Creating a Transition CCSSM Unit Example of a unit on expressions and equations SVMI

Think in Terms of Units Phil Daro has suggested that it is not the lesson or activity, but rather the unit that is the “optimal grain-size for the learning of mathematics”. Hence that was the starting point for our Scope and Sequence. Developers of High School: Patrick Callahan, Dick Stanley, David Foster, Brad Findell, Phil Daro, and Marge Cappo

New K-12 Math Curriculum Inspired by The Common Core State Standards The Gates Foundation and the Pearson Foundation are funding a large scale project to create a system of courses to support the ELA and Mathematics CCSS. These will be a modular, electronic curriculum spanning all grade levels. A Santa Cruz based company, Learning In Motion, is working to write the lessons.

Middle School Curriculum

Expression and Equations A Mathematical Big Idea Expression and Equations 3x – 5 -2x + 7 = y

The Big Idea of the Unit The seventh grade unit “Expressions and Equations” addresses the mathematical concepts of variables, expressions and equations. Students learn that variables can represent unknown quantities. An algebraic expression is a generalization of number(s), operation(s) and/or variable(s) that represents one or more quantities. An algebraic equation is a statement that indicates two expressions are equal. Students represent real situations or mathematical relationships with expressions and equations. Students solve equations using mathematical methods such as, guess and check, using tables, graphs, deductive reasoning, and algebraic methods. Student use properties of operations to change expressions and equations into different forms. They model real life situations with expressions and equations. Algebraic methods of solving equations are learned and applied to everyday and mathematical situations.

Unit of Study Around a Big Idea Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days Math Talks

Unit of Study Around a Big Idea We are Here Unit of Study Around a Big Idea Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days Math Talks

Unit of Study Around a Big Idea Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days We are Here Math Talks

MATH TALKS

Math Talks Math Talks are used to: • A daily ritual with the entire class for the purpose of developing conceptual understanding of and efficiency with numbers, operations and other mathematics such as geometry and algebra. (no more than 10 minutes per day) Math Talks are used to: • Support active student engagement through signaling • Review and practice procedures and concepts • Introduce a concept before diving into the lesson of the day • Support students in deepening their understanding of the Properties of Arithmetic and our Place Value System • Explore mathematical connections and relationships • Encourage students to construct viable arguments and critique the reasoning of others • Support students in using precise mathematical language in sharing their different strategies and approaches

Math Talk If the lime and cherries are single digits, what are their values?

Math Talk If the grape is a single digit, what values could the grape be?

Math Talk If the plum and orange are single digits What are their values?

Unit of Study Around a Big Idea We are Here Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days Math Talks

Problems of the Month A program to foster school-wide participation in math and problem solving.

CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

How are the POM be used? The POM are used school wide to promote problem solving. Each problem is divided into five levels, A-E, to meet the learning development needs of all students. A great tool for Differentiated Instruction. Students, teachers and parents learn to ask questions and persevere in solving non-routine problems. The whole school celebrates doing mathematics at school.

It’s better to solve one problem five different ways than to solve five different problems. George Polya

“A problem is not a problem if you can solve it in 24 hours.” George Polya

Creating a Poster Your concluding thoughts on an explanation poster for a level you feel you have completed AND Your current thoughts on a status poster for a level you are still exploring.

Explanation Poster: The focus of your poster should be on how your findings can be justified mathematically and how your findings make sense. Include words and visuals (such as drawings) as a part of your justification. Status Poster: The focus of your poster should be on your processes so far and where you think you want to go next and/or questions/wonderings you have about this level. Include words and visuals as a part of your justification. *Remember to justify or explain your processes you have used so far and why they make mathematical sense as clearly as you can.

Gallery Walk Each group will display their poster. Each group selects a group member to be the docent to answer questions or provide clarifications/explanations. The other group members examines, explores, reviews the other groups’ posters. There will be time for your group to re-assemble and discuss the information shared in the groups’ posters. Please mind gallery walk norms and be respectful of the work and information shared. Share the organizing schemes in a gallery walk (whole group gallery walk – 10 minutes) Whole group reflecting on findings from gallery walk (whole group – 8 minutes)

Unit of Study Around a Big Idea We are Here Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days Math Talks

Writing Algebraic Expressions Area of rectangle = _ _ _ _ _ _ _ _ _ _ _ _

Writing Algebraic Expressions Perimeter of rectangle = _ _ _ _ _ _ _ _ _ _ _ _

Writing Algebraic Expressions Which two expressions are equivalent?

Which Equations Describe The Story? A pencil costs $2 less than a notebook. A pen costs 3 times as much as a pencil. The pen costs $9 Which of the four equations opposite describe this story? Let x represent the cost of notebook.

Writing Equations To Describe A Story? Write an equation for Story 1 (S-1). Let x represent the number you are trying to find. (Solo, Partner, Class)

Writing Equations To Describe A Story? Write equations for Stories 2-6 (S-2S-6). Let x represent the number you are trying to find. Individual Think Time Partner Talk

Matching Stories and Equations Work together to match each story with an equation. Be sure to check to see whether any of the equations you and your partner have written down “match” the equations on the cards.

Sharing Matched Stories and Equations Docent/Data Collector Protocol Before we begin sharing our work, have one partner write down the agreed upon matches on the dry/erase board. Docent (Remains) Data Collectors (Visits) Discuss, revise, edit, and extend your mathematical thinking to create a Presentation Poster.

Matching Stories and Equations (Class)

Showing Steps to Solving Equations Material Management Divide your construction paper into four quadrants. Glue cards E1 to E4 on the front of your poster Glue cards E5 and E6 on the back of your poster

Showing Steps to Solving Equations Matching “E1-E4” with “Steps to Solving” Select the steps needed to solve each of the equation cards E1-E4. Write a description of the process involved for each step in solving; e.g., “divide both sides by 2” or “add 6 to both sides”. Do this for each step in the solving process. If you find that there is more than one method for solving an equation, glue the two solutions side-by-side in the appropriate quadrant. Write an explanation to show how you arrived at the equation match to your story situation.

Showing Steps to Solving Equations Once you’ve finished matching E1-E4, begin showing the steps and justifications for E5 and E6. Write a description of the process involved for each step in solving; e.g., “divide both sides by 2” or “add 6 to both sides”. Do this for each step in the solving process. If you find that there is more than one method for solving an equation, glue the two solutions side-by-side in the appropriate quadrant. Write an explanation to show how you arrived at the equation match to your story situation.

Follow-Up Lesson Original pre-assessment, “Express Yourself” Carefully look over your original work. Please write about what you have learned since you did this task. “Express Yourself (Re-visited)” Please use what you have learned to answer these questions.

Unit of Study Around a Big Idea We are Here Unit of Study Around a Big Idea Pre- assessment MARS Task Instruction Final Assessment POM or Expert Investigation CC FAL 1 day 2 days 5 - 10 days Math Talks

Apprentice Task

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