Module 3 PARTNERS for Mathematics Learning Grade 7 Partners

Fiesta Fundraiser  How many people do you think are going 2 Fiesta Fundraiser  How many people do you think are going to want hot salsa? Medium salsa? Mild salsa?  How will you decide the number of peppers and tomatoes needed? Partners for Mathematics Learning

Problem-Based Learning 3 Three-Part Format for Problem-Based Learning  Before  Get students mentally prepared  Be sure the task is understood  Establish expectations  During  Let go  Provide hints  Listen actively  Encourage testing of ideas Partners for Mathematics Learning

Fiesta Fundraiser  How many servings of each type 4 Fiesta Fundraiser  How many servings of each type of salsa did you make? What strategies did you use to determine the number of servings needed for each type of salsa?  How many peppers and tomatoes did you need for hot salsa? Medium salsa? Mild salsa? How did you determine your numbers? Partners for Mathematics Learning

Fiesta Fundraiser  Teacher thoughts as students share 5 Fiesta Fundraiser  Teacher thoughts as students share  Does the student use correct ratios and/or proportional relationships?  Can the student describe and justify their process to solve the problem?  Does the student correctly find the percentages of tomatoes and peppers in each recipe?  Does the student check for reasonableness in their number of tomatoes and peppers?  What questions would you ask students directly? Partners for Mathematics Learning

Fiesta Fundraiser  What types of ratios were 6 Fiesta Fundraiser  What types of ratios were used to solve this problem?  How would you help students transition from understanding and using ratios to understanding and using proportions? Partners for Mathematics Learning

Fiesta Fundraiser  Give examples to show how the process 7 Fiesta Fundraiser  Give examples to show how the process standards were used during this activity?  Problem-Solving  Reasoning and Proof  Communication  Connections  Representations  Which Big Idea is the focus of this activity? Partners for Mathematics Learning

Look Alike Rectangles  With a partner, group the rectangles 8 Look Alike Rectangles  With a partner, group the rectangles into three groups of three look-alikes  There will be one extra rectangle, the oddball  Compare your results within your group  Discuss how you determined your three sets Adapted from Teaching Student Centered Mathematics Grades 5-8, Van de Walle and Lovin Partners for Mathematics Learning

Look Alike Rectangles  Measure and record the side lengths 9 Look Alike Rectangles  Measure and record the side lengths of each rectangle to the nearest half centimeter  Find the ratio of the side lengths for each rectangle  Discuss the results with your partner Partners for Mathematics Learning

Look Alike Rectangles  What do you notice about the 10 Look Alike Rectangles  What do you notice about the relationship between the width and the length in each set of rectangles?  What determines if two rectangles are similar?  How does this activity help students develop an understanding of similarity? Partners for Mathematics Learning

Extended Look Alikes  Draw a first quadrant on the piece of 11 Extended Look Alikes  Draw a first quadrant on the piece of centimeter paper provided  Stack your like rectangles on the centimeter coordinate grid  Place the width of each rectangle on the y - axis and the length on the x -axis  Align the common vertex of each rectangle at the origin Partners for Mathematics Learning

Extended Look Alikes  Place a straightedge across the 12 Extended Look Alikes  Place a straightedge across the diagonals starting at the common vertex  What do you see?  Discuss your findings with your group Partners for Mathematics Learning

Look Alike Rectangles  Why is it important for students to have 13 Look Alike Rectangles  Why is it important for students to have hands-on experiences with similar figures?  Which big idea was the focus of this activity? Partners for Mathematics Learning

Monkey Mania  A video game company has asked you to 14 Monkey Mania  A video game company has asked you to design a football field for monkeys  The company has asked you to make the dimensions similar to those used in the National Football League Partners for Mathematics Learning

Monkey Mania Talk to your partner… 15 Monkey Mania Talk to your partner…  What information do you think you might need to do this task?  What mathematics do you know that will help you do the work?  What questions do you have? Partners for Mathematics Learning

Monkey Mania  What is the average height 16 Monkey Mania  What is the average height of an NFL football player?  Is there more than one way to interpret “average height”?  How did you determine the average height Partners for Mathematics Learning

Monkey Mania  Determine the number of 17 Monkey Mania  Determine the number of inches in “NFL land” equivalent to one inch in “toy monkey land”  How could you use this ratio to determine the dimensions of the Monkey Mania football field?  Compare your dimensions to others in your group. What do you notice? Partners for Mathematics Learning

Monkey Mania  What would you do to prepare 18 Monkey Mania  What would you do to prepare students before this activity?  What challenges would your students face during this activity?  How could you give clear directions and support without telling students what to do step by step?  After the activity, how will you provide all students the opportunity to share their solutions? Partners for Mathematics Learning

Reflection “It takes many varied physical experiences to 19 Reflection “It takes many varied physical experiences to develop an understanding of what a proportional relationship is…” (AIMS)  What activities do you use in your classroom to develop student learning of proportional reasoning? Partners for Mathematics Learning

Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell 20 DPI Mathematics Staff Everly Broadway, Chief Consultant Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell Carmella Fair Johannah Maynor Amy Smith Partners for Mathematics Learning is a Mathematics-Science Partnership Project funded by the NC Department of Public Instruction. Permission is granted for the use of these materials in professional development in North Carolina Partners school districts. Partners for Mathematics Learning

PML Dissemination Consultants 21 PML Dissemination Consultants Susan Allman Julia Cazin Ruafika Cobb Anna Corbett Gail Cotton Jeanette Cox Leanne Daughtry Lisa Davis Ryan Dougherty Shakila Faqih Patricia Essick Donna Godley Cara Gordon Tery Gunter Barbara Hardy Kathy Harris Julie Kolb Renee Matney Tina McSwain Marilyn Michue Amanda Northrup Kayonna Pitchford Ron Powell Susan Riddle Judith Rucker Shana Runge Yolanda Sawyer Penny Shockley Pat Sickles Nancy Teague Michelle Tucker Kaneka Turner Bob Vorbroker Jan Wessell Daniel Wicks Carol Williams Stacy Wozny Partners for Mathematics Learning

2009 Writers Partners Staff Kathy Harris Rendy King Tery Gunter 22 2009 Writers Partners Staff Kathy Harris Rendy King Tery Gunter Judy Rucker Penny Shockley Nancy Teague Jan Wessell Stacy Wozny Amanda Baucom Julie Kolb Freda Ballard, Webmaster Anita Bowman, Outside Evaluator Ana Floyd, Reviewer Meghan Griffith, Administrative Assistant Tim Hendrix, Co-PI and Higher Ed Ben Klein , Higher Education Katie Mawhinney, Co-PI and Higher Ed Wendy Rich, Reviewer Catherine Stein, Higher Education Please give appropriate credit to the Partners for Mathematics Learning project when using the materials. Jeane Joyner, Co-PI a nd Project Director Partners for Mathematics Learning

Module 3 PARTNERS for Mathematics Learning Grade 7 Partners