Unit 1 Number Sense: Numbers to 10

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1 Unit 1 Number Sense: Numbers to 10 Introduction In this unit, students will review counting (this includes equating written numerals, quantities, spoken numbers, and numbers written as words). Students will also review the notion of one-to-one correspondence, or pairing up for example, given a set of pencils and a set of erasers, there are the same number of pencils and erasers if you can pair the erasers with the pencils and are left with no unpaired pencils or erasers. This notion also leads naturally to the concepts of more, fewer, and less (in physical quantities as well as in number). Students will also review basic concepts of addition and subtraction, including adding and subtracting with zero. The focus of the unit is numbers from 0 to 10, although some questions involve numbers beyond 10. Meeting Your Curriculum Alberta Lesson NS2-8 is required. All other lessons are recommended as review of material that will be useful in later units. British Columbia Lesson NS2-8 is required. All other lessons are recommended as review of material that will be useful in later units. Manitoba Lesson NS2-8 is required. All other lessons are recommended as review of material that will be useful in later units. Ontario Lesson NS2-8 is required. All other lessons are recommended as review of material that will be useful in later units. Signalling. In these lessons, we often suggest that all students signal their answers simultaneously (e.g., by flashing thumbs up for yes or thumbs down for no or by pointing to a displayed answer). For a complete description of signalling, see p A-22. Student readiness. While this unit reviews counting, it is assumed that students can subitize (recognize quantities) up to and including 5, and that they can recognize and write numerals. BLM Writing Numbers (p B-42) provides extra practice with writing numerals. Recurring Games The following games and activities recur throughout this unit. Rules and materials may vary per lesson. Go to page. Make sure students can find the page numbers in their JUMP Math AP Books, in the bottom left and right corners. Have students turn to different pages, one at a time and in random order. Always ensure that the entire class has found the page before asking students to turn to another. Have students point to where they see each page number. This helps students grasp the order of numbers, as they learn which way to turn the pages. Number Sense B-1 CA 2.1 TG Unit 1 p1-36 V5.indd 1 6/14/17 11:48:58 AM

2 Picking pairs. Use, for example, number cards and number word cards; the deck that students use will depend on the lesson. Students can play in teams or individually. Place a 3 4 array of cards face up on the table. Students take turns picking pairs of matching cards and placing them into a common discard pile. When there are no more pairs in the array, add more cards. The goal is to place all the cards into the discard pile. If students have any non-matching cards left at the end, then some of their cards must have been matched incorrectly. Memory. Place all cards face down. Students turn over two cards at a time. If the cards match, students set these cards aside; otherwise, they turn them face down again and continue playing. Play this first as a whole class, with volunteers taking turns. Students can then play individually or co-operatively in pairs. In either case, the goal is to match up all the cards. If playing with a partner, Player 1 leads by choosing and turning over a card and Player 2 follows by choosing and turning over another card. After all pairs are found, players switch roles and play again. Players can help each other by asking questions or making suggestions (EXAMPLE: I think I know where both 3s are; should I turn one of them over? ), but they are not allowed to tell each other where specific cards are. (NOTE: It is a good idea for students to play Picking Pairs to practise making and recognizing matches before they play Memory.) Dominoes. Make paper dominoes with numbers written in different ways (EXAMPLES: random arrangements of dots, base ten blocks, addition or subtraction sentences, numerals). You can use the template on BLM Blank Domino Cards (p M-3). Decide how many different numbers you want the dominoes to have (at least seven for four players), and ensure that every number appears on the same domino with every other number, including itself (for four players, there will be at least 28 cards). Explain that the dominoes can be turned around, even though any numerals won t look like numerals any more. Lay all the dominoes face down and shuffle them. Each player draws a domino in turn. Continue drawing dominoes until all dominoes are taken. The player with either the most dominoes or the highest double (a double is a domino with both ends showing the same number) starts the game by laying a domino face up. On a turn, players either play a domino that matches an open end of a domino already in play, or play any domino to start a new train. At the end of a turn, players may join two existing trains if they wish. (This process can be made more fun by making train sound effects as the trains are being joined.) The players are a team and must help each other to place their dominoes; all dominoes in each player s hand are thus placed face up on the table for all to see. The game ends when all dominoes have been played. The goal is for all the dominoes on the table to form a single train. Easier Variation: Play without doubles dominoes. B-2 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 2 6/14/17 11:48:59 AM

3 Peace. (A co-operative version of the card game War.) Two players sit opposite each other and divide the deck into two equal piles, one on Player 1 s left and one on Player 1 s right. Player 1 begins by turning over the top card of each pile. If the cards are not equal, both cards are placed beside the pile that the greater card came from. If they are equal, they are each placed beside the pile they came from. Player 2 then takes a turn by turning over the top card of each pile. The game ends when all cards have been turned over and played. There will now be two piles on the table. Together, the players must predict, without counting, which pile has more. They count or use one-to-one correspondence to check their prediction. If they are right, they win. Variations: Peace for Less. Place both cards beside the pile that the lesser card came from. Addition Peace. Turn over the top two cards from each pile and compare the sums of each pair. Difference Peace. Turn over the top two cards from each pile and compare differences instead of sums. I Have, Who Has? Each student needs one card to play (see sample below). You can make the cards or have students make them using BLM Game Cards (p M-2). The blank spaces at the top and bottom of each card can be filled with numerals or representations of numbers: an arrangement of dots, tens blocks, an addition or subtraction sentence. The student with the card shown below would start by saying I have 3. Who has 7? The student who has 7 on top would respond with I have 7. Who has [whatever is on the bottom of the card]?, and so on. Sample Card I have 3 Who has Group Dominoes. This is a variation of I Have, Who Has? Have one student tape his or her card to the board. The person whose top matches the bottom of the card on the board adds his or her card below it, as when you play dominoes. This variation is particularly useful for students who prefer physical action to verbal answers. Materials Number cards (0 to 10) and number word cards (zero to ten). Write each numeral from 0 to 10 and each number word from zero to ten on an index card or a piece of construction paper, or have students make the cards. You will need one set of each per student. Number Sense B-3 CA 2.1 TG Unit 1 p1-36 V5.indd 3 6/14/17 11:48:59 AM

