Skill Builder. J. B. Wright A D VA N TA G E

Transcription

1 MATHS MATE Skill Builder 6 J. B. Wright THE EDUCATIONAL A D VA N TA G E

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3 THE EDUCATIONAL MATHS MATE /6 Skill Builder J. B. Wright Published by The Educational Advantage Pty Ltd PO Box 068 Echuca VIC 64 Phone: Fax: info@mathsmate.net Website: Copyright J. B. Wright 006 All rights reserved. The publisher of these worksheets gives permission for schools to photocopy the following worksheets for use by any student who has purchased a Maths Mate Student Pad. Copying for use with the Maths Mate Program The Maths Mate Skill Builder series are sets of photocopiable masters designed to help individual students gain particular skills that the Maths Mate Program may have identified as being poorly grasped. Maths Mate users can download and duplicate copies, print and file copies of Skill Builders for easy access in class or at home. Material available for use in the Maths Mate Program Maths Mate Student Pad - st Ed Maths Mate 4 Student Pad - st Ed Maths Mate Student Pad - rd Ed Maths Mate 6 Student Pad - rd Ed Maths Mate 7 Student Pad - 4th Ed Maths Mate 8 Student Pad - 4th Ed Maths Mate 9 Student Pad - 4th Ed Maths Mate 9 Gold Student Pad - nd Ed Maths Mate 0 Student Pad - 4th Ed Maths Mate 0 Gold Student Pad - nd Ed Maths Mate Teacher Resource CD - Version For use with all student pads Maths Mate Teacher Resource Book - st Ed Maths Mate 4 Teacher Resource Book - st Ed Maths Mate Teacher Resource Book - rd Ed Maths Mate 6 Teacher Resource Book - rd Ed Maths Mate 7 Teacher Resource Book - 4th Ed Maths Mate 8 Teacher Resource Book - 4th Ed Maths Mate 9 Teacher Resource Book - 4th Ed Maths Mate 9 Gold Teacher Resource Book - nd Ed Maths Mate 0 Teacher Resource Book - 4th Ed Maths Mate 0 Gold Teacher Resource Book - nd Ed Maths Mate Skill Builder /4 For use with Maths Mate & 4 Maths Mate Skill Builder /6 For use with Maths Mate & 6 Maths Mate Skill Builder 7/8 For use with Maths Mate 7 & 8 Maths Mate Skill Builder 9/0 For use with Maths Mate 9 & 0 A D VA N TA G E page i Maths Mate /6 Skill Builder

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5 FORWARD Why use Skill Builders? Too often, through the teaching, learning and assessment process, teachers identify weaknesses and gaps in student learning but the constraints of the classroom severely limit remediation opportunities. The Maths Mate Skill Builder series was prepared in response to requests from teachers and parents who want an easy but effective way to help students who identify skill deficiencies using the Maths Mate Program, and are motivated to do something about them. The Maths Mate record keeping sheets found at the start of each term in each Student Pad (and on each CD ~ Record Keeping Sheets, pages to 4) enable students to find out what they know and what they still need to learn and practise. The Skill Builders extensively target through instruction and practice, all skills within the related Maths Mate Program except the problem solving questions. The Problem Solving Hints & Solutions (see CD ~ Problem Solving Hints & Solutions) can be used by teachers to develop students problem solving skills. The Skill Builders also contain a Glossary of important facts and reference material that will provide instant help when students present with difficulties. Background to the design of Maths Mate and Skill Builders Any question on the Maths Mate sheets is part of a set of 4 similar questions in the term. For example, consider sheets,, and 4 in year 6 term. Question 0 on each sheet is similar in design, content and degree of difficulty. This grouping of question style is also true of the next set of four sheets and so on. Thus the Maths Mate tests made available in the Teacher Resource Book and CD (see CD ~ Test Masters, pages to and Test Answers, pages to ) also reflect this grouping of question style and substance. Generally too, the Skill Builders can be linked to each set of 4 similar questions. These links are identified in the grid at the title of each skill. The grid shown here for example, would relate a skill to questions in the first 4 sheets of term, the last 4 sheets of term and the first 4 sheets of term. Once understood, these links will be helpful to students in their selection of Skill Builders and to you in your allocation of Skill Builders to students. On each Maths Mate worksheet, questions through to get progressively harder. (Refer - How to use the Skill Builders, page iv) Suggestions for the preparation and organisation of Skill Builders Skill Builders can be downloaded from the internet. Teachers can either direct students to the internet to download and print their own copies or save the entire Skill Builder to disc and photocopy at will. Rather than photocopying Skill Builders one at a time, you may find it helpful to set up a file in a central area that contains perhaps five copies of each Skill Builder. In this way you will save time and be prepared in advance. The Glossary too can be downloaded or photocopied for students as a resource. How you can help We are confident that your students will be rewarded for the effort you have made in making these worksheets available to them either via the internet or through hardcopy. As with any program, however, there is always room for improvement and we place great value in feedback from people like yourself. Please, if you have any suggestions at all, contact us. page iii Maths Mate /6 Skill Builder

6 How to use Maths Mate Skill Builder. Determine which Maths Mate questions pose a difficulty If a student gets one or more incorrect answers, represented by one or more successive unshaded boxes on their worksheet results sheet, then that question requires a Skill Builder. For example, question in Sheets,, and 4 is not shaded, so Skill. from Skill Builder needs to be handed to the student. For skill builder help go to 6 MATHS MATE Worksheet Results Term Name:. Anthony Wright Class:... 6B Teacher:... Miss Bourke Skill Builder links Sheet 8 Sheet 7 Sheet 6 Sheet Skill Builder links Sheet 4 Sheet Sheet Sheet. [+ Whole Numbers to 0].,,,4.,,,4. [ Whole Numbers to 0].,,,4,.,,,4,. [ Whole Numbers to 0].,,.,,4, 4. [ Whole Numbers to 0] , ,. [Large Number +].,., 6. [Large Number ] NUMBER & ALGEBRA 7. [Powers of 0, ] 8. [Large Number ] 9. [Large Number ] 0. [Decimals] , , [Fractions]..4,. [Place Value]. [Order of Operations] 4. [Word Numbers] , ,. 4.. [Number Patterns].. MEASUREMENT & GEOMETRY 6. [Units of Measurement] 7. [Time] 8. [Measuring] 9. [Location] 0. [Exploring Geometry] , , S & P. [Statistics / Probability]..,4 PROBLEM SOLVING. [Problem Solving ]. [Problem Solving ] 4. [Problem Solving ] Hints & Solutions Hints & Solutions Hints & Solutions Hints & Solutions Hints & Solutions Hints & Solutions Total Correct 0 page Maths Mate 6 ~ Record Keeping Sheets. Find the relevant Skill Builder on the Maths Mate worksheet results sheet Check across the question that is posing difficulties on the worksheet results sheet to find the list of skills within the Skill Builder that are most relevant to that question. Obtain a copy of one or all of the skills listed for that question (pages to 40). You can also double check with the grid at the right of each skill title, that the chosen skill is appropriate. Remember, students should work through the skills in order. The skills where possible are arranged in increasing degree of difficulty.. [Order of Operations] Skill. Using order of operations involving + and/or Add ( + ) and/or subtract ( ) from left to right. Q = A = = = + 6 = 7 a) = = d) = 4 b) 6 + = e) = Start with 8 and subtract. The result is 6. Then subtract from 6. The result is. Finally add 6 to the. c) = f) 6 + = Be aware that some skills may require the knowledge of previous skills, so when a student has several areas of weakness, they should work on the lowest numbered skill builders first. For example, a student struggling with Q0 and Q will need to build skills required for Q0 before they can improve Q. g) = j) = + = = 0 h) 7 4 = k) = i) = l) = m) = n) + 7 = o) 9 = p) = q) = r) = page 7 Maths Mate /6 Skill Builder page iv Maths Mate /6 Skill Builder

7 . Look up any unknown terms in the Skill Builder glossary The glossary (pages 4 to 68) is more than just a list of definitions. It contains a wealth of relevant information that may help the students to better understand the question at hand. Weaker students may find that referring to a copy of the glossary, and even building on it, is a helpful strategy for improving their overall mathematical competency. For example, a student might need to look up the word operation before attempting to complete Skill. operation opposite order order of operations A mathematical process performed according to certain rules. The equivalent position but on the other side. Placing a group in a special arrangement. The order of doing operations. ) Simplify inside all brackets. ) Calculate and from left to right. ) Calculate + and from left to right. There are four basic operations in arithmetic: addition + subtraction multiplication division 6 The opposite: left/right +4/ 4 The aliens are arranged in order of height. Calculate 4 + (6 ) by ) = ) = 4 ) = 48 op - pe ordinal numbers A whole number that shows position. st, nd, rd, 4th, th... are ordinal numbers. orientation outcome Position relative to direction. Result. The tornado is coming from the west. N W E S The outcome (result) of 4 is 8 pair Two together. parallelogram pattern penta A special quadrilateral. Opposite sides are parallel lines. Opposite sides are equal in length. Numbers or objects that are arranged following a rule. Prefix meaning five. See pentagon pentagon A polygon with sides. Pentagon Regular pentagon page 4 Maths Mate /6 Skill Builder Glossary 4. Complete the relevant Skill Builder Work through the examples given for that skill, and complete the exercises. There are many techniques or methods that can be used to teach the same basic skills, even something as simple as adding 7 and 9. It is good for a student to be given a range of alternatives appropriate for each skill but space restrictions make this impossible. These sheets often suggest an approach that may be different to a student s past experience. If a student feels more comfortable with his current technique, that is fine. In most cases it is the end result that counts. It is possible to take a very weak student back to a Skill Builder from a lower level if this is necessary. It is also possible to use a higher level book for students to have further practice if required.. Correct the relevant Skill Builders from the Skill Builder answer sheets (from page 7) 6. Circle the completed skill numbers on the Maths Mate worksheet results sheet NUMBER & ALGEBRA 7. [Powers of 0, ] 8. [Large Number ] 9. [Large Number ] 0. [Decimals] , , [Fractions]..4,. [Place Value]. [Order of Operations] 4. [Word Numbers] , ,. 4.. [Number Patterns].. 6. [Units of Measurement] Go back and repeat previous Maths Mate questions After completing a Skill Builder, students should be encouraged to go back and attempt again those particular questions on the recently completed Maths Mate worksheets. page v Maths Mate /6 Skill Builder

8 Dear Parents As part of their Mathematics program this year, all students have been given a weekly Maths Mate worksheet. The program is now under way. The diagnostic nature of the worksheets helps students monitor their own progress. After they correct their worksheet and complete the record keeping sheet, over time, your child will be able to identify areas of strength and weakness in their mathematical learning. If your child is having difficulty with a question for consecutive weeks or believes that their understanding is not at the level they would like, then Skill Builder sheets will be made available to develop each of the skills in the Maths Mate program. Each Skill Builder focuses on and explores, one question from the Maths Mate worksheets. Your child is encouraged to make full use of these resources by taking home any sheet that will help consolidate their understanding of a particular skill. Or, for your convenience, all worksheets are available on our website. Simply go to and follow the prompts to download the appropriate Skill Builder. As each question in the Maths Mate is generally more difficult than the last, finishing with the problem solving questions, then it would be advised that, if students are concerned with more than one question, they tackle lower numbered questions first. The Skill Builders may also help to motivate students to make another attempt at mastering skills that they have found too difficult in the past, given that it will become clear to them that they will be confronted by the same type of question on a regular basis. While we will be monitoring your child s progress and supporting their skill development in the school environment, it would be appreciated if you would complete the tear off slip at the bottom of this page so that we can be sure that you are aware of our expectations regarding both the Maths Mate worksheets and the availability of Skill Builder worksheets. We ask also that you continue to sign the completed worksheets each week so that we can ensure each student is working independently and regularly but with your support. We thank you in anticipation of your involvement and remind you that you are encouraged to call and discuss your child s progress at any time. Yours sincerely Class Teacher Principal Maths Mate Program - Skill Builder Return Slip Student s Name: Class: As a parent / guardian I have signed this form to indicate that I am aware of the support Maths Mate Skill Builders can give my child in their mathematical development. Parent s Signature: Date:

9 CONTENTS Forward... iii How to use Maths Mate Skill Builders... iv Letter to Parents (sample)... vi Skill Builders... Glossary... 4 Maths Facts Symbols Conversions Zero One Answers... 7 MM SB [Maths Mate - Mathematical strand] Question Skill No. Skill Builder - Skill description. [+ Whole Numbers to 0].... Adding whole numbers from to 0 by counting on.. Adding whole numbers from to 0 using a number line.. Adding 7, 8 or 9 by making 0..4 Adding whole numbers from to 0 using an addition table.. [ Whole Numbers to 0].... Subtracting whole numbers from to 0 by counting back.. Subtracting whole numbers from to 0 using a number line.. Subtracting whole numbers from to 0 from two-digit numbers with smaller unit values (e.g. 8 = )..4 Subtracting 7, 8 or 9 by building up.. Subtracting whole numbers from to 0 using an addition table.. [ Whole Numbers to 0].... Multiplying whole numbers from to 0 by or 0.. Multiplying whole numbers from to 0 by.. Multiplying whole numbers from to 0 by or 4..4 Multiplying whole numbers from to 0 by.. Multiplying whole numbers from to 0 by 6, 7, 8 or 9..6 Multiplying whole numbers from to 0 by [ Whole Numbers to 0] Dividing by whole numbers from to 0 using a multiplication table. 4. Dividing by whole numbers from to 0 using subtraction.. [Large Number +] Adding large numbers without carry over using columns.. Adding large numbers with carry over using columns.. Adding large numbers by adding each place value, then adding the totals. 6. [Large Number ] Subtracting large numbers without carry over using columns. 6. Subtracting large numbers with carry over using columns. 6. Subtracting from a multiple of 0 (e.g. 0, 700, etc). 7. [Powers of 0, ] Multiplying a whole number by a power of 0 using zeros as place holders. 7. Multiplying a whole number by a power of 0 using columns. 7. Dividing a whole number by a power of 0 using fractions. 7.4 Dividing a whole number by a power of 0 by removing zeros or changing place values. 8. [Large Number ] Multiplying a large number by a single digit without carry over, using columns. 8. Multiplying a large number by a single digit with carry over, using columns. 8. Multiplying a large number by a two-digit number, using columns. page vii Maths Mate /6 Skill Builder

