unit 1 number sense: numbers to 10 - jump math for new cdn... · unit 1 number sense: numbers to 10...

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Number Sense B-1

Unit 1 Number Sense: Numbers to 10

IntroductionIn 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.

CA 2.1 TG Unit 1 p1-36 V5.indd 1 6/14/17 11:48:58 AM

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B-2 Teacher’s Guide for Grade 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.

5 + 2


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Number Sense B-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.



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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


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Number Sense 2-1 B-5

GoalsStudents will review counting (associating spoken numbers with the

corresponding quantities and written numerals).

PRIOR KNOWLEDGE REQUIRED

Can colourCan recognize and write numerals within 10Can subitize within 5Can join two figures with a line

MATERIALS

BLM Quantities (pp B-37–41)countersBLM Writing Numbers (p B-42)2 cm grid paper or BLM 2 cm Grid Paper (p M-1)magazines and cataloguesBLM 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

NS2-1 Counting and MatchingPages 1–2

CURRICULUM REQUIREMENTAB: recommendedBC: recommendedMB: recommendedON: recommended

VOCABULARYcounthow manynumbernumbers 0 to 10



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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.

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 (4 2 5 3 8 6 1 0 7 …). 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: 10

2. 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?

EXTRA PRACTICE

BLM Writing Numbers


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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.

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:

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.



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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:

25

Exercises: Draw a matching domino using numbers instead of dots.

a) b)

c) d)

Answers: a) 61 , b) 47 , c) 72 , d) 30

Match two quantities to numerals. Ask students to match dominoes with dots to corresponding dominoes with numbers. EXAMPLE:

6

3

4

2

1

5

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. EXTRA PRACTICE

BLM Dominoes


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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.

Extensions1. 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).



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GoalsStudents will identify which of two sets of objects has more by using

one-to-one correspondence.


Understands the concepts of more and less (or fewer)Can count

MATERIALS

two-sided countershula 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.


VOCABULARYas manymorepair

NS2-2 One-to-One CorrespondencePages 3–4


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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.

Extensions1. 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

Real World

CONNECTION

1

1 1

1 0

2 2 1

1 1

2 3 1

2 3

1 1 3 2

0 0 1



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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.


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GoalsStudents 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.


Can count, recognize, and write numerals within 10Subitizes within 5

MATERIALS

counting chart or BLM Counting Cubes (p B-50)two colours of connecting cubessquare pieces of papertapetwo-sided counters or coinsred and yellow blocksBLM Who Is Winning? (p B-51)strips of paper or index cardsdeck 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).

1 2 3 4 5 6 7 8 9 10

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


VOCABULARYfewerfewestleastlessmoremostorderright

NS2-3 More, Fewer, and LessPages 5–6



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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:

1 2 3 4 5 6 7 8 9 10

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.

1 2 3 4 5 6 7 8 9 10

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.


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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

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) 7BLM Who Is Winning?

EXTRA PRACTICE



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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)


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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.



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Extensions1. 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.


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GoalsStudents determine how much more one quantity is than another by

counting the extras.


Understands one-to-one correspondenceUnderstands the concepts of more and less (fewer)Can count up to 20 from a number less than 20

MATERIALS

two-sided countersBLM 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:

1 2 3 4 5 6 7 8 9 10

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:

1 2 3 4 5 6 7 8 9 10

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.


VOCABULARYextrahow many morepair up

NS2-4 How Many More?Pages 7–9



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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)


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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.

Extensions1. 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 4.

2. 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.”



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GoalsStudents will read the number words from zero to ten.


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.”

•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.


VOCABULARYnumber words zero to ten

NS2-5 Reading Number Words to TenPages 10–11

EXTRA PRACTICE

BLM Match Pictures to Number Words


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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.



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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.


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.

Extensions1. 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).


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GoalsStudents will solve simple addition problems.


Counts objects without skipping or counting twiceCan count to 10Knows the plus (+) and equal (=) signsUnderstands the concept of addition

MATERIALS

two-sided counters diceBLM 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 “2 + 3 = 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 “3 + 4 = 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.


VOCABULARYaddaddition sentencealtogetherequal (=)in totalplus (+)

NS2-6 AdditionPages 12–13



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Students should work in pairs for the following exercises.