4 Counters or cubes of two different colours. Two-sided counters or cubes of two different colours (for example, red and blue) are called for in this unit. In addition to the BLMs found at the end of this unit, the following Generic BLMs, found in section M, are also used in this unit: BLM 2 cm Grid Paper (p M-1) BLM Game Cards (p M-2) BLM Blank Domino Cards (p M-3) Assessment. The assessment checklist for this unit can be found in section N. The following table indicates the lessons covered by a test, which can be found in section O. Test Lessons NS2-4 to 6 Test Lessons NS2-7 to 8 B-4 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 4 6/14/17 11:48:59 AM

5 NS2-1 Counting and Matching Pages 1 2 CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended VOCABULARY count how many number numbers 0 to 10 Goals Students will review counting (associating spoken numbers with the corresponding quantities and written numerals). PRIOR KNOWLEDGE REQUIRED Can colour Can recognize and write numerals within 10 Can subitize within 5 Can join two figures with a line MATERIALS BLM Quantities (pp B-37 41) counters BLM Writing Numbers (p B-42) 2 cm grid paper or BLM 2 cm Grid Paper (p M-1) magazines and catalogues BLM Game Cards (p M-2) BLM Blank Domino Cards (p M-3) BLM Circle the Numbers (p B-43) BLM Dominoes (p B-44) Review saying the numbers from 1 to 10. Teach a counting song, such as One two, buckle my shoe. The concept of how many. Show students sets of four cards from BLM Quantities, of which three illustrate the same quantity, and ask students to identify the card that doesn t belong. Point to each card, one at a time, and ask students to raise their hands when you point to the card that doesn t belong. Repeat for each quantity from zero through nine at least once. Discuss what is the same and what is different about all the cards that do belong. Explain that you made the groups based on how many shapes are on each card. It doesn t matter what the shapes are, how big they are, where they are on the card, or what colour they are. Tap your desk a few times and ask students to identify the number of taps. Have all students signal the answer simultaneously by holding up the correct number of fingers. Then, hold up various numbers of fingers and have students say the correct number. Counting in different ways gives the same answer. Arrange nine counters in a row. ASK: Do you think I will get the same answer starting here (at the left) as I get starting over here (at the right)? Count in both directions. ASK: Why did I get the same answer? (same number of counters) Repeat with various numbers of counters between 0 and 10. Occasionally make a mistake by counting a counter twice. Wait for students Number Sense 2-1 B-5 CA 2.1 TG Unit 1 p1-36 V5.indd 5 6/14/17 11:48:59 AM

6 to discover your mistakes. Discuss strategies to ensure that you don t count objects twice; for example, move objects already counted to a separate pile or cover up each object that has already been counted. EXTRA PRACTICE BLM Writing Numbers Identifying the numeral with the sound. Draw several capital or lowercase letters and ask students to name them. Explain to students that just as we have symbols for the letters in the alphabet, we have symbols for numbers. Write some numbers on the board in order from 0 to 9, and ask students to say the numbers as you point to them. Gradually increase the difficulty by writing more and more numerals that are not in order ( ). Then write 10 on the board. ASK: Is this a number? (yes) What number is it? (ten) Identifying the numeral with the quantity. Write the numbers from 0 to 9 across the board, in order, leaving plenty of space between them. Give each student one of the quantity cards used earlier and ask volunteers to tape their card below the correct number. More than one card will go with the same number. Then write a numeral on the board and have students hold up the corresponding number of fingers. Exercises 1. Count the pictures. Write the number. a) b) c) d) e) Bonus: Answers: a) 4, b) 5, c) 8, d) 9, e) 3, Bonus: Copy the number. Draw that many dots under the number. a) 2 b) 7 c) 1 d) 6 e) 9 f) 10 Bonus: 0 ACTIVITIES 1 5 (Optional) 1. Five. Give students 2 cm grid paper or BLM 2 cm Grid Paper. Ask them to colour any five squares, but only five. Ask one student to count his or her squares, pointing to each square one by one. SAY: I see all of the squares are [describe their arrangement on the page, e.g., in the top corner, in a line]. ASK: Did anyone colour five squares in a different way? How is your five different? B-6 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 6 6/14/17 11:48:59 AM