10 MM SB [Maths Mate - Mathematical strand] Question Skill No. Skill Builder - Skill description 9. [Large Number ] Dividing a large number by a single digit, without carry over. 9. Dividing a large number by a single digit, with carry over - no remainder. 0. [Decimals] Reading a decimal number on a scale. 0. Comparing place value in decimal numbers. 0. Adding decimal numbers with carry over using columns. 0.4 Writing a fraction as a decimal number. 0. Subtracting decimal numbers with carry over using columns. 0.6 Writing a mixed number as a decimal number. 0.7 Subtracting a decimal number less than from a whole number. 0.8 Writing an improper fraction as a decimal number. 0.9 Writing a decimal number as a fraction.. [Fractions] Illustrating proper fractions.. Writing as a fraction.. Reading a fraction or a mixed number on a number line..4 Adding fractions with the same denominators.. Subtracting fractions with the same denominators..6 Illustrating and converting mixed numbers to improper fractions..7 Illustrating equivalent fractions..8 Finding equivalent fractions..9 Simplifying fractions..0 Comparing fractions.. Finding a fraction of a whole number.. [Place Value] Understanding the place value of a digit in a number.. Finding the value of a digit in a number.. Comparing whole numbers..4 Ordering whole numbers.. Comparing decimal numbers..6 Ordering decimal numbers..7 Rounding whole numbers to a given place..8 Rounding decimal numbers to the nearest whole number..9 Estimating outcomes by rounding to the nearest 0 or Estimating outcomes by rounding decimals to whole numbers.. [Order of Operations] Using order of operations involving + and/or. Using order of operations involving and/or. Using order of operations involving single or and + or.4 Using order of operations involving brackets ( ) 4. [Word Numbers] Expressing word numbers in numerals. 4. Writing -digit numbers in words. 4. Writing -digit numbers in words. 4.4 Writing 4-digit numbers in words. 4. Writing -digit numbers in words. 4.6 Writing 6-digit numbers in words.. [Number Patterns] Completing number patterns by adding the same number.. Completing number patterns by subtracting the same number.. Completing number patterns by multiplying by the same number..4 Completing number patterns by dividing by the same number.. Completing number patterns by using changing values in the rule. page viii Maths Mate /6 Skill Builder

11 MM SB [Maths Mate - Mathematical strand] Question Skill No. Skill Builder - Skill description 6. [Units of Measurement] Selecting the appropriate units of measurement. 6. Estimating length, mass etc. using units of measurement. 6. Converting length units. 6.4 Converting mass units. 6. Converting capacity units. 6.6 Working with units of measurement. 7. [Time] Expressing the time in words. 7. Expressing the time in numbers. 7. Identifying centuries. 7.4 Showing the time on an analogue clock. 7. Converting time units. 7.6 Calculating periods of time. 7.7 Reading timetables. 8. [Measuring] Estimating length. 8. Reading and using scales. 8. Comparing angles to a right angle. 8.4 Measuring angles using a protractor. 8. Calculating the perimeter of a shape using a grid. 8.6 Calculating the area of a shape by counting squares & triangles. 8.7 Describing volume by counting cubes. 9. [Location] Locating places using simple bearings (closest, left, first turn). 9. Locating places using compass bearings N, E, S and W. 9. Following directions to find a place on a map. 9.4 Reading distances on a map. 9. Using regions on a grid to describe location (e.g. A). 9.6 Using coordinates to describe location on a coordinate plane. 9.7 Measuring distances using a grid scale. 9.8 Using a linear scale to calculate distance. 0. [Exploring Geometry] Recognising D shapes. 0. Drawing D shapes. 0. Describing polygons. 0.4 Recognising D shapes. 0. Describing D shapes. 0.6 Identifying the shape of a cross-section. 0.7 Drawing symmetrical shapes. 0.8 Identifying nets of D shapes. 0.9 Describing the movement of an object.. [Statistics / Probability] Interpreting stacked bar graphs without a scale.. Interpreting stacked bar graphs with a scale.. Interpreting pictographs without a scale..4 Interpreting pictographs with a scale.. Interpreting tables..6 Interpreting bar graphs..7 Interpreting multiple stacked bar graphs..8 Recognising the relative likelihood of an event..9 Finding the likelihood of an outcome..0 Interpreting Venn diagrams. page ix Maths Mate /6 Skill Builder

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13 . [+ Whole Numbers to 0] Skill. Adding whole numbers from to 0 by counting on. Start with the largest number. Count on the smaller number. Q A counting on counting on... 0,, OR 9 + =? Start with the largest number 9. Count on more. 9 + =? a) b) c) d) page Maths Mate /6 Skill Builder

14 Skill. Adding whole numbers from to 0 using a number line. Q. A =? Start at 8. Go forward 6 places. You are at = 4 a) b) c) d) page Maths Mate /6 Skill Builder

15 Skill. Adding 7, 8 or 9 by making 0. Find the largest number. Work out what number you need to add to the largest number, to make 0. Break down the smaller number to include the number you need. Regroup the numbers to create a sum of 0. (0 s are easy!) Q. A = = = 0 + = =? 8 is the largest number. Ask: What number added to 8, will make 0? Answer: 8 +? = = 0 You need a Break down the smaller number 7, into and. + = 7 Regroup the with the 8 to make 0. a) Hint: When you add 9 the unit in the answer is always one less than the unit in the question! = = = + 0 = b) c) page Maths Mate /6 Skill Builder

16 Skill.4 Adding whole numbers from to 0 using an addition table. Q. A =? Move down the column from. Move across the row from 8. The number crossed is the result. + 8 = 8 + = a) b) c) d) page 4 Maths Mate /6 Skill Builder

17 . [ Whole Numbers to 0] Skill. Subtracting whole numbers from to 0 by counting back. Start with the first number given. Count backwards the second number. Q. A counting back OR 9 counting back... 8, 7, 6 9 =? Start with the first number given, 9. Count backwards. 9 = 6 a) b) c) d) page Maths Mate /6 Skill Builder

18 Skill. Subtracting whole numbers from to 0 using a number line Q. A =? Start at 8. Go backward 6 places. You are at. 8 6 = a) b) c) d) page 6 Maths Mate /6 Skill Builder

19 Skill. Subtracting whole numbers from to 0 from two-digit numbers with smaller unit values (e.g. 8 = ). Look at the unit value of the two-digit number. Break down the single digit number to include this number and the remainder. Subtract the number from the two-digit number, 0 will be the result. Then subtract the remainder from 0. Q. A = 7 7 The unit value of 7 is 7. You need a 7. Breakdown 8 into 7 and. 7 + = 8 = 7 7 = 0 = 9 Subtract 7 from 7 to get 0. Subtract from 0. a) = 4 4 = 4 4 = 0 = 8 b) c) d) page 7 Maths Mate /6 Skill Builder

20 Skill.4 Subtracting 7, 8 or 9 by building up. Build up 7, 8 or 9 to 0 by adding the amount needed. Build up the number being subtracted from, by adding the same amount. Then complete the subtraction from 0. Q. A = = = 9 0 = To subtract 7 from 6: Build up 7 to 0 by adding. Also build up 6 by adding. 6 becomes 9. Then subtract 0 from 9. a) = 7 0 = Hint: When you subtract 9 the unit in the answer is always one more than the unit in the question! b) c) page 8 Maths Mate /6 Skill Builder

21 Skill. Subtracting whole numbers from to 0 using an addition table. Q. A Ask: 8 =? Reword the subtraction by turning it into an addition. What number, when added to 8, will give? 8 +? = Answer: Using the addition table: = So 8 = 7 a) b) c) d) page 9 Maths Mate /6 Skill Builder

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23 . [ Whole Numbers to 0] Skill. Multiplying whole numbers from to 0 by or 0. Multiplication forms patterns. Multiplication is the same as repeated additions. Any number, multiplied by, equals the sum of of the numbers. Example: 6 = 6 Hint: The number stays the same. Any number, multiplied by 0, equals the sum of 0 of the numbers. Example: 6 0 = = 60 Hint: Add a zero to the number. Multiplication is counting by a number of times. You can multiply by by counting by that number, time. Example: 6 } time You can multiply by 0 by counting by that number, 0 times. Example: 6,, 8, 4, 0, 6, 4, 48, 4, 60 }0 times Multiplication is reversable. Example: 0 6 = 6 0 Q. A When you multiply a number by 0, add a zero to the end of the number. a) b) page Maths Mate /6 Skill Builder

24 = = = Skill. Multiplying whole numbers from to 0 by. Multiplication forms patterns. Multiplication is the same as repeated additions. Any number, multiplied by, equals the sum of of the numbers. Example: 9 = = 4 Multiplication is counting by a number of times. You can multiply by by counting by that number, times. Example: 9, 8, 7, 6, 4 } times Multiplication is reversable. Example: 9 = Hint: Multiplying by produces a value that is half that of a multiplication by = 90 9 = 4 Hint: Multiplying by produces a value that always ends in 0 or. Hint: Multiplying by produces the same values as the minutes on a clock face = = 60 = = 4 = = = = = 0 0 Q. A a) page Maths Mate /6 Skill Builder

25 Skill. Multiplying whole numbers from to 0 by or 4. Multiplication forms patterns. Multiplication is the same as repeated additions. Any number, multiplied by, equals the sum of of the numbers. Example: 7 = = 4 Any number, multiplied by 4, equals the sum of 4 of the numbers Example: 7 4 = = 8 Multiplication is counting by a number of times. You can multiply by 4 by counting by that number, 4 times. Example: 7, 4,, 8 } 4 times Multiplication is reversable. Example: 7 = 7 Hint: Multiplying by always produces an even number. Hint: Multiplying by is the same as doubling. Double 7 is 4 OR 7 = 4 Hint: Multiplying by 4 is the same as doubling the number and then multiplying by. 7 4 = 4 = 8 Q A a) = + Repeated = 0 additions b) = 6 Double = and by page Maths Mate /6 Skill Builder

26 Skill.4 Multiplying whole numbers from to 0 by. Multiplication forms patterns. Multiplication is the same as repeated additions. Any number, multiplied by, equals the sum of of the numbers. Example: 8 = = 4 Multiplication is counting by a number of times. You can multiply by by counting by that number, times. Example: 8, 6, 4 } times Multiplication is reversable. Example: 8 = Q. A a) b) page 4 Maths Mate /6 Skill Builder

27 Skill. Multiplying whole numbers from to 0 by 6, 7, 8 or 9. Number the fingers on each hand from 6 to 0 starting with the thumb as 6. Touch the appropriate fingers together to match the table you are working on. Example: 7 8 Count your thumbs, the touching fingers and any fingers in between (shaded lightly). This result makes up the tens. ( fingers on left hand, fingers on right hand) + = tens = 0 Count separately, the fingers on each hand that are beyond the touching fingers (shaded dark). Multiply the sums. This result makes up the units. ( fingers on left hand, fingers on right hand) = 6 6 units = 6 Finally add the tens and units = 6 So 7 8 = Q. A =? + = tens = 0 (light fingers) 4 = units = (dark fingers) 0 + = 4 So 6 7 = 4 a) b) c) d) page Maths Mate /6 Skill Builder

28 Skill.6 Multiplying whole numbers from to 0 by 9. Number the fingers on each hand from to 0. Bend the finger that matches the 9 table you are working on. Example: For 8 9, bend the 8th finger Count the fingers before the bent finger. This result makes up the tens. 7 fingers 7 tens = 70 Count the fingers after the bent finger. This result makes up the units. fingers 7 units = Add the tens and units = 7 So 8 9 = 7 Q. A = = = = = = = = = = 9 Hint: When multiplying by 9, the digits in the answer always add to To find 7 9 =?, bend the 7th finger. 6 fingers before the bent finger 6 tens = 60 fingers after the bent finger units = 60 + = 6 So 7 9 = 6 a) b) page 6 Maths Mate /6 Skill Builder

29 4. [ Whole Numbers to 0] Skill 4. Dividing by whole numbers from to 0 using a multiplication table. Division forms patterns Division and multiplication are inverse operations. (Division undoes multiplication) Example: If 7 8 = 8 7 = then 6 8 = or 6 7 = Q. A =? How many 7 s go into 6? Reword the division by turning it into a multiplication. Ask: 7 multiplied by what number makes 6? (7? = 6) Answer: Using the multiplication table 7 8 = 6 So 6 7 = 8 a) b) c) page 7 Maths Mate /6 Skill Builder 4

30 Skill 4. Dividing by whole numbers from to 0 using subtraction. Division is the same as repeated subtractions. Example: 6 7 =? How many 7 s go into 6? OR If you have 6, how many times can you take away 7? = 0 } 8 times If you have 6 you can take 7 away, 8 times. So, 6 7 = 8 Q. A How many s go into? Reword the division by turning it into a subtraction. Ask: If you have, how many times can you take away? = 0 } 7 times Answer: If you have you can take away, 7 times. So, = 7 a) = 0 So 6 = 8 Take away 8 times. b) c) d) page 8 Maths Mate /6 Skill Builder 4

31 . [Large Number +] Skill. Adding large numbers without carry over using columns. Always keep your working columns in line, aligning units with units, tens with tens, etc. Add from right to left. Q. + 4 A. units tens hundreds + 4 Units: + = 8 8 units Tens: + 4 = 6 6 tens 6 8 Units first! Hundreds: + 0 = hundred a) b) c) d) 7 Units first! Units first! e) f) g) h) i) j) k) l) m) n) o) p) page 9 Maths Mate /6 Skill Builder

32 Skill. Adding large numbers with carry over using columns. Always keep your working columns in line, aligning units with units, tens with tens, etc. Add from right to left. Q A. units tens hundreds Units: = = + = = ten + units 9 Units first! units Carry over the ten to the tens column. Tens: (carry over) = 9 9 tens Hundreds: + 0 = hundred a) b) c) d) Units first! Units first! e) f) g) h) i) j) k) l) page 0 Maths Mate /6 Skill Builder

33 Skill. Adding large numbers by adding each place value, then adding the totals. Add the digits in each place value. Then add the totals. Q A. units tens hundreds units tens Add the units (U): + 6 = Add the tens (T): = 0 + hundreds 9 Add the hundreds (H): = a) 8 b) U = T = U = 0... T = c) 7 U = d) T =... H =... U =... T =... H = e) 6 U f) = 4 7 T = H 00 = U =... T =... H = g) 8 U h)... = T... = H =... U =... T =... H = page Maths Mate /6 Skill Builder

