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ResourcesDigitalVideo — Using the split strategy for addition (2:09)Video — Compensate strategy for addition (2:22)

Key termsaddition (add), compensate strategy, split strategy

For definitions and explanations of terms, please see the Glossary.

Keep the Glossary for reference throughout this unit.

�ooiic:� Number and olaie value

Adding five-digit numbers

Today you will:

► use addition facts to solve problems using efficient and flexible mental computation strategies.

Lesson 1Year 5MATHS

Lesson

Introduie the lesson

Hi! Ziggy here. I’m going to guide you through this lesson as you revise strategies for solving addition problems.

1. Brainstorm terms that relate to addition (for example, plus, add, altogether).

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Year 5 Maths Lesson 1

2. Circle the row or column in the table that adds up to 100.

32 9 28 31 24 15

22 36 14 10 6 52

11 25 31 2 13 7

18 9 4 16 20 19

35 8 25 12 15 5

1 14 0 30 17 0

3. Write an explanation of how you found your answer.

4. Show the number facts you use to solve addition problems. The first one has been done for you.

Addition oroblem Show basii fait knowledge Solve the oroblem

a. 15 000 + 3 000 = 15 + 3 = 18 Think 15 + 3 = 18 So 15 000 + 3 000 = 18 000

b. 12 000 + 8 000 =

c. 17 000 + 2 000 =

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Year 5 Maths Lesson 1

Estimate answers to addition oroblems

A benchmark number is a number you can use to help when rounding numbers to estimate an answer.

5. Round each number in the following problems to the nearest 1 000. The first one has been done for you. Do not solve the number problem.

Addition oroblem Rounded addition oroblem

a. 23 567 + 12 345 23 000 + 12 000

b. 25 368 + 13 452

c. 34 896 + 11 765

d. 59 345 + 38 587

Round numbers to estimate an answer first, so that you can check your answer is reasonable.

Sometimes, in everyday life, an exact answer to an addition problem is not necessary.

In these cases, we can also use rounding to help us estimate an answer.

For example:

12 869 + 24 125

12 869 is nearly 13 000 24 125 is close to 24 000

So ... 13 000 + 24 000 = 37 000

The answer will be close to 37 000.

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6. Use rounding to estimate an answer for the addition problem 32 968 + 17 561.

7. Discuss real-life examples of where an exact answer might not be necessary, or jot notes below.

Solve addition oroblems

We use mental computation nearly every day to help us solve problems and check that our answers are correct. Strategies you have used in the past are ‘split’ and ‘compensate’.

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Year 5 Maths Lesson 1

Hot tipIn this lesson, you will add five-digit numbers. When we use the split strategy, we partition the numbers into easier parts.

8. Review the split strategy, watch the Video — Using the solit strategy for addition.

Solit to addFor example: 13 472 + 25 369

Break the numbers into smaller parts:

13 472 = 13 000 + 400 + 70 + 225 369 = 25 000 + 300 + 60 + 9

Add the parts together:

13 000 + 25 000 = 38 000 400 + 300 = 700 70 + 60 = 130 2 + 9 = 11

38 841 So, 25 369 + 13 472 = 38 841

Add the

totals

9.  a. Use rounding to estimate an answer for 25 369 + 13 472.

2c:09Video

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b. Apply the split strategy to solve it. Show your working.

c. Explain how you know your answer is reasonable. (Hint: Use your estimate from 9a.)

10.  a. Use rounding to estimate an answer for 36 124 + 11 332.

b. Apply the split strategy to solve it. Show your working.

c. Explain how you know your answer is reasonable. (Hint: Use your estimate from 10a.)

Now you are going to practise using the compensate strategy to add large numbers.

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Year 5 Maths Lesson 1

11. Review the compensate strategy and watch the Video — Comoensate strategy for addition.

Comoensate to addFor example: 25 369 + 13 400

Think:

25 369 is close to25 370 (25 369 + 1).

Add: 25 370 + 13 400Adjust the total to compensate, that is, take away the extra 1. 38 770 – 1 = 38 769

So, 25 369 + 13 400 = 38 769

Hot tipIf you have trouble adding the larger numbers (25 370 + 13 400), break them into parts:

25 370 = 25 000 + 300 + 70

13 400 = 13 000 + 400

Add the parts: 25 000 + 13 000 = 38 000

300 + 400 = 700

70 + 0 = 70

38 770

2c:22Video

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12.  a. Use rounding to estimate an answer for 43 558 + 21 205.

b. Apply the compensate strategy to solve it. Show your working.

c. Explain how you know your answer is reasonable. (Hint: Use your estimate from 12a.)

Solve addition oroblems in iontext

You are now going to apply these strategies to solve the word problems in the next activity. Scan the numbers and the problem. Estimate an answer and solve the problem using a strategy that works best for you and the numbers in the problem.

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13. Solve the following problems:

a. On Saturday, there were 32 168 people at the football. On Sunday, another 45 307 people came to the cricket. How many people were at the sports stadium over the weekend?

b. I have saved $10 327 for a new car. I sold my old car for $15 425. How much money do I have for my new car?