7 2. Posters. Give each student an old magazine or catalogue. Assign each student one number from 2 to 9 and ask students to find and cut out pictures where items are in groups of that many. Students can then form a group with other students who had the same number and pool their cut-outs to make a poster. 3. I Have, Who Has? or Group Dominoes (see unit introduction). Use numerals on top and dots on the bottom. Alternatively, use different arrangements of dots on the top and bottom. 4. Dominoes (see unit introduction). Use dots on both sides of the dominoes, but arrange the dots differently for the same quantities. 5. Go to Page (see unit introduction). Have students open their JUMP Math AP Books to page 1. Then, have them turn and point to the following page numbers in order: 2, 5, 3, 7, 10, 6, 9, 8, 6, 1, 4. NOTE: Technically, a number is the quantity and the symbol for the number is called the numeral. A digit is any symbol from 0 to 9. A numeral can consist of one digit or more than one digit. Students do not need to use the word numeral at this stage; they can use number to refer to both the quantity and the symbol. Numbers need to be right-side up. Demonstrate that a chair, no matter how you turn it, is still a chair. But, letters and numbers are not like chairs; they have to be written right-side up, otherwise they change. Write some lowercase letters, such as j or k, on cards, and turn them upside down and sideways to illustrate this. NOTE: Students may identify letters and numbers that don t change (e.g., 8) or letters that turn into other letters (e.g., d becomes p ) when written on a card and turned upside down. Point out that these are special cases; in general, numbers and letters have only one right-side up. Draw several numbers in two ways, correctly and incorrectly, and have volunteers circle the correct way. Include numbers that are upside down or on their side. Exercises: Complete BLM Circle the Numbers. Some boxes include two correctly written numbers. Match by counting. In a two-column chart, draw three different quantities (less than 10) in the first column. Draw the same three quantities, using different items in a different arrangement, in the second column. (see example in margin) Alternatively, tape cards from BLM Quantities on the board. Have volunteers match the items by quantity. Repeat several times, gradually increasing the quantities in each column, up to 10. Then, arrange and match quantities by row instead of by column. When students can comfortably match quantities, replace the quantities in one column or row with numerals, and have students match numerals to quantities. Writing numerals for two quantities. Draw on the board: Number Sense 2-1 B-7 CA 2.1 TG Unit 1 p1-36 V5.indd 7 6/14/17 11:48:59 AM

8 Point to the left side of the domino and ASK: How many dots are there on this side? (5) Students can signal their answer by holding up the correct number of fingers. After all students have signalled the correct answer, SAY: There are five dots. (If students gives an incorrect answer, point to the dots one by one as you count them together.) Repeat with the right side of the domino. (2) Draw a blank domino directly underneath the one on the board. SAY: I want to draw a matching domino by writing numbers instead of drawing dots. Point to the left side of the blank domino and ASK: What number should I write here? (5) Repeat with the right side. (2) The picture should look like this: 5 2 Exercises: Draw a matching domino using numbers instead of dots. a) b) c) d) Answers: a) 1 6, b) 7 4, c) 2 7, d) 0 3 Match two quantities to numerals. Ask students to match dominoes with dots to corresponding dominoes with numbers. EXAMPLE: Extra practice BLM Dominoes Encourage students to check both sides of the dominoes they match to verify their answers. Repeat with other sets of dominoes where each number appears only once. Then, begin to include examples where the same number occurs on one side of two different dominoes. Finally, arrange the dominoes in rows instead of columns and then scatter them B-8 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 8 6/14/17 11:49:00 AM

9 ACTIVITY 6 (Optional) 6. Play Picking Pairs and then Memory (see unit introduction) using cards from BLM Quantities. Start with two of each quantity from one to nine. Arrange the 18 cards in three rows of six. Variation: Use one quantity card and one number card for each quantity. Extensions 1. Have students match objects by number. SAY: It might be tricky. Some groups have the same objects but you have to match by number, not by object. (see example in margin) 2. Ask students to think of letters that can be turned around to make other letters. Then, ask them to think of numbers that can be turned around to make letters. Give students calculators, and have them push different numbers and then turn the calculators around to see what letters they can make. Ask them to try to make a word. Can they make any of these words: hello, goose, giggles, bees? What other words can they make? 3. Have students complete BLM Many Ways to Colour (p B-45). Number Sense 2-1 B-9 CA 2.1 TG Unit 1 p1-36 V5.indd 9 6/14/17 11:49:01 AM

10 NS2-2 One-to-One Correspondence Pages 3 4 CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended VOCABULARY as many more pair Goals Students will identify which of two sets of objects has more by using one-to-one correspondence. PRIOR KNOWLEDGE REQUIRED Understands the concepts of more and less (or fewer) Can count MATERIALS two-sided counters hula hoops (optional) Adding one to both or removing one from both doesn t change which has more. Take a pile of three red counters and a pile of four yellow counters. ASK: Are there more red counters or yellow counters? (yellow) Verify by counting. Emphasize that 4 comes after 3, so there are more yellow counters than red counters. Continue adding one to each pile, asking which pile has more, and verifying. Emphasize that adding one to each pile doesn t change which one has more. Matching chairs to people. Sit in your chair, and ask students to do the same so that everyone in the classroom is seated. ASK: Are there more people or chairs in this room? How do you know? (If there are extra chairs, then there are more chairs than people.) Draw several combinations of chairs and stick-people on the board (see examples below) and ASK: Are there more people or chairs? How do you know? Did you need to count? Explain that you can see whether there are extra chairs or extra people after pairing up chairs and people. 5 chairs and 7 people; 2 people are standing 5 chairs and 7 people, but no one is standing the first 2 and last 2 people are sharing a chair 9 chairs and 6 people; 3 chairs are empty ACTIVITY (Optional) Co-operative musical chairs. Play musical chairs, but no one sits out. Instead, every time a chair is removed, children sit two or more to a chair. Eventually, they will all have to fit on one chair. Play in groups of seven or eight. Make the connection between having more people than chairs and having to share chairs. Variation: Large hula hoops are islands. The water level is rising and islands are disappearing, one by one. People stand inside the hula hoops. B-10 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 10 6/14/17 11:49:01 AM

