Number Sense Part 1. Number Sense 1-

Transcription

1 Number Sense Part 1 Number Sense 1-1

2 Number Sense 1 Part 1 In this unit, students will explore the concept of number. They will count (match numbers with their corresponding quantities and numerals), put numbers in order, and compare quantities (more, less, fewer, as many as). They will also learn to add, subtract, and estimate. Number Cards Write the numerals 0 through 20 on separate cards. These number cards will be used throughout the unit. BLM Numbers Template (p XXX) provides a template. Daily Routines Incorporate counting into daily routines. Lining Up. When students line up for recess or lunch, they can each pick a number card and line up in order according to their number. At first, have only as many cards as students; later, there can be more cards than students so that there are gaps in the numbers held by consecutive students. Ordinal Numbers. When students learn ordinal numbers (NS1-22), use them to identify and call on students. EXAMPLE: Ask the 2nd person in line to open the door. Counting back to indicate time remaining. You might count back from 3 to 0 when you need students to quiet down, or count back from 20 to 0 when you want them to line up for lunch. Eventually, end at numbers other than 0. Students who need to be finished a task when you say 4 will learn quickly that 5 comes right before 4 when counting back. Recurring Games. The following games occur often throughout the unit. The rules and materials will vary as students learn more about numbers. Sample Card I have 3 Who has I Have, Who Has? Each student will need one card to play (see sample). The student with the card shown in the margin would begin by saying, I have 3. Who has 7? The person who has 7 on top would say, I have 7. Who has [whatever is on the bottom of the card]? At first, when only numbers 1 to 10 are available, students will have to play in smaller groups so that two people do not have the same number. Sometimes you will be asked to make the cards (see the template on BLM Game Cards, p XXX), sometimes students will be asked to make their own cards, and sometimes cards will be provided on other BLMs. The blank spaces at the top and bottom of each card are to be filled with numerals or other representations of numbers, such as an arrangement of dots, a representation using tens blocks, or an addition or subtraction sentence. Dominoes. Make domino cards with numbers written in different ways (EXAMPLES: random arrangements of dots, base ten blocks, addition or subtraction sentences, numerals). BLM Blank Domino Cards (p XXX) provides a template for you to create cards. You will need to explain that the cards can be turned around even though the numerals won t look like 2 Teacher s Guide for Workbook 1

3 numerals any more. To start, give students 3 or 4 chains of dominoes and ask them to make the longest chain they can using those dominoes. SAMPLE CHAINS: [5,4], [4,6], [6,10], [10,7], [7,3], [3,2] and [6,3], [3,7], [7,8], [8,10] and [7,4], [4,5], [5,6], [6,2]. The second chain can replace domino [6,10] and the last chain can be placed in the opposite direction at the end of the chain, so that only [6,10] is left out. Demonstrate creating a long chain like this before asking students to play. Go to Page. First, make sure students can find the page numbers in their JUMP Math workbooks in the bottom left and right corners. Then ask them to turn to different pages, one at a time, in random order. Always ensure that the entire class has found one page before you ask students to turn to another. Students should point to where they see each page number. This will help students to grasp the order of the numbers. Message Booklet. Create message booklets in which there is only one word on each page and the words are out of order. Instructions at the top of each page tell students which page to turn to next to find the next part of the message. For example, a message booklet for The pig took a bath in the mud would need 8 pages. Each page should be one-sided and should look like the sample in the margin. If you want students to turn the pages in the order 1, 5, 3, 6, 2, 4, 7, 8, then page 5 would say Go to page 3, page 3 would say Go to page 6, and so on. Go to page 5 THE 1 As students learn larger numbers, you could make longer books. VARIATION: Create a 26-page booklet with all the letters of the alphabet in random order but without the instructions regarding which page to turn to. Provide instructions orally to create an unlimited number of words and messages. Use messages that your class will enjoy. Solitaire War. Give each student a deck of cards without the face cards (Jack, Queen, King). Tell students to separate the black cards from the red cards and then shuffle both decks. Then have students turn over the top card from each pile. If the black card is more than the red one, they can take the cards; if the red card is more than the black card, they lose both cards. If the cards are equal, remove them from each pile, place them face down, and play again, either keeping or losing all the cards involved. VARIATIONS: War for Less: Players win if the black card is less than the red card. Addition War: Players play two cards at a time from each deck and keep the cards if the black sum is larger than the red sum. Difference War: Same as Addition War but players need the black difference to be larger than the red difference. Ensure that students always subtract the smaller number from the larger number. Students might find it helpful to count out the larger number in tokens or counters, and place them on the objects pictured on the smaller card (e.g., clubs, hearts) to see how many are left. Number Sense 1 3

