Unit 7 Number Sense: Addition and Subtraction with Numbers to 100

Transcription

1 Unit 7 Number Sense: Addition and Subtraction with Numbers to 100 Introduction In this unit, students will review counting and ordering numbers to 100. They will also explore various strategies and tools for solving addition and subtraction problems within 100. Students will use hundreds charts, base ten blocks, ten-frames, and number lines. Strategies will include counting forwards and counting backwards, and making use of the connection between addition and subtraction. Meeting Your Curriculum Alberta All lessons in this unit are required, except Lesson NS2-26. Lesson NS2-26 is recommended, as it reviews Grade 1 material that is used in Lesson NS2-27. British Columbia All lessons in this unit are required, except Lesson NS2-26. Lesson NS2-26 is recommended, as it covers material that is used in lesson NS2-27. Manitoba All lessons in this unit are required, except Lesson NS2-26. Lesson NS2-26 is recommended, as it reviews Grade 1 material that is used in Lesson NS2-27. Ontario All lessons in this unit are required, except Lesson NS2-26. Lesson NS2-26 is recommended, as it reviews Grade 1 material that is used in Lesson NS2-27. Recurring Games The following games and activities recur throughout this unit. Rules and materials vary per lesson. 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 students who has 7 on top would respond with, I have 7. Who has [whatever is on the bottom of the card]? and so on. I have 3 Who has Number Sense H-1 CA 2.1 TG Unit 7 p1-44 V4.indd 1 27/04/ :02:04 AM

2 Catch. You will need a small ball or paper object that students can catch. Toss the ball to a student while saying a number. The student catches the ball and repeats the number. The student then tosses the ball back to you and says whatever next number you have asked for (e.g., the next number counting backwards. Ensure that everyone gets a chance to play. Materials Hundreds charts and base ten materials. Make a copy of BLM Hundreds Chart (p M-5) for each student, and laminate it if possible. Use additional photocopies of this BLM as required. Students will often use this hundreds chart with 1 cm connecting cubes and tens and ones blocks. If you do not have such cubes or blocks, or if your students need larger manipulatives, they can use BLM Hundreds Chart Five Rows (p H-47) with paper ones and tens blocks from BLM Base Ten Materials (p M-4). Copy and laminate as many tens and ones blocks as required. Also available: a slightly larger hundreds chart on BLM A Larger Hundreds Chart (p M-13). A hundreds chart for whole-class teaching. For whole-class discussions and demonstrations, you will need a large hundreds chart. You might draw one on the board, or project a hundreds chart transparency. Tens and ones blocks. You will often need tens and ones blocks. Two different colours of blocks is ideal for demonstrating addition (e.g., 3 red blocks + 4 blue blocks is 7 blocks altogether.) As an alternative, you can use 1 cm connecting cubes, and have students link ten together to create a tens block. If you don t have 1 cm connecting cubes or tens and ones blocks, you can use BLM Base Ten Materials to make some. Photocopy the BLM onto red and blue paper, glue it to bristol board or thin cardboard (e.g., a cereal box), and cut out the materials for your students. Be aware, however, that many students will find these thin blocks hard to manipulate Long number lines. You might wish to provide students with long number lines from 0 to 100 for some of the lessons in this unit. Although metre sticks or measuring tapes can be used, you can also make a number line using a hundreds chart. Cut out a hundreds chart (you can use BLM Hundreds Chart or BLM A Larger Hundreds Chart) leaving extra space to the left of the chart. Fold the chart to make a cylinder and tape it together so that when the first row ends, the second row starts. Cut out the rows in one long spiral starting underneath the 1; this will form one long strip with the numbers in order from 1 to 100. You can make the number line yourself, or make the cylinders and have students cut them. Two-colour counters. Two-colour counters are called for in this unit. If you do not have these, you can make your own using dried beans by painting one side of the beans a different colour. As an alternative to two-colour counters, you could put two colours of connecting cubes or blocks into an opaque bag. Instead of tossing a certain number of two-colour counters, students draw a handful of cubes out of the bag without looking. H-2 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 2 27/04/ :02:04 AM

3 Shoeboxes to contain tosses of two-colour counters. It can be useful to have a container to prevent the tosses of two-colour counters from flying onto the ground when students use them. Shoeboxes or shoebox lids work well for this purpose. Generic BLMs. In addition to the BLMs found at the end of this unit, the following Generic BLMs, found in section M, are also used in Unit 7: BLM Base Ten Materials (p M-4) BLM Hundreds Chart (p M-5) BLM Game Cards (p M-2) BLM Hundreds Chart One Row (p M-6) BLM A Larger Hundreds Chart (p M-13) BLM 1 cm Grid Paper (p M-7) 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 NS2-20 to 25, 27 Number Sense H-3 CA 2.1 TG Unit 7 p1-44 V4.indd 3 27/04/ :02:04 AM

