Using Tape Diagrams Multiplicative Structures- Comparison Problems Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success Thursday February 5, 2015 4:30 – 7:30

Learning Intentions and Success Criteria We are learning to: Understand how to represent comparison problems involving multiplication with tape diagrams. Make explicit the connections between tape diagrams and symbols and equations. Success Criteria We will be successful when we can solve multiplicative comparison problems using tape diagrams.

High-leverage Teaching Practice #3 Use and Connect Mathematical Representations Verbal: Use language (words) to interpret, state, define, or describe mathematical ideas. Contextual: Situate mathematical ideas in everyday, real-world, imaginary, or mathematical situations and contexts. Physical: Use concrete objects to show, study, act upon, or manipulate mathematical ideas (e.g., cubes, counters, paper strips). Symbolic: Record or work with mathematical ideas using numerals, variables, tables, and other symbols. Visual: Illustrate, show, or work with mathematical ideas using diagrams, pictures, number lines, graphs, and other math drawings.

Multiplication Standards On your white boards, each person at your table should Explain the expectation of a standard in your own words. Provide a visual representation of what students are expected to know. Represent and solve problems using multiplication and division 3.OA.1 3.OA.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic 3.OA.8 Use the four operations with whole numbers to solve problems. 4.OA.1 4.OA.2 4.OA.3 Table Discussion: How do you see a progression of knowledge and skills developing across these standards?

Multiplication and Division Situations Compare A blue hat costs $6. The red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example: A rubber band is 6 cm long. How long is the rubber band when it is stretched 3 times as long? A red hat costs $18 and that is 3 times as much as the blue hat. How much does the blue hat cost? Measurement example: A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example: A rubber band was 6 cm long at first. Now it is stretched to 18 cm long. How many times as long is the rubber band now as it was before? a x b = ? a x ? = p and P ÷ a = ? ? x b = p and P ÷ b = ?

The Comparison Model Multiplication & Division larger quantity ÷ smaller quantity = multiple smaller quantity x multiple = larger quantity larger quantity ÷ multiple = smaller quantity

Sean’s weight is 40 kg. He is 4 times as heavy as his younger cousin Louis. What is Louis’ weight in kilograms?

There are tulips, daisies, and daffodils growing in the garden There are tulips, daisies, and daffodils growing in the garden. There are 2 times as many daisies as tulips and 3 times as many daffodils as tulips. If there are 12 daisies, how many flowers are in the garden?

The school librarian, Mr The school librarian, Mr. Marker, knows the library has 1400 books, but wants to reorganize how the books are displayed on the shelves. Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that the library has four times as many fiction books as resource books and half as many nonfiction books as fiction books. If these are the only types of books in the library, how many of each type of book are in the library? Gr6 M4 L 29

The measure of an angle is 2/3 the measure of its supplement The measure of an angle is 2/3 the measure of its supplement. Find the measure of the angle. Angle Supplement 180 ENY Gr7 M6 L4

The measure of an angle is 2/3 the measure of its supplement The measure of an angle is 2/3 the measure of its supplement. Find the measure of the angle. Angle Supplement 180 ENY Gr7 M6 L4

Stop and Jot Work with a shoulder partner. Jot down the talk moves that were used to help discuss the Comparison Tape Diagrams. Write a brief description describing the reason the talk move was used.

Learning Intentions and Success Criteria We are learning to: Understand how to represent comparison problems involving multiplication with tape diagrams. Make explicit the connections between tape diagrams and symbols and equations. Success Criteria We will be successful when we can solve multiplicative comparison problems using tape diagrams.

Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.