4 NS1-1 Counting Page xxxx Curriculum Expectations Ontario: 1m1, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20 WNCP: kn1, kn3, 1N1, 1N2, 1N3, 1N4, [R, CN, C] Goals Students will use counting to find how many and will associate numbers (spoken) with the corresponding quantities and numerals. PRIOR KNOWLEDGE REQUIRED is able to colour and to circle a group of objects Materials Vocabulary the numerals 1 to 10 number how many counting 24 quantity cards (described below) or BLM How Many? (p XXX XXX) 8 counters 5 coloured tokens or paper circles BLM How Many? Part 2 (p XXX XXX) number cards for 1 to 10 (see BLM Numbers Template (p XXX)) online guide One way to teach this using the song One, Two, Buckle My Shoe. Looking for a pattern Saying the numbers in order from one to ten. The concept of how many. Have ready six cards with two shapes on each card. Use circles, squares, and stars in different combinations. Vary the shapes on each card so that they are: sometimes both big, sometimes both small, sometimes one big and one small; sometimes close together, sometimes far apart; sometimes black, sometimes white; sometimes one black and one white; arranged various ways side by side, one on top of the other, randomly. Repeat with three shapes on each of six cards, and four shapes on each of six cards. Finally, make six cards with only one shape on each; vary the size, colour, and type of shape as before. (Alternatively, use the cards on BLM How Many?) Then show students sets of seven cards, six of which illustrate the same quantity, and ask students to identify the card that doesn t belong. Repeat for each quantity (one, two, three, and four) at least once. Discuss what is the same and different about all the cards that do belong. Explain that you made the groups based on how many shapes were on each card. It didn t matter what the shapes were, how big they were, where they were on the card, or what colour they were. You must count each object only once. Arrange eight counters in a circle. SAY: I want to know how many counters are in this circle. I m going to count them. Then demonstrate counting around the circle but keep going so that you count several dots twice. Does anyone notice? ASK: Am I allowed to count the same object twice? Emphasize that if you want to know 4 Teacher s Guide for Workbook 1

5 how many there are, you have to count each object only once. Then ask students how you can know when to stop. Suggestions might include: Cover up the first one you count with a small piece of paper. Move objects already counted to a separate pile. Change the arrangement of the counters (instead of a circle, perhaps two rows of four or a scattered arrangement) and use students suggestions. Does their method work? Counting in different ways gives the same answer. Arrange seven counters in a row. ASK: Do you think I will get the same answer if I count them starting here (at the left) and then starting over here (at the right). Demonstrate counting in both directions. ASK: Why did we get the same answer? Use five tokens or paper circles of different colours. Tape them randomly to chart paper or the board and count them, starting with the blue one. Then SAY: This time I am going to count starting with the yellow one. I am counting the same tokens. Who thinks I will get the same answer? Who thinks I will get a different answer? Have students count along with you and demonstrate getting the same answer. Repeat, starting with other colours. Identifying the numeral with the number (spoken). Draw several capital or lower case letters and ask students to name the letters. Explain to students that just as we have symbols for the letters in the alphabet (E is ee ), in math we have symbols (called numerals) for the numbers. Write the numerals 1 to 3 in order on the board, then say the numbers in order as you point to them. Erase the numbers, write the same numbers in random order, and have students say the numbers as you point to them. Gradually increase the difficulty by using more numerals. EXAMPLES: Bonus Have students put number cards in the correct order. Raise the bar by using more cards. online guide BLMs similar to Workbook p.1 for numbers 1, 2, 4, 5, 6, 7, 8, and 9. Identifying the numeral with the quantity. Write the numbers 1 to 4 on the board in order ( ), leaving plenty of space below and around each one. Give each student one of the quantity cards used earlier in the lesson and have four volunteers tape a card next to or below the right number. Repeat with more volunteers. Then write the numbers 1 to 4 in random order and repeat with the students who have not yet used their cards. Repeat with the numbers 1 to 7 by adding cards from the first page of BLM How Many? Part 2 to the set (or make your own cards.) Then repeat with the numbers 1 to 10 and the second page of the BLM or your own cards. Hold up various numbers of fingers, in random order, and ASK: How many fingers am I holding up? (Students should call out the answer.) Then write a numeral on the board and have students hold up the corresponding number of fingers. Number Sense 1-1 5

6 NS1-2 Match by Counting Page xxxx Curriculum Expectations Ontario: km10, km15, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20 WNCP: kn1, kn3, 1N1, 1N2, 1N3, [R, CN, C] Goals Students will practise counting, that is, matching numerals and quantities. PRIOR KNOWLEDGE REQUIRED understands the concept of quantity can join two figures with a line Vocabulary The numerals 1 to 10 how many number Materials number cards from 1 to 10 quantity cards or BLM How Many? (see BLM Numbers Template (p XXX XXX)), BLM How Many? Part 2 (p XXX XXX) 2-cm grid paper or BLM 2-cm Grid Paper (p XXX) various old magazines and catalogues (e.g. sports, clothing, toys) BLM Game Cards (p XXX) BLM Blank Domino Cards (p XXX) connection Literature What Comes in 2 s, 3 s, & 4 s? by Suzanne Aker. One Gray Mouse by Katherine Burton. Feast for 10 by Cathryn Falwell. One Hungry Monster by Susan Heyboer O Keefe. Journal Draw a group of 9 and a group of 10. Have a partner circle the group of 10. In a two-column chart, draw three different quantities (up to ten) in one column and the same three quantities, arranged differently and using different items, in the second column. (Alternatively, use cards from BLMs How Many? and How Many? Part 2.) For example, draw 4 stars, 5 dots, and 1 checkmark in the first column, and 1 heart, 4 squares, and 5 triangles in the second column. Have students match the items by quantity. Repeat several times, eventually including more quantities in each column and, later, arranging quantities and matching them by row instead of column. When students can comfortably match quantities, replace the quantities in one column or row with numerals, and have students match numerals to quantities. (You can write the numerals or use pre-made number cards.) ACTIVITIES A Counting Game. Pairs start counting at 1 and take turns saying the next number until they reach 5. The pair wins if the person who started counting also finishes. Demonstrate by playing the game yourself with a volunteer. Then have students play in partners. Have them repeat the game ending with 6, then 7, 8, 9, and 10. After students have played several times and counted to different numbers, ASK: Was it possible to win every time? What numbers do you need to finish with if you want to win? (5, 7, or 9) 2. Memory. Match quantities to quantities or numerals to quantities up 6 Teacher s Guide for Workbook 1