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35 6. [Large Number ] Skill 6. Subtracting large numbers without carry over using columns. Always keep your working columns in line, aligning units with units, tens with tens, etc. Subtract from right to left. Q A. units tens hundreds Units: 7 = 4 4 units Tens: 4 4 = 0 0 tens 0 4 Units first! Hundreds: 0 = hundred a) b) c) d) 4 Units first! Units first! e) f) g) h) i) j) k) l) m) n) o) p) page Maths Mate /6 Skill Builder 6

36 Skill 6. Subtracting large numbers with carry over using columns. Always keep your working columns in line, aligning units with units, tens with tens, etc. Subtract from right to left. 4 7 Q. A. units tens hundreds 4 7 Units: 7 =? units. The result is < 0. To make the answer positive break down the 4 tens. 4 tens = tens + 0 units 4 7 Re-group the 0 units with the units to make units = Units first! Tens next! Now... 7 = 8 8 units Tens: = ten Hundreds: = hundreds a) 6 b) c) Units first! Units first! d) e) f) g) h) i) j) k) l) page 4 Maths Mate /6 Skill Builder 6

37 Skill 6. Subtracting from a multiple of 0 (e.g. 0, 700, etc). Always keep your working columns in line, aligning units with units, tens with tens, etc. Subtract from right to left. Q A. hundreds tens units Units: 0 8 =? units. The result is < 0. To make the answer positive break down the hundreds (no tens available). hundreds = hundreds + 9 tens + 0 units 4 Units first! Now = units Tens: 9 = 4 4 tens Hundreds: 0 = hundreds 8 a) b) c) d) Units first! 0 4 Units first! e) f) g) h) i) j) k) l) m) n) o) p) page Maths Mate /6 Skill Builder 6

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39 7. [Powers of 0, ] Skill 7. Multiplying a whole number by a power of 0 using zeros as place holders. When multiplying by 0 move each digit one place to the left. units tens hundreds 0 units tens hundreds 0 0 Use zero as a place holder Hint: Multiplying by a power of 0 does not change the digits in the number. Example: 0 = 0 the and the remain in the answer. When multiplying by 00 move each digit two places to the left. When multiplying by 000 move each digit three places to the left. etc. Add zeros as place holders in the vacated places. Q A. units tens thousands hundreds means 9 groups of 00. Shift and 9 two places to the left Units first! Use 0 s as place holders in the vacated units and tens places a) b) c) Use zero as a place holder d) e) f) g) h) i) j) k) l) page 7 Maths Mate /6 Skill Builder 7

40 Skill 7. Q Multiplying a whole number by a power of 0 using columns. A. tens units thousands hundreds Hint: One thousand, seven hundred can also be called seventeen hundred. Units first! Units: 0 7 = 0 0 units Tens: 0 7 = 0 0 tens Hundreds: 7 = 7 7 hundreds = thousand + 7 hundreds 7 hundreds thousand a) b) c) d) 6 0 Units first! Units first! e) f) g) h) i) j) k) l) m) n) o) p) page 8 Maths Mate /6 Skill Builder 7

41 Skill 7. Dividing a whole number by a power of 0 using fractions. Convert the division to a fraction and... EITHER Divide both the numerator and the denominator by the value of the denominator. OR Cancel the zeros in the numerator against the zeros in the denominator = 40 = 40 0 = 4 = 4 40 = = 4 = = 600 = = 6 = = 600 = 6 = Q = A = = = = How many groups of 00 make up 400? Convert the division to a fraction. Divide the numerator and the denominator by groups of 00 make up 400. Hint: Five thousand, four hundred can also be called fifty-four hundred. a) = = = b) 70 0 = = c) 80 0 = = d) = e) = f) = = = = g) = h) = i) = = = = page 9 Maths Mate /6 Skill Builder 7

42 Skill 7.4 Dividing a whole number by a power of 0 by removing zeros or changing place values. EITHER Remove the same number of zeros as in the divisor from the end of the whole number. ( for 0, for 00, for 000, etc.) Example: = = = 98 OR Move the decimal point the same number of places to the left as there are zeros in the divisor. Hint: There is a decimal point and zeros which are not written, at the end of any whole number. zero place left zeros places left zeros places left Q = A = = = has zeros. To divide by 000 remove zeros from both sides of the equation. a) = = d) = b) 90 0 = =... e) 00 0 = c) 0 0 = =... f) = =... =... =... g) = h) = i) = =... =... =... j) = k) = l) = =... =... =... page 0 Maths Mate /6 Skill Builder 7

43 8. [Large Number ] Skill 8. Multiplying a large number by a single digit without carry over, using columns. Multiply the units, tens, hundreds and thousands by the single digit. Multiply from right to left. Q. A. units tens hundreds Units: = 6 6 units Tens: = tens 9 6 Units first! Hundreds: = 9 9 hundreds a) b) c) d) 9 7 Units first! e) f) g) 4 h) i) j) k) l) 6 9 Units first! m) n) o) p) page Maths Mate /6 Skill Builder 8

44 Skill 8. Multiplying a large number by a single digit with carry over, using columns. Multiply the units, tens, hundreds and thousands by the single digit. Multiply from right to left. If there is a carry over : First multiply. Then add on the carry over. 9 8 Q. A. units tens hundreds Units first! Units: 8 9 = 7 7 units = 7 tens and units units Carry over the 7 tens to the tens column. Tens: 8 = (carry over) = tens = hundred and tens tens Carry over the hundred to the hundreds column. Hundreds: 8 = (carry over) = 9 9 hundreds 4 a) b) c) d) Units first! e) f) g) h) 8 6 i) j) k) l) Units first! m) n) o) p) 4 page Maths Mate /6 Skill Builder 8

45 Skill 8. Multiplying a large number by a two-digit number, using columns. Multiply by the unit digit first, working from right to left. Reminder: Put a zero in the units place before you start multiplying by the tens. Then multiply by the ten digit, working from right to left. Add the results last. 8 4 Q. A. tens units thousands hundreds first! First multiply 8 by the 4 units. Units: 4 = 0 0 units = tens and 0 units 0 units Carry over the tens to the tens column. Tens: 4 8 = + (carry over) = 4 4 tens = hundreds and 4 tens 4 tens next! + last! Hundreds: hundreds Then multiply 8 by the ten. Units: Write 0 as a place holder for the ten. 0 units Tens: = tens Hundreds: 8 = 8 8 hundreds Add these results: = 90 4 first! 4 next! a) b) c) d) 7 4 Use zero as a place holder + last! first! next! Use zero as a place holder first! e) g) h) f) page Maths Mate /6 Skill Builder 8

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47 9. [Large Number ] Skill 9. Dividing a large number by a single digit, without carry over. Divide from left to right across the digits, one at a time. Q. A hundreds first! hundreds units tens Hundreds: 4 = hundreds Tens: 8 = 4 4 tens Units: 6 = units Read as: 486 divided by equals? OR How many s go into 486? OR 486 divides by how many times? Consider: 486 = 4 4 = 486 a) hundreds first! b) c) d) e) f) g) h) i) thousands first! j) k) l) m) thousands first! n) o) p) page Maths Mate /6 Skill Builder 9

48 Skill 9. Dividing a large number by a single digit, with carry over - no remainder. Divide from left to right across the digits one at a time. If any result is less than : Break down the number being divided into. Carry over this amount to the next column. Add on the carry. Then try dividing again. Q. A. 4 8 hundreds first! 4 8 hundreds units tens Hundreds: 4 =? The result is <. Break down the hundred into 0 tens and carry them to the tens column. Tens: + 0 (carry over) = 4 = tens Units: 8 4 = units Read as: 8 divided by 4 equals? OR How many 4 s go into 8? OR 8 divides by 4 how many times? Consider: 8 4 = 4 = 8 a) hundreds first! 0 b) hundreds first! 4 c) 4 d) 7 9 e) f) g) h) i) thousands first! j) k) l) m) n) o) p) page 6 Maths Mate /6 Skill Builder 9

49 0. [Decimals] Skill 0. Reading a decimal number on a scale. Count the number of spaces between two whole numbers. (Always one more than the number of marks.) Work out the value of each space. Example: 0 spaces between each whole number 0 = 0. Each mark is further along the scale by one tenth or Starting at the last whole number, count on by 0.. Point to each mark as you go. Q. What number is shown by the arrow on the scale? 0 A. 0.7 There are 0 spaces between 0 and. Each space is worth = 0 = 0. 0 From 0 you can count on: 0, 0., 0., 0., 0.4, 0., 0.6, 0.7 OR Knowing the middle mark is 0., count on from 0.: 0., 0.6, 0.7 a) What number is shown by the arrow on the scale? b) What number is shown by the arrow on the scale? c) Show with an arrow the number 4.8 on the scale. 4 d) Show with an arrow the number 6.6 on the scale e) What number is shown by the arrow on the scale? 0 f) What number is shown by the arrow on the scale? page 7 Maths Mate /6 Skill Builder 0

50 Skill 0. Comparing place value in decimal numbers. Line up the decimal numbers at their decimal points. Compare the size of digits in the same places, starting from the left. thousands hundreds tens units decimal point tenths hundredths thousandths Hint: Using zeros as place holders does not change the value of a number when the zeros are put: EITHER OR Before the first digit in any number Example: The digit is in the units place = 0 = 00 After the last digit of a decimal number, after the decimal point Example: 0. The digit is in the tenths place 0. = 0.0 = 0.00 Q. Which of the following are true? A ) 6.0 = 6.00 B ) 400 = 40 C ) 0.7 = D ) 0.8 = A. A and D Line up the numbers at their decimal points. Compare from the left. A) 6.0 = 6.00 True C) 0.7 = False Only A and D are true. B) 400 = D) 0.8 = 40 False True a) Which of the following are true? A ) 6 = 60.0 B ) 0.0 = 0 C ) 0. =. D ) 00. =.00 b) Which of the following are true? A ) 70 = 7 B ) 9 = 0.9 C ) 0. = 0.0 D ) 8.0 = 8.00 c) Which of the following are true? A ) 0.0 =.0 B ) 0.0 = 0 C ) 0.07 =.007 D ) 4 = 4.0 B and C and and d) Which of the following are true? A ) 90 = 90.0 B ) 4 = 40.0 C ) 0.0 =.0 D ) 0.0 = 0. e) Which of the following are true? A ) 0.0 = 0.0 B ) 0.4 = 0.40 C ) 7 = 0.70 D ) 8.0 = 8.00 f) Which of the following are true? A ).0 = B ) 0 = 0.0 C ) 0.4 = D ).0 =.0 and and and page 8 Maths Mate /6 Skill Builder 0

51 Skill 0. Adding decimal numbers with carry over using columns. Always keep your working columns in line, aligning the decimal points, the decimal places, units with units, tens with tens, etc. Add from right to left. $. 7 + $. 4 Q. A. units $. 7 + $. 4 $ 4. 0 tenths hundredths Hundredths first! Hundredths: + = 0 0 hundredths = tenth and 0 hundredths 0 hundredths Carry over the tenth to the tenths column. Tenths: (carry over) = tenths = unit and tenths tenths Carry over the unit to the units column. Put the decimal point in the answer box under the other decimal points. Units: + + (carry over) = 4 4 units a) $. 0 + $. 0 b) $ 4. + $. 4 c) $ $. 4 d) $. 7 + $ 8. 0 Hundredths $. 00 $ $ $ first! e) f) g) h) i) j) k) l) page 9 Maths Mate /6 Skill Builder 0

52 Skill 0.4 Writing a fraction as a decimal number. When the denominator is a power of 0: Say the fraction out loud using tenths, hundredths or thousandths. Write the last digit of the numerator in the place spoken of in the denominator. Fill in the numerator working backwards to the decimal point. Use zeros as place holders where necessary. Examples: twenty-seven hundredths 7 00 = units 4 Q. Write as a 000 decimal number. tenths Decimal point hundredths 0 7 Write the 7 in the hundredths place. A Work backwards filling in the. Read as: twenty-four thousandths. units sixteen thousandths tenths Decimal point = hundredths thousandths units tenths Decimal point hundredths Write the 4 in the thousandths place and work backwards. Use zeros as place holders thousandths Use zeros as place holders Hint: The number of zeros in the denominator shows the number of digits after the decimal point. 7 6 = 0.7 = a) Write as a 0 decimal number. five tenths b) Write as a 0 decimal number.... c) Write as a 0 decimal number d) Write as a e) Write as a decimal number. decimal number. eight hundredths f) Write as a 00 decimal number g) Write as a 000 decimal number. h) Write as a 000 decimal number. i) Write as a 000 decimal number page 40 Maths Mate /6 Skill Builder 0

53 Skill 0. Subtracting decimal numbers with carry over using columns. Keep the units, decimal points, tenths and hundredths in their own column. Work from right to left Q. A. units tenths hundredths Hundredths first! Hundredths: 0 = hundredths Tenths: 6 9 =? tenths. To make the answer positive break down the units. units = units and 0 tenths. Re-group the 0 tenths with the 6 tenths to make 6 tenths. Now = 7 7 tenths Put the decimal point in the answer box under the other decimal points. Units: = unit a) b) c) d) Hundredths first! Hundredths first! e) f) g) h).. 8 i).. 4 j) k) l) page 4 Maths Mate /6 Skill Builder 0

54 Skill 0.6 Writing a mixed number as a decimal number When the denominator is a power of 0: Write the whole number first. Put the decimal point. Write the fraction as a decimal number. (see skill 0.4, page 40) Example: four and.. eight hundredths = units Q. Write the mixed number 4 8 as a decimal. 00 Read as: Eight and twenty-four hundredths tenths Decimal point hundredths Work backwards filling in the 4. Write the 8 in the hundredths place. Use zeros as place holders Hint: The number of zeros in the denominator shows the number of digits 6 = 0.06 after the decimal point. 000 A. 8.4 When the denominator is not a power of 0: Change the mixed number to an improper fraction. + = Divide the numerator by the denominator. = = Hint: =.0 + = Write the whole number, 8 units. Put the decimal point. Write the numerator 4, with the last digit 4 in the hundredths place. [No zero place holders are necessary.] a) Write the mixed number 7 0 as a decimal = =....7 d) Write the mixed number as a decimal. 00 b) Write the mixed number as a decimal e) Write the mixed number 6 as a decimal. 0 c) Write the mixed number 4 0 as a decimal f) Write the mixed number as a decimal g) Write as a decimal number. h) Write 4 as a decimal number. i) Write as a decimal number page 4 Maths Mate /6 Skill Builder 0