11 connection Real World Find out which pile has more, without counting, by removing one from each pile. SAY: Sharon and Tess each have a pile of beads. (Show Sharon s pile of 24 yellow counters and Tess s pile of 26 red counters.) They want to know if they have the same number or not, but counting each pile is too much work. ASK: How can they find out without counting? Encourage students to talk over the problem with a partner before sharing ideas with the class. If no one suggests removing one from each pile until only one colour is left, suggest it yourself and then demonstrate. ASK: Which colour is left, red or yellow? (red, so there are more red counters than yellow counters) Who has more counters? (Tess) ASK: If Tess gives a counter to Sharon, do you think they will have the same number? Check the prediction. Exercise: Have students work in pairs. Give each pair a pile of red and a pile of yellow counters and have them determine if they have more red or yellow counters. Draw a model for the counters. Draw several squares, some coloured and some uncoloured, scattered on the board. Demonstrate pairing objects by drawing a circle around pairs or by joining pairs with a line. ASK: Are there more coloured or uncoloured squares? How do you know? 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 one to eight? (8) Demonstrate by counting eight cubes. Point out that each cube gets paired up with a number from 1 to 8. Since you know that there are eight numbers from 1 to 8, there are eight cubes. Emphasize that it doesn t matter which cube you pair up with each number, just like it didn t matter which red counter was paired up with which yellow counter in the exercise. Extensions Have students complete BLM Counting Starred Squares (pp B-46 48). Over the course of the BLM, students will learn to identify how many starred squares each square in a grid is touching (see examples in margin). 2. Starsweeper. To make a 4 4 or 5 5 Starsweeper grid, put at most four stars in the 4 4 grid and five stars in the 5 5 grid. Then, in each square without a star, write the number of starred squares the square is touching. You (or students) can use the templates on BLM Blank Starsweeper Grids (p B-49). Students cover all the squares on the grid with coins or tokens. Students remove the coin from any square they think does not have a star in it. If they uncover a square with a 0 in it, they know that all the squares around it are star-free and they can uncover all of those, too. When students think there are more starred squares still covered than numbered squares, they stop. Students can check if they re correct by putting the coins left on the board into two piles: one pile for the coins that cover a starred square and a second pile for the coins that cover Number Sense 2-2 B-11 CA 2.1 TG Unit 1 p1-36 V5.indd 11 6/14/17 11:49:01 AM

12 a numbered square. They win if the first pile has more than the second pile. Students can play individually or co-operatively in pairs by taking turns. Players must decide together when to stop uncovering squares. 3. Give each pair of students connecting cubes of two colours. Have students select a number of cubes of each colour and build a structure with them. Have partners exchange structures and determine if the structure contains more cubes of one of the colours, without disassembling it. B-12 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 12 6/14/17 11:49:01 AM

13 NS2-3 More, Fewer, and Less Pages 5 6 CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended Goals Students will use a number chart to count and compare numbers and quantities. Students will understand that when numbers are spoken and written in order, numbers that mean more are said later and written to the right of smaller numbers. VOCABULARY fewer fewest least less more most order right PRIOR KNOWLEDGE REQUIRED Can count, recognize, and write numerals within 10 Subitizes within 5 MATERIALS counting chart or BLM Counting Cubes (p B-50) two colours of connecting cubes square pieces of paper tape two-sided counters or coins red and yellow blocks BLM Who Is Winning? (p B-51) strips of paper or index cards deck of cards Make a counting chart for each student. Make strips of paper 2 cm wide and 20 cm long divided into 10 numbered squares (or photocopy strips from BLM Counting Cubes) Count using a chart. Give each student up to ten 2-cm connecting cubes (students should have different numbers of cubes). Ask students to count their cubes. Then, have them make a chain with the cubes and place it on their number 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. ASK: How many cubes did you count? What is the last number covered on the chart? Does anyone notice 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. ASK: Does the pattern hold? (yes) What is an easy way to find out 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 one, two, three, when picking up the cubes, just place a cube on 1, another cube on 2, another on 3, and so on) Demonstrate by picking up a cube, saying one, and placing it on Number Sense 2-3 B-13 CA 2.1 TG Unit 1 p1-36 V5.indd 13 6/14/17 11:49:01 AM

