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Outcome: NS2.2 Uses mental and written strategies for addition and subtraction involving two, three and four digit numbers.
Indicators: Students learn about:
using mental strategies for addition and subtraction involving two-, three- and four-digit numbers, including
· the jump strategy eg 23 + 35; 23 + 30 = 53, 53 + 5 = 58
· the split strategy eg 23 + 35; 20 + 30 + 3 + 5 is 58
· the compensation strategy eg 63 + 29; 63 + 30 is 93, subtract 1, to obtain 92
· using patterns to extend number facts eg 5 – 2 = 3, so 500 – 200 is 300
· bridging the decades eg 34 + 17; 34 + 10 is 44, 44 + 7 = 51
· changing the order of addends to form multiples of 10 eg 16 + 8 + 4; add 16 and 4 first
- Solve a variety of problems using problem solving strategies such as: trial and error, drawing a diagram, working backwards, looking for patterns, using a table
- Solves 2 & 3 digit addition with trading problems

Lesson 1

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Mental Strategies
Students are asked to calculate 34 + 17 in their heads. (Depending on student ability levels it may be necessary to use different numerals). They are then asked to record the strategy they used. This process is repeated for other problems, such as:
73 – 25 162 – 69
63 + 29 188 – 89
Students discuss which methods are the most efficient.
Extension: Students are given increasingly more difficult problems to solve mentally. Students explain and discuss the strategies they use eg for ‘188 – 89 = ?’ A student may say, ‘I took away 88 and that was easy because it left 100 but I had to take away one more, because 88 + 1 = 89, so the answer is 99.’ Students record the mental strategies they use.
Possible questions include:
. Is there a better strategy?
. What is the best method to find a solution to this problem?

Strategies to model and revise with students include: jump strategy, compensation strategy, bridging the decades, using patterns to extend number facts, change the order of addends to form multiples. Refer to activity sheet 1.

Students complete ‘Addition Strategies’ (activity sheet 2).


Lesson 2

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Number Lines
Students are shown the number sentence 157 + 22 and an empty number line. The teacher marks the number 157 on the number line.
Possible questions include:
. What is the next multiple of ten after 157?
. How many do you add on to get that number?
Students record their answers on the number line.
Possible questions include:
. Can you work it out with fewer steps?
. Can you visualise the number line in your head and do it?
. Can you write the numbers on paper to help you keep track?

As an additional activity, in pairs, students draw an empty number line. Student A chooses two three-digit numbers and places them on the number line. Student B uses the number line to work out and record the difference between the two numbers. Students explain the mental strategies they used to find the answer. They reflect on their method, considering whether it can be improved.
Students complete activity ‘Addition using a number line’ (Activity sheet 3). Ensure that students also use a number line to solve subtraction problems.


Lesson 3
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Base 10 Material
Begin lesson with a quick game of recall of related addition and subtraction facts. Ask one of the students to model 9-6=3 with base 10 material and have another student model the sum as a number sentence. Then choose another student to model 90-60=30 with base 10 material. Record this number sentence also. Repeat with another set of numbers. For example 8-2=6, 80-20=60. Discuss with students the pattern that they can see emerging. Work with students to extend these number facts to use hundreds and thousands.

As an additional activity, students use 2, 3 or 4 dice to generate a 2, 3 or 4 number and then represent this number using Base 10 material. Students then generate a second, smaller number by rolling one less die. Students represent this number using Base 10 material, then add the two numbers and show the result using Base 10 material. Students repeat this process, subtracting the second number from the first. Students record their solutions.

Students independently work on ‘Patterns in addition and Subtraction‘(activity sheet 4). Students can also work on Addition with Trading (activity sheet 5).



Lesson 4
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Addition With Trading
Revise with students addition 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), addition+, 2 or 3 digit with regrouping. Work through algorithms with students.
If do not have access to IWB, show students ‘Teach This’ poster demonstrating addition with trading.

Students complete ‘Addition with trading’. (Activity Sheet 6). Students can also work on 3 digit addition with trading by completing the problems from the worksheet ‘Adding with 3 digits’ (activity sheet 7).


Lesson 5
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Subtraction With Trading
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.

Students complete ‘Subtraction with trading. (Activity Sheet 8). Students can also work on 3 digit subtracting with trading by completing the problems from the worksheet ‘Subtracting with 3 digits’ (activity sheet 9 ).


Lesson 6
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Addition and Subtraction With Trading Problems
Discuss addition word problems with students. For example ‘There were 122 oranges on one tree and 37 on another tree. How many oranges were there altogether?’. Ask students for their ideas of how to solve the problem. Complete this problem and others as a whole class activity. Model and revise with students various strategies they can use to solve such problems.
Students then work independently on problems from Activity sheet 10, “Addition Word Problems/Subtraction Word Problems”. Repeat lesson with subtraction word problems.

As an additional activity, students are given an activity called “Word Problem Mix-up” (activity sheet 11). This activity requires students to complete the missing addition and subtraction number and word problems, then cut them into cards. Students can use cards to play ‘Concentration’ or ‘Snap’.

Another alternate activity is “What Went Wrong?”. Students are shown a number of completed subtraction problems with a consistent error eg subtracting the smaller number in a column from the larger number. Students correct the calculations and describe the error that was made. Students plan how to teach a person who made this mistake a correct method for obtaining solutions.