55 Skill 0.7 Subtracting a decimal number less than from a whole number. Write the whole number first, with a decimal point and one or two zeros after it. Hint: The number doesn t change. =.00 Write the decimal number underneath. Line up the decimal points. Subtract using columns. (see skill 0., page 4) Q = A. units tenths hundredths Hundredths first! Hundredths: 0 4 =? hundredths To make the answer positive break down the units: units = 4 units + 9 tenths + 0 hundredths Now = 6 6 hundredths Tenths: 9 9 = 0 0 tenths Put the decimal point in the answer box. Units: 4 0 = 4 4 units a) 0. = b) 0. = c) 0. = Tenths first! Tenths first! d) = e) 9 0. = f) = g) = h) 0.8 = i) 0.4 = page 4 Maths Mate /6 Skill Builder 0

56 Skill 0.8 Writing an improper fraction as a decimal number. When the denominator is a power of 0: Divide the numerator by 0, 00 or 000 by moving the decimal point the same number of places to the left as there are zeros. Examples: by 0 ( zero place left) by 00 ( zeros places left) by 000 ( zeros places left) Hint: Fractions are just divisions. Hint: There is a decimal point and zeros which are not written, at the end of any whole number. The number doesn t change. 6 = Example: = = = =.6 When the denominator is not a power of 0: Multiply both the numerator and denominator by the same number to make the denominator a power of 0. Example: = = power of Then divide by moving the decimal point. 48 Example: = = = =.48 Q. Write as a decimal number. 7 a) Write as a 0 decimal number = A. = 0 = = =.4 b) Write 0 as a decimal number Multiply the denominator and the numerator by to make the denominator a power of 0. 8 c) Write as a 0 decimal number d) Write as a 00 decimal number. 4 e) Write as a 00 decimal number. 8 f) Write as a decimal number g) Write as a decimal number. 9 h) Write as a decimal number. 9 i) Write as a decimal number page 44 Maths Mate /6 Skill Builder 0

57 Skill 0.9 Writing a decimal number as a fraction. From left to right (ignoring zeros if they start the number) write the digits as the numerator. Use the place value of the last digit of the decimal number to determine the size of the denominator. (See also 0.4, page 40) Q. Write 0.9 as a fraction. A. 0.9 = tenth = 0 hundredths 9 hundredths Write 9. The nine is in the hundredths place. Write 00ths as the denominator. Said as: 9 nineteen hundredths 00 a) Write 0. as a fraction. b) Write 0.9 as a fraction. c) Write 0.7 as a fraction. 0 d) Write 0.4 as a fraction. e) Write 0. as a fraction. f) Write 0.8 as a fraction. g) Write 0.9 as a fraction. h) Write 0.8 as a fraction. i) Write 0.4 as a fraction j) Write 0. as a fraction. k) Write 0.9 as a fraction. l) Write 0.4 as a fraction. m) Write 0.0 as a fraction. n) Write 0.0 as a fraction. o) Write 0.09 as a fraction. 00 p) Write 0.07 as a fraction. q) Write 0.0 as a fraction. r) Write 0.06 as a fraction. page 4 Maths Mate /6 Skill Builder 0

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59 . [Fractions] Skill. Q. What fraction of the circle is shaded? Illustrating proper fractions. Count the number of shaded parts. Count the total number of parts. Write the number of shaded parts over the total number of parts. A. 4 numerator - how many parts count denominator - how many equal parts in one whole The circle is divided into 4 equal parts so the denominator of the fraction is 4. Only parts of the circle are shaded so the numerator is. The fraction of the circle that is shaded is three fourths or. 4 a) What fraction of the bar is shaded? b) What fraction of the bar is shaded? c) What fraction of the bar is shaded? d) What fraction of the circle is shaded? e) What fraction of the sunglasses is shaded? f) What fraction of the balloons is shaded? 4 g) Shade in of the square. 9 h) Shade in of the parallelogram. 8 i) Shade in of the square. 8 j) Shade in of one half of this circle. page 47 Maths Mate /6 Skill Builder

60 Skill. Writing as a fraction. whole circle shaded 4 = = = = = 4 numerator = denominator fractions = Q. Which of the following equal? A. A and D The only fractions in which the 4 4 A) B) C) D) numerator is the same as the 4 4 denominator are and 4 = (three thirds make a whole) 4 = (four fourths or quarters make 4 a whole) a) Which of the following equal? 8 A) B) C) D) and b) Which of the following equal? A) B) C) D) and c) Write a fraction equal to that has a denominator of 8. d) Write a fraction equal to that has a denominator of 7. e) Write a fraction equal to that has a denominator of. f) Write a fraction equal to that has a denominator of 9. g) Three quarters of the lesson is over. What fraction of the lesson remains? h) Luke has spent one sixth of his pocket money. What fraction of the money is left? i) If one third of the birthday cake was eaten, what fraction of the cake remains? j) If three fifths of the show is over, what fraction of the performance is left? page 48 Maths Mate /6 Skill Builder

61 Skill. Reading a fraction or a mixed number on a number line. Count the number of spaces between two consecutive whole numbers. The number of spaces tells you the value of the denominator. Example: If there are 6 spaces between the whole numbers, then each space equals Q. Name the mixed number shown by the arrow on the number line. 4 6 A. 6 spaces denominator There are five spaces between and 6. Each space equals. The arrow points to. a) Name the fraction shown by the arrow on the number line. 0 b) Name the fraction shown by the arrow on the number line. 0 c) Name the mixed number shown by the arrow on the number line. d) Name the mixed number shown by the arrow on the number line. 0 0 e) Name the fraction shown by the arrow on the number line. f) Name the fraction shown by the arrow on the number line. 0 0 g) Name the mixed number shown by the arrow on the number line. h) Name the mixed number shown by the arrow on the number line i) Name the mixed number shown by the arrow on the number line j) Name the mixed number shown by the arrow on the number line. 4 page 49 Maths Mate /6 Skill Builder

62 Skill.4 Adding fractions with the same denominators. Add the whole numbers first. Then add the numerators (top numbers of the fractions). Don t change the denominators. Q. + = A Add the whole numbers first: + = Add the fractions: One fourth plus two fourths is three fourths. Add only the top numbers. + = 4 + = 4 4 a) + = b) + = c) = d) 4 + = e) = 6 6 f) + = 4 4 g) + = h) + = 8 8 i) + = 9 9 j) + = k) l) = + = m) = n) + = o) = p) 4 + = q) + 4 = r) = 0 0 page 0 Maths Mate /6 Skill Builder

63 Skill. Subtracting fractions with the same denominators. Subtract the whole numbers first. Hint: You may need to convert whole number to an equivalent fraction. Example: = Then subtract the numerators (top numbers of the fractions). Don t change the denominators. Q. = A. 6 6 The two can be seen as one whole and six sixths. Six sixths minus five sixths is one sixth = 6 = 6 6 a) = 4 b) = c) 6 = 9 9 d) 6 = e) = f) = g) 9 6 = 0 0 h) 8 = i) 7 = j) = k) 4 = l) = 7 m) 4 = n) = o) = 4 4 p) = q) 6 = r) 9 = page Maths Mate /6 Skill Builder

64 Skill.6 Illustrating and converting mixed numbers to improper fractions. Recognising mixed numbers To name the whole number: Count the fully shaded shapes. To name the fraction: Count the shaded parts of the last shape. Count the total parts of the last shape. Write the shaded parts over the total parts. 4 MIXED NUMBER whole number fraction Illustrating mixed numbers Consider the mixed number as two bits: A whole number. A fraction. Shade the number of whole shapes to match the whole number. Partially shade the last shape to match the fraction. = numerator - 8 parts count IMPROPER FRACTION denominator - equal parts in one whole Q. Shade the circles to show that 7 = A. 7 = + + = + + Shade two whole circles and a third of the remaining circle. In total 7 thirds have been shaded. 7 This shows that = a) Name the mixed number represented by these shaded squares. + + b) Name the mixed number represented by these shaded triangles. c) Name the mixed number represented by these shaded rectangles. d) Name the mixed number represented by these shaded hexagons. e) Shade the pentagons to show that f) Shade the circles to show that 8 = = g) Shade the rectangles to show that h) Shade the circles to show that 4 4 = 6 6 = 9 6 page Maths Mate /6 Skill Builder

65 Skill.7 Illustrating equivalent fractions. same area shaded = = = different fraction names equal value (equivalent fractions) Q. Shade the diagrams to show 6 = 8 4 = A. = Shade six eighths inside the first square. Shade three fourths inside the second square. The same area of each square has been shaded. This shows that 6 8 = 4 a) Shade the diagrams to show 8 4 = 0 b) Shade the diagrams to show 4 = 6 = = c) Shade the diagrams to show 4 = 0 d) Shade the diagrams to show 6 = 9 = = e) Shade the diagrams to show f) Shade the diagrams to show 4 = = = = page Maths Mate /6 Skill Builder

66 Skill.8 Finding equivalent fractions. same area shaded = = = different fraction names equal value (equivalent fractions) Q. Complete to form equivalent fractions: A. 4 = = 4 = The rectangle on the left has 4 equal parts. Shade one part. The rectangle on the right has equal parts. Shade the same area as in the first rectangle. Three out of twelve parts have been shaded. One fourth is the same as three twelfths. are equivalent fractions. 4 = a) Complete to form equivalent fractions: 4 6 = 0 b) Complete to form equivalent fractions: 6 = = c) Complete to form equivalent fractions: 9 d) Complete to form equivalent fractions: 6 = g) Complete to form equivalent fractions: 8 = e) Complete to form equivalent fractions: = 8 h) Complete to form equivalent fractions: 6 = f) Complete to form equivalent fractions: 4 = 0 i) Complete to form equivalent fractions: 4 = j) Complete to form equivalent fractions: k) Complete to form equivalent fractions: l) Complete to form equivalent fractions: = 8 9 = = 0 8 page 4 Maths Mate /6 Skill Builder

67 Skill.9 Simplifying fractions. Decide if the fraction can be simplified. If both numbers, top (numerator) and bottom (denominator), can be divided by the same number then the fraction can be simplified. Hint: If the numbers are both even then you can start with dividing by. 6 8 Divide both the numerator and the denominator by the same number. 6 8 numerator (even) denominator (even) = 4 6 Q. Simplify A. 0 Both 6 and 0 are even numbers. They can be divided by. The fraction can be simplified = 0 = a) Simplify 8 b) Simplify 4 6 c) Simplify 9 8 = 6 9 =... d) Simplify 0 e) Simplify 6 9 f) Simplify g) Simplify h) Simplify 8 0 i) Simplify j) Simplify 4 0 k) Simplify 0 l) Simplify page Maths Mate /6 Skill Builder

68 Skill.00 Comparing fractions. First shade each fraction on the identical shapes. Then compare the shaded areas to decide which is the largest. Q. Shade the diagrams below to compare and. 9 Which fraction is larger? A. 9 Shade two thirds of the first rectangle. Shade five ninths of the second rectangle. The fractions are close in value however is slightly greater than. 9 a) Shade the diagrams below to compare and. 4 Which fraction is larger? b) Shade the diagrams below to compare and. 4 Which fraction is larger? 4 c) Shade the diagrams below to compare and. Which fraction is smaller? d) Shade the diagrams below 7 to compare and. 4 8 Which fraction is larger? e) Shade the diagrams below 4 4 to compare and. 7 Which fraction is larger? f) Shade the diagrams below to compare and. 4 6 Which fraction is smaller? e) Shade the diagrams below to compare and. 9 Which fraction is larger? f) Shade the diagrams below 4 to compare and. 8 7 Which fraction is smaller? page 6 Maths Mate /6 Skill Builder

69 Skill. Finding a fraction of a whole number. First find one fraction of the number by dividing by the denominator. Then multiply the number of fractions you need by the result. Example: Three fifths of 0? First find one fifth of 0 by dividing 0 by. 0 = Then find three fifths of 0 by mulyiplying by. = 6 So three fifths of 0 is 6. Q. Eric kicked two thirds of his team s goals. How many goals did he kick? A. 8 Find one third of. Divide by. = 4 Find two thirds of. Multiplying by 4. 4 = 8 a) Three fourths of the 8 students in the class are boys. How many boys are in the class? one fourth of 8 = 8 4 = 7... three fourths of 8 = 7 =... b) Two fifths of the 0 children at the nursery had the flu. How many children were ill? one fifth of 0 =... two fifths of 0 =... c) Ian scored five eighths of the 40 points on the test. How many points did he score? one eighth of 40 =... five eighths of 40 =... d) Of the 4 students in a class, one third are chosen for the school play. How many students are chosen for the play? one third of 4 =... e) Five sixths of the 0 horses in the race jumped over the first hurdle. How many horses passed the first hurdle? one sixth of 0 =... five sixths of 0 =... f) Of the 00 cakes at a party, seven tenths were eaten in the first hour. How many cakes were eaten in the first hour? one tenth of 00 =... seven tenths of 00 =... page 7 Maths Mate /6 Skill Builder

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71 . [Place Value] Skill. Understanding the place value of a digit in a number (). When writing numbers the following is true: Each digit in a number occupies a special place or column. Larger numbers have their largest digits first (ordered from left to right). Smaller numbers have their smallest digits first (ordered from left to right). Even numbers have as their last digits either 0,, 4, 6 or 8. Odd numbers have as their last digits either,,, 7 or 9. continues on page 60 Place value thousands hundreds tens units tenths hundredths thousandths Q. What is the largest odd, 4 digit number, that contains the digits 0, 4, and 7? A. 740 To make the largest odd number, move the smallest odd digit to last place. Both and 7 are odd but is smallest, so goes last. Order the remaining digits 0, 4 and 7 from largest to smallest: 740 a) What is the smallest even, digit number that contains the digits, 6 and 7? 76 b) What is the smallest odd, digit number that contains the digits, 6 and 9? c) What is the smallest even, 4 digit number that contains the digits,, 6 and 7? d) What is the largest odd, 4 digit number that contains the digits 0,, 8 and 9? e) What is the largest even, digit number that contains the digits, 4 and 8? f) What is the largest odd, digit number that contains the digits 4, and 8? g) What is the largest odd, 4 digit number that contains the digits,, and 6? h) What is the smallest even, digit number that contains the digits 0, 4 and 7? page 9 Maths Mate /6 Skill Builder