7 to 10. See BLM How Many? and BLM How Many? Part 2 for pre-made cards. 3. Have students make the numerals 1 through 10 out of clay, playdough, or pipe cleaners. Reflecting on other ways to solve a problem 4. Give students 2-cm grid paper and have them colour any five squares. Discuss the differences between the various answers. Display the various arrangements on a poster titled Give each student an old magazine or catalogue. Assign each student a number from 2 to 6. Students will find and cut out pictures where items are in groups of that many. Students can then form groups with other students who had the same number and pool their cut-outs to make a poster for each number. 6. Bring in packages that are labelled with numbers. (EXAMPLES: puzzles, marbles, cookies, pencils, pens, erasers, crayons, chalk, paper, Ziploc bags, garbage bags) Have students identify the numbers on the packages. Discuss why numbers are important. Students might wish to package a product themselves and write how many on the package. online guide BLMs for more Tic Tac Toe boards 7. I Have, Who Has? (see NS Part 1 Introduction). Use the template on BLM Game Cards to make cards with numerals on top and dots on the bottom or different arrangements of dots on the top and bottom. 8. Dominoes (see NS Part 1 Introduction). Use BLM Blank Domino Cards. Extensions connection Literacy SAMPLE: 1. Hold up pictures of various objects (or the objects themselves) and ask students to say what number the object rhymes with. EXAMPLES: a pen (10), a zoo (2), sticks (6), a line (9), a tree (3), a beehive (5), a gate (8), a door (4). Give each student one number to focus on, from 1 through 10 (exclude 7). Students draw that number of an object that rhymes with the number (EXAMPLE: three trees). Use the students work to build a class poem on a poster. Students can read the poem together as a class, with each student reading his or her own line. 2. Have students match by number, but tell them you are going to try to trick them by having groups of the same object. Remind students to match by number, not object. 3. BLM Many Ways to Colour 3 shows one way to colour three of the five given circles and allows students to find five more ways to do the same. Number Sense 1-2 7

8 NS1-3 There s Order Here Page xxxx Curriculum Expectations Ontario: km6, 1m1, 1m3, 1m5, 1m11 WNCP: kn1, 1N1, [R, CN] Goals Students will become familiar with the order of the numbers through exploration. PRIOR KNOWLEDGE REQUIRED Vocabulary order can associate the numerals 1 to 10 with the corresponding quantities can read the numerals 1 to 10 Materials number cards for 1 to 10 for each student (see BLM Numbers Template) number cards for 1 to 10 with letters on the other side (details below) JUMP Math Workbook (1 per student) BLM Find the Missing Numbers (p xxx) Making an organized list. Extra practice BLM Find the Missing Numbers Reflecting on the reasonableness of an answer. Using order to find numbers quickly. Start by giving students number cards for 1, 2, and 3 and have them find and hold up the card that matches the number when you say it aloud. Suggest that they order their cards to make it easier. Add cards 4 and 5, then 6 and 7, and finally 8, 9, and 10. Using order to solve puzzles. Students will work together in small groups for this part of the lesson. Mark the other side of several sets of number cards with the letters shown below (you will need one set with which to demonstrate and one set for each group). Front Back B D E G L N O R U W Distribute your set on the board with the numerals facing the class in order spread them as far apart as you can and have students arrange their cards in the same way. Then tell students to find the 1 and turn it over. What letter do they see? Turn your card over and reattach it to the board in a new row: B Explain that if students turn over the numbers 5, 9, and 3 in that order, they will make a colour word. Do this together as a class you with your cards and each group with theirs B L U E ASK: What word do you see? Have students show you something that is that colour. Have students repeat the task for each of the following groups of numbers: (red), (brown). Encourage students to check 8 Teacher s Guide for Workbook 1

9 the words they make against known colour words. Explain how checking that the words are spelled correctly is a way of checking that they have uncovered the numbers in the right order. SAMPLE WORDS: sat the pig a hat in wig cat big has SAMPLE MESSAGES: (the big pig has a wig) (the cat sat in a hat) Bonus ACTIVITY 1 Repeat with words and a message instead of letters. (You will need to make new cards.) See the margin for a sample. Go to page (see NS Part 1 Introduction) Use numbers up to 10. Observe students as they work. Do they look in the correct direction? For example, to find the number 2 after finding the number 6, do they know to look left, or do they look right first and then go back to the beginning? Putting the numbers in order. Have cards numbered 1 through 10 arranged on the board in order, but with some cards missing. (You can put the missing cards aside or on the ledge in random order.) Have volunteers move the missing cards into the correct positions. Repeat for increasingly more complex arrangements, first having no two consecutive numbers missing and eventually asking students to order all the cards Joining dots in order. Draw numbered dots on the board for students to join in order. You might wish to have the dots spell a word for students to read. (The example in the margin reads MATH. ) ACTIVITIES 2 5 online guide More message ideas. 2. Message Booklet. (see NS Part 1 Introduction). Make a 10-page booklet that clearly shows a page number and a letter on each page. You can combine many on the same ten-page book by providing oral instructions instead of having the instruction Go to page in the booklet. A B E G I L M N R U: (animal); (bear); (green); (number) 3. Provide pairs of students with cards numbered 1, 2, 3, 4, 5. Player 1 shuffles the 5 cards. Player 2 removes one of the cards. Player 1 orders the remaining cards and Player 2 inserts his or her card in the right place. Progress to cards numbered 1 through 10. connection Visual Art Students use different kinds of lines to make a puzzle. 4. On a long piece of thick paper, write the numbers from 1 to 10 equally spaced. Have students make a puzzle by cutting out jagged, curved, or straight lines between each pair of numbers. Partners can then solve each other s puzzles. Discuss how knowing and using the order of the numbers helped them solve the puzzle. 5. Put a deck of cards in order as though it is brand new. Number Sense 1-3 9

