docs/yr6_worddocs... · web viewto. think functionally. march mtl meeting. march 3 and 5 2009....

Using Repeating Patterns

toThink Functionally

March MTL MeetingMarch 3 and 5 2009

DeAnn HuinkerKevin McLeodConnie LaughlinMelissa HedgesBeth Schefelker

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. EHR-0314898.

Session Goals:

To connect repeating and growing patterns to their underlying functional relationships

To examine recursive and explicit functional relationships in patterns

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. EHR-0314898.

Concept Map for Patterns

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. EHR-0314898.

Recursive

Strategi

Patterns

Explicit or Functional Strategies

Functional Relationships

Assessment Resource Banks English, Mathematics and Science arb.nzcer.orgnz

Mathematical Knowledgefor Teaching (MKT)

What do we want Kindergarten students to know about AB patterns?

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. EHR-0314898.

Using repeated patterns to think

Repeating Patterns

What do we want 2nd, 3rd, and 4th graders to know about AB patterns?

What do we want 8th graders to understand?

Pattern exploration leads naturally to the development of rules to describe patterns and strategies to work a given pattern.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. EHR-0314898.

Investigating an AB Pattern

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. EHR-0314898.

Use the tiles to build a pattern of yellow, blue.

Analyze the patterno Identify the unit.o What comes next?

Share out your insights about the structure of the pattern.

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. EHR-0314898.

Research shows that students tend to use the recursive strategy in their pattern work…however its usefulness in the type of pattern work students will encounter in their school years is limited.

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. EHR-0314898.

What is the unit?What comes next?What are the next three shapes in this pattern?

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. EHR-0314898.

How would children answer these questions using recursive thinking?

What would the 10th shape look like?

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. EHR-0314898.

What would the 21st shape be?

Draw the 35th shape?

What should we be doing with patterns between Kindergarten and Grade 8?

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. EHR-0314898.

Moving toward Functional strategies

Use the yellow, blue tile pattern you built. Create a number sequence associated

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. EHR-0314898.

with the repeating pattern.

1 2 3 4 5

Discuss relationships that emerge. What do you notice about the yellow tiles? blue tiles?

What color is the 17th tile?

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. EHR-0314898.

Is the 20th tile blue? Why?What color is the 100th tile? What number is the

100th blue tile? What number is the

100th yellow tile?

Explain the differences among these questions

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. EHR-0314898.

and how you solved them

Functional strategies and rules are very powerful because they allow the user to work out any number in a pattern without knowing its predecessor.

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. EHR-0314898.

What can you say about the position of any blue tile?

What can you say about the position of any yellow tile?

Video: 8th Grade Yellow/Black Tile Pattern

What struggles are the 8th graders 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. EHR-0314898.

demonstrating as they work on this pattern?

How does the teacher move their recursive strategy to a functional strategy?

Investigating Red, Blue, Green

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. EHR-0314898.

Build an ABC pattern using red, blue, and green tilesCreate a number sequence associated with the repeating pattern.Use the relationships of the ordinal position and the constant increment to analyze the pattern.

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. EHR-0314898.

Consider the following questions as you work. What color is the 25th tile? What position on the

number line is the 13th green tile?

What position on the number line is the 19th blue?

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. EHR-0314898.

ROYGBIV Think about a repeating pattern with the unit shown above…

Where would you find the 30th yellow?

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. EHR-0314898.

Where would you find the 45th indigo ?

What do we need our teachers to do in order to transition children from recursive thinking to functional thinking?

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. EHR-0314898.