72 Skill. Understanding the place value of a digit in a number (). Q. In the number 89 which of the digits, 8, 9 or lies in the hundreds column? A. 8 continued from page 9 The digit three places to the left of the decimal point is in the hundreds place. So 8 is in the hundreds column. i) In the number 0 which of the digits, or 0 lies in the tens column? j) In the number 47 which of the digits, 4, 7 or lies in the hundreds column? k) In the number 006 which of the digits, 0 or 6 lies in the thousands column? l) In the number 0 which of the digits,, 0 or lies in the units column? m) In the number 447 which of the digits, 4 or 7 lies in the thousands column? n) In the number 64. which of the digits, 6, 4 or lies in the units column? o) In the number 70 which of the digits 7,, or 0 lies in the hundreds column? p) In the number.6 which of the digits,, or 6 lies in the hundredths column? q) In the number 49 which of the digits, 4, 9 or lies in the tens column? r) In the number 4.7 which of the digits 4,, 7 or lies in the tenths column? s) In the number 76 which of the digits 7,, 6 or lies in the thousands column? t) In the number.80 which of the digits,, 8 or 0 lies in the units column? u) In the number.0 which of the digits, 0, or lies in the hundredths column? v) In the number 78.9 which of the digits 7, 8, 9 or lies in the tenths column? page 60 Maths Mate /6 Skill Builder

73 Skill. Finding the value of a digit in a number. Compare the position of the digit to that of the decimal point. Hint: There is a decimal point which is not written, at the end of any whole number. Place value Value thousands 000 hundreds tens units tenths 8 0 hundredths 00 thousandths Decimal point Q. What is the value of the numeral 6 in the number 4.96? Q. In which number does the digit have the greater value? A) B) 900 A = 0.06 A. B Consider the position of the numeral 6 to that of the decimal point. 6 is two places to the right so it is in the hundredths place. The 6 represents 6 hundredths or 6 00 Check the position of the digit. In 900 the is in the thousands place. In the is in the hundreds place. So has greater value in 900. a) What is the value of the numeral in the number 467? 00 b) What is the value of the numeral 7 in the number 7? c) What is the value of the numeral 6 in the number 9.6? d) What is the value of the numeral in the number.0? e) In which number does the digit 8 have lesser value? A) 987 B) 8 f) In which number does the digit have greater value? A) 67 B) 49 g) In which number does the digit have greater value? A) 9 B) 67 h) In which number does the digit 4 have lesser value? A) 40 B) 647 i) Which digit in 4087 is in the same place as the in 6? j) Which digit in 8. is in the same place as the 4 in.47? page 6 Maths Mate /6 Skill Builder

74 Skill. Comparing whole numbers. Compare the size of the digits in the same place, one at a time. Work from left to right across each number. Q. Which number is greater? 46 or 64? A. 64 Thousands: Both numbers have the digit in the thousands place. Hundreds: Both numbers have the digit in the hundreds place. Tens: In the tens place 6 is greater than 4. So 64 is greater than 46. a) > True or false? c) 677 < 766 True or false? false b) 64 < 46 True or false? d) > True or false? e) 878 > 887 True or false? f) 646 < 646 True or false? g) 404 < 404 True or false? h) 00 > 00 True or false? i) Which number is smaller? or j) Which number is smaller? or k) Which number is greater? 788 or 778 l) Which number is smaller? 4 or 4 m) Which number is greater? 77 or 77 n) Which number is smaller? or o) Which number is greater? 64 or 64 p) Which number is smaller? 747 or 774 page 6 Maths Mate /6 Skill Builder

75 Skill.4 Ordering whole numbers. Compare the size of the digits in the same place, one at a time. Work from left to right across each number. Q. Place in order from largest to smallest: 00, 98, 08, 0 A. 08, 0, 00, 98 Hundreds: 00 is larger than 00. Tens: All of the three numbers starting with have zero in the tens place. Units: The three numbers starting with have the digits 0, 8 and in the units place. Ordering from largest to smallest gives 8,, and 0. So far in order we have 08, 0, 00. Then place 98. a) Place in order from largest to smallest:, 7,, 7, 7 b) Place in order from smallest to largest: 78, 87, 8, 7, 77 c) Place in order from largest to smallest:, 4, 4, 4, d) Place in order from smallest to largest: 46, 4, 4,, 4 e) Place in order from largest to smallest: 768, 786, 776, 787 f) Place in order from smallest to largest: 46, 46, 46, 64 g) Place in order from largest to smallest: 00, 00, 00, 00 h) Place in order from smallest to largest: 0, 0, 00, page 6 Maths Mate /6 Skill Builder

76 Skill. Comparing decimal numbers. Line up the decimal numbers at their decimal points. Compare digits in their same place values, starting from the left. Q..6 <.07 True or false? Q. Which number is greater? 4.0 or 4.0 A. False A. 4.0 Remember < means less than. Units: They are both. Tenths: 6 is greater than 0. OR 6 > 0 Therefore.6 is not less than.07 and the statement is false. Units: They are both 4. Tenths: is greater than 0. OR > 0 Therefore 4.0 is greater than 4.0 a) 4. > 4. True or false? false b). <.0 True or false? c). <.0 True or false? d) 4. > 4. True or false? e) 89.9 < 400 True or false? f) > 0.66 True or false? g) Which number is greater? 6.8 or h) Which number is smaller?.4 or.4 i) Which number is greater?. or. j) Which number is smaller?.88 or.78 k) Which number is greater?. or. l) Which number is smaller?.7 or.07 page 64 Maths Mate /6 Skill Builder

77 Skill.6 Ordering decimal numbers. Line up the decimal numbers at their decimal points. Compare digits in their same place values, starting from the left. Q. Place in order from largest to smallest: 9.8, 8.9, 8.8, 9 A. 9.8, 9, 8.9, 8.8 Units: 9 is larger than 8. Tenths: 9 is larger than 8. When the number is whole like the 9 then think of it as is larger than 8, which is larger than 0 a) Place in order from smallest to largest:.,,.,.,.,.,. b) Place in order from largest to smallest:.,.,.,. c) Place in order from smallest to largest: 6.7, 7.7, 6.6, 6, d) Place in order from largest to smallest: 4.9, 9.4, 9, 4.4 e) Place in order from smallest to largest: 4.0, 40., 4.4, 40.4 f) Place in order from largest to smallest:.,.0,., g) Place in order from smallest to largest:.4, 4,.4,.04 h) Place in order from largest to smallest:.6,.6, 6.,.6 page 6 Maths Mate /6 Skill Builder

78 Skill.7 Rounding whole numbers to a given place. If the digit to the right of the place is 0,,, or 4 - round down - keep the digit in the requested place unchanged., 6, 7, 8 or 9 - round up - add to the digit in the requested place. Keep the number of digits in the answer the same as in the question by using zeros to fill the vacated spaces. Q. Round 448 to the nearest ten. A. 40 The digit to the right of the tens place is 8 so round up. Add to the 4 in the tens place. Use a zero in the units place. a) Round 7 to the nearest ten. 60 b) Round 7 to the nearest ten. c) Round 66 to the nearest ten. d) Round 69 to the nearest ten. e) Round 804 to the nearest ten. f) Round 49 to the nearest ten. g) Round 77 to the nearest hundred. 800 h) Round 09 to the nearest hundred. i) Round 4 to the nearest hundred. j) Round 48 to the nearest hundred. k) Round to the nearest hundred. l) Round 48 to the nearest hundred. m) Round 78 to the nearest hundred. n) Round 44 to the nearest hundred. page 66 Maths Mate /6 Skill Builder

79 Skill.8 Rounding decimal numbers to the nearest whole number. If the digit to the right of the decimal point is 0,,, or 4 - round down - keep the digit in the unit place unchanged., 6, 7, 8 or 9 - round up - add to the digit in the unit place. Leave off all digits after the decimal point. Q. Round 8. to the nearest whole number. A. 8 The digit to the right of the decimal point is. Round down by keeping the 8 in the units place unchanged. a) Round.08 to the nearest whole number. b) Round 9.06 to the nearest whole number. c) Round 4.9 to the nearest whole number. d) Round 6.7 to the nearest whole number. e) Round.7 to the nearest whole number. f) Round 4. to the nearest whole number. g) Round.8 to the nearest whole number. h) Round 4. to the nearest whole number. i) Round 0.7 to the nearest whole number. j) Round 0.9 to the nearest whole number. k) Round. to the nearest whole number. l) Round 8.6 to the nearest whole number. m) Round.79 to the nearest whole number. n) Round 4.8 to the nearest whole number. page 67 Maths Mate /6 Skill Builder

80 Skill.9 Estimating outcomes by rounding to the nearest 0 or 00. If the digit to the right of the requested place is 0,,, or 4 - round down - keep the digit in the requested place unchanged., 6, 7, 8 or 9 - round up - add to the digit in the requested place. Keep the number of digits in the answer the same as in the question by using zeros to fill the vacated spaces. Q. Estimate the difference between 48 and 0 by rounding to the nearest ten before subtracting. A Round 48 up to 40 and 0 down to 00. Subtract these answers to estimate the difference. a) Estimate the product of 8 and by rounding to the nearest ten before multiplying c) Estimate the sum of and 49 by rounding to the nearest ten before adding b) Estimate the sum of 7 and 9 by rounding to the nearest ten before adding d) Estimate the sum of 48 and by rounding to the nearest ten before adding.... e) Estimate the difference between 888 and 4 by rounding to the nearest hundred before subtracting.... f) Estimate the difference between 4 and 49 by rounding to the nearest ten before subtracting.... g) Estimate the product of 8 and 64 by rounding to the nearest ten before multiplying.... h) Effie swam 8 km, rode her bike km and ran km. Estimate the total distance travelled by rounding to the nearest tens.... page 68 Maths Mate /6 Skill Builder

81 Skill.00 Estimating outcomes by rounding decimals to whole numbers. If the digit to the right of the decimal point is 0,,, or 4 - round down - keep the digit in the unit place unchanged., 6, 7, 8 or 9 - round up - add to the digit in the unit place. Leave off all digits after the decimal point. Q. Estimate the total cost by rounding to the nearest whole dollars: $. + $.0 + $ $6.9 A. $. + $.0 + $ $6.9 $ + $ + $ + $7 $0 Round each dollar value, then add to estimate the total cost. a) Estimate the sum of the decimals.4 and 8.7 by rounding to the nearest whole numbers c) Estimate the difference of the decimals.8 and.9 by rounding to the nearest whole numbers.... e) Estimate the perimeter of a rectangular yard with a length of 4.7 m and a width of 8. m by rounding to the nearest whole metres g) Estimate the total cost by rounding to the nearest whole dollars: $0.0 + $. + $8.9 + $6. b) Estimate the difference of the decimals 9. and 6.8 by rounding to the nearest whole numbers d) Estimate the sum of the decimals 7.6 and 6. by rounding to the nearest whole numbers.... f) Estimate the difference of the decimals 6.7 and.0 by rounding to the nearest whole number.... h) Estimate the total cost by rounding to the nearest whole dollars: $4.9 + $9.8 + $. + $ page 69 Maths Mate /6 Skill Builder

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83 . [Order of Operations] Skill. Using order of operations involving + and/or Add ( + ) and/or subtract ( ) from left to right. Q = A = = = + 6 = 7 Start with 8 and subtract. The result is 6. Then subtract from 6. The result is. Finally add 6 to the. a) = b) 6 + = c) = = 4 d) = e) = f) 6 + = g) = h) 7 4 = i) = j) = k) = l) = + = = 0 m) = n) + 7 = o) 9 = p) = q) = r) = page 7 Maths Mate /6 Skill Builder

84 Skill. Using order of operations involving and/or Multiply ( ) and/or divide ( ) from left to right. Q. = A. = = 4 = 0 Start with and divide by. The result is 4. Then multiply 4 by. a) = b) = c) 6 4 = 0 = 0 d) 4 = e) = f) = g) 4 4 = h) 8 6 = i) 7 7 = j) 4 = k) 9 6 = l) 0 = 8 = 6 m) 6 = n) 4 = o) 4 4 = p) 4 = q) 8 7 = r) 4 6 = page 7 Maths Mate /6 Skill Builder

85 Skill. Using order of operations involving single or and + or Multiply ( ) and/or divide ( ) from left to right. Add ( + ) and/or subtract ( ) from left to right. Q. 6 + = A. 6 + = = = 0 First do divided by. The result is 4. Then add 6 and 4. a) = b) 4 + = c) = 7 = d) = e) 4 = f) 6 + = g) = h) = i) = j) = k) = l) 0 = 9 = 4 m) 7 = n) = o) = p) 8 = q) = r) 8 6 = page 7 Maths Mate /6 Skill Builder

86 Skill.4 Using order of operations involving brackets ( ) Simplify within the brackets. Multiply ( ) and/or divide ( ) from left to right. Add ( + ) and/or subtract ( ) from left to right. Q. 9 + (9 ) = A. 9 + (9 ) = = = 9 + = Simplify inside the brackets and subtract from 9. The result is 4. Then divide by 4. The result is. Finally add 9 and. a) 7 (4 ) = b) 9 (4 + ) = c) ( ) + 7 = 7 = 4 d) 8 + ( ) = e) (4 + 4) = f) ( ) = g) 7 (6 ) = h) (8 6) = i) 8 ( 7) = j) 8 + ( + ) = k) 4 + ( ) = l) ( + ) = = 8 + = m) (9 + 7) 4 = n) 8 (9 ) + = o) 9 + (8 4) = page 74 Maths Mate /6 Skill Builder

87 4. [Word Numbers] Skill 4. Expressing word numbers in numerals. Rule : Leave a space, or put a comma, between the thousands and the hundreds. : Write a zero in any place that is left empty between other digits. Q. Express in numerals: Eighteen thousand, seven hundred and two. a) Express in numerals: Six thousand, three hundred and fifty-four. A Tens of thousands 8 7 The digits and 8, 7 and will be in the number. Numbers read from left to right so start with 8 thousand. The last digit of this number goes in the thousands position. The seven goes in the hundreds position. There is no ten, so put a 0. Write as the unit. b) Express in numerals: Two hundred and eighteen. Places Thousands Hundreds Tens Units 0 c) Express in numerals: Nine hundred and twenty-seven. d) Express in numerals: Eight thousand, four hundred and six. e) Express in numerals: Three thousand and thirteen. f) Express in numerals: Seven thousand and eight. g) Express in numerals: Eighty thousand. h) Express in numerals: Seventy thousand, nine hundred. i) Express in numerals: Sixteen thousand, two hundred and three. j) Express in numerals: Ninety-six thousand. k) Express in numerals: Four hundred thousand. l) Express in numerals: Five hundred thousand and one. page 7 Maths Mate /6 Skill Builder 4