Exercises: Read the addition sentence aloud to your partner in two different ways.

a) 2 + 1 = 3 b) 2 + 4 = 6 c) 1 + 5 = 6

d) 3 + 3 = 6 e) 4 + 5 = 9 f ) 3 + 5 = 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) 4 + 2 = b) 6 + 1 = c) 3 + 4 =

d) 8 + 2 = e) 5 + 3 = f ) 3 + 5 =

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. 4 + 3 = 7 B. 6 + 2 = 8 C. 7 + 3 = 9 D. 4 + 6 = 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 “5 + 1 is the same number as 6” (write “5 + 1 = 6” on the board) means the same thing as saying “6 is the same number as 5 + 1” (write “6 = 5 + 1” on the board).

Exercises: Write the addition sentence with the answer on the left.

a) 3 + 4 = 7 b) 2 + 6 = 8 c) 1 + 4 = 5

Bonus: 33 + 66 = 99

Answers: a) 7 = 3 + 4, b) 8 = 2 + 6, c) 5 = 1 + 4, Bonus: 99 = 33 + 66


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Have students use counters to model the equations in the following exercise and find which one is incorrect.

Exercise: Which equation is incorrect?

A. 6 = 3 + 2 B. 7 = 2 + 5 C. 8 = 7 + 1 D. 9 = 3 + 6

Answer: A

Add three things together. Tell students that three adults, two children, and two babies went on a picnic. Write on the board:

3 adults + 2 children + 2 babies = people.

ASK: How many people went on the picnic? Using stick people, have one volunteer draw the three adults, another volunteer draw the two children, and another draw the two babies. ASK: How many people are there altogether? (7) Have students find the totals in similar problems by drawing their own pictures or dots, or by using counters.

Exercises: Add.

a) 3 basketballs + 2 volleyballs + 4 soccer balls = balls

b) vehicles = 3 buses + 2 fire trucks + 3 police cars

Bonus: animals = 2 lions + 1 bear + 3 cats + 2 dogs + 4 hamsters

Answers: a) 9, b) 8, Bonus: 12


1. If students can count to 12, have pairs of students roll two dice—one each—and add the numbers they roll. Students should add the numbers independently and compare their answers. If students’ answers do not agree, they should add again or count the dots until they do. If students can count to 18, have them work in groups of three.

2. I Have —, Who Has —? (see unit introduction). Use a number on top and an addition question (for example, 3 + 4) with a picture on the bottom. Use BLM Game Cards to make cards for numbers up to 10.

3. Dominoes or Group Dominoes (see unit introduction). Use BLM Blank Domino Cards to make dominoes with a number on top and an addition problem with a picture on the bottom.

4. Play Addition Peace (see unit introduction).

Write addition sentences another way. Explain that addition sentences can be written up and down, too (see example in margin).

2 apples+ 7 bananas

9 fruits



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Exercises: Add.

a) b) c)

3

+ 5 1

+ 4 2

+ 7

d) e) f )

2

+ 3 2

+ 6 6

+ 4

Bonus: 8+ 3


Extensions1. Students can use the cards on BLM Add Roman Numbers (p B-62) to

write and add Roman numbers.

2. Find the missing number. Draw pictures or dots to help.

a) 4 apples + oranges = 6 fruits

b) red crayons + 5 blue crayons = 8 crayons

c) carrots + 3 peas = 5 vegetables

d) 9 cars = 6 big cars + small cars

Answers: a) 2, b) 3, c) 2, d) 3

3. Draw dots to find the missing number.

a) 4 + = 5 b) + 3 = 7

c) 9 = 1 + d) 10 = 4 +

Answers: a) 1, b) 4, c) 8, d) 6

BLM Add the Dots

EXTRA PRACTICE


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GoalsStudents will understand subtraction as “taking away” and will draw

and use pictures to solve subtraction problems.


