MULTIPLICATION AND DIVISION PROBLEM SOLVING Nick Meyer and

MULTIPLICATION AND DIVISION PROBLEM SOLVING Nick Meyer and Kathy Jones, District Elementary Math Coaches October 26, 2017

Overview 3 Examine multiplication and division problem types 1 4 2 Model concrete and pictorial representations 3 Investigate progression across grade levels Understand how parents can help

4 Multiplication and Division § Review the problem-solving cards. § Sort the cards by the type of problem they represent. § Arrange them according to the grid on the next slide.

Multiplication and Division Structure 5 Unknown Product Equal Groups Area/Arrays Compare Size of Group Unknown Number of Groups Unknown (How many in each (How many groups? ) group? )

6 Multiplication and Division Structure Unknown Product Equal Groups There are A bags with B plums in each bag. How many plums are there in all? Area/Arrays Compare Size of Group Unknown Number of Groups (How many in each Unknown (How many group? ) groups? ) If C plums are shared If C plums are to be equally into B bags, then packed B to a bag, how many plums will be then how many bags in each bag? are needed?

Multiplication and Division Structure 7 Equal Groups Area/Arrays Compare Unknown Product Size of Group Number of Groups Unknown (How many in each group? ) groups? ) There are A bags with B plums in each bag. How many plums are there in all? If C plums are shared If C plums are to be packed equally into B bags, then B to a bag, then how many plums will be in bags are needed? each bag? There are A rows of apples with B apples in each row. How many apples are there? If C apples are arranged into A equal rows, how many apples will be in each row? If C apples are arranged into equal rows of B apples, how many rows will there be?

Multiplication and Division Structure 8 Unknown Product Equal Groups Area/Arrays Compare There are A bags with B plums in each bag. How many plums are there in all? There are A rows of apples with B apples in each row. How many apples are there? A blue hat costs $B. A red hat costs A times as much as the blue hat. How much does the red hat cost? Size of Group Number of Groups Unknown (How many Unknown in each group? ) (How many groups? ) If C plums are shared equally into B bags, then how many plums will be in each bag? If C apples are arranged into A equal rows, how many apples will be in each row? A red hat costs $C and that is A times as much as a blue hat costs. How much does a blue hat cost? If C plums are to be packed B to a bag, then how many bags are needed? If C apples are arranged into equal rows of B apples, how many rows will there be? A red hat costs $C and a blue hat costs $B. How many times as much does the red hat cost as the blue hat?

Structure 9 Number of Groups x Size of Group = Product Nx. S=P

10 Division Read Problems A and B. (next slide) Make a math drawing for each problem. Write a number sentence. How are these problems similar and different?

Division 11 Problem A Rick puts 12 tennis balls into cans. Each can has 3 tennis balls. How many cans does Rick use? Problem B Rick puts 12 tennis balls equally into 3 cans. How many balls will be in each can?

12 Continuum of Representations

13 Fact Strategies Ms. Booker has 18 stickers in her sticker book. She puts 3 stickers on each page. How many pages will she use?

14 If I had 8 boxes of peaches with 6 peaches in each box, how many peaches would I have? Fact Strategies

15 Fact Strategies I have 6 bags of books with 7 books in each bag. How many books do I have?

16 Fact Strategies

17 23 x 8

18 23 x 18 184 +230 414

19 “Long” Division Bailey’s Bakery donated 596 cupcakes to the school bake sale. They packaged them in groups of 4. How many packages of cupcakes did they donate?

20 Much larger numbers… Michael has a collection of 1, 404 sports cards. He hopes to sell the collection in packs of 36 cards and make $633. 75 when all the packs are sold. If each pack is priced the same, how much should Michael charge per pack?

21 Much smaller numbers… Joanne has 2 ½ oranges. She wants to give 1/3 of an orange to each of her friends on the soccer team. How many of her friends can get 1/3 of an orange? How much of an orange will Joanne have left over?

22 How can you help? u Ask your student about his/her math drawing. u Where does each quantity appear? u Ask your student about his/her method for multiplying and dividing. u How do they decide to break the numbers into manageable parts?

questions and answers 23 ? We are happy to answer any questions.