4 NS2-18 Counting to 100 Pages CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required VOCABULARY numbers to 100 ten-frame Goals Students will count orally to 100. Students will check their counting and identify mistakes in counting by keeping track. PRIOR KNOWLEDGE REQUIRED Can count on Can count to 20 MATERIALS ball or paper object large hundreds chart for demonstration BLM Hundreds Chart (p M-5, optional) tens and ones blocks for demonstration Count orally to 30. Review counting to 20. Then write the numbers from 20 to 30 on the board, point to each number, and say it aloud. Repeat, but this time emphasize the last part of the word while underlining the ones digit. ASK: Which two numbers end with the same digit? (20 and 30 both end with 0) Do the words for the numbers sound the same in any way? (they both end with a tee sound) Look at the other numbers, from 21 to 29 what are the last digits? (1 to 9) On the board, write 30 and 13. Have students listen carefully while you say the numbers, then ASK: What part sounds the same? ( thir or thirt or thirtee ) Emphasize that for numbers in the teens thirteen, fourteen, fifteen, and so on we hear the last digit first. Point to and say thirteen : we hear a sound that s close to three and then teen. SAY: It s the same for the number fourteen we hear four and then teen for fifteen, and so on. However, the pattern changes for numbers in the 20s. First we hear a sound that s close to two and then the ones digit. Say the numbers again to demonstrate. Continue counting orally to 100. Write 31 on the board and say it aloud. Then write 32. ASK: How would you say this? Continue through the 30s, first in numerical order and then in random order. Repeat with the 40s, 50s,..., 90s. Emphasize the connection between how we say 40 and 14, 50 and 15, and so on (just take the n sound off teen to get the other number). Ask students to say 20, 30, 40, 50, 60, 70, 80, and 90, first in numerical order and then in random order. ACTIVITY 1 (Essential) 1. Catch. (see unit introduction) Say any number less than 100 and ask students to say the next number. Do not include numbers ending in 9. H-4 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 4 27/04/ :02:04 AM

5 The number after numbers ending in 9. SAY: The numbers you say after 29, 39, and 49 are the hardest to remember. Once you remember that 30 comes after 29, you can easily count to 39 (count from 30 to 39 together). It s remembering what comes after 39 that s hard. Look at a hundreds chart together or give one to each student (see BLM Hundreds Chart). Point to the 2 and 3 in the 20s and 30s. SAY: We know the 20s start with a sound that s close to two ( tw ). The thirties start with a sound that s close to three ( th ); remember how it sounds more like 13 than 3 (take off the n sound). ASK: What comes after 3? (4) What should the number after the 30s sound like? (forty) (PROMPT: Think of the number that comes after 13, but take off the n sound. Then chant the numbers from 40 to 49 as a class. Continue to 100. NOTE: Some languages group numbers differently. We count by grouping in tens. Tell students that you heard someone count like this: one, two,, twenty,, twenty-nine, twenty-ten, twentyeleven,, twenty-twenty. ASK: Is this right? What s different about this counting? Why do you think the person counted like this? (they were grouping numbers in groups of twenty) Explain that in English we start counting over at ten and groups of ten numbers sound the same. That s why numbers twenty to twenty-nine have twenty in common; thirty to thirty-nine have thirty in common, and so on. ACTIVITY 2 (Optional), ACTIVITY 3 (Essential) EXAMPLES: 23, 32; 6, 16, 60; 65, 55, Have students stand in a line. The first person in line says one, the next person says two, and so on to 100, with one catch: any student who says a word that has the sound four in it (EXAMPLES: 14, 24, 40 49) has to move to the front of the line. (EXAMPLE: I say 14 and move; the student who stood behind me before I moved says 15.) Repeat with the sound five. (NOTE: and have a fif sound, not a five sound.) VARIATION: Students stand in a circle and whisper the next number to the next person; special numbers are said out loud. 3. Catch. (see unit introduction) Say any number less than 100 and ask students to say the next number. Include two-digit numbers ending in 9. Say and write two-digit numbers. Display a large hundreds chart and ask students to first say, and then write, numbers as you point to them. Point to numbers one after the other that look or sound similar. Say the number given groups of tens and ones. Draw or present various objects grouped by 10s and 1s (e.g., crayons or dots). Have students say what number is represented. Point out that counting in this way, where objects are grouped by 10s and 1s, is like counting using tens and ones blocks. Show a couple of examples using tens and ones blocks. Repeat using ten-frames. Number Sense 2-18 H-5 CA 2.1 TG Unit 7 p1-44 V4.indd 5 27/04/ :02:05 AM

6 Extensions 1. Teach students to count to 200, or even Which is longer? Measure a chain of 100 paper clips against the height of one school floor. Students can hang the chain from the top of a stairway. 3. Count by keeping track. Remind students how to count and keep track of all the letters in a sentence, as they did in Unit 2, but use longer words and sentences. EXAMPLES (see below for subtotals): 1. Sara likes to jump rope with her sister. 2. John likes to bake chocolate chip cookies with his father. 3. Matt likes to jump rope with his brother and bake chocolate chip cookies with his mother. SUBTOTALS: 1. 4, 9, 11, 15, 19, 23, 26, , 9, 11, 15, 24, 28, 35, 39, 42, , 9, 11, 15, 19, 23, 26, 33, 36, 40, 49, 53, 60 Students can compare their answers. As before, discuss how counting letters in this way gives students an opportunity to check their work and find mistakes. CONNECTION Have students complete BLM Counting and Colours (p H-45). Art On BLM Counting and Colours, students discover how mixing colours can make brown. NOTE: Extensions 4 6 should be done in order. 4. Number words for multiples of 10. Teach students to read the number words for multiples of ten, up to one hundred. First review the number words from one to twenty. Then focus on ten and twenty. Write these two words on the board and ask what number each word represents. (10 and 20) Write 10 above ten, and 20 above twenty. Then write thirty on the board. Have the class read the word, and write 30 above thirty. Ask students which number words the word thirty reminds them of. (three, thirteen) Ask students which letters these words have in common (th, or thirt) and what is the same about all of the numbers. (all the numbers have a 3) Repeat with forty, fifty, sixty, seventy, eighty, and ninety. Then write one hundred on the board. Have students read the word, and then write 100 above it. Ask students which smaller number word they recognize from one hundred. (one) Ask students where they see one (1) in the number 100. (the first digit) Write the numeral above the word. a) thirty b) ten c) eighty d) twenty e) ninety f) seventy g) forty h) sixty i) fifty j) one hundred Answers: a) 30, b) 10, c) 80, d) 20, e) 90, f) 70, g) 40, h) 60, i) 50, j) 100 H-6 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 6 27/04/ :02:05 AM