88 Skill 4. Writing -digit numbers in words. General Rules for writing a number in words Rule : Consider one digit at a time starting from the left. : First write the word for the digit (unless it is a 0). Next write the place of the digit. Exceptions for -digit numbers Multiples of 0 have their own words: 0 ten 0 twenty 0 thirty 40 forty 0 fifty 60 sixty 70 seventy 80 eighty 90 ninety For the numbers to 9 use: eleven twelve thirteen 4 fourteen fifteen 6 sixteen 7 seventeen 8 eighteen 9 nineteen For all numbers to 99 use a hyphen (-) to separate the word for the tens from the word for the units. Q. Write the number 7 in words. A. Twenty-seven word first! 00 = Two hundred place next Tens of thousands Places Thousands Hundreds Tens Units 7 Starting from the left the is in the tens position. As a multiple of 0 it has its own word and is written as twenty. The next digit 7 is written as seven. 7, is between and 99, so it has a hyphen - when written in words. a) Write the number in words. thirty-five b) Write the number 8 in words. c) Write the number 69 in words. d) Write the number 6 in words. e) Write the number in words. f) Write the number 74 in words. g) Write the number in words. h) Write the number 48 in words. page 76 Maths Mate /6 Skill Builder 4

89 Skill 4. Writing -digit numbers in words. Rule : Consider one digit at a time starting from the left. : First write the word for the digit (unless it is a 0). Next write the place of the digit. : Always write hundred not hundreds. 4: Place the word and after the word hundred if other values follow. AND Consider the rules for -digit numbers on page 76. Q. Write the number 94 in words. A. Nine hundred and forty-three Tens of thousands Places Thousands Hundreds 9 Tens Units 4 Start from the left. The 9 is in the hundreds position so write nine hundred. Include and as other values follow. The next digit is 4. It is in the tens position so it is written as forty. The is a unit and written as three. 4, is between and 99, so it has a hyphen - when written in words. a) Write the number 60 in words. six hundred and ten b) Write the number 800 in words. c) Write the number 400 in words. d) Write the number 60 in words. e) Write the number 90 in words. f) Write the number 78 in words. g) Write the number 67 in words. h) Write the number 90 in words. i) Write the number 06 in words. j) Write the number 8 in words. page 77 Maths Mate /6 Skill Builder 4

90 Skill 4.4 Writing 4-digit numbers in words. Rule : Consider one digit at a time starting from the left. : First write the word for the digit (unless it is a 0). Next write the place of the digit. : Always write thousand not thousands and hundred not hundreds. 4: Place the word and after the word thousand if there are no hundreds. : Place the word and after the word hundred if other values follow. AND Consider the rules for -digit numbers on page 76. Q. Write the number 60 in words. A. Two thousand, six hundred and ten Tens of thousands Places Thousands Hundreds Tens Units 6 0 Start from the left. The is in the thousands position so write two thousand. The 6 is in the hundreds position so write six hundred. Include and as other values follow. The next two digits are and 0 in the tens and units places. They are written as ten. a) Write the number 08 in words. three thousand and eighteen b) Write the number 6000 in words. c) Write the number 400 in words. d) Write the number 700 in words. e) Write the number 8070 in words. f) Write the number 9090 in words. g) Write the number 00 in words. h) Write the number 4006 in words. i) Write the number 09 in words. j) Write the number 0 in words. page 78 Maths Mate /6 Skill Builder 4

91 Skill 4. Writing -digit numbers in words. Rule : Consider one digit at a time starting from the left. : First write the word for the digit (unless it is a 0). Next write the place of the digit. : Always group the tens of thousands digit to the thousands digit using the -digit rules. 4: Always write thousand not thousands and hundred not hundreds. : Place the word and after the word thousand if there are no hundreds. 6: Place the word and after the word hundred if other values follow. AND Consider the rules for -digit numbers on page 76. Q. Write the number 078 in words. A. Fifteen thousand and seventy-eight Tens of thousands Places Thousands Hundreds 0 Tens Units 7 8 Start from the left. The is in the tens of thousands position and the is in the thousands position so consider them together. Write fifteen thousand. Include and as there are no hundreds. The next digit is 7. It is in the tens position so it is written as seventy. The 8 is a unit and written as eight. 78 is between and 99, so it has a hyphen - when written in words. a) Write the number in words. b) Write the number 000 in words. twenty-seven thousand and six c) Write the number in words. d) Write the number in words. e) Write the number in words. f) Write the number 00 in words. g) Write the number in words. h) Write the number 0 06 in words. page 79 Maths Mate /6 Skill Builder 4

92 Skill 4.6 Writing 6-digit numbers in words. Rule : Consider one digit at a time starting from the left. : First write the word for the digit (unless it is a 0). Next write the place of the digit. : Always group the hundreds of thousands digit and the tens of thousands digit to the thousands digit using the -digit and -digit rules. 4: Always write thousand not thousands and hundred not hundreds. : Place the word and after the word thousand if there are no hundreds. 6: Place the word and after the word hundred if other values follow. AND Consider the rules for -digit numbers on page 76. Q. Write the number in words. A. Nine hundred and fifty thousand and seventy-three Hundreds of thousands 9 Tens of thousands Places Thousands Hundreds Tens Units Start from the left. The 9 is in the hundreds of thousands position, the is in the tens of thousands position and the 0 in the thousands position so consider them together. Write nine hundred and fifty thousand. Include and as there are no hundreds. The next digit is 7. It is in the tens position so it is written as seventy. The is a unit and written as three. 7 is between and 99, so it has a hyphen - when written in words. a) Write the number in words. b) Write the number in words. one hundred thousand and thirty c) Write the number in words. d) Write the number in words. e) Write the number in words. f) Write the number 0 04 in words. g) Write the number in words. h) Write the number in words. page 80 Maths Mate /6 Skill Builder 4

93 . [Number Patterns] Skill. Completing number patterns by adding the same number. Find the number used to get from term to term. Find the operation used to get from term to term. Hint: Every number pattern is created by a rule involving numbers and operations. Q., 7,, 9,, _,, _ A., 7,, 9,, 7 Ask: Answer: Are the numbers increasing or decreasing? How can you get from to 7? To get from to 7, add 6. To get from 7 to, add 6. To get from to 9, add 6 and so on. So the rule of the pattern is: Add 6 to the previous number. Apply this rule to the last given number. + 6 = + 6 = 7 a), 9,, 7,, _, 9 _ b) 9, 4, 9, 4, 9, _, _ Rule: Add 4 to the previous number Rule: c) 8,, 4, 7, 0, _, _ d) 6, 6, 6, 6, 46, _, _ Rule: Rule: e), 0, 7, 4,, _, _ f), 4,,, 4, _, _ Rule: Rule: page 8 Maths Mate /6 Skill Builder

94 Skill. Completing number patterns by subtracting the same number. Find the number used to get from term to term. Find the operation used to get from term to term. Hint: Every number pattern is created by a rule involving numbers and operations. Q. 9, 0, 4,,, _,, _ A. 9, 0, 4,,, Ask: Answer: Are the numbers increasing or decreasing? How can you get from 9 to 0? To get from 9 to 0, subtract 9. To get from 0 to 4, subtract 9. To get from 4 to, subtract 9 and so on. So the rule of the pattern is: Subtract 9 from the previous number. Apply this rule to the last given number. 9 = = a) 4, 8,, 4, 7, 0 _, _ b) 6, 4,, 0, 8, _, _ Rule: Subtract 7 from the previous number Rule: c) 4, 6, 0, 4, 8, _, _ d), 8,, 8,, _, _ Rule: Rule: e), 4,, 7, 9, _, _ f), 47, 4, 9,, _, _ Rule: Rule: page 8 Maths Mate /6 Skill Builder

95 Skill. Completing number patterns by multiplying by the same number. Find the number used to get from term to term. Find the operation used to get from term to term. Hint: Every number pattern is created by a rule involving numbers and operations. Q.,,,, _, _ A.,,,, 6, Ask: Answer: Are the numbers increasing or decreasing? How can you get from to? To get from to, multiply by. To get from to, multiply by. To get from to, multiply by etc. So the rule of the pattern is: Multiply the previous number by. Apply this rule to the last given number. = 6 6 = a), 8,, 8, _, 048 _ b),, 4, 8, _, _ Rule: Multiply the previous number by 4... Rule:... c),, 9, 7, _, _ d) 9, 8, 6, 7, _, _ Rule: Rule: e),, 8,, _, _ f) 0.,,,, _, _ Rule: Rule: page 8 Maths Mate /6 Skill Builder

96 Skill.4 Completing number patterns by dividing by the same number. Find the number used to get from term to term. Find the operation used to get from term to term. Hint: Every number pattern is created by a rule involving numbers and operations. Q. 8, 7, 9,, _, _ A. 8, 7, 9,, _, _ Ask: Answer: Are the numbers increasing or decreasing? How can you get from 8 to 7? To get from 8 to 7, divide by. To get from 7 to 9, divide by. To get from 9 to, divide by and so on. So the rule of the pattern is: Divide the previous number by. Apply this rule to the last given number. = = a) 64,, 6, 8, 4_, _ b) 4,, 6, 8, _, _ Rule: Divide the previous number by Rule: c) 4096, 04, 6, 64, _, _ d) 70, 70, 0, _, _ Rule: Rule: e) 97, 4, 08, 6, _, _ f) 4,,,, _, _ Rule: Rule: page 84 Maths Mate /6 Skill Builder

97 Skill. Completing number patterns by using changing values in the rule. Find the number used to get from term to term. Find the operation used to get from term to term. Hint: Every number pattern is created by a rule involving numbers and operations. Counting numbers, even numbers and odd numbers have patterns themselves that will create changing numbers in the rule. Q. 0, 49, 46, 4, 4, _, _ A. 0, 49, 46, 4, 4, _, 4 _ Ask: Answer: Are the numbers increasing or decreasing? How can you get from 0 to 49? To get from 0 to 49, subtract. To get from 49 to 46, subtract. To get from 46 to 4, subtract and so on. So the rule of the pattern is: Subtract consecutive odd numbers from the previous number. Apply this rule to the last given number. 4 9 = = 4 a),, 6, 8,, _, 0 _ b), 4, 8, 4,, _, _ Rule: Add consecutive counting numbers Rule: c) 4, 0, 0,, 6, _, _ d),,, 0,, _, _ Rule: Rule: e), 0, 8,,, _, _ f), 9,, 0, 4, _, _ Rule: Rule: page 8 Maths Mate /6 Skill Builder

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99 6. [Units of Measurement] Skill 6. Selecting the appropriate units of measurement. Compare the size, mass or capacity to that of common objects (tennis court, bag of flour or carton of milk). Consider any standard units you know, chosen because they are sensible and accurate. Example: Carpenters measure wood lengths in millimetres. Height of a person is measured in centimetres. Mountains are measured in metres. Q. Choose the appropriate units: grams, kilograms or tonnes. The total amount of salt a healthy person should eat each day is 6... a) Choose the appropriate units: millilitres, litres or megalitres. A water tap that drips every second would, each year, waste litres c) Choose the appropriate units: centimetres, metres or kilometres. The highest peak in the Antartic is Mt Vinson with a height of A. grams The weight of the nutritional elements of food are usually measured in grams or milligrams. Compare the amount of salt to known amounts of a single unit e.g. kilogram of sugar or a tonne truck. b) Choose the appropriate units: millilitres, litres or megalitres. The capacity of one cup is about 0... d) Choose the appropriate units: grams, kilograms or tonnes. The heaviest animal, the blue whale, weighs about e) Choose the appropriate units: centimetres, metres or kilometres. From the Snowy Mountains to the Southern Ocean, the Murray River has a length of 0... f) Choose the appropriate units: centimetres, metres or kilometres. The world s tallest waterfall is Angel Falls in Venezuela measuring g) Choose the appropriate units: millilitres, litres or megalitres. The amount of juice in an average lemon is about... h) Choose the appropriate units: grams, kilograms or tonnes. The average amount of rubbish produced by every Australian each year is... page 87 Maths Mate /6 Skill Builder 6

100 Skill 6. Estimating length, mass etc. using units of measurement. Q. How many of these objects are likely to have a capacity of less than litre? A soap dispenser A bath A perfume bottle A hand basin A. Compare the capacity of each object to that of a standard object that you know e.g. litre of milk. Only the soap dispenser and perfume bottle would be likely to have a capacity of less than litre. a) How many of these objects are likely to have a capacity of greater than litre? A human mouth A soft drink can A bird bath A salt shaker b) How many of these objects are likely to have a mass of less than kilogram? A dozen eggs A block of chocolate A loaf of bread A box of washing powder c) How many of these objects are likely to have an area of more than square metre? An open book A doona A cinema screen A bath mat d) How many of these objects are likely to have a temperature of greater than 0 degrees Celsius? A lake A person A furnace A cellar e) How many of these objects are likely to have a mass of less than tonne? An ocean liner A helium balloon A Great Dane A Murray Grey bull f) How many of these places are likely to have an area of less than hectare? Tooronga Zoo Kakadu National Park Centre court - Wimbledon Melbourne Cricket Ground g) How many of these objects are likely to have a temperature of less than 0 degrees Celsius? A salad An ice cream A bowl of soup A glass of tap water h) How many of these objects are likely to have a capacity of less than litre? A cattle trough A toilet cistern A baby s bottle A wheel barrow page 88 Maths Mate /6 Skill Builder 6

