(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 Use tests of divisibility and factors of numbers to inform and check division calculations.

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

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

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

Mental Learning Task 1 347  2 2196  5 22 211  3 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.

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

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

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.

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.

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

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.

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.

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.

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

All these numbers are divisible by 4 Main Learning Task All these numbers are divisible by 4 124 128 264 304 144 1 000 024 312 636 484 23 446 344 What do you notice about all the numbers you can see?

All these numbers are divisible by 4 Main Learning Task All these numbers are divisible by 4 124 128 264 304 144 1 000 024 312 636 484 23 446 344 All the 2- digit numbers can be divided by 4.

All these numbers are divisible by 4 Main Learning Task All these numbers are divisible by 4 124 128 264 304 144 1 000 024 312 636 484 23 446 344 If you know this, the rest of the number must be divisible by 4, no matter how big it is!

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

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

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

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

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.

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.

Plenary 4 441  8 11 105  15 26 416  4 Is 11 105 divisible by 3? 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.

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

All these numbers are divisible by 6 Plenary All these numbers are divisible by 6 624 102 456 2 448 216 270 As all numbers are even, the numbers must be divisible by 2.

All these numbers are divisible by 6 Plenary All these numbers are divisible by 6 624 102 456 2 448 216 270 Add up the digits. As these sums are divisible by 3, they are in the 3 times table.

All these numbers are divisible by 6 Plenary All these numbers are divisible by 6 624 102 456 2 448 216 270 As these numbers have the factors of 2 and 3, they are divisible by 6.

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.

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