Counts objects without skipping or counting twiceCan count to 10Knows the plus (+) and equal (=) signsUnderstands the concept of addition

MATERIALS

countersdeck of cardsdominoes

Taking away 3 objects from 5 always leaves 2 objects. Draw five circles in a row on the board. SAY: I want to remove three circles, but instead of erasing them, I am going to cross them out; please watch carefully and tell me to stop when you think I’ve crossed out enough circles. Cross out the first three circles. If students don’t tell you to stop, ASK: How many have I crossed out? Have I crossed out enough? How many are left? Repeat with five squares in a row, but this time take away the last three squares. Repeat with five triangles scattered randomly and take away any three. ASK: If you had five apples and someone took three of them away, how many would be left? (2) SAY: No matter which objects we use, if we start with 5 and take away 3, we have 2 left.

The minus sign (−). ASK: Does anyone know how mathematicians write this fact using numbers and signs? Encourage students to come to the board to show you if they want to. If no one volunteers, write “5 − 3 = 2” on the board. Ask if students know the way mathematicians say this. Tell them that we say “5 minus 3 equals 2,” or “5 take away 3 equals 2,” or “subtract 3 from 5 to get 2.” Point to the corresponding sign as you say each part. SAY: What we really mean is that when we start with five things and we take away three of them, we get the same number as if we’d started with only two things.

Write subtraction sentences from a picture. Draw seven circles and tell students you want to remove four. SAY: Tell me when to stop. Cross out four circles. Ask a volunteer to write a “take away” sentence on the board for your drawing. (7 − 4 = 3) Write “take away,” “subtract,” and “minus” on the board. Ask another volunteer to read the sentence in two different ways, one using “take away” and another using a different word that means the same thing. Repeat this several times with different numbers, asking students to write the sentence and then read it using “subtract” or “minus.”


VOCABULARYminus (−)subtractsubtraction sentencetake away

NS2-7 SubtractionPages 14–15



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Do not include examples with zero yet (students will subtract with zero in the next lesson).

Write a few subtraction sentences on the board, such as 4 − 1 = 3, 7 − 2 = 5, and 10 − 8 = 2. Point to the equations on the board and tell students that these are called “subtraction sentences.” Subtraction sentences have a minus sign and an equal sign.

Students should work in pairs for the following exercises.

Exercises: Read the subtraction sentence aloud to your partner in two different ways.

a) 2 − 1 = 1 b) 8 − 5 = 3 c) 6 − 5 = 1

d) 9 − 3 = 6 e) 10 − 7 = 3 f ) 7 − 5 = 2

Sample answer: a) 2 minus 1 equals 1, 2 take away 1 equals 1

Colouring to subtract. Tell students that instead of crossing out circles, you will colour the circles you want to take away and then ask how many are not coloured. Draw the picture shown in the margin on the board. ASK: How many circles did I draw? How many did I colour? How many are not coloured? Write “5 − 3 = 2” on the board. Repeat for various examples.

For the exercises below, have students draw circles and either colour or cross out the ones they need to subtract. Students count the remaining circles to find the answer.

Exercises: Complete the subtraction sentence.

a) 7 − 3 = b) 6 − 2 = c) 4 − 3 =

d) 5 − 1 = e) 8 − 6 = f ) 9 − 4 =

Answers: a) 4, b) 4, c) 1, d) 4, e) 2, f ) 5

Draw a picture of a subtraction. Write a subtraction on the board, such as 5 − 2. SAY: Please draw shapes to show 5 − 2. You might draw circles, squares, triangles, or hearts. Your shapes should be big enough so that the whole class can see them when you hold them up. Have volunteers show their work to the class; emphasize how all the drawings are different and how they are the same. Differences may include shapes drawn, size of shapes, where they are on the page, and colour.

Use counters to check that subtraction sentences are correct. Give students counters. Have students count out 7 counters, and ask them to take away 3, see how many they have left, and write the subtraction sentence. Repeat for other examples. Write these subtraction sentences on the board: 8 − 2 = 6, 8 − 3 = 4, 7 − 5 = 2. Challenge students to find the one that’s incorrect and to prove it incorrect using their counters. (8 − 3 = 4)


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Have students use their counters to model the subtraction sentences in the following exercise and find which one is incorrect.

Exercise: Which subtraction sentence is incorrect?

A. 6 − 3 = 3 B. 7 − 2 = 5 C. 8 − 6 = 3 D. 9 − 3 = 6

Answer: C

Write the difference on the left. Emphasize that 7 − 3 = 4 (7 take away 3 is the same number as 4) means the same things as 4 = 7 − 3 (4 is the same number as 7 take away 3).