101 Skill 6. Converting length units. To change from smaller units to larger units Divide by the conversion factor (because you need less). Example: To change 40 mm to cm by 0 Hint: Conversion Facts km = 000 m = cm = mm m = 00 cm = 000 mm cm = 0 mm To change from larger units to smaller units Multiply by the conversion factor (because you need more). Example: To change 4 cm to mm by 0 mm cm 4 Q. Which is greater? 600 cm or mm A. 600 cm 0 = 6000 mm mm Decide which unit to convert. To convert cm to mm, multiply by 0. a) Write in metres: 000 cm = 0 m 00 cm = m so =... b) Write in centimetres: 00 mm = cm... c) Write in metres: d) Write in millimetres: km = m 60 cm = mm e) Express in metres: f) Express in millimetres: 00 cm + m = m 4 cm + 00 mm = mm g) Which is greater? km or 00 m h) Which is greater? 4000 cm or m i) Place the following in order of increasing length: 60 m, 6 km, cm. j) Place the following in order of increasing length: m, mm, 000 cm page 89 Maths Mate /6 Skill Builder 6

102 Skill 6.4 Converting mass units. To change from smaller units to larger units Divide by the conversion factor (because you need less). Example: To change 000 g to kg by 000 To change from larger units to smaller units Multiply by the conversion factor (because you need more). Example: To change kg into g by 000 Hint: Conversion Facts tonne = 000 kg = g kg = 000 g 000 g kg Q. Express in grams: 4 g + kg = A. 4 g + kg = = g = 004 g To convert kg to g, multiply by 000. kg 000 = 000 g a) Write in grams: 0 kg = g kg = 000 g so =... b) Write in kilograms: t = kg... c) Write in tonnes: d) Write in grams: 000 kg = t 4 kg = g e) Express in grams: f) Express in tonnes: g + 4 kg = g 7 t kg = t g) Which is greater? 9 kg or 000 g h) Which is greater? 7 t or 800 kg i) Place the following in order of increasing mass: kg, 0 t, 4000 g. j) Place the following in order of increasing mass: 000 kg, 0 t, g page 90 Maths Mate /6 Skill Builder 6

103 Skill 6. Converting capacity units. To change from smaller units to larger units Divide by the conversion factor (because you need less). Example: To change 000 ml to L by 000 To change from larger units to smaller units Multiply by the conversion factor (because you need more). Example: To change L to ml by 000 Hint: Conversion Facts ML (megalitre) = 000 kl = L kl = 000 L L = 000 ml (millilitre) L L = 000 ml 000 ml Q. Place the following in order of increasing capacity: 6000 ml, L, 600 ml. A ml L 000 = 000 ml 600 ml 600 ml, L, 6000 ml Change each amount to the same unit. To convert L to ml, multiply by 000. a) Write in megalitres: kl = 0 ML b) Write in millilitres: L = ml 000 kl = ML so = c) Write in litres: d) Write in kilolitres: 000 ml = L L = kl e) Express in litres: f) Express in millilitres: L ml = L ml + L = ml g) Which is greater? ml or 4 L h) Which is greater? 000 kl or L i) Place the following in order of increasing capacity: 6000 ml, kl, 700 L. j) Place the following in order of increasing capacity: 000 ml, 9 L, 900 ml page 9 Maths Mate /6 Skill Builder 6

104 Skill 6.6 Working with units of measurement. Q. One lap of the oval fountain in Hyde Park, London is 000 cm. How many metres is this? A = 0 m To convert cm to m divide by 00. a) How many metres above sea level is Arthurs Seat, the highest point on Victoria s Mornington Peninsula, if it is 00 times the height of a 00 cm person? = cm = m b) How many basketballs, each with a mass of 60 g, can be taken by the coach on to the plane if there is only two and a half kilograms allowed? c) How many 0 ml cups are necessary to fill a L vase? d) An average orange has a mass of 00 g. How many oranges would you expect to find in a kg bag? e) A half flush of a toilet uses 6 L of water. How many millilitres is this? f) Charlie s average stride length is 80 cm. At this rate, how many steps would he take to run the 400 m? ml g) How many metres above ground is Uluru if it is 6 times the height of a 0 cm tree? m h) A 0 piece is about mm wide. How many 0 pieces, end to end, would you need to run the length of a table that is cm long? page 9 Maths Mate /6 Skill Builder 6

105 7. [Time] Skill 7. Expressing the time in words. To say the minutes first: If the bigger hand is between and 6 you say past the hour. Example: twenty past eight. If the bigger hand is between 6 and you count back to the next hour. Example: ten to nine. Or say a quarter past eight Q. Express in words the time shown on this watch. FRI 6 half past ten a quarter to two a) Express in words the time shown on the wall clock. To say the hours first: Say the number that the smaller hand is on or just past. Hint: Hours (h) Minutes (min) Smaller hand Bigger hand number = h mark = min lap = h number = min lap = h = 60 min A. Five to five or Four fifty-five past 0 past 0 to or 4 past quarter to 40 past 0 to past to to o clock past 0 past 0 past past 0 or half past or quarter past The big hand has turned minutes. It is nearly back to the o clock. The little hand is almost, but not quite up to the five. b) Express in words the time shown on the watch. OR two twenty-five twenty-five past two c) Express in words the time shown on the mantle clock. 9 d) Express in words the time shown on the clock. IX X XI XII I II III 6 VIII VII VI V IV page 9 Maths Mate /6 Skill Builder 7

106 Skill 7. Expressing the time in numbers. Write the hours first. The smaller hand will be exactly on or just past a number. Then put the symbol : Count clockwise by s from (or 0 minutes) to the smaller hand. Write the minutes. Example: The clock shows 8:0 (eight twenty) and 0 8:0 (eight fifty) Hint: 0 0 Hours (h) Minutes (min) 4 Smaller hand Bigger hand 40 0 number = h mark = min lap = h number = min 0 lap = h = 60 min Q. Express in numerals the time shown on the clock face. IX X XI VIII VII XII VI I V II IV III A. : 0 XII XI X IX VIII VII VI 0 I 0 II III IV 0 V Counting from, the big hand has turned minutes. The little hand is just past or midway between the (II) and the (III). a) Express in numerals the time shown on the clock. b) Express in numerals the time shown on the clock. 9 6 : 0 : c) Express in numerals the time shown on the watch. d) Express in numerals the time shown on the clock. SAT : : e) Express in numerals the time shown on the clock. f) Express in numerals the time shown on the watch. : : page 94 Maths Mate /6 Skill Builder 7

107 Skill 7. Identifying centuries. Say the year number, hundreds first and then say the rest. Example: eight hundred and nine. 9 - nineteen hundred and thirty-two. Add to the hundreds number to find the century. Example: Television started in 9, in the 0th century. + Hint: Years in the first century do not start with a. Years in the nd century start with a. Similarly years in the 0th century start with a 9. Because of the first century the names of centuries seem like they are 00 years ahead of the numbers. Years Century st nd rd 4th 9th 0th st Q. In which century did the Ming Dynasty (68-644) become the ruling dynasty of China? a) Christopher Columbus discovered America in 49. Which century was this? th century A. 4th century Counting from year one, 68 is in the 4th block of 00 years so the Ming Dynasty began in the 4th century. b) In 066 the Vikings and the Normans invaded England, trying to claim the throne. Which century was it? c) In which century was telephone inventor Alexander Graham Bell (847-9) born? d) The last shipment of convicts to Tasmania arrived fifty three years into the 9th century. Which year was this? e) Inventor David Unaipon (87-967) of the Ngarringdjeri people was the first Aboriginal writer to be published. In which century did he die? f) Renaissance artist Sandro Botticelli (44-0) died in Florence, Italy in which century? g) Eleven years before the end of the th century eye glasses were invented. What year was this? h) The first school was established in Australia years before the start of the 9th century. What was the year? page 9 Maths Mate /6 Skill Builder 7

108 Skill 7.4 Showing the time on an analogue clock. Drawing the minute (min) hand. If the time says past : Count clockwise by s, touching as you go, the clock numbers starting with. Example: twenty past eight 8:0 Hint: Quarter past is min past. If the time says to : Count anti-clockwise by s touching as you go, the clock numbers starting with. Example: ten to nine Hint: Quarter to is min to. If the time given is digital: Count clockwise by s from (or 0 min) Example: eight twenty 8:0 or eight fifty 8:0 Q. Draw hands on the clock to show that the time is quarter past eight. a) Draw hands on the alarm clock to show that the time is 9:40. c) Complete the clock face to show the time 8:0. X 9 XI 6 XII I II 9:40 is 4 hour time. An analogue clock shows hours. Once the time goes past noon, subtract to get back to hour time. To show 9:40 you would set the hands at 7:40 Drawing the hour (h) hand. If the time says past : Draw the smaller hand after the hour. If the time says to : Draw the smaller hand before the hour. If the time given is digital: Draw the hour hand on or past the hour and moving toward the next number. Example: eight fifty 8:0 A. past to 0 past 0 to or 4 past quarter to 40 past 0 to past to o clock past 0 past 0 past past 0 or half past or quarter past One quarter of 60 is. 9 So the big hand is at 6 minutes past. Counting by s the big hand is pointing to the. The little hand is quarter of the way past the eight and toward the nine. b) Complete the clock face to show that the time is half past ten. d) Draw hands on the watch to show that the time is :0. IX III VIII VII VI V IV e) Complete the clock face to show the time hours and 0 minutes later. f) Complete the clock face to show the time 4 hours and minutes earlier page 96 Maths Mate /6 Skill Builder 7

109 Skill 7. Converting time units. Hint: Conversion Facts century = 00 years decade = 0 years year = months = weeks = 6 days leap year = 66 days fortnight = weeks week = 7 days day = 4 hours hour = 60 minutes minute = 60 seconds Days in the month: 0 days have September April June and November. All the rest have except for February alone which has 8 days clear and 9 in each leap year. Q. Write in days: Month of July =. A. days July has days as in the rhyme. a) Write in years: b) Write in days: decade = 0 years 4 hours = day c) Write in days: d) Write in minutes: Month of May = days hour = min e) Write in weeks: f) Write in seconds: fortnight = weeks min = s g) Write in years: century = years h) Write in hours: 60 minutes = hours i) Write in days: j) Write in days: year = days week = days page 97 Maths Mate /6 Skill Builder 7

110 Skill 7.6 Calculating periods of time. When calculating hours forward: Change from am to pm when you pass noon. Change from pm to am when you pass midnight. When calculating minutes forward: After 60 minutes go to the next hour. When calculating hours backward: Change from pm to am when you pass noon. Change from am to pm when you pass midnight. When calculating minutes backward: After 60 minutes go to the previous hour. Q. The movie A hitchhiker s guide to the galaxy runs for 0 minutes. If the movie finishes at :0 pm, at what time does it start? A. :0 am Convert 0 minutes to hours and minutes. 0 min = h + 0 min. The finish time is h + 0 min after midday. So, the start time would be 0 min before midday or :0 am. a) The Australian F Grand Prix starts at :00 pm. At what time will it finish if it goes for hour and minutes? :00 + :... b) Clarke woke at 6:0 am after 0 hours sleep. At what time did Clarke go to sleep? : pm :... c) The movie started at :40 and played for 0 minutes. At what time did the movie finish?... e) A fruit cake requires 7 minutes baking time. It is :0 am when the mix is put in the oven. At what time will the cake be cooked?... g) Queen s Bohemian Rhapsody plays for nearly 6 minutes. If the song finishes when the clock strikes 0:00 pm, at what time did it start?... : : : d) Samantha was in a queue for hours and minutes and purchased concert tickets at :0 pm. At what time did she join the queue?... f) Fred made an appointment for :0 pm. It is now 9: am. How long does Fred have to wait?... h) The women s world record for the 000 m is 8:06.. The youth world record for girls over the same distance is 8:6.4. How much faster are the women?... : : s page 98 Maths Mate /6 Skill Builder 7

111 Skill 7.7 Reading timetables. Q. According to the schedule, what is the longest amount of time the Yarraville Library is open for in any one day? Yarraville Library Opening Hours Monday Tuesday Wednesday Thursday Friday Saturday Sunday A. hours Check the number of open hours for each day. 0 am till pm is hours. pm till pm is hours. Closed 0am - pm0am - pm pm - pm pm - pm 0pm - noon Closed a) How much time do you spend watching TV if you watch Jakers through to the end of Roller Coaster? ABC :0 Play School (R) 8786 : Todd World (R) :0 Jakers! (R) 98 4: Basil Brush 778 :00 Roller Coaster 6:0 Doctor Who (R,S) :0 Beat The Chef (S) 844 7:00 News (S) 67 You watch from 4:0 to 6:0. There are 0 min from 4:0 until :00 and h and min after that. b) What train would you need to catch from Central station to be at Bondi station by : am? Eastern Suburbs & Illawarra Line to Bondi Junction Weekdays Redfern 4:9 am 4:49 am :04 am Central 4:4 am 4: am :07 am Town Hall Martin Place Kings Cross Edgecliff Bondi Junction 4:44 am 4:46 am 4:48 am 4:0 am 4: am 4:4 am 4:6 am 4:8 am :00 am :0 am :09 am : am : am : am :8 am h min : c) According to the schedule, what day is it if the Footscray Library is opening at pm? Footscray Library Opening Hours Monday Tuesday Wednesday Thursday Friday Saturday Sunday 0am - 8pm0am - 8pm0am - 8pm0am - 8pm0am - 8pm pm - pm pm - pm d) According to the session times, in what state am I if my showing of Bewitched ends at :4 am? Bewitched (PG) 0 mins Rockingham (WA) 0:00 am Brisbane Regent (QLD) 0: am George St Cinemas (NSW) 0:0 am e) Using hour am/pm time, when is the 6:4 pm flight from Melbourne scheduled to arrive in Mildura on the nd of August, 0? Flights Out: Melbourne to Mildura - Friday Aug 0 Time From Time To Flight Duration 08: Melbourne :0 Melbourne :0 Melbourne 8:4 Melbourne 09:40 Mildura QF078 h m :0 Mildura QF08 h m 6: Mildura QF084 h m 9:0 Mildura QF086 h m f) What is the actual time of arrival at Dean Street if the 8:0 am bus from Wodonga is running 7 minutes late? Hovell St Wodonga Dean St Albury Mylon s Wodonga/Albury Bus Timetable (am) 7:0 7:0 8:00 8:0 9: 9:4 0:0:4::4 7:0 7:40 8:0 8:4 9:0 0:000:0:00:0:00 : page 99 Maths Mate /6 Skill Builder 7

