Think of a number Multiply it by 3

Think of a number. Multiply it by 3. Add 12. Multiply by 2. Divide by 6. Subtract your original number. Your answer is 4.

Multiplication v. Break Apart Method v. Area Model v. Bowtie Method

Break Apart Method 17 x 8 Step 1: Break apart the larger factor into expanded form 17 = 10 + 7 Step 2: Multiply both parts of 17 (10 & 7) by our other factor - - 8 17 x 8 = (10 x 8) + (7 x 8) 17 x 8 = 80 + 56 17 x 8 = 136

Here’s a Visual… 17 10 x 8 7 x 8 8

Area Model Step 1: Draw a rectangle to represent your equation. 24 x 13 24 13

Step 2: Break each factor in the equation into expanded form. 24 x 13 20 + 4 10 + 3

Step 3: Label your array with each factor in expanded form. 20 10 3 4

Step 4: Solve the area for each array that we created by breaking apart the factors. 20 10 20 x 10 = 200 3 3 x 20 = 60 4 10 x 4 = 40 3 x 4 = 12

Step 5: Add each product together to find the total area of the rectangle. 200 + 60 + 40 + 12 = 312 24 x 13 = 312

Bowtie Method is a great strategy to break a double by double digit multiplication equation into four simpler equations. 36 x 52

Step 1: Break apart both factors into expanded form. 36 x 52 30 + 6 50 + 2

Step 2: Write the expanded form of the numbers across from each other. 36 52 30 50 6 2

Step 3: Create a bowtie design to figure out your four multiplication equations. Then, solve each equation and add the products together. 30 50 30 x 2 = 60 50 x 6 = 300 30 x 50 = 1, 500 6 x 2 = 12 6 2 1, 500 300 60 12 1, 872

Division v. Hangman Division v. Long Division

Hangman Division Another name for Hangman Division is Partial Quotients. To find the quotient, we look at the numbers as a whole and use what we know to solve the equation one part at a time. 165 ÷ 3

165 ÷ 3 3 165

Step 1: Since we don’t know exactly how many times 3 can go into 165, we are going to start with something we do know. I know that 3 x 20 = 60. That will get me part way there. 3 165 60 105 ct of u d o y pr act 60 m t e Ig btr Once eed to su to reach n d 60, I 65. I nee t 60, how 1 ’m a t to get I from r a so f e lef v a h 165, do I h c u m tal? my to 20

. t a e Rep 3 165 60 20 105 60 20 45 45 0 15

he t f o all de d i d s a e , h ly Last s along t amount l or fact the tota o into t g to ge es 3 can 3 m i t f o 165. 55 165 60 20 105 60 20 45 45 15 0 55