Exercises: Write the subtraction sentence with the answer on the left.

a) 7 − 4 = 3 b) 9 − 5 = 4 c) 10 − 2 = 8

Bonus: 88 − 40 = 48

Answers: a) 3 = 7 − 4, b) 4 = 9 − 5, c) 8 = 10 − 2, Bonus: 48 = 88 − 40

Have students use their counters to model the subtraction sentences in the following exercise and find which one is incorrect.

Exercise: Which subtraction sentence is incorrect?

A. 5 = 9 − 4 B. 7 = 9 − 2 C. 3 = 8 − 4 D. 6 = 10 − 4

Answer: C

Write subtraction sentences another way. Explain that, like addition sentences, subtraction sentences can be written up and down instead of side to side (see example in margin).

Exercises: Subtract.

a) b) c)

8

− 5 6

− 4 10

− 7

d) e) f )

9

− 3 9

− 6 10

− 2

Bonus: 13− 12



1. Play Difference Peace (see unit introduction).

2. Give students dominoes. Have pairs play as follows: Player 1 picks a domino, counts the total dots, tells Player 2 how many dots are on the domino, and hides one half. Player 2 guesses how many dots are on the hidden half. Player 1 then reveals the hidden half. Players switch roles and play again.

10 cats− 3 cats

7 cats



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Extensions1. Have students complete BLM Subtract! (p B-63), which shows various

models of subtraction.

Answers: 2, 6; 3, 7; 3, 2

2. Have students complete BLM Subtract Using Dominoes (p B-64).

Answers: 9; 5; 7 − 3 = 4; 2; 4; 6, 5; 2 = 7 − 5

3. Have students solve the problem using counters or by drawing dots. Explain that they will need to subtract more than once.

a) 9 − 2 − 1 = b) 10 − 6 − 2 = c) 8 − 3 − 1 =

d) 7 − 4 − 2 = e) 10 − 2 − 5 = f ) 10 − 5 − 2 =

Bonus: 16 − 1 − 2 − 3 − 4 − 5 =



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GoalsStudents will solve simple addition and subtraction problems

involving zero.


Counts objects without skipping or counting twiceCan count from 0 to 10Knows the plus (+), minus (−), and equal (=) signsUnderstands the concepts of addition and subtraction

MATERIALS

large paper dominoes dominoes or BLM Blank Domino Cards (p M-3)BLM Game Cards (p M-2)

Write addition sentences with 0 using dominoes. Tape a large paper domino on the board with a 5 on one side and nothing on the other side. Ask students to count the number of dots on each side. SAY: I would like to write an addition sentence for the total number of dots on this domino. Remind students that there is a number that means none: 0. Invite answers. Write “5 + 0 = 5” under the domino. Tape a second domino on the board or add dots to the first to show 7 on one side and nothing on the other side. Have a volunteer write the corresponding addition sentence.

Give each student several dominoes, real or paper, that are blank on one side. (You can use BLM Blank Domino Cards to make them.) Have students record the number sentences for their dominoes. ASK: What do you notice? (the first number is the same as the answer) Explain that when students add zero objects, they don’t add anything, so the result is the same as the number they started with.

Practise adding zero without dominoes. ASK: If I start with three things and add zero things, how many do I have in total? (3) Write the corresponding addition sentence on the board: 3 + 0 = 3. Repeat with more addition sentences. EXAMPLES: start with five things and add zero things, start with two things and add zero things. Invite volunteers to write the corresponding addition sentences on the board: 5 + 0 = 5, 2 + 0 = 2. ASK: What if I start with zero things and then add three things? Now how many do I have? (3) Have a volunteer write the addition sentence on the board: 0 + 3 = 3. Continue with more similar questions. Then, mix questions with zero as the first number or the second number. ASK: What do you think 0 + 15 will be? Repeat with 12 + 0, 0 + 18, and 10 + 0.