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113 8. [Measuring] Skill 8. Estimating length. EITHER Compare the length of the object to a known length. Example: The line segments shown. OR Measure the length against an everyday object. Example: Your thumb. 0 mm Q. Estimate the length of the eraser. A. 0 mm 0 mm 0 mm The eraser looks to be about five times the length of the 0 mm line. A reasonable estimate would be 0 mm. a) Estimate the length of the tweezers. b) Estimate the length of the postage 0 mm stamp. cm Accept 8 to 9 90 mm cm c) Estimate the length of the lipstick. d) Estimate the length of the hi-liter. 0 mm 0 mm mm mm e) Estimate the length of the lips. f) Estimate the length of the leaf. cm 0 mm cm mm page 0 Maths Mate /6 Skill Builder 8

114 Skill 8. Reading and using scales. Determine the value of each mark and... EITHER Start at zero and count by that amount, pointing to each mark as you go. OR Count on from a known point. Q. At what speed is the car travelling? A. 6 km/h km/h The darker calibrations mark every 0 km. The arrow is between 40 and 60 but after 0 km. The lighter calibrations mark every km. The arrow is at marks after 0. Counting, 4 to 6. The car is travelling at 6 km/h. a) Using the ruler measure the length of the line in centimetres. b) Using the ruler measure the length of the line in centimetres. cm cm cm cm c) Using a ruler measure the length of a side of the square in millimetres. d) According to the thermometer what is the temperature of the room? room temperature -0 C -0 C 0 C 0 C 0 C 0 C 40 C 0 C mm C e) At what speed is the car travelling? f) How much water is in the measuring cylinder? km/h 80 0 ml ml ml 0 ml km/h 0 ml ml page 0 Maths Mate /6 Skill Builder 8

115 Skill 8. Comparing angles to a right angle. Match the point of the angle and a corner of a Maths Mate. Align one line of the angle with a side of the page. If the other line of the angle extends beyond the page, then the angle is greater than a right angle. Example: Turning a quarter of the way around a circle is turning at right angles. Hint: A right angle measures 90 (degrees). It is marked with a corner. Q. Is the angle shown less than, equal to or greater than a right angle? A. greater than The angle appears greater than 90. Check by placing the corner of a Maths Mate inside the angle. a) Is the angle less than, equal to or greater than a right angle? b) Is the angle less than, equal to or greater than a right angle? less than c) Is the angle less than, equal to or greater than a right angle? d) Is the angle less than, equal to or greater than a right angle? e) Is the angle less than, equal to or greater than a right angle? f) Is the angle less than, equal to or greater than a right angle? page 0 Maths Mate /6 Skill Builder 8

116 Skill 8.4 Measuring angles using a protractor. Place the centre of the protractor at the corner (vertex) of the angle. Align one line of the angle with a zero line on the protractor. Take the reading from where the second line of the angle crosses the scale on the protractor. Hint: Protractors can be read using either the inside or outside scale depending on which zero is used. Q. Using the protractor measure the size of the angle shown. A Read from the outside scale. One line of the angle is at 0 and the other line of the angle extends around to a) Using the protractor measure the size of the angle shown. b) Using the protractor measure the size of the angle shown c) Using the protractor measure the size of the angle shown. d) Using the protractor measure the size of the angle shown page 04 Maths Mate /6 Skill Builder 8

117 Skill 8. Calculating the perimeter of a shape using a grid. Q. Find the perimeter of the shape. A. 4 cm cm cm Each grid length measures cm. Mark a starting point. Count the number of grid lengths around the outside of the shape. There are 4 lengths or centimetres. Start here a) Find the perimeter of the shape. b) Find the perimeter of the shape. cm cm cm 4 cm cm cm cm Start here 8cm c) Find the perimeter of the shape. d) Find the perimeter of the shape. cm cm cm cm cm cm e) Find the perimeter of the shape. f) Find the perimeter of the shape. cm cm cm cm cm cm page 0 Maths Mate /6 Skill Builder 8

118 Skill 8.6 Calculating the area of a shape by counting squares & triangles. Q. Find the area of the shape. A. 6 cm cm cm First count the number of complete squares. 4 There are complete squares. Then count the triangles. Each triangle doubled forms square. There are triangles in the shape. Together they make more square. + = 6 cm cm a) How many small squares are needed to cover the shape? b) How many small triangles are needed to cover the parallelogram? c) Find the area of the shape. d) Find the area of the shape. Area cm = cm cm cm cm e) The shapes below have the same: A) perimeter and area B) perimeter C) area P =... A =... f) The shapes below have the same: A) perimeter and area B) perimeter C) area P =... A =... page 06 Maths Mate /6 Skill Builder 8

119 Skill 8.7 Describing volume by counting cubes. Count the number of cubes needed to fill the top layer. unit Multiply this amount by the number of layers. unit cubic unit unit Q. How many cubes were used to make the prism? A. = 4 = 60 First count the cubes in the top layer. There are rows of cubes. Then count the number of layers. There are 4 layers of cubes. a) How many cubes were used to make the prism? 4 4 = 6. 6 =... b) How many cubes were used to make the prism?.... c) How many cubes were used to make the prism?. d) How many cubes were used to make the prism? e) How many cubes were used to make the prism?. f) How many cubes were used to make the prism? g) How many cubes were used to make the prism?. h) How many cubes were used to make the prism? page 07 Maths Mate /6 Skill Builder 8

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121 9. [Location] Skill 9. Locating places using simple bearings (closest, left, first turn). Q. In our Solar System which planet is between Mars and Neptune but closest to Mars? SUN Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune A. Jupiter Check the meaning of any unknown terms used to describe location. Between means somewhere in the middle of the boundaries. Closest means the shortest distance from. a) A dog enters a shed and goes into the pen that is second on the right. What animal is it now with? second b) At Sovereign Hill, which building is between the Ballarat Times and the Tent Maker but closest to the Tent Maker? MAIN STREET Sovereign Hill left first right pig Ballarat Times Confectioner Grocer Tent Maker Clock Maker c) On the Central Line in London which station is between White City and Bond Street but closest to Bond Street? d) From the main entry of the church in the Alamo compound you take the second opening on the left and then the first on the right. Where are you? White City Shepherd s Bush Holland Park Notting Hill Gate London s Central LineQueensway Lancaster Gate Marble Arch Bond Street Confessional Main Entry Nave Sacristy ALAMO - Church Texas USA Chancel Transepts Baptistry page 09 Maths Mate /6 Skill Builder 9

122 Skill 9. Locating places using compass bearings N, E, S and W. Refer to the 4 point compass to find your bearings. Hint: (Clockwise) - Never Eat Sea Weed - North, East, South, West. Q. Which capital city is east of Skopje, the capital of Macedonia? CAPITAL CITIES of EUROPE Warsaw Luxembourg Prague Bern Vienna Ljubljana Zagreb Bratislava Budapest Sarajevo Belgrade Adriatic Rome Sea Skopje Bucharest Sofia Moscow W Istanbul N S Black Sea E A. Istanbul Find Skopje on the map. Consider that you are there. Imagine the central point of a compass on Skopje. Turn and face the direction of the arrow pointing east. Which capital city would you be looking at? a) Hansel and Gretel left a trail along the forest path. In which direction did they walk when they first left their house? W N E Hansel & Gretel s house b) Hermione s house is on the north side of Separation Street. On which side of the street is Ron s house? Hermione Sam Charlotte N S Separation Street Witch's house Lee Ron Sally Lu south c) Of the Queensland cities shown below, which city is the most northerly? d) In which direction is the Red Sea from Saudi Arabia? Mt Isa QUEENSLAND W Cairns Townsville Mackay N S E GREECE TURKEY Crete CYPRUS SYRIA Mediterranean Sea LEBANON ISRAEL LIBYA JORDAN IRAQ Middle East IRAN KUWAIT Longreach Rockhampton EGYPT Red Sea SAUDI ARABIA N Birdsville Goondiwindi Brisbane Gold Coast W S E page 0 Maths Mate /6 Skill Builder 9

123 Beach Blvd Skill 9. Following directions to find a place on a map. Q. Head south from the starting point. Take the first road west and the second south. What beach is at the end of the road? Riverside Fwy Start Long Beach Fwy W LONG BEACH N S E HUNTINGTON BEACH SOUTHERN CALIFORNIA Pacific Coast Hwy ANAHEIM San Diego Fwy NEWPORT BEACH SANTA ANA a) You head south towards E street and turn west. To which number Independence Square are you headed? 4th Street Design Centre Garden Grove Fwy Two Independence Square E Street Harbor Blvd Orange Fwy Costa Mesa Fwy Santa Ana Fwy WASHINGTON D.C. You are here Washington Office Centre One Independence Square Two Independence Square N A. Newport Beach Enlargement ANAHEIM nd south NEWPORT BEACH Riverside Fwy SANTA ANA Consider one movement at a time. Mark your position as you go. b) From the corner of Kiewa and Dean Street you walk east for two blocks and then walk south for two blocks. If you then go west, what street are you in? ALBURY Stanley Street Wodonga Place Townsend Street Kiewa Street To Melbourne Clive Street Dean Street Smollett Street Hume Street Harbor Blvd Orange Fwy Costa Mesa Fwy Swift Street David Street Santa Ana Fwy Young Street Start st west To Sydney W N S E c) Head north on Morphett St. Turn east into North Terrace. Then take the second turn south. Which square are you approaching? ADELAIDE West Tce W N S E Morphett St North Tce Light Square Grote St Whitmore Square South Tce King William Rd Victoria Square Wakefield St Pulteney St Hindmarsh Square Hurtle Square East Tce Hutt St d) Start at the compass. Go east on E th Ave and take the second road north. Turn east again at the next corner. Which street are you in? W Williams St N S E High St E 6th Ave Race St E th Ave Vine St E 4th Ave Denver - Colorado Gaylord St YorkSt page Maths Mate /6 Skill Builder 9

124 Skill 9.4 Reading distances on a map. Q. What is the shortest distance from Winchelsea to Anglesea, via Geelong? Inverleigh Deans Marsh 0 Winchelsea Great Ocean Rd Lorne 8 8 Hamilton Hwy Princes Hwy Surf Coast Hwy Torquay 8 Anglesea 0 Aireys Inlet Port Phillip Bay GEELONG Bellarine Hwy Barwon Heads Bass Strait Ocean Grove W Queenscliff Pt Lonsdale N S E A. Trial A: = 77 km Trial B: = 86 km The shortest distance is 77 km Winchelsea Inverleigh 0 Winchelsea Find the possible paths. Trial each path by adding the distances between each place in order. Compare the totals for each trial. 8 8 Surf Coast Hwy Torquay 8 Anglesea Surf Coast Hwy Torquay 8 Anglesea GEELONG GEELONG a) What is the distance from Carnavon to Mt Magnet via Geraldton? Carnavon = 8 km Geraldton Gascoyne Junction 4 Glenburgh Mullewa 00 Meekatharra Mt Magnet km c) Outline the shortest path by road from Echuca to Tocumwal. What distance is that trip? Trial A:... Trial B:... Deniliquin 60 Finley NSW Mathoura Tocumwal Echuca 4 48 VIC Undera Shepparton 48 Numurkah 7 8 km km km b) What is the distance from St Arnaud to Warracknabeal via Minyip?... Warracknabeal Donald Minyip Dimboola Rupanyup 4 St Arnaud 6 HORSHAM km d) Trace the shortest path by road from Nightcaps to Wallacetown. What distance is that trip? Trial A:... Trial B:... Clifden 0 km Tuatapere 9 km 8 km Wallacetown Nightcaps 7 km 9 km 0 km Winton km 48 km INVERCARGILL Gore km km km 0 km Mataura km page Maths Mate /6 Skill Builder 9

125 Skill 9. Using regions on a grid to describe location (e.g. A). Start at the bottom left corner of the grid. First read across the horizontal axis to find the letter that matches the column you need. Then read up the vertical axis to find the number that matches the row you need. The grid space that is common to both lines marks the position you are locating. Q. Which Island is found at E? A. Churchill Island The Nobbies Seal Rock Penguin Reserve Cowes Phillip Island Grand Prix Circuit Maze Koala Reserve Cape Woolamai Reserve A B C D E Churchill Island San Remo Bridge nd Start here The Nobbies Seal Rock Penguin Reserve Cowes Phillip Island Grand Prix Circuit Maze Koala Reserve Cape Woolamai Reserve A B C D E st Churchill Island San Remo Bridge a) Where is the Australian Racing Museum located on the grid? 4 Federation Square - Melbourne Flinders Street Station Swanston Street Visitor s Centre Flinders Street Civic Plaza Transport Cinemedia Centre Aus. Racing Museum National Gallery of Vicrtoria Atrium BMW Edge Cross bar Russell Street b) Which Australian animal is located at C? Princes Bridge Yarra River A B C D E F G E A B C D c) What is the location of the drain on the tiled bathroom floor? 4 d) Alaska is located at A on this map. Where is New Zealand located? A B C D E F A B C D E F G H I J A B C D E F page Maths Mate /6 Skill Builder 9

126 Skill 9.6 Using coordinates to describe location on a coordinate plane. Read the coordinate along the horizontal or x-axis first. Then read the coordinate on the vertical or y-axis. Hint: x comes before y in the alphabet. Q. What are the coordinates of the shark and the surfer on the grid? Y X a) What are the coordinates of the football on the oval? Y 4 A. shark = (,) surfer = (4,) Trace down from the shark to the x-axis. Write the 0 number (, ). 0 is the x-coordinate for the shark. Trace across from the shark to the y-axis. Add the number to the coordinate pair (,). is the y-coordinate for the shark. Repeat for the surfer. (4,) b) Find the coordinates for the only two identical icecreams. [Hint: cone type, cone colour, scoop type and scoop number all vary.] Y Y X (6,4) X and X c) What are the coordinates of the person coming first? Y 0 0 Start X Finish d) What are the coordinates of the ship and the tug boat on the grid? Y X ship = tug boat = page 4 Maths Mate /6 Skill Builder 9

127 Skill 9.7 Measuring distances using a grid scale. Q. In this game of snake, how long is the snake? unit A = 8 grid lengths 8 unit = 8 units Count the number of unit lengths the snake covers in each direction. unit Add the lengths. Calculate the distance according to the grid scale. For every grid length, unit is covered. a) What distance has the ant tunnelled? [Give your answer to the nearest 00 m.] = 7 grid lengths m = m b) How far does the ornithologist walk from lookout to lookout 4 observing birds? grid lengths km Lookout Lookout Lookout Lookout 4 00 m grid km grid c) How long is the path shown below? grid lengths km d) What is the length of segment AB? Y 4 A B X km grid units page Maths Mate /6 Skill Builder 9