math workshop 2009

Mary WalterElementary SchoolMath Workshop

by Beth Buchholz & Kateri Thunder

Our Purpose

To help students become stronger learners and mathematicians by thinking deeply and flexibly about authentic problems that make connections across the curriculum

Why a Math Workshop?

Predictable yet flexible structure

Time for students to work and revise

Sharing with community of learners

Deeper thinking

Agenda

A Math Task: The Neighborhood Problem Things to Consider When Choosing a

Task Plan a Math Task Throughout - Sharing Student Work

Alex revises his work multiple timesTo learn alternate strategies from his peers as students share during lessons over multiple days focused on revision

Alex struggles to communicate

The problem:

The Chicago Bulls starting

line-up jogs out onto the court.

Harper, Pippen, Rodman,

Longley, and Jordan each slap

high fives to each other

player. How many high-fives are given in all?

Alex Draft #1

Revision after group share

Alex Draft #2

Revision after focused conversation

Alex Draft #3

Making math connections

The NEW problem:

“Groups of campers are going to island. On the first day two people went over and one decided it was to cold and came back. One the second day, four went over and two came back. On the third day six went over to the island and three camp back. If this pattern continues, how many people would be on the island at the end of seven days?”

Applying strategy in new context

Third draft of previous problem

First draft of NEW

problem

Our Math Workshop

Read Talk Think Write Share Revise

The Neighborhood Problem Our Plan

The original task from Investigations

The REVISED task

Task 1: Building a Neighborhood

You are an architect. The city of Charlottesville is planning a new neighborhood. The city planners want to have space for exactly 60 families. The city of Charlottesville wants all the buildings to be the same size. You have been asked to find all the possible designs for the neighborhood.

Task 1: Building a Neighborhood Use the multi-link cubes to help you find all the

possible ways to create housing for 60 families. Only one family can fit in each cube. You may stack cubes on top of each other to make tall apartment buildings. Remember, for each possible design each apartment building must be the same height. The design must hold exactly 60 families. How can you make sure that you have found all the possible ways? The city of Charlottesville wants a report of ALL the possible solutions at their next meeting. You should record each design in your notebook using words, pictures, and numbers.

Task 2: Make a recommendation

The city planners now want your recommendation for the best possible design of the neighborhood. Remember, each building must be exactly the same height. Which building size do you think is the best? You should use the grid of the neighborhood to create your design. One box on the grid is the size of one multi-link cube. Don’t forget to include all the things besides buildings that a neighborhood needs.

Design considerations:

Below are some suggestions from the families that will be living in the neighborhood:

Cindy Gola “I am a mom. I have a large family and I want my

children to have lots of room to ride their bikes, play baseball, and go swimming.”

Dwight Smith “I want to have my own backyard where my dog can

run around.” Jessica Hardy

“I want to live next to a large park with lots of trees so I can go hiking and mountain biking.”

Task 3: Write a persuasive speech

After you design your neighborhood, you need to write a speech justifying your design to the Charlottesville city council. They will want to know why you chose the buildings size and locations. Also, they will look at how well your neighborhood will work for the families that will be moving in.

Task 4: Revising

When we observe, talk, and learn about other’s ideas it can help us rethink and revise our own ideas to make them even better.

A few things I’d like to revise about my neighborhood:

Beth’s Class & the Neighborhood ProblemHere’s what Beth’s class did.

Lyndsey uses pictures and words

Anand uses multiplication

Anand noticed that you can “reverse” the numbers

Anand’s recommendation

Anand’s design and map key

Eric uses addition & multiplication

Eric notices a pattern

Eric organized his findings using a chart based on “opposites”

Eric writes to explain his choices

Isaac’s design and map key

Isaac explains his choices

Isaac revises his design

Choosing a Math Task

How does this problem challenge students on various levels?

How might the authentic context engage and motivate students in deep problem-solving?

What mathematics concepts and skills do students engage in through this problem?

How does this problem connect to concepts and skills across the curriculum (reading, writing, oral language, social studies, science, etc.)?

What questions could you ask to extend the problem for students who finish early?

How does this task fit into your pacing guide? SOLs?

Henry revises his quarterly math prompt

To clearly and efficiently communicate his strategy after peer feedback and self assessment based on a rubric

Henry’s first draft

Henry uses rubric to assess work

“How do you know, or how will

others know, if you have

done quality math

thinking and recording on

this problem?”

Peer & Self Feedback

Henry revises based on rubric

Draft #1

Draft #2

Your Turn

Work for 30 minutes (Individually or with partners).

Share with the whole group for 30 minutes.

Find one problem and develop a plan.

You might revise the problem. Consider the planning

questions we explored through the Neighborhood Problem.

To clarify his thinking and to make connections between concepts in response to his peers’ and his own thinking

Jeremy revises and continues his thinking about odd & even numbers

Jeremy’s Writing in October

Jeremy’s Writing in November

Jeremy’s Writing in November

Jeremy’s Writing in February

October

February

Jeremy’s Writing in February