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Multiplication and Division 21 Patterns and Algebra 26

Explore patterns and algebra through investigations on creating equivalent multiplication and division number sentences. Practice problem-solving scenarios and reflect on simplification techniques.

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Multiplication and Division 21 Patterns and Algebra 26

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  1. 144 12 = ÷ Factors of 12: 1, 12, 2, 6, 4, 3 Factors of 144: 1, 144, 2, 3, 4, 6, 12 144 4 = 25 + 11 = 36 ÷ ÷ 12 4 = 3 100 + 44 ÷ ÷ 144 12 = 36 3 = 12 ÷ 144 4 3 = 144 12 ÷ ÷ Multiplication and Division 21 Patterns and Algebra 26

  2. 16 x 4 = ? Multiply by 2 16 x 4 = 32 x 2 = 64 Divide by 2 Multiplication and Division 21 Patterns and Algebra 26

  3. Investigation: Use cards to create a division number sentence. Create an equivalent division number sentence by dividing both numbers by a common factor. Check that the number sentences are equivalent by performing the 2 divisions. Reflection: How can we simplify division by creating equivalent divisions by dividing by a common factor? Problem Solving 256 ÷ 8 has the same value as: 256 ÷ 4 64 ÷ 8 64 ÷ 4 64 ÷ 2 Multiplication and Division 21 Patterns and Algebra 26

  4. Investigation: • Problem Solving • Three of these calculations give the same value. • Which one gives a different value? • 244 × 2 • 122 × 4 • 61 x 8 • 366 x 1 Use cards to create a multiplication number sentence. Create an equivalent multiplication number sentence by dividing one number and multiplying the other number by the same number. Check that the number sentences are equivalent by performing the 2 multiplications. Reflection: How can we create equivalent multiplications by dividing and multiplying by a factor? Problem Solving Complete the missing number sentence: 62 x 16 =___ x 8 Problem Solving 23 x 8 has the same value as: 23 x 4 23 x 16 46 x 4 46 x 16 Multiplication and Division 21 Patterns and Algebra 26

  5. Multiplication and Division 21 Patterns and Algebra 26

  6. Investigation: Sit with a friend. Construct a rectangle using square centimetres. Work out the rectangle’s area. Halve the length of one dimension while doubling the length of the other dimension. Work out the new rectangle’s area. Discuss why the area remained the same. Reflection: How can we create shapes with equivalent areas by dividing one dimension and multiplying the other dimensions by a factor? Multiplication and Division 21 Patterns and Algebra 26

  7. Investigation: Sit with a friend. Create areas of hectares in shapes other than squares by halving the length of one dimension while doubling the length of the other dimension. For example, a square hectare is 100 m by 100m. If we halve 1 dimension and double the other dimension, we get 50 m by 200 m. Does this shape still have the area of a hectare? Why? Reflection: How can we create shapes with equivalent areas by dividing one dimension and multiplying the other dimensions by a factor? Multiplication and Division 21 Patterns and Algebra 26

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