Multiplicative Strategies progression, 4th step
The purpose of the activity
In this activity, the learners develop mental strategies for solving multiplication problems with single-digit multipliers. Sticky notes are used to demonstrate strategies.
The teaching points
There are a variety of mental strategies available for solving multiplication problems. These include:
using tidy numbers with compensation (6 x 37 can be solved as (6 x 40) – (6 x 3))
place value partitioning (6 x 37 can be solved as (6 x 30) + (6 x 7))
deriving from known facts (8 x 25 = 200 because 4 x 25 = 100 is known and 2 x (4 x 25) = 200)
using equivalent expressions (8 x 25 = 200 because 4 x 50 = 200; 9 x 15 = 135 because 3 x 45 = 135).
Different problems lend themselves to different strategies. Competent learners have a range of strategies and choose the most appropriate in a given situation.
It is not intended that you name and ‘teach’ a range of strategies. This activity is designed to encourage the learners to explore and share strategies in order to increase their range.
Using materials to demonstrate strategies helps develop understanding.
Discuss some examples of everyday situations where the learners may need to use different strategies.
The guided teaching and learning sequence
1. Use sticky notes to show six groups of 37 on the board and ask the learners to think of a way to find the total.
2. Ask the learners to share their strategies. If the strategies only include using a calculator or algorithm, ask the learners if they can think of any other ways. Model the strategies used on the board with sticky notes.
Possible strategies include:
a) Adding 3 to each group of 37 to make 6 forties. That makes 240. Take away the 6 threes (18). That makes 222. (Using tidy numbers with compensation.)
b) Six thirties are 180. Six sevens are 42. 180 and 42 are 222. (Place value partitioning.)
c) Using the algorithm. Ask the learners who use an algorithm to model it on the board and check their understanding of the underpinning place value ideas.
For example, if they say 6 times 7 equals 42, carry the 4, 6 times 3 equals 18, add the 4, etc. check they understand that the 4 is actually 4 tens or 40, that 6 times 3 is actually 6 times 30 and equals 180, etc.
3. Use sticky notes to show 8 groups of 25 on the board and ask the learners to think of a way to find the total.
4. Ask the learners to share their strategies. Again, if strategies only include using a calculator or algorithm, ask the learners if they can think of any other ways. Model the strategy they use on the board with the sticky notes. (If they use strategies that have already been demonstrated, encourage them to think of further strategies.)
Possible strategies include:
a) “I know 4 groups of 25 makes 100 so 8 groups of 25 must be twice that. The total is 200.”
b) “Eight groups of 25 are the same as 4 groups of 50 because 2 lots of 25 are 50.”
c) Using the algorithm: ask the learners who use an algorithm to model it on the board and check their understanding of the underpinning place value ideas.
Write further problems on the board, for example, 5 x 68, 4 x 97, 9 x 44, 3 x 99, 7 x 26. Have the learners work in pairs and ask them to share their strategies for solving each problem. If they are unable to understand the strategy their partner uses, ask the partner to demonstrate it with the sticky notes.
When the learners appear comfortable with sharing and understanding strategies without using sticky notes, challenge them by introducing larger numbers, for example, 5 x 999, 7 x 306, 4 x 275, 8 x 179.
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