Sample: Do Not Reproduce RAT3 STUDENT PAGES. RATIONAL NUMBERS Student Pages for Packet 3: Ordering and Equivalence.

Transcription

1 Name Period Date RATIONAL NUMBERS Student Pages for Packet : Ordering and Equivalence RAT. RAT.2 Ordering Fractions on a Number Line Use sense-making strategies to compare and order fractions. Identify unit fractions. Use benchmark fractions to locate other fractions on a number line. Equivalent Fractions Use splitting, replicating, and grouping diagrams to show equivalent fractions. Use equivalent fractions to solve problems. Connect visual representations of equivalent fractions to the multiplication property of the big. RAT. Fractions Greater Than Represent fractions greater than as mixed numbers and improper fractions. Convert mixed numbers to improper fractions and viceversa. Link a customary measurement unit (inches) to mixed numbers. RAT STUDENT PAGES RAT. Vocabulary, Skill Builders, and Review 20 6 Rational Numbers Unit (Student Pages) RAT SP

2 WORD BANK (RAT) Word Definition Example benchmark fraction proper fraction improper fraction mixed number splitting replicating ratio unit fraction RAT SP0

3 . Ordering Fractions on a Number Line ORDERING FRACTIONS ON A NUMBER LINE Ready (Summary) We will use sense-making strategies to order fractions on a number line. These are unit fractions: These are not unit fractions: Go (Warmup),, 9,. Give three more examples of unit fractions. Set (Goals) Use sense-making strategies to compare and order fractions. Identify unit fractions. Use benchmark fractions to locate other fractions on a number line., 9,, 2, 2. Explain what a unit fraction is in your own words. RAT SP

4 . Ordering Fractions on a Number Line STRATEGIES FOR ORDERING FRACTIONS Use the symbol for is less than to order each group of fractions, and explain a general strategy for comparing the fractions within each group. Fractions Ordering Strategy ,,,,,, 2 2 2,, 2, 0, These are called fractions. Describe a sense making strategy for comparing these kinds of fractions. These fractions all have a common. Describe a sense making strategy for comparing these kinds of fractions. These fractions all have a common. Describe a sense making strategy for comparing these kinds of fractions. These fractions are all minus a unit fraction. Describe a sense making strategy for comparing these kinds of fractions. Simplify This is called a fraction because it is easily recognizable. Describe a sense making strategy for comparing other fractions to this fraction. Word Bank numerator denominator benchmark unit one RAT SP2

5 . Ordering Fractions on a Number Line NUMBER LINE A Estimate the location of each number on the number line: What benchmark fractions did you locate on your number line? 2. Explain how you located 6 on the number line.. Explain how you located 6 and on the number line. RAT SP

6 . Ordering Fractions on a Number Line NUMBER LINE B Estimate the location of each number on the number line: What benchmark fractions did you locate on your number line? 2. Explain how you located and 9 on the number line.. Explain how you located 6 20 and on the number line. 2 RAT SP

7 . Ordering Fractions on a Number Line NUMBER LINE C Estimate the location of each number on the number line: What benchmark fractions did you locate on your number line? 2. Explain how you located 2 and on the number line.. Explain how you located 0 2 and on the number line. RAT SP

8 .2 Equivalent Fractions Ready (Summary) We will use diagrams to illustrate equivalent fractions. We will connect the diagrams to computations. We will compare fractions in a problem solving setting. EQUIVALENT FRACTIONS Go (Warmup) Match each model for illustrating fractions to its example.. Linear model ( of the length is bold) A. 2. Area Model ( of the big rectangle is shaded) B.. Set model ( of the shapes are stars) C. Set (Goals) Use splitting, replicating, and grouping diagrams to show equivalent fractions. Use equivalent fractions to solve problems. Connect visual representations of equivalent fractions to the multiplication property of (the big ). Interpret the meaning of the numerator and denominator for each model. Model Meaning of the numerator Meaning of the denominator. Linear model. Area model 6. Set model RAT SP6

9 .2 Equivalent Fractions EQUIVALENT FRACTIONS: REPLICATING The first set contains circles. The shaded portion is 2 of the set. To show that 2 20, make four copies of this set of circles. The shaded portion is of the set. We will call this the replicating method for showing equivalent fractions.. In the example above, why was the set of circles replicated four times to show that 2? In the replicating method, does the ratio of the part to the whole stay the same?. In the replicating method, does the size of the whole stay the same?. In the replicating method, does the size of the part stay the same? Use the replicating method to show the following equivalent fractions. Use a set model RAT SP

10 .2 Equivalent Fractions EQUIVALENT FRACTIONS: SPLITTING The area of the large rectangle is one whole. The shaded part represents Diagram To show that, 9 Diagram 2 divide each of the one-third sections into three equal parts. 9 We will call this the splitting method for showing equivalent fractions.. In diagram 2 above, how many parts are shaded? How many parts are in one whole? of the whole. 2. In the splitting method, does the ratio of the part to the whole stay the same?. In the splitting method, does the size of the whole stay the same?. In the splitting method, does the size of the part stay the same? Use the splitting method to show that the following fractions are equivalent RAT SP

