The Strategy Strut

Activities One and Two

For these activities, students are exploring strategies for adding and subtracting 2- and 3-digit numbers.
The activities encourage the students to use a variety of mental strategies to solve addition and subtraction problems and to think about which is the best strategy for solving a particular problem.
The best strategy for any problem depends on:
1. The numbers involved. Some numbers lend themselves to certain strategies more readily than others. For example, for question 1a, because 99 is so close to 100, Hamish’s rounding and Erin’s tidy number strategies seem much easier to work with than Sui’s number line (100 + 50 or 100 + 47 seems easier or quicker than 99 + 1 + 40 + 8). In Activity Two, using Taufa’s strategy of changing subtraction to addition also depends on the numbers involved. For example, for 103 – 99 =  it’s easy to go 99 +  = 100, 99 + 1 = 100, 100 + 3 = 103, so 99 + (1 + 3) = 103 and 99 + 4 = 103. So 103 – 99 = 4. But for 103 – 28 = , changing to addition isn’t so efficient.
2. The student’s preferences. Students tend to use the strategy or strategies they feel
comfortable with, as the students in the students’ book have. But it’s very important that you don’t just accept any strategy that the students use. You should encourage the students to look for and use the most efficient strategy for the problem.
The purpose of these activities is to give students experience with different strategies and see what’s most useful for a particular problem. As a student’s number sense develops, they will be able to more quickly see which are the most efficient strategies to use. Students need to be flexible enough to change the strategy they use according to the problem.
In rounding and compensation, numbers are rounded to the nearest tidy number like 10, 20, 100, or 150 and then added. The answer is adjusted according to whether the numbers were rounded up or down.
In number lines, jumps are made along a number line to a tidy number (for example, 30) and then to other tidy numbers, such as multiples of 10, and then a small jump is made to finish if necessary.
The jumps are then added (or subtracted) to find the answer. After the students get used to using number lines on paper, they should be able to visualise (or image) them to solve problems.
In the place value strategy, numbers are broken into place value parts (tens and ones), each part is then added, and adjustments (renaming) through part–whole methods (for example, 7 is seen as 8 – 1) are made.
Tidy numbers relate to part–whole thinking, in which numbers are broken into parts so that tidy numbers are made.
Activity One gives the students four number strategies and asks them to use each strategy to solve the two problems in question 1. Encourage the students to record each strategy as they use it because many may just slip back to using the strategy they are most comfortable with.
Before the students look at the strategies given in the activity, you could give them the problem that the students on the page are working on and have them brainstorm various strategies. Ask the students to name the strategy they suggest. The students could then go on to look at the strategies given on the page in the students’ book.
After using the strategies, the students are asked to decide which strategy they found the “best”.
The students’ choices of the best strategy will vary depending on their knowledge of strategies and their recall of basic facts and part–whole thinking. Be aware that some students may revert to using written forms that are not asked for.
There are many different contexts that you can use for this type of question to give your students the opportunity to practise choosing and using various strategies.
Activity Two approaches subtraction in a similar way. Strategies offered in the examples include number lines, tidy numbers, place value, part–whole, and a new strategy: converting subtraction to addition.
Many students may not have realised that subtraction problems can be solved by using the opposite operation (addition). This may be their first introduction to this idea, and some students may have difficulty grasping the concept. Work through Taufa’s strategy with them and help them apply it to one of the problems in question 1a.

Further discussion and investigation

As an extension, the students could use the same strategies to apply to 4- and 5-digit addition. For example, using a rounding and compensation strategy:
2 643 + 1 298 =
2 643 + 7 = 2 650
1 298 + 2 = 1 300
2 650 + 1 300 = 3 950
3 950 – 7 – 2 = 3 941.
Have them make a table of all the different strategies that can be used for addition and subtraction and then see if some strategies are better for some types of numbers. For example, numbers close to a 10, such as 19 and 32, might be best suited to a tidy number strategy, large numbers might be suited to a rounding and compensation strategy, and all numbers might be suited to a place value strategy.

Answers to Activities

Activity One
1. The strategies should be similar to the ones below.
a. 99 + 48 = 147

Hamish: Round 99 up 1 to 100.
Round 48 up 2 to 50.
100 + 50 = 150
Take off 3 = 147.

Taufa: 90 + 40 = 130
9 + 8 is 9 + 9 – 1 = 17
130 + 17= 147

Erin: 99 + 1 = 100
48 – 1 = 47
100 + 47 = 147

b. 238 + 598 = 834. The strategies should be similar to the ones below.

Sui:

Hamish: Round 238 up 2 to 240.
Round 596 up 4 to 600.
240 + 600 = 840
840 – 6 = 834
 

Taufa: 200 + 500 = 700
30 + 90 = 120
8 + 8 – 2 = 14
700 + 120 + 14 = 834
 

Erin: Take 4 from 238 to make
596 + 4 = 600.
234 + 600 = 834
 

2. Answers will vary. The best strategy for each problem will depend on the numbers involved  in the problem and which strategy or strategies you feel most comfortable using.
3. Preferred strategies will vary (see comment in 2 above). The answers are:
a. 73
b. 93
c. 84
d. 176
e. 180
f. 54
Activity Two
1. a. i. 51 – 19 = 32. The strategies should be similar to the ones below.
Hamish: 51 – 10 = 41
41 – 1 = 40
40 – 8 = 32
Sui:

Erin: 51 – 20 = 31
31 + 1 = 32
Taufa: 19 +  = 51
19 + 1 = 20
20 + 30 = 50
50 + 1 = 51
1 + 30 + 1 = 32
 

ii. 74 – 37 = 37. The strategies should be similar to the following:
Hamish: 74 – 30 = 44
44 – 4 = 40
40 – 3 = 37

Erin: 74 – 40 = 34
34 + 3 = 37
Taufa: 37 +  = 74
37 + 3 = 40
40 + 30 = 70
70 + 4 = 74
3 + 30 + 4 = 37
b. Answers will vary. (See comment for Activity One, question 2.)
2. Preferred strategies will vary. The answers are:
a. 25
b. 22
c. 37
d. 45
e. 37
f. 38
g. 38
h. 64
i. 106
j. 135
k. 75
l. 68