NS2-8 Adding and Subtracting 0Page 16

CURRICULUM REQUIREMENTAB: requiredBC: requiredMB: requiredON: required

VOCABULARYaddaddition sentenceminusplussubtractsubtraction sentencetake away



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Exercises: Add.

a) 4 + 0 = b) 0 + 6 = c) = 9 + 0

Bonus

d) 0 + 55 = e) = 89 + 0 f ) = 0 + 0

Answers: a) 4, b) 6, c) 9, Bonus: d) 55, e) 89, f ) 0

Subtract 0 using pictures. Draw three circles on the board. ASK: How many circles do I have? (3) Write “3” underneath the circles. ASK: If I want to take away no circles, or zero circles, how many circles would I have left? (3) Count how many are left when no circles are taken away and write the subtraction sentence under the circles, starting with the “3” already written on the board. (3 − 0 = 3) Repeat with five circles and one circle, taking away zero circles each time. Have volunteers write the subtraction sentences underneath the drawings: 5 − 0 = 5, 1 − 0 = 1. Explain that when you take zero things away, you are left with the number you started with.

Practise subtracting zero without using pictures. ASK: If I start with eight things and zero things are taken away, how many things are left? (8) Have a volunteer write the subtraction sentence on the board: 8 − 0 = 8. Repeat with more subtraction sentences. EXAMPLES: start with seven things and take away zero things, start with two things and take away zero things. Have volunteers write the subtraction sentences on the board.


a) 8 − 0 = b) 3 − 0 = c) = 10 − 0

Bonus

d) 40 − 0 = e) = 65 − 0 f ) = 99 − 0


Write subtraction sentences that equal 0 using pictures. Draw seven circles on the board. ASK: How many circles do I have? (7) Write “7” underneath. SAY: I want to take away seven circles. Then draw an “X” through each of the seven circles. ASK: How many circles do I have left? (0) Write the subtraction sentence under the circles, beginning with the “7” already written: 7 − 7 = 0. Draw two circles on the board and cross out two circles. Have a volunteer write the subtraction sentence underneath: 2 − 2 = 0.

Practise subtracting without drawing circles. ASK: If we start with four things and take away four things, how many things are left? (0) Write the subtraction sentence on the board: 4 − 4 = 0. Repeat with six things take away six things, then nine things take away nine things.


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a) 9 − 9 = b) 3 − 3 = c) = 7 − 7

Bonus

d) 48 − 48 = e) = 89 − 89 f ) = 0 − 0


Subtracting with zero. Have students write the subtraction sentences for pictures in which either all the objects are crossed out (0 is the difference) or none are crossed out (0 is the subtrahend, the number being subtracted).


1. I Have —, Who Has —? (see unit introduction). Use a number on top and a subtraction question where the number being subtracted is zero with a picture on the bottom. Use BLM Game Cards to make cards for numbers up to 10.

2. Dominoes or Group Dominoes (see unit introduction). Use cards with a number on top and a subtraction problem with a picture on the bottom. Include 0 in the problems.

Extensions1. Darcy has some grapes. She eats all of them.

a) How many grapes does Darcy have left?

b) Do you know how many grapes Darcy started with?

c) Explain why you don’t need to know how many grapes Darcy started with in order to answer part a).

Answers: a) 0, b) no, c) You don’t need to know how many grapes Darcy started with because she eats all the grapes. Any number minus the same number equals zero.

2. Read the following questions carefully before answering.

a) Rob has 5 apples. His dad gives him a bowl of fruit. Rob still has 5 apples. How many apples were in the bowl of fruit?

b) Iva has some toy cars. Ed has no toy cars. Altogether, Iva and Ed have 8 toy cars. How many toy cars does Iva have?

c) Jun has 15 red marbles and some blue marbles. Jun gives some marbles to his sister. Jun still has 15 red marbles. How many red marbles did Jun give to his sister?



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d) Aputik has 10 crayons. She gives some crayons to her friend. Aputik has no crayons left. How many crayons did Aputik give to her friend?

Answers: a) 0, b) 8, c) 0, d) 10

3. Write an addition or subtraction sentence for each part of Extension 2.

Answers: a) 5 + 0 = 5, b) 8 + 0 = 8, c) 15 − 0 = 15, d) 10 − 10 = 0


unit 1 number sense: numbers to 10 - jump math for new cdn... · unit 1 number sense: numbers to 10...

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