14 the 1. Pick up another cube, say two, and place it on the 2. Repeat until all the cubes are counted. The chart helps you make sure that each cube is counted once. ASK: How does the chart help you make sure that you don t count any cube twice? (once a cube is placed on the chart, it s been counted) How does the chart help you make sure you don t miss any cubes? (each cube is placed on a number, so each cube gets counted) 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: Explain to students that because 8 is the last number covered, you think that you put eight squares on the chart. ASK: Am I correct? (no) Why not? (the squares must cover every number in order; you can t skip numbers) Take the squares off and demonstrate counting them incorrectly: 1, 3, 4, 5, 7, 8. SAY: Even when I count them, I still get eight. What did I do wrong now? (you missed two numbers; you didn t say all the numbers in order) 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 (Optional) Give each student 10 two-sided counters or coins. Have students toss the counters/coins and then use a sequence of numbers 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 row and the yellow counters (or tails) below the row The concept of more. Ask students to try to explain what more means without using the word. Then, explain that more in math means a larger number. Write more on the board. Show lots of counters in one hand and two or three in the other. ASK: Which hand has more counters? Draw lots of little circles on the right side of the board and two big circles on the left. ASK: Are there more circles here or there? Explain that the circles are bigger on one side, but there are more of them on the other side. B-14 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 14 6/14/17 11:49:05 AM

15 The number you say last means more. Show students two piles of blocks, one with eight and one with nine. ASK: Which pile has more blocks? How can we find out for sure? Count the pile with eight blocks. Choose a student who said that the pile with nine blocks has more. SAY: You said that the other pile has more. Do you think I will get to eight when I count the second pile? Emphasize that you should get to eight before finishing the second pile because it has more. Count together and stop at eight. ASK: Was [student s name] right? Explain that because you were not finished counting the other pile when you said eight, that pile has more. Show five red counters and seven yellow counters. Count the pile of seven, and then check to see if you say seven when you count the other pile. ASK: Are there more red counters or yellow counters? (yellow) How do you know? (when counting the red pile, you did not get to 7, you stopped earlier) It s easier to count two piles together. SAY: It s so much work to count each pile separately; let s try to count two piles at the same time. Show a pile of six red cubes and eight yellow cubes. Count up to 6, holding up one red cube and one yellow cube with each number. Explain that you have to stop because you have run out of red cubes. Since there are extra yellow cubes, you know there are more yellow than red cubes. Write red 6 on the board. Finish by counting the two extra yellow cubes. Emphasize that you can start at 7 because you already counted six cubes. Write yellow 8 on the board. Exercise: Give students red and yellow cubes to count in the manner described above. 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 one time. When numbers are written in order, the number on the right means more. Write the numbers from 1 to 10 in order on the board. ASK: Are the numbers written in the same order as you say them when counting aloud? (yes) How could you use this order to say if a number is more than another number? (the one on the right means more, just as the number you say later when counting means more ) Which number means more? Write two numbers on the board. Have students show the greater of the two numbers by holding up the correct number of fingers. Have an ordered list of numbers displayed for reference. Eventually, challenge students to indicate which is more without referring to an ordered list. Exercises: Circle the larger number. a) 5 9 b) 8 4 c) 7 6 d) 1 9 Extra practice BLM Who Is Winning? e) 8 7 f) 8 10 g) 3 2 h) 6 7 Answers: a) 9, b) 8, c) 7, d) 9, e) 8, f) 10, g) 3, h) 7 Number Sense 2-3 B-15 CA 2.1 TG Unit 1 p1-36 V5.indd 15 6/14/17 11:49:05 AM

16 Which number means the most? Explain that most means more than all the others. Write most on the board. 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 (EXAMPLE: 3, 6, 7), and then give examples where the numbers are not in order (EXAMPLE: 7, 1, 4). Students might find it helpful to refer to a list of the ordered numbers at first. They can circle all three numbers that they are asked to consider on the list and then choose the one furthest to the right as the most. Exercises: Which number means the most? a) 3, 8, 9 b) 9, 7, 8 c) 6, 8, 5 d) 3, 10, 1 e) 7, 0, 10 f) 2, 1, 4 g) 5, 3, 6 h) 8, 2, 0 Bonus i) 7, 6, 3, 9 j) 4, 6, 2, 3, 7, 1 k) 7, 0, 2, 8, 4, 9, 6, 1, 5 Answers: a) 9, b) 9, c) 8, d) 10, e) 10, f) 4, g) 6, h) 8, Bonus: i) 9, j) 7, k) 9 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; that means there are fewer yellow counters than red counters. Explain that fewer is used for amounts that you can count and less is used for amounts that you cannot count. Draw two students with different amounts of cake: One has two small pieces, the other has one large piece bigger than both small pieces put together. ASK: Who has more pieces? Fewer pieces? More cake? Less cake? Write fewer and less on the board, spaced apart, and ask 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). Identifying groups with fewer objects. Show students two piles of blocks, one with three red blocks and the other with nine yellow blocks. ASK: Are there more red blocks or yellow blocks? (yellow) Students all point to the pile with more blocks. ASK: Are there fewer red blocks or yellow blocks? (red) Students all point to the pile with fewer blocks. Count the piles as a class, and write the numbers of blocks on the board: 3 9 ASK: Which number means more, 3 or 9? (9) Which number means less? (3) Repeat with several similar examples. Write on the board: There are red blocks than yellow blocks. 3 is than 9. Point to the first blank. ASK: Which word should I write in the blank, more, less, or fewer? (fewer) Repeat with the second blank. (less) B-16 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 16 6/14/17 11:49:05 AM