7 5. Number words up to 100. Teach students to read any number word from 20 to 100. Write on the board the number words from twentyone up to twenty-nine. Read the words as a class, and write the matching numerals above the number words. Guide students to see the connection between the number words and the numerals. For example, for twenty-four, SAY: The twenty part means we write 2 and the four means we write 4. Point out that there is always a hyphen (-) between the word twenty and the word for the one-digit number. Repeat with thirty-one to thirty-nine, and so on, up to ninety-nine. Write the numeral above the word. a) thirty-seven b) fifty-three c) thirty-five d) twenty-nine e) ninety-six f) seventy-two g) forty-one h) sixty-six i) fifty-eight j) forty-four k) eighty-five l) ninety m) thirty-four n) fifty o) eighty-eight p) ninety-nine Answers: a) 37, b) 53, c) 35, f) 29, e) 96, f) 72, g) 41, h) 66, i) 58, j) 44, k) 85, l) 90, m) 34, n) 50, o) 88, p) I Have, Who Has? (see unit introduction) Make game cards using BLM Game Cards (p M-2) with numerals on the top and number words on the bottom. Use numbers from 20 to 100. Number Sense 2-18 H-7 CA 2.1 TG Unit 7 p1-44 V4.indd 7 27/04/ :02:05 AM

8 NS2-19 Hundreds Charts Page 104 CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required Goals Students will use patterns to find numbers on a hundreds chart. PRIOR KNOWLEDGE REQUIRED Can count to 10 using a hundreds chart VOCABULARY hundreds chart MATERIALS 10 tokens or coins per student BLM Hundreds Chart One Row (p M-6) BLM A Larger Hundreds Chart (p M-13) BLM Hundreds Chart (p M-5) BLM Hundreds Chart Pieces (p H-46) number cards to 100 (optional) Review finding numbers in the first row of a hundreds chart. Give each student 10 tokens and a large strip of paper with the first row of a hundreds chart (e.g., from BLM Hundreds Chart One Row). Ask students to place a token on each number from 1 to 10 as you say the numbers in random order. Stop when the row is full. Review finding numbers in the second row of a hundreds chart. Draw the first two rows of a hundreds chart on the board and review how to find numbers in the second row using the first row as a guide, e.g., to find 17, find 7 and move down a row. Have volunteers use this method to find various numbers in the second row. Hand out BLM A Larger Hundreds Chart. Have students find and lightly colour the first two rows. Ensure that all students colour the correct rows. Call out the numbers in the exercises below, and check that students are covering the correct numbers. NOTE: You might have students clear the tokens off the hundreds chart after completing part a) to make part b) slightly more challenging. Exercises: Place a counter on the numbers. a) 17, 14, 9, 16, 18 b) 12, 15, 7, 20, 13 Find numbers on the entire hundreds chart. Tell students to look at the third row. ASK: How can we find 27 if we know where 7 is? (find 7, then move down until you find 27) How can we find 57 if we know where 7 is? (move down from 7 until you find the 57) Repeat with various numbers, including numbers that end in 0. Once again, call out the numbers in the exercises below, and check that students are covering the correct numbers. H-8 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 8 27/04/ :02:05 AM

9 Exercises: Place a counter on the numbers. a) 35, 75, 95, 85, 15, 65, 25, 55 b) 17, 67, 87, 97, 47, 57 c) 30, 60, 50, 90, 10, 70, 80, 20 d) 53, 46, 81, 42, 75, 90, 45, 33, 77 Use the hundreds chart to find the next number, the previous number, and the number in between. Tell students to find the number 37 and place a token on that square. ASK: What is the next number? (38) Write 37 on the board. Have a volunteer fill in the blank. Repeat with various numbers. Have students write the number you say and the number that comes next in their notebooks. Repeat with numbers that come before a given number, and then with numbers that come in between two given numbers. Exercises: Use a hundreds chart to find the numbers. 1. Write the number that comes after. a) 47 b) 51 c) 79 d) 90 Answers: a) 48, b) 52, c) 80, d) Write the number that comes before. a) 58 b) 43 c) 80 d) 71 Answers: a) 57, b) 42, c) 79, d) Write the number that is in between. a) b) c) d) Answers: a) 39, b) 54, c) 69, d) 90 Find groups in a hundreds chart. Arrange cut-out pieces of a hundreds chart on the board. Label each piece with a colour. Have students find and colour the pieces on BLM Hundreds Chart. EXAMPLES: Blue Red Yellow Green Purple Orange ACTIVITY (Optional) Students cut out the pieces from BLM Hundreds Chart Pieces and glue them in the correct place on BLM A Larger Hundreds Chart. Number Sense 2-19 H-9 CA 2.1 TG Unit 7 p1-44 V4.indd 9 27/04/ :02:05 AM

10 Find missing numbers in a hundreds chart. Create part of a hundreds chart with cards. Withhold three cards. See the margin for an example. Give each missing card to a volunteer to put in the correct place. Remove different cards from the chart, shuffle them, and have volunteers put them back. Repeat with a different part of the hundreds chart. Remove more and more cards from the chart. Finally, have volunteers write the missing numbers in the empty spaces instead of referring to the cards. Eventually, you should have no cards on the board only numbers written in by students. NOTE: Instead of using cards you can draw a piece of a hundreds chart on the board leaving some squares blank. Extensions 1. Give students BLM Hundreds Chart Five Rows (p H-47). Have students use the hundreds chart to add: 5 + 3, , (EXAMPLE: shade 5 and circle the next 3 numbers). ASK: What pattern is in the answers? Can you predict ? ? ? Verify the prediction on a large hundreds chart. Repeat with , , m a u O e p n t o c i n e 2. The reading pattern in Japanese is top to bottom and then right to left. Show students the phrase Once upon a time written using the Japanese reading pattern (see margin). Together, fill out a blank hundreds chart using this reading pattern. Answer: Have students make their own hundreds chart, using grid paper or BLM 1 cm Grid Paper (p M-7) that has three errors in other words, three squares in the chart have an incorrect number. Students exchange charts with a partner and try to find the errors in their partner s chart. H-10 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 10 27/04/ :02:05 AM

