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(National Numeracy Strategy) (Based on DFES Lesson plans)

Properties of and reasoning about number 1. (National Numeracy Strategy) (Based on DFES Lesson plans). Resources. Whiteboards and pen OHP calculator Set of calculators. Vocabulary. multiple factor divisible by. Learning Objective.

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(National Numeracy Strategy) (Based on DFES Lesson plans)

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  1. Properties of and reasoning about number 1 (National Numeracy Strategy) (Based on DFES Lesson plans)

  2. Resources • Whiteboards and pen • OHP calculator • Set of calculators

  3. Vocabulary • multiple • factor • divisible by

  4. Learning Objective • Use tests of divisibility and factors of numbers to inform and check division calculations.

  5. Mental Learning Task • 1 347  2 • 2196  5 • 22 211  3 Each of these division calculations will have a remainder. Is this true or false?

  6. Mental Learning Task • 1 347  2 • 2196  5 • 22 211  3 For A: 1347 is an odd number, so 1347 is not divisible by 2.

  7. Mental Learning Task • 1 347  2 • 2196  5 • 22 211  3 For B: 2196 does not end in a 5 or a 0, so 2196 is not divisible by 5.

  8. Mental Learning Task • 1 347  2 • 2196  5 • 22 211  3 The digits sum to 8 and as 8 is not divisible by 3, so 22211 is not divisible by 3.

  9. Mental Learning Task • 1 347  2 • 2196  5 • 22 211  3 Use a calculator to confirm these slides.

  10. Helpful Reminder A number that divides into another number without a remainder is called a factor.

  11. By the end of the lesson children should be able to • Use tests of divisibility and factors of numbers to inform and check division calculations.

  12. Key idea • Any odd number cannot be divisible by an even number. • A number is divisible by 3 if the digits sum to a number that is divisible by 3. • A number is divisible by 4 if its last 2-digit number is divisible by 4. • If the number 24 divides into a number all factors of 24 will divide into that number.

  13. Main Learning Task • Give out the calculators. • Check this sum: 156  12 = 13 • This means 12 is a factor of 156

  14. Main Learning Task • Is 3 a factor of 156? • As the digits of 156 add up to 12, and 12 is divisible by 3, 156 is divisible by 5. • Check this using a calculator.

  15. Main Learning Task • What are the factors of 12? • This means which numbers divide exactly into 12. • The factors are 1, 2, 3,4, 6 and 12.

  16. Main Learning Task • We know the factors of 12 are 1, 2, 3, 4, 6, and 12. • Which of these factors do we know will divide exactly into 156? • Check these with your calculators.

  17. Main Learning Task 198 18 = 11 • List the factors of 18 on your whiteboards. • Which of these factors also divide into 198?

  18. Main Learning Task What do you notice about all the numbers you can see?

  19. Main Learning Task All the 2- digit numbers can be divided by 4.

  20. Main Learning Task If you know this, the rest of the number must be divisible by 4, no matter how big it is!

  21. Main Learning Task • Think of a 2-digit number that is divisible by 4. 34579

  22. Main Learning Task Put your two digit number on the end of this number. Divide the seven digit number by 4 using the calculator. 34579

  23. Main Learning Task • Four is a factor of this number. • Is 4 a factor of any number where four is the factor of the last two digits? 34579

  24. Plenary • 4 441  8 • 11 105  15 • 26 416  4 • Do any of these division calculations leave a remainder?

  25. Plenary • 4 441  8 • 11 105  15 • 26 416  4 • For D: Any number divisible by 8 must be even. As 4441 is odd, it will not be divisible by 8.

  26. Plenary • 4 441  8 • 11 105  15 • 26 416  4 • For E: The factors of 15 are 1, 3, 5 and 15. If 11 1105 is divisible by 15, it must be divisible by all factors of 15.

  27. Plenary • 4 441  8 • 11 105  15 • 26 416  4 • Is 11 105 divisible by 3? • Establish that 11 105 is not divisible by 3 because the digits do not sum to a multiple of 3, so 15 is not a factor of 11 105.

  28. Plenary • 4 441  8 • 11 105  15 • 26 416  4 • For F: Are the last two digits of this number (16) divisible by 4?

  29. Plenary • As all numbers are even, the numbers must be divisible by 2.

  30. Plenary • Add up the digits. As these sums are divisible by 3, they are in the 3 times table.

  31. Plenary • As these numbers have the factors of 2 and 3, they are divisible by 6.

  32. Key idea • Any odd number cannot be divisible by an even number. • A number is divisible by 3 if the digits sum to a number that is divisible by 3. • A number is divisible by 4 if its last 2-digit number is divisible by 4. • If the number 24 divides into a number all factors of 24 will divide into that number.

  33. Children should now be able to…. • Use tests of divisibility and factors of numbers to inform and check division calculations. Click here to go back to the start of the show

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