10 NS1-4 The Number That Means None Page xxxx Curriculum Expectations Ontario: 1m1, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20 WNCP: 1N1, [R, CN, C] Goals Students will learn that the numeral 0 stands for no objects. Students will distinguish between numerals written correctly and incorrectly. Vocabulary zero (0) none number letter PRIOR KNOWLEDGE REQUIRED knows the numerals, sounds and quantities associated with numbers one through ten knows the alphabet Materials number cards for 0 to 10 for each student BLM Count and Match (p XXX) BLM Circle the Numbers (p XXX) Introduce zero. Hold up three fingers and ASK: How many fingers am I holding up? Repeat with different numbers of fingers. Then hold up no fingers and repeat the question. If students say none, tell them that mathematicians have come up with a number that means none. Ask if anyone knows what that number is. Does anyone know how to write that number? (0) Does anyone know how to say the number? (Say zero. ) ASK: How many apples am I holding? (zero) How many grapes am I holding? Draw squares showing groups with different numbers of dots on the board, including zero dots. Ask how many dots are in each group. ACTIVITY 1 Everyone stands up. You ask a question (EXAMPLE: How many younger sisters do you have?) and all the students who answer zero sit down. Play until everyone is sitting down. You ask the first one or two questions, then let students who are sitting down take turns asking the questions. The goal is to try to get everyone sitting down in exactly three turns. If no-one answers zero, it doesn t count as a turn. After each question, remind students how many turns are left. When there is only one turn left, students should try to think of a question that everyone will answer zero to. (EXAMPLE: How many tails do you have?) Challenge students to not repeat questions. Identifying the numeral 0 with the number (spoken). As in NS1-1, but include 0. Taking away to make zero. Hold up three crayons. Drop one on the floor and SAY: One fell. How many are left in my hand? (two) Repeat until you get to zero crayons. Have three volunteers stand up. Tell each of them to sit down, one at a time, and ask students how many are left standing each time, until you get to zero people standing. 10 Teacher s Guide for Workbook 1

11 Looking for a pattern Extra practice BLM Count and Match Where does zero go on the number line? Write the numbers 1 to 10 in order on a number line and ASK: Where should 0 go? How do you know? When we counted from 3 to 0, which way did we go in the numbers left or right (this way or that way)? Write 0 in the correct place to the left of the 1. Counting zero objects. Draw several sets of squares and circles on the board. ASK: How many squares? How many circles? Include examples where there are no squares or no circles. Students can hold up the corresponding number of fingers to show the answer. Then write different numerals on the board (including 0) and again have students hold up the corresponding number of fingers. Drawing zero objects. Have a volunteer draw three circles on the board, then another volunteer draw four stars, and then another volunteer draw zero hearts. Emphasize that drawing zero things is easy you don t have to draw any! Repeat with having students colour objects. online guide Activity and BLM asking students to identify numbers in postal codes and licence plates. Numbers cannot be turned around. Bring a chair to the front of the room. Ask your students what object it is. Then turn the chair around to face the other way. Is it still a chair? Now put it on its side. Is it still a chair? Draw the chair in all three positions on the board. ASK: Are all of these chairs? When all students see that the chair is still a chair, ask them if they can do the same thing with letters. Draw a c on the board. Then draw it backward. Is it still a c? Then put it on its side. Repeat with z which looks like N when turned. It might be helpful to have the letters written on cards so that you can physically turn them around. Then draw a 3 on the board or hold it up on a card. ASK: Is 3 still a 3 when you turn it around? On its side? (Demonstrate doing so.) Are there any numbers that are still numbers when you turn them upside down? (8 and 0; 1 when it is drawn as a straight line) Draw several numbers two ways correctly and incorrectly and have volunteers circle the correct way. ACTIVITIES Invite students to use numbers around the room to help them identify which numbers are written correctly on BLM Circle the Numbers. Students should carry the BLM with them on a clipboard as they walk around the room. 3. Using pipe cleaners, playdough, or clay, have students make the shape of the numeral Memory, I Have, Who Has? and Dominoes. (see NS Part 1 Introduction) Play as in NS1-2, but include zero. Extension On BLM Join Dots and Stars, students join dots to dots and stars to stars. Number Sense