11 NS2-20 More Tens and Ones blocks Pages CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required Goals Students will use tens and ones blocks to represent numbers and to find numbers on a hundreds chart. PRIOR KNOWLEDGE REQUIRED Can find a given number on a hundreds chart VOCABULARY ones digit tens digit MATERIALS ones and tens blocks BLM Hundreds Chart (p M-5) overhead projector transparency of BLM Hundreds Chart (p M-5) BLM Hundreds Chart and Base Ten Materials (p H-48) BLM Game Cards (p M-2) BLM 1 cm Grid Paper (p M-7) Count past 20 using the hundreds chart. Review counting to 20 using the first two rows of a hundreds chart. Then give each student at least 40 ones blocks and BLM Hundreds Chart. Have students count their blocks by using the chart. ASK: How many blocks did you count? How many full rows did your blocks cover? How many blocks in the next row did you need? Record answers on the board. (EXAMPLE: 35 blocks, 3 rows and 5 more blocks) Have students predict how many full rows they will fill and how many more blocks they will use to make these numbers: 28, 32, 23, 31, 13, 30, 36. Verify their predictions on an enlarged hundreds chart. Exercises 1. Guess how many rows and how many extra squares the number will fill. a) 33 full rows b) 29 full rows 33 extra squares 29 extra squares c) 25 full rows d) 38 full rows 25 extra squares 38 extra squares Answers: a) 3, 3; b) 2, 9; c) 2, 5; d) 3, 8 2. Check your guesses in Exercise 1 using ones blocks and a hundreds chart. Tens blocks. ASK: How many full rows and how many more blocks do we need to show 74? Record the students predictions. To verify the predictions, begin placing ones blocks in order on a transparency of BLM Hundreds Chart on an overhead projector. After you finish a few rows, SAY: I m tired of placing so many ones blocks in order. ASK: Does anyone Number Sense 2-20 H-11 CA 2.1 TG Unit 7 p1-44 V4.indd 11 27/04/ :02:05 AM

12 remember what we used before to cover an entire row? (a tens block) Show students a tens block. Count the individual ones blocks visible within a tens block to verify that there are ten. Then cover one full row with a tens block. ASK: Do we need to cover another full row or is 74 in the next row? (repeat until 74 is in the next row) How many ones blocks do we need in the next row? (4) How many full rows did we cover? (7) Record the answer on the board: 74 is 7 full rows and 4 more blocks. Repeat with various numbers, using tens blocks for full rows. Find numbers on a hundreds chart. SAY: How many full rows do I have to cover before I get to 63? (6) Where is 63 in the next row? (the third one) Count six full rows using tens blocks and then count three in the next row using ones blocks to demonstrate finding 63. Invite volunteers to find various numbers, then have students find numbers on their own hundreds chart. ACTIVITY 1 (Optional) 1. Assign each student a number up to 49. Students display their number on a hundreds chart by cutting the correct blocks from BLM Hundreds Chart and Base Ten Materials. Compare two methods of finding numbers on a hundreds chart. Compare the first method students learned with the method they learned in this lesson. Use the number 45 as an example: Find 5 in the first row, then move down until you find 45. Move down or cover four full rows and then count across five squares. Point out that you re really doing the same two steps but in different order. Whether you move across then down, or down then across, you end up in the same place. Show numbers using tens and ones blocks without a chart. SAY: You can use blocks without the hundreds chart to represent a number. Show students 3 tens blocks and 7 ones blocks. Draw a T-chart on the board and label the columns tens and ones. ASK: How many tens blocks do I have? (write 3 in the tens column) Repeat for ones blocks and the ones column. ASK: If we placed these on the hundreds chart, what number would we get? (37) Check by counting each cube, including the 10 in each tens block. Then place the blocks on a hundreds chart and emphasize that 37 is the last square covered. Repeat with various numbers, this time having students fill in the chart and write the number. For the following exercises, give each student 9 tens blocks and 9 ones blocks. H-12 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 12 27/04/ :02:05 AM

13 Exercises: Show the number using tens blocks and ones blocks. Write how many tens blocks and ones blocks you used. a) 47 tens blocks b) 59 tens blocks 47 ones blocks 59 ones blocks c) 62 tens blocks d) 74 tens blocks 62 ones blocks 74 ones blocks e) 89 tens blocks f) 98 tens blocks 89 ones blocks 98 ones blocks Answers: a) 4, 7; b) 5, 9; c) 6, 2; d) 7, 4; e) 8, 9; f) 9, 8 Tens digits and ones digits. Write 27 on the board. ASK: Which digit shows me the number of tens blocks I need to make 27 the 2 or the 7? (the 2) Which digit shows me the number of ones blocks I need to make 27 the 2 or the 7? (the 7) Explain that the 2 is called the tens digit and the 7 is called the ones digit. Ask students to tell you the tens digit and the ones digit in various numbers. Exercises: Write the ones digit. a) 54 ones digit: b) 68 ones digit: c) 38 ones digit: d) 76 ones digit: e) 74 ones digit: f) 91 ones digit: Bonus: 8 ones digit: Answers: a) 4, b) 8, c) 8, d) 6, e) 4, f) 1, Bonus: 8 Write 7 on the board and tell students you want to represent the number using tens and ones blocks. ASK: How many ones blocks will I need? (7) Will I need any tens blocks? (no) Show the number 7 using seven ones blocks and no tens blocks. ASK: How many ones blocks did I use? (7) What is the ones digit of the number 7? (7) How many tens blocks did I use? (0) What is the tens digit in the number 7? (0) Explain to students that they can write the number 7 as 07 (write 07 on the board) to show that the tens digit is 0, but usually people leave out the 0 and write just 7. Repeat with the number 5. Exercises: Write the tens digit. a) 54 tens digit: b) 68 tens digit: c) 38 tens digit: d) 76 tens digit: e) 14 tens digit: f) 91 tens digit: Bonus g) 9 tens digit: h) 03 tens digit: Answers: a) 5, b) 6, c) 3, d) 7, e) 1, f) 9, Bonus: g) 0, h) 0 Number Sense 2-20 H-13 CA 2.1 TG Unit 7 p1-44 V4.indd 13 27/04/ :02:05 AM

