3.OA.3 Multiplication and Division Strategies Arrays and Drawings

Group size unknown - Array If 18 apples are arranged into 3 equal groups. How many apples will be in each group? 6 apples in each of the 3 equal groups

Number of Groups unknown - Array I have 28 pieces of gum for my friends. Each friend gets 4 pieces. How many friends do I have? 7 friends It is important here for students to see the array in a table with columns and rows. However, the vocabulary of columns and rows is not important. It is also important to see the array in pictures. This word problem depicts that the number of groups is unknown.

Unknown Product - Array What multiplication problem is represented by the drawing below? 4 x 5 = 20 And/ or 5 x 4 = 20

Product Unknown– Area Model Array I have 18 packs of markers. Each pack has 4 markers in it. How many markers do I have in total? 10 + 8 4 72 total markers 40 32 Since students do not have the traditional algorithm as a strategy yet. An area model array can be used. Students can actually see the area grid of 10 x 4 which is 40 plus 8 x 4 which is 32. From there they can see the total area or 18 x 4 = 72 markers.

True or False My friend multiplied these two numbers. Below is their reasoning. Are they correct? If not, what advice do you have for this student? 18 x 6 = 116 10 + 8 6 60 56 Have student analyze and explain the “friend’s” reasoning or thought process. Perhaps have student discuss with a partner, they can use paper or a white board to describe their thinking. They are not correct. 18 x 6 = 108 10 x 6 = 60 8 x 6 = 48 not 56, that is the mistake.

Write a word problem represented by the drawing We are looking for students to know how to create a word problem based on an array. A teacher could ask for some student to create a product unknown word problem, a group unknown word problem and the number of groups unknown word problem. Examples, Product unknown = I have 4 pairs of socks. How many socks do I have in total? 8 socks Group Unknown = If 8 socks are shared equally among 4 siblings. How many socks does each sibling get? 2 socks Number of groups unknown = If 8 socks are paired together then how many people will get a pair of socks? 4 socks

Division - Area Model Array Group Size unknown If you have 48 inches of ribbon cut into 6 pieces, how long will each piece measure? 48 inches of Ribbon 6 pieces 3 X 6 = 18 5 X 6 = 30 8 inches These are new strategies. Teacher must help facilitate the division problem here. What is the question asking? How can we think about this? If we divide 6 by 48 how long will the pieces be?

Division – Array Number of groups unknown If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Use a drawing or array to solve. Be prepared to share your answer and explain. Let students try on their own. They can use a drawing to divide the fruit or a division area model array.

Division – Array Number of groups unknown Same Problem - If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Can you explain this drawing? Is it correct? Is there anything missing? The answer is missing. 14 bags needed

Division – Array Number of groups unknown Same Problem - If 56 pieces of fruit are to be packed 4 to a bag. How many bags will be needed? Can you explain this array? Is it correct? Is there anything missing? The answer is not indicated. Explain the 10 + 4 to get 14 bags needed

Given the array write a word problem 72 buttons 8 buttons

Given the array write a word problem How many shirts can I make if a shirt requires 8 buttons and I have a total of 72 buttons? 9 shirts 72 buttons 4 x 8 buttons 5 x 8 buttons 8 buttons 32 buttons 40 buttons