Here are a 4cm by 6cm rectangle, a 12cm by 2 cm rectangle, and a 3cm by 8cm rectangle. What’s the same? What’s different? What’s the same, what’s different?

These are both 4cm by 6cm rectangles. What’s the same? What’s different? What’s the same, what’s different?

6cm 3.8cm 10cm 2cm 2.3 cm Each of these rectangles is 3cm by 8cm 8 × 3 ≡ 6 × × 3

Draw pictures to represent that A.16 × 6 ≡ 10 × × 6 B.16 × 6 ≡ 12.5 × × 6 C.16 × 6 ≡ 20 × 6 – 4 × 6 D.16 × 6 ≡ 16 × × 4 E.16 × 6 ≡ ☐ × 3 F.16 × 6 ≡ ☐ × 4 Representing multiplication

A.15 × × 9 ≡  × 9 B.  × × 8 ≡ 17 × 8 C.17 ×  –  × 5 ≡ 12 × 6 D.11 × 4.3 –  × 4.3 ≡ 5 ×  E.21 ×  –  ≡ 20 × 19 F.3.6 ×  + 7 ×  ≡ 36 G.15 × 9 +  × 18 ≡ 21 × 9 H.7 ×  +  × 6 ≡ 21 × 12 Representing multiplication

A.47 × 8 ≡ 47 × × 3 B.52 × 9 ≡ 30 × × × 9 C.87 × 8 ≡ 87 × × 5.7 D.100 × 6 – 7 × 6 ≡ 93 × 6 E.49 × 7 ≡ 50 × 7 – 7 F.60 × × 13 ≡ 73 × 8 True or False? ✓ ✗ ✓ ✓ ✓ ✓

A.47 × 8 ≡ 47 × × 3 So 47 × (5 + 3) ≡ 47 × × 3 B.52 × 9 ≡ 30 × × × 9 So ( ) × 9 ≡ 30 × × × 9 C.100 × 6 – 7 × 6 ≡ 93 × × 6 – 7 × 6 ≡ (100 – 7) × 6 The Distributive Law of Multiplication

We say that “multiplication is distributive over addition and subtraction”. A × B + A × C ≡ A × (B + C) A × (B – C) ≡ P × (Q + R – S) ≡ The Distributive Law of Multiplication

51 × × 14 ≡ 51 × × 72 – 6 × 72 ≡ 72 × × × 11 – 58 × 5 ≡ 58 × × × 9.2 ≡ 6.3 × ( ) 12 × 26 – 4 × 13 ≡ 13 × (24 – 4) 6.2 × × 4 ≡ 4 × ( ) True or False? ✗ ✓ ✓ ✗ ✗ ✗

“Division is distributive over addition and subtraction”. Can you give a “number sentence” as an example of this? Can you give a “symbol sentence” as an example of this? Is your “symbol sentence” always, sometimes or never true? Convince yourself. Convince me! Agree or Challenge?