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Investigating chains of numbers.
Analysing and explaining complex patterns, and patterns within patterns.
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| Resources |
Vocabulary |
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At least 15 strips of 2 cm squared paper cut into strips of 4
Felt tips
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double, doubling, halve, halving, add 1, odd, even, 4times table, multiples of 4, pattern, exception to the pattern, reverse, inverse, opposite, going backwards |
| Organisation |
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Near achievement pairs to work on sets of four numbers. Higher numbers will go to the more confident pairs
Pairs will need strips of 2 cm squared paper marked with the four numbers for display later
Plan your use of the board to accommodate the table of results from 1 to 60 and space to jot down key words
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| Whole Class Preparation: (about 10 mins) |
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On the board, draw a caterpillar with a head and several segments.
Write 18 in the caterpillar’s head.
Explain the rules. If the number is even, you halve it. If the number is odd, you add 1, until you reach 1.
Demonstrate the rule until you get to 1, for example, 18, 9, 10, 5, 6, 3, 4, 2,1.
Will 10 make a longer or shorter caterpillar? Ask a child to try it on the board.
Will 6 make a longer or shorter caterpillar? Ask a child to try it on the board.
Why are these shorter?
Let’s try 9, will it be longer or shorter than 10? Ask a child to try it on the board.
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| Paired Work: (about 15 mins) |
Give each pair four consecutive numbers to work on starting from 1: give one pair 1-4, another pair 5-8, the next pair 9-12, and so on.
Give out the strips of squared paper. Record your caterpillars on these paper strips with felt tips, to use as display later. Keep some blank strips spare for children who make mistakes.
Ask the children to think about the following questions and make notes. Write the questions on the board:
– Why are some caterpillars longer than others?
– What do you notice about the numbers for the shorter caterpillars?
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| Class Sharing: (about 15 mins) |
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Display the 2 cm squared strips in order on the board, from 1 to 60.
What do you notice? Ask identified pairs to share their ideas, such as odd and even numbers, or patterns within groups of four. Record their ideas on the board.
Which were the shorter and longer caterpillar numbers?
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| Paired Work: (about 15 mins) |
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In your pairs, find out which caterpillars from the whole list are longer and why.
What do you notice about the shorter caterpillar numbers?
What is the link between the shorter caterpillar numbers and the longer caterpillar numbers?
Test your ideas with a larger number that is not on the whole class list.
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| Class Sharing: (about 15 mins) |
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Ask pairs to share ideas and record as many as possible on the board.
What was special about the numbers of the shorter caterpillars? They contain all even numbers except for 1.
How do we describe these numbers? Not just even, not just multiples of 4.
Introduce cognitive conflict, for example, What about 12?
What do we call that pattern? Doubles, doubling pattern, times 2.
How could we write 4 using 2s? 2 x 2. How long is the 4 caterpillar?
What about the other doubles? 16 = 2 x 2 x 2 x 2. Why is the length 5?
What is special about the pattern of number in the longer caterpillars? Odd-even-odd-even pattern. How can we make longer caterpillars?
What was the relationship between the longer and shorter caterpillars?
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