Integrating the Mathematical Practices in

Problem SolvingGrades 1 - 4

Monica HartmanAugust 28 and 29, 2012

Port Huron Back to School Professional Development

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.

Pre & Post Teacher Survey

Complete the left side “Before Attending

Mathematical Practices Workshop”

Learning Target

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

8 Mathematical Practices

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

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.

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 #3 and #62. Discuss what a classroom might look

like where the teacher is using these practices during instruction.

Implementing the Standards of Mathematical Practice

In the Gum and Pretzel problem, we will focus of Mathematical Practices 3 and 6.

MP3 – Construct viable arguments and critique the reasoning of others.

MP6 – Attend to precision

Review the Mathematics Classroom Visitation Recording Form

Content Focus

1.OA and 2.OA Cluster Statements: Represent and solve problems

involving addition and subtraction2.OA.3 Standard:Determine whether a group of objects

has an odd or even number of members; write an equation to express an even number as a sum of equal addends.

Content Focus

3.OA Cluster Statement: Solve problems involving the four

operations, and identify and explain patterns in arithmetic.

4.OA Cluster Statement: Use the four operations with whole

numbers to solve problems.

The Gum and Pretzel Problem

Mark has 30 cents in his pocket and he wants to spend it all and not have any

change left in his pocket.

What can he buy for 30 cents?What different choices does he have? Why?

big pretzel 7¢gum 2¢

The Gum and Pretzel Problem

What can he buy for 30 cents?What different choices does he have? Why?

big pretzel 7¢gum 2¢

Work independently (2-3 minutes) Share your strategies with your partner

and with your group Each group should be ready to explain

their method for solving this problem.

Sharing Strategies

Remember, 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

Sean’s Numbers

What mathematical practices do you observe in this video of a third grade class discussing odd and even numbers after doing the Gum and Pretzel problem?

Video and Supporting Documents found at http://deepblue.lib.umich.edu/handle/2027.42/65013

Remodeling Tasks • Tasks can be remodeled to make them

more intellectually challenging.• Look at the problem you wrote at the

beginning of the session• Does it fit into one of the categories from

Table 1, Common addition and subtraction situations?

• Look at Remodeling Tasks in Mathematics Classroom Handout.

• Use one of the suggestions listed, or another one, to remodel your task.

Remodeling Tasks • Get into groups of 4.• Rewrite your original problem to

make it more challenging, if needed• Share your original problem and

revision with your group.• The group chooses one to remodel

using the two page, Remodeling a Mathematical Task handout.

• Groups will give a 2 minute 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

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

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

Monica