14 Then write 25, 34, and 35 on the board and ask a volunteer to circle the two numbers with the same tens digit and underline the two numbers with the same ones digit. Repeat with similar sets of numbers. Exercises: Circle the two numbers with the same tens digit. Underline the two numbers with the same ones digit. a) b) c) d) Bonus: Answers: a) , b) , c) , d) , Bonus: ACTIVITIES 2 3 (Essential) 2. I Have, Who Has? (see unit introduction) Use BLM Game Cards to make cards with numerals and base ten models. EXAMPLE: 38 on the top and 2 tens blocks with 5 ones blocks on the bottom (I have 38, who has 25?). 3. Have students represent the numbers using tens and ones blocks, and then have them draw a model of the tens and ones blocks using grid paper or BLM 1 cm Grid Paper. a) 23 b) 37 c) 22 d) 45 Sample answer: a) Extensions 1. Have students stack as many ones blocks as they can in a given time interval. Then ASK: Did you stack more than 10 or less than 10? How can you tell? (compare to a tens block) More than 20 or less than 20? (compare to two tens blocks) Have students determine how many ones blocks they stacked by counting the number of tens blocks and then the number of extra ones blocks they need to build an equivalent stack. Repeat several times. 2. Write 22 on the board. Explain that there are two 2s in the number, but they mean different things. Point to the first 2 and ASK: What does this 2 mean? (2 tens) Point to the second 2 and ASK: What does this 2 mean? (2 ones) Emphasize that the tens digit in any number always tells how many tens, and the ones digit tells how many ones. Repeat with more two-digit numbers that have the same tens digit as ones digit, such as 55, 77, and 99. H-14 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 14 27/04/ :02:06 AM

15 3. Write 45 and 54 on the board. ASK: What does the number 5 mean in 45? (5 ones, or 5) What does the number 5 mean in 54? (5 tens, or 50) Emphasize that what the 5 means depends on the position of the 5. If 5 is the tens digit, it means 5 tens; if 5 is the ones digit, it means 5 ones. Repeat with 57 and 74, asking what the 7 means in each number. Then have students write what the 9 means in each number below. a) 19 b) 94 c) 39 d) 9 e) 90 f) 09 Answers: a) 9 ones, or 9; b) 9 tens, or 90; c) 9 ones, or 9; d) 9 ones, or 9; e) 9 tens, or 90; f) 9 ones, or 9 Number Sense 2-20 H-15 CA 2.1 TG Unit 7 p1-44 V4.indd 15 27/04/ :02:06 AM

16 NS2-21 Ordering Numbers to 100 Pages CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required Goals Students will compare and order numbers to 100. PRIOR KNOWLEDGE REQUIRED Can find numbers in a hundreds chart VOCABULARY hundreds chart larger largest smaller smallest MATERIALS red and blue tens and ones blocks BLM 1 cm Grid Paper (p M-7) metre sticks or tape measures to 100 cm BLM Hundreds Chart (p M-5) tokens or counters Use tens and ones blocks to compare numbers to 100. Write 29 on the board in blue and 34 in red. Give students more than enough tens and ones blocks to make 29 using blue and 34 using red. Remind students that 1 tens block is the same as 10 ones blocks. Have students select red and blue tens and ones blocks to represent the two numbers. Then have students place the blue blocks beside the red blocks. Emphasize that students must place tens blocks with tens blocks and ones blocks with ones blocks. ASK: Which number is larger, 29 or 34? How do you know? (There is 1 red tens block left over and 5 blue ones blocks left over. The number with more left over is larger. Ten is more than 5, so 34 is larger than 29.) Repeat with 42 (blue) and 37 (red). ASK: Do you have more red or blue left over? (blue) Which number is more? (42) Repeat with various numbers. Have students use the same method for the exercises below. Exercises: Which number is larger? a) 16 or 21 b) 83 or 38 c) 38 or 74 Answers: a) 21, b) 83, c) 74 Use tens and ones blocks symbolically to compare two numbers. Write two numbers on the board, say 36 and 43. Ask students to predict which number is bigger. Draw the base ten representation for the majority vote on the board. Then have a volunteer try to make the other number by colouring the picture on the board. For example, if students predict that 43 is bigger, the volunteer will colour 3 tens blocks and 6 ones blocks for the smaller number. If students predict that 36 is bigger, the volunteer will not be able to colour 4 tens blocks and 3 ones blocks; there won t be enough blocks drawn on the board. Repeat with various numbers. Have students use this same method for the following exercises, using grid paper or BLM 1 cm Grid Paper. H-16 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 16 27/04/ :02:06 AM