12 NS1-5 Writing Numbers Page xxxx Curriculum Expectations Ontario: km10, 1m1, 1m3, 1m5, 1m7, 1m11, 1m13 WNCP: kn1, kn3, 1N1, 1N3, [R, CN, C] Goals Students will write the numerals, first by tracing, then independently. Students will also write numerals as they appear on digital clocks and calculators (using only straight lines). PRIOR KNOWLEDGE REQUIRED Vocabulary the numerals from 0 to 10 can hold a pencil and trace lines can join dots with a straight line Materials BLM Calculator Numbers (p XXX) or BLM 2-cm Grid Paper (p XXX) a calculator for each student (to be used during the lesson and when students are completing Workbook pages 18, 19) online guide Extra practice Copies of the first two worksheets and four new BLMs, for students who need additional practice with counting and writing numbers. connection Technology. Draw numbers by starting at the big dot and following the arrow. Ask students to watch carefully as you draw a 7 on the board. ASK: Did I start drawing the 7 from the top or the bottom? Draw several more 7s to give every student a chance to see what you are doing. Ask a volunteer to come to the board and draw a big dot to show where you started. Ask for a suggestion on how you could show the direction to move in when drawing the 7. Tell students you will draw an arrow, and do so. Have volunteers draw a 7 the same way you did. Then tell them to watch carefully as you draw a 1. Draw several more 1s before asking a volunteer to add both the dot and the arrow showing where you started and what direction you went in. Repeat with a, emphasizing that it needs two starting points. Then move on to numbers with only curved lines (0, 3, 6, 8, 9) and then numbers with both straight and curved lines (5, 2). Have volunteers draw numbers the same way you did. How calculators show numbers. Give each student a calculator. Draw the number 2 on the board and have students press the number 2 on their calculators. Compare the two numbers. (On a calculator, all lines are straight and only go up and down or side to side. The number 2 is usually curly or curved, with a more pointy corner at the bottom left. One or the other might be easier to draw.) Repeat with various numbers from 0 to 9. Have a dotted square 8 on the board (see below) that students can trace to show what they see on their calculators. 12 Teacher s Guide for Workbook 1

13 ACTIVITY I Have, Who Has? (p XXX). Include numerals as they appear on digital devices. Investigate malfunctioning calculators. Tell students that your calculator doesn t work it s not showing the numbers properly. Draw for them what you see when you hit 0, 1, 2, 3, and 4 or use a transparency of BLM Calculator Numbers. (See margin) Looking for a pattern. Reflecting on the reasonableness of an answer. Using logical reasoning. Ask students what part of each number is missing. Have a volunteer draw it in. Ask another volunteer to draw how they think your calculator will show 5. Have the dotted square 8 outlined for them to draw on. ASK: Why does the calculator show this number correctly? (Because the 5 doesn t have the top right line in it.) Which numbers does the calculator show correctly? (5 and 6) Which numbers does the calculator show incorrectly? (0, 1, 2, 3, 4, 7, 8, 9) Are there two numbers that look the same on your calculator? (Yes, 6 and 8, and 5 and 9.) Tell students that another calculator you have is missing the top left line: Challenge students to draw each number from 0 to 9 as it would appear on this calculator. Students can record their answers on BLM Calculator Numbers or on 2-cm grid paper. ASK: Which numbers does the calculator show correctly? (1, 2, 3, 7) Incorrectly? (0, 4, 5, 6, 8, 9) Are there two numbers that look the same? (Yes, 3 and 9.) Repeat for other malfunctioning calculators. (When the middle line is deleted, 8 and 0 look the same. When the top line is deleted, 1 and 7 look the same. When the bottom left line is deleted, 5 and 6 look the same, as do 8 and 9. When the bottom right or bottom lines are deleted, no numbers look the same.) online guide BLM How Many Things? (students count two different quantities in the same picture) and BLM Calculator Fun (a sample lesson which involves malfunctioning calculators) Extensions 1. On BLM Roman Numbers, students will count the shapes on playing cards to translate Roman numbers to English numbers. 2. BLM Counting Dots asks students to count the corners (marked by dots) of various shapes. 4. On BLM Missing Numbers, students fill in the missing number in Sudoku-like rows, columns, and boxes. 5. BLM Fractions asks students to count first the shaded squares and then all the squares, and to write the answer as a fraction. 6. Trace a number on a friend s back. Can your friend guess the number? Number Sense

14 NS1-6 Counting Using a Chart Page xxxx Curriculum Expectations Ontario: km6, km10, 1m1, 1m2, 1m5, 1m7, 1m11, 1m21 WNCP: kn1, kn3, 1N1, 1N3, [R, CN, C] Vocabulary number line Goals Students will use a chart in place of counting orally. PRIOR KNOWLEDGE REQUIRED can say the numbers from 0 to 10 and can write the corresponding numerals in sequence can count to 10 Materials counting strips (details below) or BLM Counting Cubes (p XXX) lots of 2-cm connecting cubes two-colour counters or coins pre-cut square pieces of paper (details below) number lines or BLM Number Lines 0 to 10 (p XXX) Make a counting strip for each student. Make strips of paper 2 cm wide and 20 cm long divided into numbered squares, as follows: Alternatively, copy and cut strips from BLM Counting Cubes. Looking for a pattern Making and investigating conjectures. Teach students to count using a chart. Provide each student with several 2-cm connecting cubes (different numbers of cubes for each student). Ask students to count their cubes. Then have them make a chain with the cubes and place it on the chart, so that each cube covers one square and the chain starts on the 1. Students should exchange cubes with different partners and repeat the exercise several times. Then ASK several students: How many cubes did you count? What is the last number covered on the chart? Ask students if anyone notices a pattern. (The last number covered is always the number of cubes in the chain.) Have students repeat the exercise with this pattern in mind. Does it hold? ASK: What is an easy way to know how many cubes there are without counting? (Look at the last number covered.) The chart does the counting for you. ASK: How is the chart doing the counting for you? (Instead of saying 1, 2, 3, as I pick up the cubes, I can just place a cube on 1, another cube on 2, another on 3, and so on.) Demonstrate picking up a cube, saying one, and placing it on the 1. Pick up another cube, say two, and place it on the 2. Repeat until all the cubes are counted. 14 Teacher s Guide for Workbook 1

