Outcomes: NS2.2 Uses mental and written strategies for addition and subtraction involving two, three and four digit numbers. WMS2.5 Links mathematical ideas and makes connections with, and generalizations about, existing knowledge and understanding in relation to Stage 2 content WMS2.1 Asks questions that could be explored using mathematics in relation to Stage 2 content Indicators: Students learn about:

using mental strategies for addition and subtraction involving two-, three- and four-digit numbers, including

uses the formal written algorithm to solve addition or subtraction problems

students will use decomposition and equal addends strategies to solve subtraction algorithms

reflect on own method of solution for a problem, considering whether it can be improved (Reflecting)

Asks ‘What is the best method to find a solution to this problem?’ (Questioning)

Lesson 1

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Mental Strategies

Have students write the number 78 in the middle of the board have students suggest many number sentences or problems that equal 78.
Have students do their own in their books or on a piece of scrap paper using a different number.

Revise mental strategies. Ask students to mentally calculate 28 + 52 = and 55 + = 81. Have students record the strategies that they used to get their answers. Students are encouraged to share their ideas. Repeat this step with four or five more examples.

Have students complete (choosing appropriate strategies worksheet).

Students discuss which strategy they chose and why they chose to use that strategy.

Lesson 2

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Formal Addition with Trading

Model 462 + 125 with MAB materials. Complete the addition with MAB materials. Draw a table on the board with hundreds, tens and ones columns. Write the corresponding numbers into the correct columns e.g.

Hundreds

Tens

Ones

4

6

2

+1

2

5

5

8

7

Repeat with the equation 187 + 224. Demonstrate trading by replacing ten ones blocks with a ten block and trading it to the tens column.

Hundreds

Tens

Ones

1

8

7

+2 1

2 1

4

4

1

1

Choose students to demonstrate the process.
Complete (3 – digit addition with trading to the tens and hundreds) worksheet.

Lesson 3

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4 Digit Addition

Write the numerals 8, 1, 0, 9, 4, 6, 3 and 5 on the board and have the students suggest 4 digit plus 4 digit addition problems from those numerals e.g.
1096
+8545
Use a student to demonstrate how to solve the problem for the class. Emphasise the importance of showing the trading. Use language like (we have 11 ones so we need to trade 10 ones into 1 ten etc).

In their books have students write 3 different problems using the numbers on the board and then answer the following questions:

What trading did you have to make to complete the addition above?

Why do you think it is important to record the trading in a formal algorithm for addition?

Complete Addition with (Trading to the Thousands) worksheet.

Lesson 4

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Decomposition Strategy

Revise with students subtraction with trading. If have access to an IWB teachers can use Rainforest Maths on the school server to demonstrate to students how to trade. When on Rainforest Maths Select Year 3 or 4 (depending on your year), subtraction +, 2 or 3 digit. Work through algorithms with students.

If do not have access to IWB, show students ‘Teach This’ poster demonstrating subtraction with trading.

Complete 3 digit subtraction with trading worksheet.

Lesson 5

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Equal Addends

Use MAB’s to make the equation 229 – 98. Have a student use a calculator to get the answer. Demonstrate equal addends by rounding 98 to 100 and doing the same on the other side to get 231 – 100 have students work this out and compare the answer.
Have students complete (Equal Additions) worksheet.

Model 235 – 176 using MAB Materials. Draw a table on the board with hundreds, tens and ones columns. Write the corresponding numbers into the correct columns e.g.

Hundreds

Tens

Ones

2

13

15

- 11

17

6

(2-2=0)

5 (13-8=5)

9 (15-6=9)

Complete Study ladder worksheet

Lesson 6

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Formal Subtraction

Write some word problems on the board e.g. Australia scored 482 runs at cricket and New Zealand scored 198 less. How many runs did New Zealand score? Have students identify the key information and write the problem as a formal algorithm.

Use this problem and others as a whole class activity. Model and revise with students various strategies they can use to solve such problems. In their books have students answer the following questions:

What strategy did you use to solve the problems?

Why do you think it is important to record the trading in formal algorithms for subtraction?

Outcomes:NS2.2Uses mental and written strategies for addition and subtraction involving two, three and four digit numbers.WMS2.5Links mathematical ideas and makes connections with, and generalizations about, existing knowledge and understanding in relation to Stage 2 contentWMS2.1Asks questions that could be explored using mathematics in relation to Stage 2 contentIndicators: Students learn about:using mental strategies for addition and subtraction involving two-, three- and four-digit numbers, includinguses the formal written algorithm to solve addition or subtraction problemsstudents will use decomposition and equal addends strategies to solve subtraction algorithmsreflect on own method of solution for a problem, considering whether it can be improved (Reflecting)Asks ‘What is the best method to find a solution to this problem?’ (Questioning)Mental StrategiesHave students write the number 78 in the middle of the board have students suggest many number sentences or problems that equal 78.

Have students do their own in their books or on a piece of scrap paper using a different number.

Revise mental strategies. Ask students to mentally calculate 28 + 52 = and 55 + = 81. Have students record the strategies that they used to get their answers. Students are encouraged to share their ideas. Repeat this step with four or five more examples.

Have students complete (choosing appropriate strategies worksheet).

Students discuss which strategy they chose and why they chose to use that strategy.

Formal Addition with TradingModel 462 + 125 with MAB materials. Complete the addition with MAB materials. Draw a table on the board with hundreds, tens and ones columns. Write the corresponding numbers into the correct columns e.g.

Complete (3 – digit addition with trading to the tens and hundreds) worksheet.

4 Digit AdditionWrite the numerals 8, 1, 0, 9, 4, 6, 3 and 5 on the board and have the students suggest 4 digit plus 4 digit addition problems from those numerals e.g.

1096

+8545

Use a student to demonstrate how to solve the problem for the class. Emphasise the importance of showing the trading. Use language like (we have 11 ones so we need to trade 10 ones into 1 ten etc).

In their books have students write 3 different problems using the numbers on the board and then answer the following questions:

What trading did you have to make to complete the addition above?

Why do you think it is important to record the trading in a formal algorithm for addition?

Complete Addition with (Trading to the Thousands) worksheet.

Decomposition StrategyRevise with students subtraction with trading. If have access to an IWB teachers can use Rainforest Maths on the school server to demonstrate to students how to trade. When on Rainforest Maths Select Year 3 or 4 (depending on your year), subtraction +, 2 or 3 digit. Work through algorithms with students.

If do not have access to IWB, show students ‘Teach This’ poster demonstrating subtraction with trading.

Complete 3 digit subtraction with trading worksheet.

Equal AddendsUse MAB’s to make the equation 229 – 98. Have a student use a calculator to get the answer. Demonstrate equal addends by rounding 98 to 100 and doing the same on the other side to get 231 – 100 have students work this out and compare the answer.

Have students complete (Equal Additions) worksheet.

Model 235 – 176 using MAB Materials. Draw a table on the board with hundreds, tens and ones columns. Write the corresponding numbers into the correct columns e.g.

Complete Study ladder worksheet

Formal SubtractionWrite some word problems on the board e.g. Australia scored 482 runs at cricket and New Zealand scored 198 less. How many runs did New Zealand score? Have students identify the key information and write the problem as a formal algorithm.

Use this problem and others as a whole class activity. Model and revise with students various strategies they can use to solve such problems. In their books have students answer the following questions:

What strategy did you use to solve the problems?

Why do you think it is important to record the trading in formal algorithms for subtraction?