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Chris Clements

Properties of Number. Divisibility tests. 3’s. 6’s. Chris Clements. <date>. Learning Objective:. <Steps to success>. Divisibility Tests. In this lesson you will learn divisibility tests for multiples of 3 and 6. Divisibility tests help us

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Chris Clements

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  1. Properties of Number Divisibility tests 3’s 6’s Chris Clements

  2. <date> Learning Objective: <Steps to success>

  3. Divisibility Tests In this lesson you will learn divisibility tests for multiples of 3 and 6. Divisibility tests help us identify if a whole number is in a specified times table Today you will find out how you can test if large whole numbers are multiples of 3 and 6.

  4. Divisibility Tests for multiples of 3 Lets start by looking at the first ten multiples of 3. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 The numbers go; odd, even, odd, even but that’s not going to help us today. Can you see what happens to the sum of the 2 digit numbers. 3, 6, 9, 1+2=3, 1+5=6, 1+8=9, 2+1=3, 2+4=6, 2+7=9, 3+0=3

  5. This pattern continues; 3+3=6, 3+6=9, 3+9=1+2=3, 4+2=6, 4+5=9 The pattern goes 3, 6, 9 (all multiples of 3) So the test must be; that the sum of the digits must equal a multiple of 3 (usually 3, 6 or 9). Let’s test this with a large whole number, e.g. 23,301 2+3+3+0+1 = 9 Check on a calculator! 23,301 ÷ 3 = 7,767

  6. Divisibility test for finding large multiples of 3 is; • add up the sum of the digits • it must equal a multiple of 3 Give it a go; 157 157 171 1,932 111 2,682 1,150 262 1,150 705 262 9,993

  7. Divisibility Tests Now we will look at multiples of 6 Lets have a look at the first ten multiples of 6. 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 Notice anything? All even numbers! 6, 1+2=3, 1+8=9, 2+4=6, 3+0=3, 3+6=9, 4+2=6, 4+8=1+2, 5+4=9, 6+0=6 Just like the test for the 3’s but in a different order; 6, 3, 9…

  8. Divisibility Tests • So the test for multiples of 6 is; • is the whole number even • is the sum of digits a multiple of 3 • Give it a go, find the multiples of 6! 621 621 2, 456, 076 2,640 1, 350 31, 464 180, 330 18, 000 828 3, 535 3, 535 1,602 5,092 5,092

  9. Divisibility tests for multiples of 3 and 6 • For multiples of 3; add up the digits to see if it is a multiple of 3 (usually 3, 6 or 9) • 2) For multiples of 6; first see if it is even, then see if the sum of it’s digits is also a multiple of 3 (usually 3, 6 or 9) Divisibility tests Steps to success

  10. Activity <type here>

  11. Many answers but the lowest possible would be 210 because it is a multiple of 5 (ends in a 0) and it’s digits equal 3. Accept any number that satisfies this criteria. Plenary 3 6 9 12 15 18 21 5 10 15 20 25 30 35 Look at the two number sequences; can you say a number greater than 200 which will be in both sequences? 2 3 6 Use the 6 digit cards to make three multiples of 3. 4 5 7 More ways possible! 5 3 4 6 7 2 2 4 6 5 3 7

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