15 The chart makes sure that you count all the cubes without counting any twice. ASK: How does the chart help to make sure that you didn t count any cube twice? (By placing a cube on the chart, I can see that I already counted that cube.) How does the chart help to make sure you didn t miss any cubes? (If any cubes are left off the chart I know I ve missed them.) Demonstrate using the chart incorrectly. Draw the same chart on the board and use square pieces of paper to represent cubes. Place six squares on numbers as shown: Connecting. Explain to students that because 8 is the last number covered, you think that you put 8 squares on the chart. ASK: Am I right? (no) Why not? (Because you have to put the squares on every number in order you can t skip numbers.) Then take the squares off and demonstrate counting them incorrectly: 1, 2, 4, 5, 6, 8. SAY: Even when I count them, I still get 8. What did I do wrong now? (You missed two numbers you didn t say the numbers in order the right way.) Explain that just as you re not allowed to miss numbers when counting, you re not allowed to miss any numbers when using the chart. Repeat with various incorrect placements, always asking students to tell you how this is like missing numbers when counting. EXAMPLE: 2, 3, 4, 5. ACTIVITY Give each student 10 two-colour counters or coins. Have students toss the counters/coins and then use a chart to count how many turned up red and how many turned up yellow (or heads and tails). Students could place the red counters (or heads) above the chart and the yellow counters (or tails) below the chart. Counting using a number line. Show a number line on the board and introduce the term number line. Use the paper squares from the previous exercise to demonstrate counting with a number line. (Place some squares over the numbers in order, starting at 1. What is the last number with a square over it?) Demonstrate counting incorrectly by starting at 0 instead of 1. ASK: When I count the squares and I start counting at 0, will I get the right answer? (no) Demonstrate incorrectly counting the fingers on one hand by starting with 0 and ending with 4. SAY: I get 4 fingers but I really have 5 fingers. How come? Explain that using the number line is just like counting out loud except that we are counting in writing; in either case, you have to start at 1. Provide each student with several (less than 10) counters and have them count the counters using a number line (they can use the number lines on the third worksheet or BLM Number Lines 0 to 10). Students then exchange counters with a partner and check to see if they get the same answer for the same counters. Number Sense

16 NS1-7 More and Less Page xxxx Curriculum Expectations Ontario: km6, km7, 1m1, 1m3, 1m5, 1m11, 1m20 WNCP: kn5, 1N5, [R, CN] Goals Students will understand that the number that means more (less) is written to the right (left) when the numbers are written in counting order. PRIOR KNOWLEDGE REQUIRED Materials Vocabulary right left more most less least fewer fewest order is able to say the numbers from 0 to 10 in sequence can match, and translate between, numbers spoken orally and numerals objects to count, such as blocks, counters, and pennies 1-cm connecting cubes BLM Counting Cubes (p XXX) BLM Extra Practice with More and Less (p XXX) Check that all students understand the concept of more. Show a pile of 5 blocks and a pile of 20 blocks and ASK: Which pile has more blocks? If students don t know the answer, explain that the word more is used to compare how much or how many. EXAMPLE: If you like chocolate, you probably want more chocolate than your parents want to give you. Changing into a known problem. Reflecting on other ways to solve a problem. When the numbers are written in counting order, the number on the right means more. Write the numbers 1-10 in order on the board or refer to a list already posted in the room. Ask students if the numbers are written in the order you say them when counting. Ask students how they could use this order to say if a number is more than another number. (The one on the right, or further along in the list, will mean more, just like the number you say last when counting means more.) Give each student a handful of 1-cm connecting cubes and ask them to make a chain. Then have students work in pairs to determine who was given more cubes, using the charts on BLM Counting Cubes or on the second worksheet for NS1-6. Students place their chains on the chart starting at 1. Which chain is longer? Which number is under the rightmost cube? Have partners link their chains together and then pair up, so that there are four students in each group. Which pair s chain has more cubes? Challenge students to find the answer without using numbers. (e.g. by laying the chains side by side) Which number means more? Write two numbers on the board or on chart paper, and ask a volunteer to circle the number that means more. Have an ordered list of numbers on display for students to refer to at first. Write some pairs out of order and others in order. Then have students show the larger of the two numbers by holding up the correct number of fingers. 16 Teacher s Guide for Workbook 1

