When you return from lunch

Grades 6 – 9 - Room 257 CMP Glencoe Holt Discovering Algebra

Expressions and other curricula - Room 258

Scott Foresman & Everyday Math - Room 261

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Reflecting and Connecting

Recognizing mathematical ideas and supporting MKT in our classrooms

Math Teacher Leader MeetingMarshall Complex

February 17 & 23, 2010

Session Goals:

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Review and reflect on content that was emphasized using MKT as a lens.

Explore current textbook series to make connections to fraction concepts explored this year.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Content Goals for the2009-2010 School Year

Develop conceptual understanding of rational numbers and proportional reasoning.

Develop an understanding of student misconceptions of rational numbers and identify teacher moves needed to remediate and address the errors.

Support MTLs in linking content ideas to the curricular resources in their buildings.

Recognize levels of cognitive demand and transfer to classroom practice.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Rational Numbers: October FocusFraction as Quotient:

“How much is a fair share?”

(1) Fractions As More Than Part Whole

Mariah’s cat has 24 kittens. Mariah kept 1/4 of the kittens. How

many kittens does Mariah have?

(2) “This box contains something that we will share.”

?

“If we share the contents of this box equally among 4 people, how much will each person get?”

(3) A fair share:Total amount of what is being shared is used up.

Each share contains the same amount.

How many ______ is one share?

(4) Missing Part:What goes in the box?

4 x = 3

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Rational Numbers: December FocusMultiplication of Fractions

The Challenge of Computation vs. Conceptualization

Julie is making the family dinner. She buys 4 packages of meat for the spaghetti. Each package weighs 5/8 lb. How many pounds of meat does she buy?

I wanted to run 4 miles. I ran 5/8 of the distance before I stopped for water. How many miles did I run before I had to stop for water?

Combining Parts“4 parts of 5/8 lbs each”

vs.Finding Parts of a Group“5/8 parts of 4 miles”

Multiplication of fractions involves: Combining equal parts Finding a part of a whole or part of a group

ie: Mariah's Kittens Doing both – combining equal parts and finding part

of a whole.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Rational Numbers January Focus

Addition and Subtraction“Making sense of adding & subtracting fractions”

Folding Fraction Strips Reasoning through 1, ½ , ¼, 1/3 & 1/6

Exploring Operation Sense Using Benchmark Fractions If you add 2 fractions and the sum is greater than ½, what can

you say about the fractions?

Making connections to whole number operation sense If you add 2 whole numbers together and the sum is larger than

10, what do you know about those 2 numbers?

Exploring Equalities Using your fraction strips find combinations to represent your

target number.

Exploring Difference (K - 6) Estimate the difference. State answer as a unit fraction.

2/3 or ¼

The Dangerous Rush to Rules and Problem-Based Number Sense Approach

“A firm understanding of fractions is the most critical foundation for fraction computation. Without this foundation, students will most certainly be learning rules without reasons.”

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Developmental Progressions

Review the 3rd– 5th grade Revised WI Model Academic Standards for Number and Operations Sense with Fractions (pp. 7-10 v.6.0)

Make connections between our MTL content focus of rational numbers and the big ideas, strategies, and models discussed in the narrative, Learning Priorities, and Focus Areas?

What do you notice about the development progression of skills in the accompanying continuums?

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Developmental Progressions

Review the 6th – 8th grade Revised WI Model Academic Standards for Number and Operations Sense with Fractions (pp. 4 -19 v.6.0).

Make connections between our MTL content focus of rational numbers and the big ideas, strategies, and models discussed in the narrative, Learning Priorities, and Focus Areas?

What do you notice about the development progression of skills in the accompanying continuums?

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Rational Numbers (2 – 5)

As a table group please complete the following:

Select a Focus Area research: Conceptual Foundations Equivalence Relative Magnitude Meaning of Operations Flexible Estimation of Strategies

Directions: (20 minutes)1. As a textbook group, identify the focus area you will be exploring.

2. Grade levels (within that textbook group) use the note taking guide to explore the development of the focus area.

Sharing out…(20 minutes) Share your findings from grade level to grade

level. Note developmental progressions.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Rational Numbers (6-8)

As a table group please complete the following:

Select a Focus Area research: Modeling Order Equivalence Computational Strategies, including Estimation

Directions: (20 minutes)1. As a textbook group, identify the focus area you will be exploring.

2. Grade levels (within that textbook group) use the note taking guide to explore the development of the focus area.

Sharing out… (20 minutes) Share your findings from grade level to grade

level. Note developmental progressions.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

Implications of this work

As a leader in mathematics, your role in supporting your teachers’ growth with MKT is to help them to…

Define a big idea in mathematics.Know how the authors of your textbook have

chosen to develop that idea.

You will know you are successful when… Teachers can communicate the “Big Idea”

as found their curricular materials.

Teachers can articulate its development across grade levels.

Teachers can identify pivotal instructional experiences students need in order to develop their understanding.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. 0314898.