11 .2 Equivalent Fractions EQUIVALENT FRACTIONS: GROUPING This area of the rectangle on the left is one whole. The shaded part is of the whole. 2 To show that 2, draw lines to make six equal groups with four parts shaded We will call this the grouping method for showing equivalent fractions.. Circle groups of objects to show that 2 using a set model In the grouping method, does the ratio of the part to the whole stay the same?. In the grouping method, does the size of the whole stay the same?. In the grouping method, does the size of the part stay the same?. How are the splitting method and the grouping method related? Use the grouping method to show the following equivalent fractions. Use an area model RAT SP9

12 .2 Equivalent Fractions THE BIG Two fractions are equivalent if they have the same value. To find equivalent fractions, multiply (or divide) by a form of one, which we call the big. This is the multiplication property of. Equivalent fractions Diagram Big calculation X X O O O X X O O O X X O O O X X O O O RAT SP0

13 .2 Equivalent Fractions THE FLOWER GARDEN PROBLEM Four students have gardens of different sizes and shapes. Below are scale drawings of the gardens, where each square represents one square yard. The shaded portions below represent the part of each garden that is planted. Number of Total number Fraction of garden Student name and garden square of that is planted yards planted square yards. Omar 2. Bailey. Melissa. José Bailey says that her garden has the largest fractional part planted. Omar, Melissa, and José disagree with Bailey. Settle the disagreement. Use diagrams, big calculations, and sense making arguments to help each student understand your answer.. Who has the larger fractional part planted: Bailey or Omar? 6. Who has the larger fractional part planted: Bailey or Melissa? RAT SP

14 .2 Equivalent Fractions THE FLOWER GARDEN PROBLEM (continued). Who has the larger fractional part planted: Bailey or Jose?. Does Bailey have the largest fractional part planted? How do you know? Here are some other ways to compare the gardens. 9. Write an inequality that compares the sizes of the whole gardens. Who has the largest garden? How big is it? 0. Write an inequality that compares the sizes of the planted portions of the gardens. Who has the largest amount of their garden planted? How big is it?. Write an inequality that compares the fractional parts of the gardens that are planted. Who has the largest fractional part of their garden planted? How much is it? RAT SP2

15 . Fractions Greater than FRACTIONS GREATER THAN Ready (Summary) We will represent fractions greater than one as mixed numbers and improper fractions using an area model, a set model, and a linear model. We will explore how mixed numbers are used on a ruler that is marked off in inches. Go (Warmup) Set (Goals) Represent fractions greater than as mixed numbers and improper fractions. Convert mixed numbers to improper fractions and vice-versa. Link a customary measurement unit (inches) to mixed numbers. Complete the table. Each figure below represents one whole brownie. Amount in words Shade the appropriate amount Write the number. One-half brownie 2. One and one-half brownies. Two and one-half brownies RAT SP

16 . Fractions Greater than MIXED NUMBERS AND IMPROPER FRACTIONS A proper fraction is a fraction between zero and. A mixed number is the sum of a whole number and a fraction. An improper fraction is a fraction greater than or equal to. Fill in the missing sections. Ex Shaded Brownies Sum Mixed Number Conversion whole brownie Improper Fraction 2 RAT SP

17 . Fractions Greater than. Change MIXED NUMBERS AND IMPROPER FRACTIONS (continued) into an improper fraction: +. A common shortcut for this can be depicted by the following diagram: To find the number of eighths, x + x (0 eighths) ( eighths) 9. Change into a mixed number remember that with a remainder of Change each mixed number into an improper fraction Change each improper fraction into a mixed number. 2.. so 2.. : RAT SP

18 . Fractions Greater than MUFFIN PROBLEMS. This picture represents one whole pack of muffins. Shade 2 of the pack. 2. Draw pictures to represent the following: Number of packs of muffins Sketch packs 2 2 packs a. b. c. packs 6. If muffins represents three-fourths of a pack of muffins, draw pictures to represent the following. Number of packs of muffins Sketch whole pack packs 2 a. b. c. 9 packs RAT SP6

19 . Fractions Greater than Add mentally MENTAL ADDITION AND ESTIMATION Use estimation. Circle the correct answer. 2. Less than 6 Greater than Less than 0 Greater than Less than Greater than. 6 2 Less than 9 Greater than Closer to 6 Closer to Closer to Closer to 2 2. Closer to Closer to Closer to Closer to 2 RAT SP

20 . Fractions Greater than 0 inches CUSTOMARY UNITS OF LENGTH: THE INCH A scaled down one foot ruler. Although most of the world uses metric units for measurement, the United States relies mostly upon customary units of measurement. For measuring length, we use inches, feet, yards, and miles. The Greeks used the width of 6 fingers to find one foot. The Romans adopted the foot from the Greeks and divided it into 2 sections. The picture above is a standard one-foot ruler ( scaled down to fit on the page). The picture below is one inch ( scaled up to illustrate its parts). A very good estimate for one inch is the diameter of a quarter.. The inch is divided into how many equal parts? 2. Write the fractional amount for each part under its marking.. Write three equivalent fractions that relate to these markings. Example: 2 $0.2 inch RAT SP

