KDG Problem Solving with8 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.

Teaching KDG All Day

1. Make group with at least one member being a teacher that has taught all day K last year.

Three Step Interview2. Questions about teaching all day & Questions about teaching Math

Expressions3. Report out on the most important

thing you heard in your group.

Teaching KDG All Day

Review1. Time Standards for Elementary

Instruction

2. New Math Pacing Guide

3. Emphases in CCSS (where to spend your time)

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

Revised 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

Operations and Algebraic ThinkingK.OA.1 – K.OA.5

Cluster Statement: Understand addition as putting

together and adding to, and understand subtraction as taking apart and taking from.

How Does MP Look in ActionYour Story Problem

6 girls were riding their bikes. Some girls go home for lunch. How many girls were left riding bikes?

1. How many different answers can we find? Find 2 different strategies to solve the problem.

2 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 Problem (pg.261 MX book)8 girls jump rope. 6 girls go home. How

many girls are jumping rope now?

How did I make it more intellectually challenging?

**** Review the Remodeling Tasks in

Mathematics Classrooms Handout

Analysis of My TaskPart 1: Selecting and Setting up a Mathematical TaskGoals: K.OA Cluster Statement: Understand addition as putting together and adding to, and

understand subtraction as taking apart and taking from.

All Task Answers: 6-1=5, 6-2=4, 6-3=3, 6-4=2, 6-5=1,6-6=0

Representations Used: inch titles, counters, circle drawings, act out, ten frames, number titles, cm cubes, other objects

Record and Report work: Independently- 3 min. using whiteboardSmall Group– 5 to 10 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. Are we going to add or subtract? How do you know?3. Can you come up with another equation that could be

right?4. What other ways can we show the solution?5. How do you know you can’t take any more away?6. Can you draw it another way?7. Are you taking apart or taking from?8. Did you touch all the circles as you counted?

Look at Common Errors pg. 372 to help think of questions.

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

discussion?*take one away, *take two away, *take three away, *take four

away, *take five away, *take six away – everyone is homeLooking for different strategies and representations with number

titles correctly naming equations.Mathematical ideas: subtraction- largest number first. Addition

bonds, should your numbers be bigger than 6Expand on debate, and question the solutions being sharedSolve and Discuss (Solve-Explain-Question-Justify it)Questions to build mathematical ideasWhy did you start where you did?Can anyone retell what that group just said?How are _____’s pictures same/different than ____’s pitcutes?

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?

Ten Frame Video

How to use Mathematical Practices when introducing numbers.

Watch Number Talks video with Ten Frames

Let’s discuss how to use Mathematical Practices when you are introducing numbers.

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