5th Grade Problem Solving with

8 Mathematical Practices

Laura ChamblessSt. Clair RESA Consultant

www.protopage.com/lchambess

Pre & Post Teacher Survey

Complete the left side “Before Attending

Mathematical Practices Workshop”

Write Your Own Story Problem

1. Think of a story problem you would use with your students.

2. Write it down on a 3x5 card.3. Place the card under your name

tag.

Learning Target

I can integrate the Mathematical Practices in my teaching to develop deeper mathematical knowledge within my students.

8 Mathematical Practices

www.protopage.com/lchambless

From: Teaching Children Mathematics, March 2012, Getting Started in K – Grade 2, pg. 440-445.

CCSS for Mathematical Practice Student-friendly Language

Make sense and persevere in solving problems.

I don’t mind trying many times to understand and solve a math problem.

Reason abstractly and quantitatively. I can think about the math problem in my head, first.

Construct viable arguments and critique the reasoning of others.

I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies too.

Model with mathematics. I can use pictures, objects, math symbols, and numbers to show how to solve a problem.

Use appropriate tools strategically.

I can choose the best math tool like calculators, rulers, pictures, or objects to solve the problem.

Attend to precision. I can check to see if my strategy and calculations are correct. I use clear mathematical language.

Look for and make use of structure.

I can use what I already know about math to solve the problem.

Look for and express regularity in repeated reasoning.

I can use different strategies or find a pattern from a similar problem to solve a new math problem.

8 Mathematical Practices Posters

http://departments.jordandistrict.org/curriculum/mathematics/elementary/CCSSM6/SMPposters.pdf

Solve and Discuss Structure

• Some children go to board and solve a problem

• Other children solve the problem at their desk.

• Teacher asks two children at the board to explain their method.

Solve and Discuss Structure

The explaining student:• Relates solution to a math drawing• Asks if there are any questions• Responds to the questionsThe listening student:• Asks questions • Suggests edits to the explanation or

solution

Solve and Discuss Structure

• The Solve and Discuss Structure is actually a Solve, Explain, Question, and Justify structure

• Aspire to make your classroom a place where all children listen to understand each other, not just being quiet while someone else is talking.

Content Focus

5.NF.65.OA.6 Standard:Solve real world problems involving

multiplication of fractions and mixed numbers

How Does MP Look in ActionYour Story Problem

Liz put 2/5 of her money in the bank and spent ½ of the remainder. If she had $30 left, how much money did Liz have at first? Write an equation.

3 min. by yourself15 min. with a small group (2 or 3)Report out 2 min per group

Mathematical Practice Rubric

3 min. Review Rubric (from: Institute for Advanced Study)

http://www.ocf.berkeley.edu/~mimiyang/misc/rubric.pdf

Pair Share1. Look at Math Practice #1 and #22. Discuss where your story problem fell

on the rubric.3. Group Discussion

Remodeling Tasks

Original ProblemLiz had $100. She put 2/5 in the bank and spends ½

of what is left. How much did she spend? Write an equation.

How did I make it more intellectually challenging?

*** Review Level of Cognitive Demand Handout

Analysis of My TaskPart 1: Selecting and Setting up a Mathematical TaskGoals: 5.NF. 6 StandardSolve real world problems involving multiplication of fractions

All Task Answers: $100 should see different representations

Representations Used: array drawings, fraction bars, comparison bars, …

Record and Report work: Independently- 5 min. using whiteboardSmall Group– 5 to 15 min. - adding to each students whiteboardWhole Group Report: 2 min.

Analysis of My TaskPart 2: Supporting Students’ Exploration of the TaskQuestions to help get started:1. Can you tell me what is happening in the story?2. Is there another ways can write the equation?3. Can you make a list of all the steps needed to solve the

problem?4. What representation are you thinking about using?5. Which operation do you think you need to use?6. What are you being asked to find?7. How can you break apart the problem?

Look at Common Errors pg. 126 to help think of questions.

Analysis of My TaskPart 3: Sharing and Discussing the TaskWhat solution paths do you want shared during class

discussion?*How many steps are in the problem, *Where to start in the

problem,*Once you knew how much she spent, how did you figure out the missing 2/5s?

Looking for different strategies and representations.Mathematical Ideas: fractions broken into equal partsExpand on, debate, and question the solutionsSolve and Discuss: (Solve-Explain-Question it- Justify it)EvidenceQuestions to build mathematical ideas connectionsWhy did you start where you did? Did anyone else start there?Can anyone retell what that group just said?How are _____’s pictures same/different than ____’s pictures?

Your Story Problem

1. Get into groups of 4.2. Everyone reads their story problem

they wrote at beginning of session.3. The group chooses one to remodel.4. Each person fills in the Remodeling

a Mathematical Task sheet while group is collaborating.

5. Groups will give a 2 min. report to class.

2 Minute ReportRequirements

• Original Problem• Remodeled Problem• Mathematical Practice- refer to rubric• Part 1: Setting up the mathematical

task• Part 2: Questions to supporting

students’ during task• Part 3: Questions to use during class

discussion

Setting Up Norms

What Norms do we need to have in place?

Problem Solving withBar Diagrams

1. Understand: Identify what is known and what is unknown. Draw the bar diagram to promote comprehension and demonstrates understanding. (Situation vs. Solution Equation)

2. Plan: Decide how you will solve the problem (find the unknown). Analyze the bar diagram to find a solution plan.

3. Solve: Execute the plan. Use the bar diagram to solve.

4. Evaluate: Assess reasonableness using estimation or substitution. Substitute the solution for the unknown in the bar diagram.

Bar Diagrams

Watch Introduction Videohttp://www.mhschool.com/math/common/pd_video/mathconnects_bardiagram_p1/index.html http://www.mhschool.com/math/common/pd_video/mathconnects_bardiagram_p2/index.html

Thinking Blocks

http://www.mathplayground.com/thinkingblocks.html

Explore the site

When done exploring go to my Protopage and look at your grade level math tab.

Other Resources

Check out my Protopage for content websites. How will you use the 8

Mathematical Practices with them?

www.protopage.com/lchambless

Learning Target

I can integrate the Mathematical Practices in my teaching to develop deeper mathematical knowledge within my students.

Exit Ticket

On the back of your name tent write:

What is your take-away from today’s session?

Pre & Post Teacher Survey

Complete the right side“After Attending Mathematical

Practices Workshop”&

Post Event Questions

Thanks for another great session

Laura