17 Exercises: Which number is larger? a) 22 or 17 b) 65 or 56 c) 49 or 71 Answers: a) 22, b) 65, c) 71 Use a number line to order numbers. Give students a long number line to 100 (such as a metre stick, a tape measure, or a number line made from a hundreds chart as described in the unit introduction) and challenge them to find these numbers: 38, 12, 25. ASK: Which is the smallest number? (12) Which is the largest number? (38) How do you know? (the numbers farther along on the number line are larger) How do we write the numbers in order from smallest to largest? (12, 25, 38) How do we write the numbers from largest to smallest? (38, 25, 12) Repeat with more groups of three numbers. Exercises 1. Write the numbers from smallest to largest. a) 28, 24, 31 b) 41, 39, 40 c) 78, 29, 56 Bonus: 42, 14, 74, 41, 32, 73 Answers: a) 24, 28, 31; b) 39, 40, 41; c) 29, 56, 78; Bonus: 14, 32, 41, 42, 73, Write the numbers from largest to smallest. a) 47, 53, 19 b) 59, 61, 58 c) 87, 68, 79 Bonus: 3, 57, 32, 25, 46, 91 Answers: a) 53, 47, 19; b) 61, 59, 58; c) 87, 79, 68; Bonus: 91, 57, 46, 32, 25, 3 Discuss how ordering numbers using a number line is harder or easier than using blocks. (possible answers: it is harder to find numbers on the number line than to make them using blocks, but once we find the numbers, it is easier to compare them; it is much easier to compare many numbers on a number line) Use a hundreds chart to order numbers. Review finding numbers on a hundreds chart. Students can compare many numbers at a time by first finding each number on the chart and then writing them in order. Give each student a copy of BLM Hundreds Chart for the exercises below. Students can place tokens or counters on the numbers in the chart and then write the numbers in order on a separate sheet of paper. Exercises: Write the numbers from smallest to largest. Use a hundreds chart. a) 34, 21, 26, 19, 7, 45 b) 21, 12, 33, 9, 41, 14 c) 31, 62, 77, 80, 43, 52 Answers: a) 7, 19, 21, 26, 34, 45; b) 9, 12, 14, 21, 33, 41; c) 31, 43, 52, 62, 77, 80 Number Sense 2-21 H-17 CA 2.1 TG Unit 7 p1-44 V4.indd 17 27/04/ :02:06 AM

18 ACTIVITY (Optional) Find page numbers. Have students open their JUMP Math AP books to page 1. Then have them turn and point to the page numbers in the following order: 24, 29, 26, 21, 28, 20, 25, 27, 30, 34, 31, 38, 36, 39, 35, 37, 41, 48, 96, 45, 49, 82, 47, 44. Ensure students are turning the pages in the correct direction. Compare numbers with the same number of tens. Tell each student to take 3 red ones blocks and 5 blue ones blocks. ASK: Which is more, 3 or 5? Have a volunteer show the answer by matching the blocks. Repeatedly have students add a tens block to each group. After each addition, ask students what numbers they have and which number is bigger. Emphasize that by adding a tens block to each, we never change which number is bigger. When two numbers have the same number of tens, the number with more ones is bigger. Exercises: Write the numbers from largest to smallest. a) 42, 48, 45 b) 56, 52, 59 c) 98, 90, 91 Bonus: 59, 52, 58, 51, 56, 55 Answers: a) 48, 45, 42; b) 59, 56, 52; c) 98, 91, 90; Bonus: 59, 58, 56, 55, 52, 51 Compare numbers with different numbers of tens. Tell each student to take 3 red ones blocks and 6 blue ones blocks. ASK: Which is more? How do you know? Tell each student to add 2 red tens blocks and 1 blue tens block. Repeat the questions. This time, the colour of the larger number changed: even though there are more blue ones blocks, there are more red blocks altogether. ASK: How can a number with 3 ones blocks be more than a number with 6 ones blocks? (it has more tens blocks) Repeat with more numbers such as: 31 and 26; 37 and 45. Emphasize that the number with more tens is bigger. Exercises 1. Circle the larger number. a) b) c) 60 8 d) e) 9 61 f) Answers: a) 52, b) 51, c) 60, d) 81, e) 61, f) Write the numbers from smallest to largest. a) 24, 59, 6, 28, 61, 52 b) 79, 91, 75, 49, 80, 90 c) 51, 2, 27, 36, 65, 50 Answers: a) 6, 24, 28, 52, 59, 61; b) 49, 75, 79, 80, 90, 91; c) 2, 27, 36, 50, 51, 65 H-18 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 18 27/04/ :02:06 AM

19 Extensions 1. Give each student 9 tens blocks and 9 ones blocks. Challenge students to find as many answers as they can for the following problems. a) Find a number between 42 and 82 that can be made with exactly 9 blocks. b) Find a number between 12 and 45 that can be made with exactly 7 blocks. c) Find a number between 73 and 91 that can be made with exactly 8 blocks. d) Find a number between 73 and 91 that can be made with exactly 11 blocks. Answers: a) 45, 54, 63, 72, 81; b) 16, 25, 34, 43; c) 80, d) 74, Provide each student with 10 ten-frames, or show students how to cut their own ten-frames from grid paper (they can use BLM 1 cm Grid Paper). Have students write the numbers below in order from smallest to largest, and verify their answers using ten-frames. Students can use ones blocks to fill part of a ten-frame. a) 45, 32, 49 b) 52, 31, 49 c) 87, 78, 76 d) 91, 89, 90 Answers: a) 32, 45, 49; b) 31, 49, 52; c) 76, 78, 87; d) 89, 90, Marko ordered the numbers from smallest to largest. He made some mistakes. Find Marko s mistakes and explain them. a) 43, 45, 54, 50, 61 b) 73, 81, 28, 93, 99 c) 29, 35, 72, 81, 79 Bonus: 29, 37, 84, 91, 100, 99 Answers: a) 54 and 50 are in the wrong order; 54 is larger than 50 since they have the same number of tens and 54 has more ones; b) 28 should be the first number; 28 has fewer tens than all the other numbers; c) 81 and 79 are in the wrong order; 79 is smaller than 81 since it has fewer tens; Bonus: 100 should be the last number since it is larger than all the other numbers (it has 10 tens) Number Sense 2-21 H-19 CA 2.1 TG Unit 7 p1-44 V4.indd 19 27/04/ :02:06 AM

