To look at strategies for generating numbers using multiplication and addition.
To explore systematic ways of organising numerical data.
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Resources |
Vocabulary |
Sixteen slips of paper with four numbers on each (see teachers’ notesheet). One of the numbers should be impossible with one stroke
A3 paper
Thick felt tips
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multiply, times, lots of,product, add on, addition,going back, subtraction, going further, further, greater, more, shorter, nearer, distance, possible, impossible, brackets, ordered lists, arranging |
Organisation |
Near ability pairs on mixed ability tables
Pre-prepared enlarged slips of paper for each pair
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Whole Class Preparation: (about 10 mins) |
What games do you know that involve bats or clubs? Tennis, cricket, golf...
What affects how far the ball with go? Focus on the relationship between the strength of hit, the type of club and the distance travelled.
Introduce the idea of a simple mathematical golf game. On the board, list the numbers of the different types of club 2, 4, 6, 8, 10. On the board, list the strength of the hit 1/2, 1, 3, 5, 7.
Explain that the overall distance is a multiplicative relationship; the type of club multiplied by the strength of the hit. Club 2, strength 3 = 2 x 3: distance is 6.
What is the greatest distance possible in one hit? What is the least?
How could we get a ball to travel 13? 2 x 5 then 6 x 1/2. Are there any other ways? 2 x 7 then back 2 x 1/2. Repeat with a different distance,
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Paired Work: (about 15 mins) |
Give each pair three or four distances to work out on a slip of paper.
Numbers worked on by different pairs should overlap, in order to check accuracy.
Find more than one way to get each distance.
In pairs, choose one of your distances and record your strokes onto the A3 paper. Children may decide to use brackets at this point.
You may need to remind children to record the type of bat first
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Class Sharing: (about 15 mins) |
Ask pairs to explain their calculations. Two or three pairs to demonstrate them for one-stroke distances, and another two of three pairs to demonstrate them for two-stroke distances.
Focus attention on common strategies and record them (‘the largest number to the target’, ‘looking for easy numbers’, ‘going through the times table’, ‘trial and improvement’).
How can you find all the 'easy numbers’ (those that can be made with one stroke)?
Why are brackets useful? Move from informal bracketing to formal pairs.
Set the scene for a second round. How can we make sure that we have discovered all of the one-hit numbers?
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Paired Work: (about 15 mins) |
Distribute Ask pairs to find the distances between 1 and 100 that can be covered with two hits. They will need first to clarify their way of recording the 'easy numbers' – those that can be made with one calculation, systematically.
Explain the strategy you’re using.
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Class Sharing: (about 15 mins) |
Children first share their system of recording all 'easy numbers'. They should realise that they have listed the numbers in order either by weights or by hits. Pupils with grids or tree diagrams should explain their methods.
What patterns are there in the grid? They should notice the diagonal increase and explain it. Share the ways that listing the easy numbers helps find the 'difficult numbers' between 1 and 100.
Extensions: Are there any distances impossible to reach with two strokes? Why? How do we find these systematically between 1 and 100? What are the least and most useful weights, and least and most useful hit strengths?
How is this activity similar to finding coin or stamp
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