17 Bonus Use longer lists of numbers (e.g , ) online guide Individual dart-like game with BLM Target Practice Doing a simpler problem first. Extra Practice BLM Extra Practice with More and Less. Which number means the most? Explain that the most means which one is more than all the others, just like biggest means bigger than all the others. Write three numbers on the board and have students choose the number that means the most. Start with examples where the numbers are already in order (e.g ) then give examples where the numbers are not in order. (e.g ). Students might at first find it helpful to use a list of ordered numbers. They can circle the three numbers they are asked to consider and then choose the rightmost one. Introduce fewer and less as the opposite of more. Have two piles of counters: five red and three yellow. Tell students there are more red counters than yellow counters, which means there are fewer yellow counters than red counters. Explain that the number 3 is less than the number 5, but 3 counters is fewer than 5 counters. Fewer is used for amounts that you can count; less is used for amounts that you cannot count. Show two people, a girl and a boy, with different amounts of cake. The boy has 2 small pieces and the girl has 1 large piece that is bigger than both of the boy s pieces put together. ASK: Who has more pieces? Fewer pieces? More cake? Less cake? Write fewer on one side of the board and less on the other. Tell students to point to the correct word to finish various sentences (or make cards for the students to hold up). EXAMPLE: I have more coins, so you have coins. (fewer) Repeat with carrots (fewer), juice (less), pie (less), pizza (less), pieces of pizza (fewer). Repeat the exercises for more with less and fewer. At first, guide students to decide which pile has fewer by first asking which pile has more. Explain that least means less than all the others and fewest means fewer than all the others. Repeat the exercise above (Which number means the most?) with fewest instead of most. Adding one to each pile doesn t change which has more. Show students a pile of 3 red counters and a pile of 4 yellow counters. ASK: Are there more red counters or yellow counters? (yellow) How do you know? (Because 4 comes after 3.) Add one counter to each pile and repeat the question. Have students predict which pile will have more when you add another counter to each pile (the yellow pile will always have more). Removing one from each pile doesn t change which has more. Repeat the exercise above but remove one at a time from each pile. Start with 7 red and 8 yellow counters. ACTIVITY Play Solitaire War (p XXX). connection Literature More, Fewer, Less by Tana Hoban. Number Sense 1-7 Extension On BLM Who s Winning?, students can compare the scores of two hockey teams and decide who is winning (who has more points). 17

18 NS1-8 One-to-One Correspondence Page xxxx Curriculum Expectations Ontario: km7, km16, 1m1, 1m3, 1m5, 1m6, 1m7, 1m11, 1m13, 1m20 WNCP: kn5, 1N5, [R, CN, V, C] Vocabulary more less pair enough as many Journal Draw 2 more hearts than circles. Draw as many pencils as erasers. Making a model. connection Real World Goals Students will identify which of two sets has more by using one-to-one correspondence. PRIOR KNOWLEDGE REQUIRED understands the concepts of more and less (fewer) can count Materials objects to count, such as counters and connecting cubes How to count two piles together. Show a pile of 6 red cubes and a pile of 8 yellow cubes. Demonstrate taking one at a time from each simultaneously, counting the 6 red cubes and 6 of the yellow cubes together. Then finish counting the yellow cubes. Give students piles of red and yellow cubes to count in this way. Repeat by having students trade handfuls of cubes with each other. Bonus Give students 4 blue, 8 red, and 7 yellow cubes and ask them to count all three piles by saying the counting sequence only once. To see which pile has more without counting, you can remove one from each pile. Tell the class that Sayaka and Jenn are playing a game and the person with the most counters wins. Show Sayaka s pile of 24 yellow counters and Jenn s pile of 26 red counters (but don t tell students the number of counters). Explain that you want to know which pile has more without counting. Encourage students to discuss the problem with a partner. Then, demonstrate removing one counter from each pile until only one colour is left. ASK: Which colour is left red or yellow? (red, so there are more red counters than yellow counters) Who won? (Jenn) Let students work in pairs. Give each pair a pile of red and yellow counters and have them determine if there are more red counters or yellow counters without counting. Drawing a model for the counters. Draw blank circles and coloured circles scattered on the board. Ask students how you could check, without counting, whether there are more blank circles or more coloured circles. ASK: How could I show removing one of each? If students suggest alternately erasing one of each, explain that it might be hard to remember which one (blank or coloured) they erased first. Take other suggestions, then demonstrate circling pairs of circles (one of each kind) in several examples. Matching people to determine which group has more. Tell students you want to find out if there are more boys or girls in the class. Ask them how 18 Teacher s Guide for Workbook 1

19 connection Goldilocks. In this story, were there enough beds for both Goldilocks and the three bears? online guide Match chairs to people and then play Cooperative Musical Chairs. Using logical reasoning. Using logical reasoning, Reflecting on the reasonableness of an answer. you could find out without counting. Then tell the class to pair up, one boy with one girl. Are there any boys or girls left without a partner? Are there more boys or girls? Which group has extra? Repeat with 5-year-olds and 6-year-olds. As many as. Draw three hearts and three circles and ASK: Are there more hearts or circles? Tell students that since there are the same number of each, we say there are as many hearts as circles. Have students draw on a separate piece of paper a different example of as many hearts as circles and then discuss the various ways of doing so. ASK: If you draw 4 hearts, how many circles do you have to draw? If you draw 1 heart, how many circles do you have to draw? If someone decides to draw no circles and no hearts, have they drawn as many hearts as circles? (yes) Have students take one pencil and one workbook and get into groups of four. ASK: Are there as many people as pencils? How do you know? (Yes, because each person has a pencil.) Are there as many people as workbooks? (Yes, because each person has a workbook.) As many workbooks as pencils? (Yes, because there are the same number of workbooks as people and the same number of pencils as people, so there are the same number of workbooks as pencils.) Build a set that has more, fewer, or as many elements as a given set. Give each student five connecting cubes of each colour: red, white, blue, green. Ask students to build a set of connecting cubes so that there are more red than white, fewer blue than white, and as many green as red (give these criteria one at a time). ASK several students: How many green cubes do you have? Do you have more green or white? Why did everyone get the same answer to the second question but not to the first? (Students could choose different numbers of green cubes, but if there are more red than white and as many green as red, everyone s set will have more green than white.) Are there more green or blue? How do you know? (There are more green than white, and more white than blue, so more green than blue.) Connect one-to-one correspondence with counting. Explain that when you count, you are really pairing up each object with a number. ASK: How many numbers do I say when I count from 1 to 10? (10) When I count from 1 to 5? (5) When I count from 1 to 8? (8) Demonstrate counting 7 cubes, while explaining that each cube gets paired up with a number from 1 to 7. Since you know that there are 7 numbers from 1 to 7, there are 7 cubes. Extension Draw the Olympic rings on the board (see margin) and show students 4 chalks of different colours. ASK: Can I colour each circle a different colour? Do I have enough colours? Number Sense

