1. Implementation 1.Review the mathematical concept. 2.Review the problem solving steps. 3.READ: Children read the part that is asking them to find something out. 4.UNDERSTAND: Children explain what they need to find out. 5.Children identify what information they will need to find it out. 6.Remove the coloured rectangle. 7.Children find the information they need to find it out. 8.CHOOSE A STRATEGY: Children identify strategies that they could use to find it out. 9.USE A STRATEGY: Children use a strategy to find it out. 10.Children record their thinking as they find it out. 11.CHECK: Children reread the part that asked them to find something out. 12.Children check that they have found it out. 13.Children check they have recorded their solution correctly. 14.Children follow the problem solving steps to solve the 2 nd level of the problem, with minimal teacher guidance. 15.Children who solve the 2 nd level, follow the problem solving steps to solve the 3 rd level of the problem independently. 16.Children use the problems as a guide to create their own problem, either alone or in pairs/small groups. 17.Children solve their own problem. Throughout the lesson, children share solution strategies. At the end of the lesson, children explain how they created their own problems.

2. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 256 ÷ 8 has the same value as: 256 ÷ 4 64 ÷ 8 64 ÷ 4 64 ÷ 2 630 ÷ 42 has the same value as: 315 ÷ 21 315 ÷ 42 630 ÷ 84 630 ÷ 21 816 ÷ 12 has the same value as: 816 ÷ 24 408 ÷ 24 408 ÷ 6 204 ÷ 2

3. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 23 x 8 has the same value as: 23 x 4 23 x 16 46 x 4 46 x 16 52 x 12 has the same value as: 52 x 24 104 x 24 26 x 6 104 x 6 71 x 18 has the same value as: 142 x 9 36 x 36 142 x 36 71 x 36

4. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 Three of these calculations give the same value. Which one gives a different value? 244 × 2 122 × 4 61 x 8 366 x 1 Three of these calculations give the same value. Which one gives a different value? 26 × 42 52 × 21 546 x 1 13 x 84 Three of these calculations give the same value. Which one gives a different value? 18 × 14 9 x 28 36 x 9 36 x 7

5. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 Complete the missing number sentence: 62 x 16 = ____ x 8 Complete the missing number sentence: 58 x 32 = 29 x ____ Complete the missing number sentence: 108 x 14 = ___x 7

6. Problem Solving Equivalent Division and Multiplication Multiplication and Division 21, Patterns and Algebra 26

7. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 Gail constructed a square with an area of 16 cm2. She constructed a new quadrilateral by halving the length of one dimension, and doubling the length of the other. What does Gail’s new quadrilateral look like? What is the area of Gail’s new quadrilateral? Gail constructed a square with an area of 30 cm2. She constructed a new quadrilateral by halving the length of one dimension, and doubling the length of the other. What does Gail’s new quadrilateral look like? What is the area of Gail’s new quadrilateral?

8. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 Toni and Marc each had some land. Marc’s land measured 500 m by 200 m. Toni’s land measured 100 m by 100 m. Both Marc and Toni said their land measured 1 hectare. Are they right? Toni and Marc each had some land. Marc’s land measured 250 m by 250 m. Toni’s land measured 1000 m by 100 m. Both Marc and Toni said their land measured 1 hectare. Are they right?

9. Problem Solving Equivalent Division and Multiplication Create your own problem! Now solve it! Multiplication and Division 21, Patterns and Algebra 26 Toni and Marc each had 1 hectare of land. Toni’s land was a square measuring 100 m by 100 m. Marc’s land was a rectangle, with one pair of opposite sides each measuring 500 m. What was the length of each of the other opposite sides of Marc’s land? Toni and Marc each had 1 hectare of land. Toni’s land was a square measuring 100 m by 100 m. Marc’s land was a rectangle, with one pair of opposite sides each measuring 250 m. What was the length of each of the other opposite sides of Marc’s land?

10. Problem Solving Equivalent Division and Multiplication Multiplication and Division 21, Patterns and Algebra 26 Carrie and Donna constructed models of the same area. Carrie’s model was 22 cm wide by 20 centimetres long. Donna’s model was half as long. What were the dimensions of Donna’s model? Carrie and Donna constructed models of the same area. Carrie’s model was 14 cm wide by 16 centimetres long. Donna’s model was half as long. What were the dimensions of Donna’s model? Create your own problem! Now solve it!