17 Give each student three blank strips of paper or index cards and have them write the words more, less, and fewer, one word on each strip of paper. Have students hold up the correct word that goes in the blank in the exercises below. Exercises: Which word goes in the blank, more, less, or fewer? a) 4 red blocks, 2 yellow blocks There are red blocks than yellow blocks. b) 4 red blocks, 2 yellow blocks 4 is than 2. c) 5 red blocks, 8 yellow blocks There are red blocks than yellow blocks. d) 5 red blocks, 8 yellow blocks 5 is than 8. e) 6 red blocks, 7 yellow blocks There are red blocks than yellow blocks. f) 6 red blocks, 7 yellow blocks 6 is than 7. Answers: a) more, b) more, c) fewer, d) less, e) fewer, f) less Introduce least and fewest as the opposite of most. Explain that least means less than all the others and fewest means fewer than all the others. Exercises 1. Which number of blocks is the fewest? a) 3, 8, 9 b) 9, 7, 8 c) 6, 8, 5 d) 3, 10, 1 Answers: a) 3, b) 7, c) 5, d) 1 2. Which number is the least? a) 7, 0, 10 b) 2, 1, 4 c) 5, 3, 6 d) 8, 2, 0 Bonus e) 7, 6, 3, 9 f) 4, 6, 2, 3, 7, 1 g) 7, 0, 2, 8, 4, 9, 6, 1, 5 Answers: a) 0, b) 1, c) 3, d) 0, e) 3, f) 1, g) 0 ACTIVITY (Optional) Play Peace and Peace for Less (see unit introduction). Use only the red cards from A to 10 and count A as 1. Number Sense 2-3 B-17 CA 2.1 TG Unit 1 p1-36 V5.indd 17 6/14/17 11:49:05 AM

18 Extensions 1. Complete BLM Mr. Fish (pp B-52 54). 2. Have students draw two groups of objects (for example, stars and happy faces), so that they have a different number of stars and happy faces. Have them describe the picture using the words more and fewer. Sample answer: I drew 5 stars and 3 happy faces. I drew more stars than happy faces. I drew fewer happy faces than stars. B-18 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 18 6/14/17 11:49:06 AM

19 NS2-4 How Many More? Pages 7 9 CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended VOCABULARY extra how many more pair up Goals Students determine how much more one quantity is than another by counting the extras. PRIOR KNOWLEDGE REQUIRED Understands one-to-one correspondence Understands the concepts of more and less (fewer) Can count up to 20 from a number less than 20 MATERIALS two-sided counters BLM Counting Cubes (p B-50) Find out how many more by lining up objects above and below a sequence of numbers. Draw the numbers 1 to 10 on the board, and then line up eight squares above the numbers and six triangles below the numbers in one-to-one correspondence: Remind students how to pair objects by pairing one square to one triangle. ASK: Are there more squares or triangles? (squares) SAY: If there is more of one shape, I m going to call the additional number of shapes extra. Write the word extra on the board. Draw a circle around each extra square and the number below it: ASK: How many extra squares are there? (2) Write the following sentence on the board and ask a volunteer to fill in the blank: There are more than. Repeat with similar pictures (for example, five squares and nine triangles, seven squares and four triangles). For the following exercises, give each pair of students a number chart from 1 to 10 (for example, from BLM Counting Cubes) and 20 two-sided counters. Partner 1 models the red above the number strip and Partner 2 models the yellow below the number strip. Partners count the extras together. Number Sense 2-4 B-19 CA 2.1 TG Unit 1 p1-36 V5.indd 19 6/14/17 11:49:06 AM

20 Exercises: Write how many more red than yellow. a) 5 yellow, 7 red b) 4 red, 3 yellow c) 2 yellow, 8 red d) 7 yellow, 10 red e) 9 red, 6 yellow d) 10 red, 1 yellow Answers: a) 2 more red, b) 1 more red, c) 6 more red, d) 3 more red, e) 3 more red, d) 9 more red Counting the extra numbers you say. Write the numbers 1 to 5 on the board, and have a volunteer continue writing the numbers until 8. ASK: How many extra numbers did you write? (3) How many more is 8 than 5? (3) Tell students that they can keep track of how many extra numbers there are by counting on their fingers. Tell students you are going to count to 8, but only raise a finger when you say an extra number after 5. Remind students that you want to know how many more 8 is than 5. Count from 1 to 5 with your fist closed, and then raise your thumb and say 6 ; raise your index finger and say 7 ; and raise your middle finger and say 8. SAY: Because I raised three fingers when counting to 8 after I counted 5, I can see that 8 is 3 more than 5. As a class, use this method to find how many more 9 is than 7. Start counting at 1; students only raise fingers when they get to the extra numbers. Repeat with 8 and 4, 10 and 5, 9 and 6, 10 and 7. NOTE: Make sure students tuck their thumbs under their other fingers when they make a fist. If the thumb is not tucked under and sticks out, students may start counting the extras with their other fingers but include the thumb when they total the extras. To ensure that students keep their fists closed while saying the first number, you can pretend to throw them the first number which they have to pretend to catch. Counting on. Show students an easier way to find how many more 10 is than 7. Instead of saying 1, 2, 3, 4, 5, 6, 7 with their fists closed, they can just say 7 with their fists closed, and count the extra numbers 8, 9, and 10. Discuss why this works. SAY: You are going to get to 7 anyway, by saying all the numbers from 1 to 7, so you might as well save time by starting at 7. Give students lots of practice with this type of question. Eventually, include questions where students need to count the extra numbers on both hands, but use only one-digit numbers. EXAMPLE: 9 is how many more than 3? Write on the board: 8 is more than 5. Read or have a volunteer read the sentence aloud, saying blank for the blank line. ASK: How do we find the number that goes in the blank? (count on using your fingers) Have students find the answer together. (3) Have a volunteer write 3 in the blank. Repeat with 6 is more than 2. (4) B-20 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 20 6/14/17 11:49:06 AM