20 NS2-22 Adding, Subtracting, and Order Pages CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required Goals Students will see that changing the order of the numbers in addition does not change the total; however, changing the order of numbers in subtraction sentences does change the situation. PRIOR KNOWLEDGE REQUIRED VOCABULARY addition sentence subtraction sentence take away from total Knows the plus (+) and minus ( ) signs Can add and subtract within 20 Can distinguish between right and left MATERIALS two-colour counters or blocks of two different colours large blank paper domino dominoes Switch objects between hands to show that the total stays the same. Make sure students can correctly identify their left and right hands. Hold 3 objects in your left hand and 4 in your right hand. ASK: How many do I have in each hand? How many do I have in total? Write on the board: + = left hand right hand total Have a volunteer fill in the correct numbers. Then switch hands and have the volunteer write the new corresponding addition sentence (left hand first again). ASK: What is the same about the two addition sentences? (the numbers that are added together and the totals) What is different? (the order of the numbers added together) Repeat with several examples. ACTIVITY 1 (Essential) 1. Have students work in pairs, facing each other. Partner 1 holds up some fingers on their left hand (for example, 4), and some fingers on their right hand (for example, 3). Reading from left to right, one partner sees 4 + 3, the other sees Students record the two sentences and the totals. Students alternate roles and repeat several times. ASK: Does the order you add the numbers change the total? (no) Add three numbers and switch the order. Students work in pairs. One partner picks up some counters with one hand and some with the other hand. The other partner picks up some counters only with the non-writing hand. The person with a free hand records different number sentences H-20 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 20 27/04/ :02:06 AM

21 to show the total number in all three hands by counting different hands first. Challenge students to find at least three different number sentences. NOTE: If two of the numbers are the same (e.g., 2, 3, 3), there will only be three number sentences. If all numbers are the same, there will only be one number sentence. If the three numbers are different, there will be a total of six number sentences. Turn dominoes around and add. Tape a blank paper domino to the board. Have a volunteer draw dots on the domino to show ASK: What could I do to this domino to make it show instead of 6 + 4? (turn it around) Does turning the domino change the total number of dots? (no) How does turning the domino change the addition sentence? (6 + 4 = 10 becomes = 10) What stays the same? (the three numbers used and the total) What is different? (the order of the other two numbers) Give students dominoes. Have them turn the dominoes around to write two addition sentences. ACTIVITY 2 (Essential) 2. Toss 8 two-colour counters. ASK: How could the colours show an addition sentence? Could we count red first and then yellow? What number sentence would we get? What if we counted yellow first and then red what number sentence would we get? Give each pair of students up to 10 two-colour counters. Partner 1 tosses the counters and Partner 2 writes two addition sentences (yellow + red = total, red + yellow = total). Students switch roles and repeat several times. Order doesn t matter in addition. Students have seen that the order of numbers does not matter in addition. As a reminder, write on the board: = Emphasize that we always read from left to right, so means start with 6 and add 2, and means start with 2 and add 6. Verify that these are equal with a picture (e.g., draw 6 circles and then add 2 more, then draw 2 circles and add 6 more, for a total of 8 both times). Does order matter in subtraction? Write on the board: 6 2 = 2 6. SAY: 6 2 means start with 6 and take away 2. What does 2 6 mean? Emphasize that we start from the left, so we have to start with 2 things and try to take away 6 of them. Show 2 objects. Ask a volunteer to take away 6 of them. Explain that the question doesn t make sense: if you start with 2 things, you can t take away 6 of them. Give students counters and have them decide whether they can subtract the following: 3 4 and 4 3. Have volunteers show and explain their answers using the counters. (Sample answer: 4 is more than 3, so you cannot subtract 4 from 3. So 3 4 doesn t make sense. Since 3 is less than 4, 4 3 makes sense; you can take 3 away from = 1) Draw on the board: Number Sense 2-22 H-21 CA 2.1 TG Unit 7 p1-44 V4.indd 21 27/04/ :02:06 AM

22 ASK: How many circles are on the board? (4) Can you take 6 away from 4? (no) Why not? (because 6 is more than 4) Ask if there is any student who thinks they can take 6 away from 4. If there is no volunteer, say that you will try. Start crossing out circles and counting 1, 2, 3, 4 as you cross out each circle: SAY: Now I m stuck. I need to take away two more circles, but there are no more circles to take away. Write on the board: 4 6 = 6 4 = ASK: Which problem makes sense? (6 4) Circle that problem. ASK: Which problem does not make sense? (4 6) Cross out that problem. Have a volunteer draw a picture with circles to solve the problem that makes sense. The final picture should look like this: 4 6 = 6 4 = 2 Exercises: Solve the problem that makes sense. a) 4 7 = or 7 4 = b) 5 3 = or 3 5 = c) 1 9 = or 9 1 = d) 10 7 = or 7 10 = Answers: a) 7 4 = 3, b) 5 3 = 2, c) 9 1 = 8, d) 10 7 = 3 Extensions 1. Have students count the number of letters in each sentence by adding the number of letters in each word: More sentences: The blue hat is big The big hat is blue. Is the big hat blue? Is the blue hat big? Jin s birthday is today. ( = 19) Today is Jin s birthday. ( = 19) Is today Jin s birthday? ( = 19) ASK: What do you notice? (the total is always 19, the same 4 numbers are in all the sentences) Do you know why the answer is always the same? (the same 4 words are in all the sentences, just rearranged) 2. Solve the problem that makes sense. Use base ten blocks to help you. a) = or = b) = or = c) = or = d) = or = Answers: a) = 15, b) = 25, c) = 14, d) = 1 H-22 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 22 27/04/ :02:06 AM