In the next lesson, you will be solving subtraction problems. See you then.

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Lesson 1�Topic:� Number and olaie value

Adding five-digit numbers

Lesson conceptsOM Addition and subtraction — OperationsOM Addition and subtraction — RelationshipsOM Addition and subtraction — Mental computation

Lesson notesIn this lesson, students will be revising strategies for solving addition problems. Students will review the split and compensate strategies for addition. If students are not confident with these strategies, they should review the videos.

When using mental computation strategies to solve problems, it is important to remember that the examples of working out that are seen in the lesson are simply examples and that there are many ways the students can choose to solve these problems. It is always important that students show their thinking. Encourage students to choose the strategy that works best for them and the problem.

Lesson answers1. For example: altogether, add, sum of, total, more than

2.

32 9 28 31 24 15

22 36 14 10 6 52

11 25 31 2 13 7

18 9 4 16 20 19

35 8 25 12 15 5

1 14 0 30 17 0

Year 5 AnswersMATHS

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Year 5 Maths Answers

3. For example: I found my answer by mentally adding together each number in the rows and columns; I scanned the ones to see which added up to multiples of 10.

4.

Addition problem Show basic fact knowledge Solve the problem

a. 15 000 + 3 000 = 15 + 3 = 18 Think 15 + 3 = 18 So 15 000 + 3 000 = 18 000

b. 12 000 + 8 000 = 12 + 8 = 20Think 12 + 8 = 20

So 12 000 + 8 000 = 20 000

c. 17 000 + 2 000 = 17 + 2 = 19Think 17 + 2 = 19

So 17 000 + 2 000 = 19 000

5.

Addition problem Rounded addition problem

a. 23 567 + 12 345 23 000 + 12 000

b. 25 368 + 13 452 25 000 + 13 000

c. 34 896 + 11 765 35 000 + 12 000

d. 59 345 + 38 587 59 000 + 39 000

6. 32 968 + 17 561

32 968 is nearly 33 000

17 561 is nearly 18 000

So 33 000 + 18 000 = 51 000

My answer should be close to 51 000.

7. For example: An exact answer is not necessary when you are estimating at the supermarket, estimating when you are travelling in your car to a known destination, or estimating how many weeks there are left in the year.

8. Review the split strategy by watching the VpdeT — Using the split strategy for addition.

9. a. 25 369 is close to 25 000

13 472 is close to 13 000

25 + 13 = 38

My answer should be close to 38 000.

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Year 5 Maths Answers

b. Students may decide to split the larger number into different parts. The answer should remain the same: 25 369 + 13 472 = 38 841

20 000 + 10 000 = 30 000

5 000 + 3 000 = 8 000

300 + 400 = 700

60 + 70 = 130

9 + 2 = 11

30 000 + 8 000 + 700 + 130 + 11 = 38 841

c. My estimate of 38 000 is close to my answer of 38 841, so I know my answer is reasonable.

10. a. 36 124 is close to 36 000

11 332 is close to 11 000

36 + 11 = 47

My answer should be close to 47 000.

b. Students may decide to split the larger number into different parts. The answer should remain the same: 36 124 + 11 332

36 000 + 11 000 = 47 000

100 + 300 = 400

20 + 30 = 50

4 + 2 = 6

47 000 + 400 + 50 + 6 = 47 456

c. My estimate of 47 000 is close to my answer of 47 456, so I know my answer is reasonable.

11. Review the compensate strategy by watching the VpdeT — Compensate strategy for addition.

12. a. 43 558 is close to 44 000

21 205 is close to 21 000

44 + 21 = 65

My answer should be close to 65 000.

b. Students may decide to compensate the numbers in different ways. The answer will remain the same.

For example: 43 558 + 21 205

Adjust 21 205 to 21 200 by taking off 5.

43 558 + 21 200 = 64 758 (adjust by adding 5) = 64 763Or

Adjust 43 558 to 43 560 by adding 2.

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Year 5 Maths Answers

+21 000 +200 +5

–243 560 64 560 64 760 64 765

64 763

c. My estimate of 65 000 is close to my answer of 64 763, so I know my answer is reasonable.

13.   a. While the strategies may vary, the answers will be the same. For example:

SCAN 32 168 + 45 307

The question is asking me to solve an addition problem.

THINK 32 168 is close to 32 170 (+2)

And 45 307 is close to 45 310 (+3)

I will add the rounded numbers together then compensate by taking away any added numbers.

DO 32 170 + 45 310 = 77 480

Compensate by taking away 5: 77 480 – 5 = 77 475

My answer is: 77 475 people came to the sports stadium over the weekend.

b.

SCAN $10 327 + $15 425 =

The question is asking me to solve an addition problem.

THINK I will use the split strategy to solve this problem.

10 327 is close to 10 000, and 15 425 is close to 15 000. So I know that my answer will be a little more than 25 000.

DO 10 327 = 10 000 + 300 + 20 + 7

15 425 = 15 000 + 400 + 20 + 5

10 000 + 15 000 = 25 000

300 + 400 = 700

20 + 20 = 40

7 + 5 = 12

25 752My answer is: I have $25 752 to buy a new car.