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Understanding ‘inverse’ as the mathematical word meaning to reverse.
Finding missing digits by using place value relationships in addition and subtraction number sentences.
Developing a feel for the size of numbers, leading to an understanding of maximum or minimum values.
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| Resources |
Vocabulary |
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Calculators
Digit Detective notesheet enlarged to A3 – one per pair
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ones, tens, hundreds, digit, figure, numeral, inverse, opposite,
number, place value, position, value
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| Organisation |
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Near ability pairs on mixed ability tables
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| Whole class Preparation: (about 5-10 mins) |
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What is the difference between a digit and a number?
Write 12 + ? = 19 on the board. Explain that the ? is a missing digit between 0 and 9. How will you find the missing digit?
Share ideas as a class:
‘counting on in 1s, 2s’ ‘just knew’ ‘subtracting 12 from 19’ (why?) ‘because 2 + 7 = 9’ Write ??? + 150 = 257 and ? + 8 = ?4 on the board.
Try these with your partner.
Jot down how you worked these out.
Share strategies for working these out, as a class.
As a last question, ask Where did people start and why?
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| Paired Work and Sharing: (about 10 mins) |
Give out the top half of notesheet with questions 1, 2 and 3. Work in pairs on these questions.
Make notes of the questions that you asked yourselves and how you worked the puzzles out.
Focus on the strategy and not the specific details of the calculation.
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| Class sharing: (about 10-15 mins) |
Now let’s share your results. Why is it that you couldn’t find the digits in question 1?
What about Question 2? How many solutions did you find? Get answers from a variety of pairs.
How could we check that we haven’t missed any solutions out?
For question 3, invite children to share ideas arising from both examples.
Start with a pair who have randomly tried digits and trial and improvement. Then ask a pair who have used previous knowledge and understanding of place value.
Collect a variety of contributions. Emphasise the usefulness of starting with the ones, then moving onto tens.
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| Paired Work: (about 10 mins) |
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Now give out the bottom half of the notesheet with Question 4.
You may use any of the digits 0-9 but each can only be used once. Each ? must represent a different digit.
Find the largest answer and explain why this is the largest and then find the smallest and explain why this is the smallest.
Pairs of children could work on either smallest or largest.
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| Class sharing: (about 10 mins) |
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How can you be sure that you have made the largest possible number? (97 + 86 or 96 + 87).
What other combinations did you try?
Why will the position of the digits effect the answer?
What about the smallest possible answer? What digits did you choose this time? 13 + 20 or 10 + 23. Why can’t zero be used in the tens position?
What ideas did you use to help you solve the puzzles?
Share solutions and strategies for ?? x ?? and discuss maximum and minimum values.
Here it makes a difference which digit is used in the ones position – discuss why this is.
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