23 3. Solve the problem that makes sense. Write the answer as a number word. a) five minus three or three minus five b) nine minus eleven or eleven minus nine c) eighteen minus twelve or twelve mine eighteen d) six minus twenty or twenty minus six Answers: a) five minus three equals two, b) eleven minus nine equals two, c) eighteen minus twelve equals six, d) twenty minus six equals fourteen 4. Provide each student with a copy of BLM Subtract Two Ways (p H-49). Work through the first example together, which shows how to solve 9 2 4, and ASK: What is the same about these two problems? (the three numbers are the same: 9, 4, and 2; also, the answer is the same: 3) What is different? (the order of 4 and 2) When you are subtracting two smaller numbers (like 2 and 4) from a larger number (like 9), do you think the order of the two smaller numbers will matter? Accept yes or no answers at this point. After students complete the BLM, discuss this question again. Remind students that when subtracting two numbers (a smaller number from a larger number), the order of the numbers matters: the larger number must be written first otherwise the problem doesn t make sense. However, when subtracting two smaller numbers from a larger number, as long as the larger number is written first, the order of the two smaller numbers doesn t matter. Number Sense 2-22 H-23 CA 2.1 TG Unit 7 p1-44 V4.indd 23 27/04/ :02:06 AM

24 NS2-23 Adding with a Number Line Pages CURRICULUM REQUIREMENT AB: required BC: required MB: required ON: required VOCABULARY number line leap Goals Students will locate numbers on a partial number line and then use number lines to add. PRIOR KNOWLEDGE REQUIRED Can count to 100 Can order numbers Understands the concept of more Can add by counting on MATERIALS BLM Frog (p H-50) BLM Blank Number Lines (p H-51) BLM Finding Missing Numbers (p H-52) Locating numbers on a number line. Draw a partial number line from 34 to 41: Tell students that you want to find 39. Start at 34 and ASK: Is this it? (no) Try 35, 36, and 37. SAY: I wonder if we missed 39. I m at 37 now and we haven t found it yet. How can we be sure we didn t miss it? (39 is greater than 37) PROMPT: What comes first, 37 or 39? Emphasize that as long as you re still at numbers that come before 39, then you know you didn t miss it. Continue searching one at a time for 39 until you find it. Repeat with other numbers on partial number lines. Introduce the strategy of starting in the middle. Draw a number line from 46 to 56 and tell students you want to find 53. Explain that instead of starting at 46 and checking all the numbers until you get to 53, you re going to take a shortcut. Start in the middle of the number line (at 51) and decide whether to go right or left. ASK: Is 53 more than 51 or less? (more) Which way should I go on the number line: right or left (this way or that way)? Look to the right of 51 because 53 is more than 51. Explain that now you have fewer numbers to check. Repeat for various number lines and numbers. Adding 1 on a number line. Remind students that to find 3 + 1, they can find the number they say after 3 it is the number that is one more than 3. Draw a number line on the board and tell students that instead of counting on from 3 and saying the next number, they can draw a leap from 3 to the next number. Cut the frog out of BLM Frog. Place the frog on the 3 and move it one leap forward to the 4. H-24 Teacher s Guide for Grade 2 CA 2.1 TG Unit 7 p1-44 V4.indd 24 27/04/ :02:06 AM

25 The frog ends up at the next number after 3, or Write: = 4. Add 1 to several other numbers. Use partial number lines that begin at larger numbers. EXAMPLE: On a number line from 34 to 41, find At first, place the frog on the number line where students need to start and have them just add 1. Then have students both locate the starting number and add 1. Students can draw a dot (instead of a frog) at the starting number and draw arrows for the leaps. (as shown in the margin) For the following exercises, provide each student with BLM Blank Number Lines. Write the numbers 0 to 10 on each number line before photocopying, or have students write these numbers. Students draw a dot for the starting number and arrows for leaps. Exercises: Use the number line to add 1. a) = b) = c) = d) = Answers: a) 4, b) 8, c) 6, d) 10 Adding 2 or 3 on a number line. Start by drawing two leaps in order to add 2. EXAMPLES: 4 + 2, , , , Then draw three leaps in order to add 3. EXAMPLES: 5 + 3, , , At first, draw a big dot where students need to start, then have students do both steps (finding the place to start and drawing the leaps). Then mix up examples that require adding 1, 2, or 3. Students need to decide how many leaps to add 1, 2, or 3 depending on the second addend. Connect adding on a number line to adding by counting on. Draw a number line from 0 to 10 on the board and tell students that you want to add Have a volunteer demonstrate by counting on starting from 5 using their fingers. Then tell students you will add using the number line. ASK: What number should I start at? (5) Draw a big dot at the 5. ASK: What part of counting on to add is this like? (saying 5 with your fist closed) How many leaps should I draw starting at the 5? (3) What part of counting on is this like? (saying the next three numbers after 5) Connect the number sentence to the number line. Write the addition sentence (5 + 3 = 8) below the number line. Point out that leaps start and end at numbers that we see in the addition sentence. Show that 5 is where the leaps start and 8 is where they end. Connect the numbers in the number sentence to the numbers on the number line = 8 Number Sense 2-23 H-25 CA 2.1 TG Unit 7 p1-44 V4.indd 25 27/04/ :02:06 AM