21 Exercises: Count on using your fingers. Fill in the blanks. a) 7 is more than 4. b) 8 is more than 3. c) 9 is more than 7. d) 10 is more than 4. e) 5 is more than 1. f) 10 is more than 2. Bonus: 13 is more than 4. Answers: a) 3, b) 5, c) 2, d) 6, e) 4, f) 8, Bonus: 9 Counting on with pencil and paper. Tell students that you want to know what number is 4 more than 5. Instead of saying the next four numbers, you can write them. Write on the board: 5 Have a volunteer fill in the blanks. (6, 7, 8, 9) ASK: What number is 4 more than 5? (9) Repeat with other numbers, always ending with at most 10. Then write the numbers from 1 to 20 in order on the board and repeat the above, this time including questions that involve counting to 20. Leave this number sequence visible while students complete AP Book 2.1 p 8. ACTIVITY (Optional) Set up a hiding area at the front of the room. Ask four volunteers to hide and ask for three more volunteers to stand at the front where everyone can see them. ASK: How many children are at the front of the room? SAY: I know there are four children hiding even though we can t see them, so we will count on to count the others. ASK: What number do we say with our fists closed? (4) Demonstrate counting on, then ask the hidden students to come out and count all the students, starting at 1. Repeat with various numbers of volunteers. Variation: Hide a known number of counters in a container. Extensions 1. Have students complete BLM More Than (p B-55). Students discover patterns by changing the order of numbers: 7 is 4 more than 3, but 7 is also 3 more than Have students complete BLM Keeping Score (p B-56). 3. Students work in pairs. Each partner chooses a number between 1 and 10. Students then write a sentence stating how much more the larger number is than the smaller number. For example, if students choose 5 and 7, they write 7 is 2 more than 5. Have students repeat this process several times. If both partners choose the same number, then they write, for example, 9 is 0 more than 9. Number Sense 2-4 B-21 CA 2.1 TG Unit 1 p1-36 V5.indd 21 6/14/17 11:49:06 AM

22 NS2-5 Reading Number Words to Ten Pages CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended VOCABULARY number words zero to ten Goals Students will read the number words from zero to ten. PRIOR KNOWLEDGE REQUIRED Can write the alphabet Knows the sounds associated with each letter of the alphabet MATERIALS BLM Match Pictures to Number Words (p B-57) number word cards for zero to ten and number cards for 0 to 10 (one set of each per student) Sound out number words to read. Write on the board: two four zero three five one SAY: These are the number words for 0, 1, 2, 3, 4, and 5, but they are out of order. Write the numerals on the board. Have students say each number aloud. Use sound to match the numerals to the number words in this sequence: 4 ASK: What sound does it start with? What other words start with the same sound? What letter makes that sound? What sound does the word four end with? What letter do you think it ends with? Can you choose the correct word? (Circle four. ) 0 Repeat the questions above. Circle zero. Show students how to check their choice using information given. ASK: The word that you circled has an r in it does this make sense? 5 SAY: There are two ways to see that five is 5. First, it s the only word left that begins with the f sound. Second, look at all the words in the list; five is the only one that has a v sound. 3 Remind students that sometimes two letters make one sound. Ask them which two letters are making one sound in words, such as throw, thanks, and think. Encourage students to search for the words in a book, point to words on the word wall, or write some of them on the board. Underline the th in some of these words. ASK: Which number word starts with th? (three) 2 SAY: It starts with t but not th. EXTRA PRACTICE BLM Match Pictures to Number Words 1 SAY: It has an n sound; also, it s the only word left! Repeat with the words six through ten. EXAMPLE: Use the t sound at the end of eight to help students match it to 8. B-22 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 22 6/14/17 11:49:06 AM

23 For Exercise 1 below, hold up the indicated number word card and have students hold up the corresponding number of fingers (remind students that they can show zero by holding up a closed fist). For Exercise 2, distribute a set of number word cards labelled zero through ten to each student. When you hold up the indicated number of fingers, have students hold up the corresponding number word card. Exercises 1. How many? a) six b) three c) seven d) two e) one f) five g) zero h) nine i) four j) eight k) ten 2. How many? a) 10 b) 7 c) 3 d) 8 e) 4 f) 0 g) 2 h) 9 i) 1 j) 6 k) 5 Answers: a) ten, b) seven, c) three, d) eight, e) four, f) zero, g) two, h) nine, i) one, j) six, k) five Find the number word in a sentence. Write the number words from zero to five on the board and the sentence Four friends played together. ASK: Can you find the number word in that sentence and say it? Ask a volunteer to write the number above the number word: 4 Four friends played together. Repeat with several more sentences, using zero to five. Erase the number words on the board and have students find the number word without having the list to refer to. Continue with sentences using number words six to ten, again starting with a list of the number words on the board and then erasing it. Finally, give students sentences using any number from zero to ten. Start with simple sentences, such as There are nine monkeys, and move on to more complex sentences, such as Rani bought two tennis rackets and three tennis balls. EXAMPLES: Four children played hockey. Recess lasts ten minutes. Rani bought three tennis balls. Kathy has five erasers. John is seven years old. Karen is five years old. Cody is three years old and Lela is five years old. Ana has eight fingers and two thumbs. Luc is two years younger than Sara. Number Sense 2-5 B-23 CA 2.1 TG Unit 1 p1-36 V5.indd 23 6/14/17 11:49:06 AM