21 . Fractions Greater than INCHES AND MIXED NUMBERS For each scaled up inch below, use mixed numbers to label each marking.. An inch that begins at inch and ends at 2 inches. 2. An inch that begins at inch and ends at inches. Rewrite each measurement as an improper fraction.. in.. in.. in. 6. in. Locate each length on a ruler. Then use the symbols <,, or > to order each pair of lengths inches inches 2 0. inch inches inches 2 inches. inches 2 inches inches inches 2 inches inches 2. 2 inches inches 2 inches inches RAT SP9

22 . Vocabulary, Skill Builder, and Review Match the words to the clues. FOCUS ON VOCABULARY (RAT) Words. benchmark fraction 2. proper fraction. improper fraction. mixed number. splitting 6. replicating Clues a. This model shows equivalence by keeping the ratio of part to whole the same and changing the size of the whole. b. This model shows equivalence by keeping the size of the whole constant. c. This is a comparison of two numbers by division. d. The fractions, 6 and 2 2 are examples of this type of fraction. e. A fraction whose numerator is one and whose denominator is a natural number. f. A fraction that is easily recognizable.. ratio g. A fraction between zero and.. unit fraction h. is a shorthand way of writing +, which is an example of this type of number. RAT SP20

23 . Vocabulary, Skill Builder, and Review SKILL BUILDER Shade each fractional amount inside a dot paper square. Label the location of each pair of fractions on a number line. Complete number sentence by writing < or > in the blank RAT SP2

24 . Vocabulary, Skill Builder, and Review SKILL BUILDER 2 Use the multiplication property of to find each equivalent fraction Find each sum or difference. Use the fraction array chart (in RAT) to find equivalent fractions or use the big as needed RAT SP22

25 . Vocabulary, Skill Builder, and Review SKILL BUILDER Express each fraction as a decimal and a percent.. 0. % 00 Fraction Decimal Percent Write each expanded form number in its standard form Ê Ê % Fraction Decimal Percent () +(0.) + (0.00) Compute. 6. (00) + () + (0.) Label each marking on the number line. Then, estimate the placement of each number below. A) 0.6 B) 0.0 C) 0. D) 0.9 E) RAT SP2

26 . Vocabulary, Skill Builder, and Review SKILL BUILDER. Order the fractions in from least to greatest Estimate the location of each number on the number line. 0.. Explain how you located and 9. Use a splitting, replicating, or grouping diagram to show that these fractions are equivalent RAT SP2

27 . Vocabulary, Skill Builder, and Review SKILL BUILDER. Estimate the location of each number on the number line Use a splitting, replicating, or grouping diagram to show that these fractions are equivalent RAT SP2

28 . Vocabulary, Skill Builder, and Review SKILL BUILDER 6 Rewrite each mixed number as an improper fraction Rewrite each improper fraction as a mixed number.. Use <, >, or to make each statement true RAT SP26

29 . Vocabulary, Skill Builder, and Review SKILL BUILDER. Estimate the location of each number on the number line. Use a splitting, replicating, or a grouping diagram to show that these fractions are equivalent. 2.. Rewrite each mixed number as an improper fraction.. 6. Rewrite each improper fraction as a mixed number RAT SP2

30 . Vocabulary, Skill Builder, and Review TEST PREPARATION (RAT) Show your work on a separate sheet of paper and choose the best answer.. Place the fractions listed below in order from least to greatest. A. C.,,, 0 2,,, 0 2,,, Which symbol makes this statement true? 2 B. D.,,, 2 0,,, 2 0 A. < B. > C. D. +. Which of the following fractions is equivalent to A. 20 B. 2. Which number is equivalent to 9? A. B. C. C. 20? D. 2 D. RAT SP2

31 . Vocabulary, Skill Builder, and Review KNOWLEDGE CHECK (RAT) Show your work on a separate sheet of paper and write your answers on this page.. Ordering Fractions on a Number line. Which is greater, or? Explain. 2. Which is greater, or 2? Explain..2 Equivalent Fractions. Use the replicating method to show that 2 6. Use the multiplication property of to show that Fractions Greater Than. Rewrite 6 as an improper fraction. 6. Use <, >, or to make the statement true: 2 RAT SP29

32 Home-School Connection (RAT) Here are some questions to review with your young mathematician.. Order the following fractions from least to greatest.,,, Use the splitting, replicating or grouping method to how the 6 is greater than 2.. Rewrite each measurement as an improper fraction. inches inches Parent (or Guardian) signature Selected California Mathematics Content Standards NS 2.. Recognize, name, and compare unit fractions from /2 to /2. NS.. Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., /2 of a pizza is the same amount as 2/ of another pizza that is the same size; show that / is larger than /). NS..2 Add and subtract simple fractions (e.g., determine that / / is the same as /2). NS.. Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. FIRST PRINTING DO NOT DUPLICATE 200 RAT SP0