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Session 1: The Meaning of Multiplication and Division. Jennifer Suh jsuh4@gmu.edu July 23 – 25, 2015 Chicago Institute. https://www.youtube.com/watch?v=aU4pyiB-kq0. What comes in these sets?. Introductions (Name tent) What is your name ? Grade you teach? Chat with your neighbor-
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Session 1: The Meaning of Multiplication and Division Jennifer Suh jsuh4@gmu.edu July 23 – 25, 2015 Chicago Institute https://www.youtube.com/watch?v=aU4pyiB-kq0
What comes in these sets? Introductions (Name tent) What is your name? Grade you teach? Chat with your neighbor- Where are you from? What do you do there? Finding setsWork in your teams to find at least one interesting things that come in these sets.
Dr. Jennifer Suh Jennifer M. Suh, PhD, jsuh4@gmu.edu Associate Professor, Mathematics Education George Mason University Interests: Developing students’ mathematics proficiency & teachers' mathematics knowledge through Lesson Study and representational fluency through mathematics tools and emerging technologies Highlight of my summer: Spending the summer with my boys (Two sons) mom who traveled here with me. Will head to the beach in 3 weeks
SETS by NUMBERSWhat comes in these sets? Like Scategory-add only new ideas to the category for points or to generate many examples
How to play: Players take turns rolling a number cube After each roll, a player decides which column to place the digit. That player then adds the value to his/her total. The player who is closest to the target (in the last total) without going over the target wins. Adapted from Fundamentals, Creative Publications, 4-5
Choose 1 to discuss with a partner • How might you use this game in your mathematics classroom? • How might you modify this game for your students? • What would you look for while your students played the game?
Other versions… Target 1 --> tenths, hundredths Target 10 --> tenths, ones Target 1,000 --> hundreds, tens Target 10,000 --> thousands, hundreds But can we still use tools?
Putting Essential Understanding of Multiplication and Division into Practice The way in which you teach a foundational concept or skill has an impact on the way in which students will interact with and learn later related content. For example, the types of representations that you include in your introduction of multiplication and division are the ones that your students will use to evaluate other representations and ideas in later grades.
About the Institute… 1. Explore the meaning of multiplication/division 1. Examine problem solving situations of multiplication/division 2. Apply the properties of multiplication and division 3. Establish the concepts of multi-digit computation 4. Identify strategies for developing mental computation 4. Revisit approaches to basic facts
Principles to Action Think-Pair-Share • Take a look at the 8 practices. • Consider which practice is easiest for you to implement in your classroom. • Consider which practice is most challenging for you to implement. We will circle back to these practices throughout the institute.
Write a multiplication or division word problem that has the solution 24 golf balls.
With a partner… 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.
Let’s look back at the problems we wrote.Which problem solving structure does your problem represent?
What might our results tell us about problem solving structures in our classrooms?
Using “KEY” words The clown gave my little brother 7 red balloons and some green balloons. Altogether my brother got 13 balloons. How many green balloons did he get? Clement, L. and Bernhard, J. (2005) “A Problem-Solving Alternative to Using Key Words” Mathematics Teaching in the Middle School, March 2005, 10-7 p. 360, NCTM
Using “KEY” words The clown gave my little brother 7 red balloons and some green balloons. Altogether my brother got 13 balloons. How many green balloons did he get? Elliott ran 6 times as far as Andrew. Elliott ran 4 miles. How far did Andrew run? Clement, L. and Bernhard, J. (2005) “A Problem-Solving Alternative to Using Key Words” Mathematics Teaching in the Middle School, March 2005, 10-7 p. 360, NCTM
Using “KEY” words The clown gave my little brother 7 red balloons and some green balloons. Altogether my brother got 13 balloons. How many green balloons did he get? Elliott ran 6 times as far as Andrew. Elliott ran 4 miles. How far did Andrew run? How many legs do 6 elephants have? Clement, L. and Bernhard, J. (2005) “A Problem-Solving Alternative to Using Key Words” Mathematics Teaching in the Middle School, March 2005, 10-7 p. 360, NCTM
The reason many of us have used a key word or a steps approach to teaching problem solving is that we have not had any alternative instructional strategies!
K-W-S for Problem Solving The store has 13 cans of tennis balls on the shelf. Each can has 3 balls in it. How many tennis balls does the store have?
More on this later… Understanding through Context, Connection, and Children’s Literature
Think to yourself… Which representation of 4 x 6 do you think is “best”? Why? 6 + 6 + 6 + 6 C A B E D
Let’s start with multiplication • What can multiplication look like?
What might it look like? Each chocolate chip cookie had 6 chocolate chips. The mouse ate 4 cookies. How many chocolate chips did he eat?
So • Multiplication can describe equal groups. • 6 x 4 would tell the total number of chocolate chips • 9 x 4 would tell the total number in 9 groups of 4 penguins.
What might it look like? Sammy ate 6 crayons during each of his first 4 classes. How many crayons did Sammy eat?
So multiplication… • Can also describe repeated addition. • For example, 6 x 4 would mean 4 + 4 + 4 + 4 + 4 + 4.
Number Line Jumps • Each jump is a whole number amount. • All jumps are equal length. • What number could [?] to be? • What number could [?] not be? 0 [?]
What Might It Look Like? 24 ants went off on their own. They were marching in rows and columns. How many ants were in a row? How many were in a column? How do you know?
What might it look like? In class, the worms built rectangles with exactly 24 color tiles. What might the length and width of their rectangles have been?