24 A tip for struggling students. When you ask students to write the numbers above the number words here and on AP Book 2.1 p 11, some students may find it helpful if you underline the number word first. Once students are able to find and write the number this way, try more sentences without underlining the number word. Exercises: Make up your own sentences with number words. Have a partner write the numbers above the number words. ACTIVITIES 1 2 (Optional) 1. Play Picking Pairs and Memory (see unit introduction) using cards for 0 to 10 and zero to ten. 2. Play Go to page (see unit introduction). Write the page numbers on the board using number words: two, seven, one, nine, six, ten, four, eight, five, three. Extensions 1. Have students complete BLM How Many More Than (p B-58). Students write how many more one number is than another. Bonus: Write the number word above the numeral in the blank. 2. Have students complete BLM Stars (p B-59). Students join the dots in order, according to the number words. 3. Give each student number word cards for zero to ten. Students shuffle the cards and order them. Students can then re-shuffle the cards and exchange with a partner. 4. Complete BLM Reading Numbers (p B-60). B-24 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 24 6/14/17 11:49:06 AM

25 NS2-6 Addition Pages CURRICULUM REQUIREMENT AB: recommended BC: recommended MB: recommended ON: recommended VOCABULARY add addition sentence altogether equal (=) in total plus (+) Goals Students will solve simple addition problems. PRIOR KNOWLEDGE REQUIRED Counts objects without skipping or counting twice Can count to 10 Knows the plus (+) and equal (=) signs Understands the concept of addition MATERIALS two-sided counters dice BLM Game Cards (p M-2) BLM Blank Domino Cards (p M-3) deck of cards BLM Add the Dots (p B-61) Starting with 2 and adding 3 more always gives 5 in total. Draw two circles in a row on the board. ASK: How many circles did I draw? Then, ask students to watch carefully. Draw three more circles. ASK: How many more did I draw? (3) SAY: I started with two circles. I drew three more. ASK: How many do I have in total? (5) Repeat with squares in a row and then triangles arranged not in a row, again starting with two and adding three more. SAY: No matter what I count, if I start with two and add three more, I get five. The plus (+) and equal (=) signs. ASK: If you have two apples and someone gives you three more apples, how many would you have in total? (5) Tell students that mathematicians have a way to say that if you have two of something and you add three more, you always have five in total. Ask if anyone knows the way mathematicians write this. If no one does, write = 5 on the board. Ask if students know the way mathematicians say this. Tell them that we say 2 plus 3 equals 5, but what we really mean is starting with 2 things and adding 3 more is the same number as having 5 things ; point to the corresponding symbol as you say each part. Emphasize that the plus sign (+) means adding and the equal sign (=) means is the same number as. Read addition sentences two ways. Write = 7 on the board. ASK: How could I read this? ( 3 plus 4 equals 7 or starting with 3 things and adding 4 things is the same number as having 7 things ) Say it both ways after volunteers respond. Repeat with more sentences, but don t include zero yet (students will add and subtract zero in Lesson NS2-8). Point to the equations on the board, and tell students that these are called addition sentences. SAY: Addition sentences have a plus sign and an equal sign. Number Sense 2-6 B-25 CA 2.1 TG Unit 1 p1-36 V5.indd 25 6/14/17 11:49:06 AM

26 Students should work in pairs for the following exercises. Exercises: Read the addition sentence aloud to your partner in two different ways. a) = 3 b) = 6 c) = 6 d) = 6 e) = 9 f) = 8 Selected answer: a) 2 plus 1 equals 3, starting with 2 things and adding 1 thing is the same number as having 3 things Have students use counters, draw pictures, or draw dots to find the totals in the exercises below. Exercises: Complete the addition sentence. a) = b) = c) = d) = e) = f) = Answers: a) 6, b) 7, c) 7, d) 10, e) 8, f) 8 Use counters to check that addition sentences are correct. Give students two-sided counters. Have students make, for example, a pile of two yellow counters and another pile of four red counters and then see how many they have altogether. Emphasize that starting with two counters and then adding four more counters is the same number as having six counters (i.e., starting with both piles put together). SAY: Notice that we are adding counters, not colours; colour doesn t matter. Have students use counters to model the addition sentences in the following exercise and find which one is incorrect. Exercise: Which addition sentence is incorrect? A = 7 B = 8 C = 9 D = 10 Answer: C Write the total on the left. Tell students that when you say two things are the same, it doesn t matter which you say first. SAY: For example, My shirt is the same colour as your crayon and Your crayon is the same colour as my shirt mean the same thing. We can do that with numbers, too. Saying is the same number as 6 (write = 6 on the board) means the same thing as saying 6 is the same number as (write 6 = on the board). Exercises: Write the addition sentence with the answer on the left. a) = 7 b) = 8 c) = 5 Bonus: = 99 Answers: a) 7 = 3 + 4, b) 8 = 2 + 6, c) 5 = 1 + 4, Bonus: 99 = B-26 Teacher s Guide for Grade 2 CA 2.1 TG Unit 1 p1-36 V5.indd 26 6/14/17 11:49:06 AM

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