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Writing Equations Using the Distributive Property MAFS.3.OA.2.5 Lesson Opening 1. If you combined the arrays below, what multiplication equation could represent it? 2×3 2×3 2. If the two equations below were combined, what multiplication equation could represent it? (Use square tiles to model if needed) 2 × 5 = 10 2 × 5 = 10 Lesson Opening 1. If you combined the arrays below, what multiplication equation could represent it? 2×3 2×3 2. If the two equations below were combined, what multiplication equation could represent it? (Use square tiles to model if needed) 2 × 5 = 10 2 × 5 = 10 or Yesterday, we learned… 3×2 3×2 3×4 can be broken apart Yesterday, we learned… 3×2 3×2 3×4 can be broken apart Here is how we would write it as an equation: 3 x 4 = (3 × 2) + (3 × 2) 3 x 4 = (3 x 2) + (3 x 2) Put parentheses around each multiplication array to show that it NAMES the array. Also, if we solve the equation we have to do the operation inside the parentheses first! 3 x 4 = (3 x 2) + (3 x 2) Then, put an addition sign in between the arrays to show that you ADD the products of the array to find the TOTAL product. Write the equation for this array: 4 x 5 = (4 x 2) + (4 x 3) Write the equation for this array: 4 x 5 = (4 x 2) + (4 x 3) 2 3 The 5 was decomposed into 2 and 3. Then each part was multiplied by 4. Write the equation for this array: 6 x 5 = (3 x 5) + (3 x 5) = 30 3 3 The 6 was decomposed into 3 and 3. Then each part was multiplied by 5. Here’s another way to think about it… 6 6 4 6 x 10 tens 2 This is a number bond that shows 6 decomposed into 4 and 2. 4 2 tens tens 4 x 10 2 x 10 This is a number bond that shows 6 tens decomposed into 4 tens and 2 tens. 6 x 10 = (4 x 10) + (2 x 10) Let’s try another one. 7 7x4 This is a number bond that shows 7 fours decomposed into 5 fours and 2 fours. fours 7 x 4 = (5 x 4) + (2 x 4) 5 2 fours fours 5x4 2x4 On your dry-erase board, write an equation for the following: 8 8x3 threes 8 x 3 = (5 x 3) + (3 x 3) = 24 or 8 x 3 = (4 x 3) + (4 x 3) = 24 5 3 threes threes 5x3 3x3 or 8 x 3 = (6 x 3) + (2 x 3) = 24 or 8 x 3 = (7 x 3) + (1 x 3) = 24 Use the Distributive Property to write an equation (think of a number bond or an array). 6×6 (3 × 6) + (3 × 6) = 36 (4 × 6) + (2 × 6) = 36 (5 × 6) + (1 × 6) = 36 (6 × 3) + (6 × 3) = 36 (6 × 4) + (6 × 2) = 36 (6 × 5) + (6 × 1) = 36 Use the Distributive Property to write an equation (think of a number bond or an array). 7×8 (5 × 8) + (2 × 8) = 56 (4 × 8) + (3 × 8) = 56 (6 × 8) + (1 × 8) = 56 (7 × 4) + (7 × 4) = 56 (7 × 5) + (7 × 3) = 56 (7 × 6) + (7 × 2) = 56 Your Turn • Draw the array that represents the multiplication expression. • Use two different colors to represent how you can break apart the array. • Write the equation that represents how you broke apart the array. • Don’t forget to write the product. Bonus Questions 1. The following equation represents an array broken apart into 3 smaller arrays. What is the equation for the original array? How do you know? (5 × 3) + (5 × 3) + (5 × 2) = 40 2. Can you break apart this array into 3 smaller arrays? What would the equation be? 3 × 12 Bonus Questions 1. The following equation represents an array broken apart into 3 smaller arrays. What is the equation for the original array? How do you know? rows columns rows columns rows columns (5 × 3) + (5 × 3) + (5 × 2) = 40 Since there are 5 rows in each of the arrays, I know the array has 5 rows. So then I add up all the columns. 3 + 3 + 2 = 8. So the original array is 5 × 8. 2. Can you break apart this array into 3 smaller arrays? What would the equation be? 3 × 12 Bonus Question #2 Answer Choose to decompose either the 3 or the 12. 3 × 12 3 12 12 threes threes twelves 10 1 1 twelve 1 twelve twelve (1 x 12) + (1 x 12) + (1 x 12) = 36 threes 1 three 1 three (10 x 3) + (1 x 3) + (1 x 3) = 36 4 4 threes 4 threes threes (4 x 3) + (4 x 3) + (4 x 3) = 36 Exit Ticket: Which expressions could represent the array? a) 6 × 4 b) 4 × 6 c) (6 × 4) + (6 × 4) d) (3 × 4) + (3 × 4) e) (6 × 2) + (6 × 2) f) (6 × 4) × (6 × 2)