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Repeated Addition Partial Products used to combine groups of the same size Symbols: x,, ( ) Each student in Ms. Bonnie’s class needs 6 sheets of colored paper for their art project. There are 28 students in Ms. Bonnie’s class. How many colored sheets of paper will she need in all? 28 +28 168 28 x 6 = 20 x 6 =120 8 x 6 = 48 120+48 = 168 Open Array Arrays are rectangular pictures of equal groups; of factors and the multiple 5x4=20 4x5=20 Factor: 5 Factor: 4 multiple or product Square Numbers: numbers that can be made into a square array; a multiplied double 4x4=16 Prime Numbers: A number that only has 1 and itself as factors; makes only one kind of array 1x7=7 OR 20 +20 120 6 +6 48=168 + 208 612048 120+48 = 168 multiple: the number you count by factor: a number that you multiply with

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For teacher-talk related to each strategy, see other charts 1764 4 x 5 = 20- 20 156 4 x 25 = 100 - 100 56 4 x 10 = 40- 40 16 4 x 4 = 16- 16 44 1764 176 = 160 + 16 160 = 4 x 4 x 10 16 = 4 x 4 Maria has 176 stickers to give away to each of her 4 cousins. How many will each cousin get? How many each? How many equal groups? OR Answers 2 types of questions: Partial Quotients “small groups at a time” 4 8 12 16 20 24 28 32 36 40 80 120 160 200 240 280 320 360 400 44 Quotient Distributive Division “break it into friendly numbers” 4 different math symbols 176 ÷ 4 = or 176 / 4 or 4 176 or 176 4 used to separate a total into equal groups = another name for the solution Divisor = the factor you divide by Dividend = the factor you divide up Are the extras… things? parts of a whole?

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1764given problem 1764 This is our thinking line. We think it through on one side and record our thinking on the other. Let’s record that this way… If I subtract out that 20 we found, we are left with 156. What can I multiply by 4 to get close to 156? 4 x 5 = 20- 20 156 4 x 25 is 100. Let’s record that this way… If I subtract out that 100 we found, we are left with 56. What can I multiply by 4 to get close to 56? 4 x 25 = 100 We don’t know how many sets of 4 will fit in 176, so will have to keep breaking up into chunks we know. What is one multiple of 4 we know?. - 100 56 4 x 10 is 40. Let’s record that this way… If I subtract out that 40 we found, we are left with 16. What can I multiply by 4 to get close to 16? 4 x 10 = 40- 40 16 4 x 4 is 16. Let’s record that this way… If I subtract out that 16 we found, we are left with 0. 4 x5 is 20. Since we finished breaking up our number into groups of 4, all that is left is to record how many groups we found. What is 5+25+10+4? 4 x 4 = 16- 16 44

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176 = 160 + 16 16 = 4 x 4 16 0= 4 x 4 x 10 1764given problem This is our thinking line. We think it through on one side and record our thinking on the other. Since none of our numbers are close to 176 yet, let’s multiply all these multiples by 10 and generate another list of friendly numbers. Can anyone see a way we could combine 2 or more of these numbers to compose 176? We don’t know how many sets of 4 will fit in 176, but we can use multiples of 4 to help us identify friendly numbers that compose 176. First let’s list multiples of 4. 160+16=176 or 120+40+16= 176 or 120+36+20= 176 Let’s record all of those ideas with arrows this way. Now let’s take one of those solutions and identify how many groups of 4 were in each friendly number…. Since 4x10 is 40 and 40+4 is 44, our solution is 44 because we found 44 equals groups of 4 in our friendly numbers. 1764 4 8 12 16 20 24 28 32 36 40 80 120 160 200 240 280 320 360 400 44

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