20 NS1-9 How Many More? Page xxxx Curriculum Expectations Ontario: km2, km16, 1m1, 1m7, 1m11, 1m14 WNCP: kn5, 1N5, [R, C] Goals Students will determine how many more by pairing objects up and counting the extras. Students will also understand how much more one number is than another. Vocabulary extra how many more PRIOR KNOWLEDGE REQUIRED understands one-to-one correspondence understands the concepts of more and less (fewer) can count Materials two-colour counters BLM Pairing Them Up (p XXX) BLM 2-cm Grid Paper (p XXX) OR BLM Counting Cubes (p XXX) 2-cm connecting cubes Counting the extras to find how many more. Give students two-colour counters. Have them toss their counters. ASK: Did more counters land with the yellow face up or the red face up? Have students pair up their counters. Are any counters left unpaired? What colour are the extras? Have several volunteers present their answers and show their pairings. Repeat several times. Draw the following picture on the board: Changing into a known problem. ASK: Are there more circles or squares? How many more? (i.e., How many extras are there?) Remind students how to pair objects up in drawings by joining them with a line. Students can colour any shapes not joined to identify the extras and then count the extras to find how many more. Students can complete BLM Pairing Them Up for additional practice. Counting extras when objects are lined up in grids. Display the following picture on the board: 20 Teacher s Guide for Workbook 1

21 online guide Activity with BLMs based on popular computer game Minesweeper. ASK: Are there more circles or triangles? How many more? Explain to students that the grid does the pairing for them. Have a volunteer colour the extra triangle (the one that isn t paired up). Repeat with more examples. Have the triangles sometimes in the top row and sometimes in the bottom row. Then draw only the triangles and have volunteers add the circles so that there are: 2 more circles than triangles; 3 more triangles than circles; 1 fewer triangle than circles; 2 fewer circles than triangles. Then give students connecting cubes of two colours and ask them to use BLM 2-cm Grid Paper or BLM Counting Cubes to determine which colour of cubes they have more of and how many more. You could then have students choose a combination of cubes (e.g., 3 more red than blue) and use the grid to show that they have done so correctly. How much more is one number than another? Display three circles and four squares in a grid as shown: ASK: How many circles are there? How many squares are there? How many more squares than circles are there? Summarize as follows: more than Looking for a pattern. Draw several similar grids using different shapes but always 3 of one and 4 of the other. Write the summary statements one below the other, so that 1 more and than create clear columns. ASK: What is always the same? Emphasize that the group of 4 always has one extra, so 4 objects is always 1 more than 3 objects. Explain that mathematicians shorten this to saying 4 is 1 more than 3. Repeat with 5 shapes and 3 shapes and have a volunteer fill in the blank: 5 is more than 3. Find the number that is 2 more than another number by drawing circles and triangles. Draw 4 triangles in a grid and have a volunteer draw 2 more circles than triangles. ASK: How many circles did she/he draw? What number is 2 more than 4? Repeat with other numbers of triangles. Then have students draw 5 triangles and 2 more circles than triangles on grid paper or BLM Counting Cubes. ASK: How many circles did you draw? What number is 2 more than 5? Repeat with various examples of 2 more than and then ask for examples of 1 more than and 3 more than. Number Sense

22 NS1-10 Counting On Page xxxx Curriculum Expectations Ontario: km13, 1m1, 1m3, 1m7, 1m11, 1m14 WNCP: 1N5, [R, C] Vocabulary extra how many more counting on Goals Students will determine how many more by counting on. PRIOR KNOWLEDGE REQUIRED understands one-to-one correspondence understands the concepts of more and less (fewer) can count can determine how many more Materials counters bedsheet BLM Counting On (p xxx) Counting extras when objects are lined up with numbers. Draw or display the following picture on the board ASK: How many circles are there? How many squares? Are there more circles or squares? Have a volunteer circle the extra circles. ASK: How many extras are there? Have a volunteer fill in the blanks in this sentence: There are more than. Repeat with similar pictures. How many more than another number? Draw the numbers in between the rows, as shown, but with all the numbers dotted for the students to trace ASK: How many circles are there? How many squares? Have a volunteer trace the extra numbers. ASK: How many numbers did you trace? How many more squares than circles are there? Repeat with pictures of different objects but with the same numbers, 3 and 5. Emphasize that the group of 5 always has 2 extra, so 5 objects is always 2 more objects than 3 objects. Mathematicians say that 5 is 2 more than 3. Write on the board: Have a volunteer continue writing the numbers up to 7. ASK: How many numbers did the volunteer write? Explain that 7 is 3 more than 4 because the volunteer had to write 3 more numbers after 4 to get to 7. Repeat with various examples. 22 Teacher s Guide for Workbook 1