2. Multiplication and Division 13 Patterns and Algebra 18 Multiplying by 5 - additively Multiplying by 5 – multiplicatively

3. 5 x 7 = 5 + 2 5 x 5 = 25 5 x 2 = 10 25 + 10 = 35 Distributive property- distribute multiplication over addition 5 x 7 = 35 5 = of 10 10 x 7 = 70 x 70 = 35 5 x 7 = 5 x 7 = 35 Multiplication and Division 13 Patterns and Algebra 18

4. Multiplication and Division 13 Patterns and Algebra 18

5. Multiplication and Division 13 Patterns and Algebra 18 1.Select cards to make a number to multiply by 5, for example, or 2.Multiply the number by 5 using the distributive property, for example, 3.Record the product, for example, 5 x 7 = 35 5 x 57 = 285. 4.If you multiplied a single-digit number by 5, learn the multiple of 5 (table). 5.Explain to a friend how you used the distributive property to multiply the number by 5. Reflection: How can we use the distributive property to multiply by 5? Problem Solving The teacher made 5 teams of 8 children. How many children altogether? Investigation: Problem Solving The school had 5 classes of 28 children. How many children altogether?

6. Multiplication and Division 13 Patterns and Algebra 18 Dividing by 5 - additively Dividing by 5 – multiplicatively

7. 20 + 15 partition and divide by 5 35 ÷ 5 = 20 ÷ 5 = 4 15 ÷ 5 = 3 4 + 3 = 7 35 ÷ 5 = 7 ÷ 5 = fifth ÷ 5 = partition and fifth 1 5 of 35 = 20 + 15 1 5 of 20 = 4 of 15 = 3 4 + 3 = 7 1 5 of 35 = 7 1 5 1 5 Multiplication and Division 13 Patterns and Algebra 18

8. 20 + 17 partition and divide by 5 37 ÷ 5 = 20 ÷ 5 = 4 15 ÷ 5 = 3 4 + 3 = 7 35 ÷ 5 = 7 r2 ÷ 5 = fifth ÷ 5 = partition and fifth 1 5 of 37 = 20 + 17 1 5 of 20 = 4 of 15 = 3 4 + 3 = 7 1 5 of 35 = 7 r2 1 5 1 5 15 + 2 Multiplication and Division 13 Patterns and Algebra 18

9. Multiplication and Division 13 Patterns and Algebra 18

10. 1.Select cards to make a number to divide by 5 / fifth, for example, or or 2.Divide your number by 5 by partitioning it into multiples of 5 that you do know, for example, 3.Record the quotient. 4.Explain to a friend how you divided by 5 / fifthed. Reflection: How can we divide by 5 / fifth? Multiplication and Division 13 Patterns and Algebra 18 Problem Solving 45 children are divided into 5 teams. How many in each team? Problem Solving The school divided 125 children into 5 classes. How many children in each class? Investigation:

11. Multiplication and Division 13 Patterns and Algebra 18

12. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Use a calculator to multiply numbers by 5. 2.Check using the distributive property. 3.Explain your strategy to a friend. Reflection: How can we use the distributive property to multiply by 5?

13. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Use a calculator to divide numbers by 5 / fifth. 2.Check by partitioning into multiples of 5 that you know. 3.Explain your strategy to a friend. Reflection: How can we divide by 5 / fifth?

14. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Sit with a friend. 2.Each of you has 2 cards. 3.Place your cards face down and record each number’s product when multiplied by 5, on paper next to the card, for example, 4.Take turns to tell your friend what number you think is on each card, explaining using multiplication, by saying ‘I think the number on the card is 8 because 5 times 8 equals 40’. 5.If correct, you take the card. Reflection: How can we use the distributive property to multiply by 5? 25 40

15. 1.Sit with a friend. 2.Each of you has 2 cards. 3.Places your cards face down and record each number’s product when multiplied by 5 on paper next to the card, for example, 4.Take turns to tell your friend what number you think is on each card, explaining using division, by saying ‘I think the number on the card is 8 because 40 divided by 5 equals 8’. 5.If correct, you take the card. Reflection: How can we divide by 5 / fifth? Multiplication and Division 13 Patterns and Algebra 18 Investigation: 25 40

16. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Sit with a friend. 2.Lay out 5 cards in a row. 3.Take turns to secretly select cards and to name a number that, when divided by 5, gives that number as the quotient. 4.If you friend works out the quotient, they keep the card. 5.For example, you may secretly select 6 and say, ‘When I divide 30 by 5, the quotient is this number’. 6.For example, you may secretly select 4 and 1 to make 41, and say, ‘When I divide 205 by 5, the quotient is this number’. Reflection: How can we multiply and divide by 5?

17. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Sit with a friend. 2.Lay out 5 cards in a row. 3.Take turns to secretly select cards. 4.Describe the number after it has been multiplied by 5. 5.For example, you may secretly select 8 and say, ‘When my number is multiplied by 5, the product is 40’ 6.For example, you may secretly select 4 and 1 to make 41 and say, ‘When my number is multiplied by 5, the product is 205’. Reflection: How can we multiply and divide by 5?

18. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Select a card to make single-digit numbers to multiply by 5. 2.Record the multiplication number sentence. 3.Use the commutative property to record another multiplication sentence. 4.Use the inverse relationship between multiplication and division to record 2 division number sentences. 5.For example, flip 6 and record 6 x 5 = 30 and 5 x 6 = 30. Then record 30 ÷ 5 = 6 and 30 ÷ 6 = 5. Reflection: How can we multiply and divide by 5?

19. Multiplication and Division 13 Patterns and Algebra 18 Investigation: Have a multiplication by single-digit numbers array and use it to recall multiples of 5 (tables!) through properties and relationships. For example, 5 x 6 could be represented using 2 sheets of card as, for example, Reflection: How can we multiply and divide by 5?

20. Multiplication and Division 13 Patterns and Algebra 18 Investigation: 1.Flip cards one at a time and name the product when the number is multiplied by 5. 2.If you know the product when multiplied by 5 efficiently (quite quickly, without skip count), place the card in the ‘know’ pile. 3.If you do not know the product when multiplied by 5 efficiently, place the card in the ‘learn’ pile. 4.Once you have 2 cards with different numbers in the ‘learn’ pile, stop flipping cards. 5.Look at the numbers that you cannot yet multiply by 5, and use multiplicative place value to assist you to efficiently multiply the number by 5. 6.If you cannot think of any strategies yourself, ask your classmates in either a structured sharing session, or while investigating multiplying and dividing by 5. 7.Record the multiplication facts, and related division facts, for example, 6 x 5 = 30 5 x 6 = 30 30 ÷ 5 = 6 30 ÷ 5 = 3 Reflection: How can we multiply and divide by 5?