Making Algebraic ConnectionsMaking Algebraic ConnectionsMath Science Partnership GrantMath Science Partnership Grant

Funded byFunded by

the United States Department of Education the United States Department of Education

through through

the Kentucky Department of Educationthe Kentucky Department of Education

Fraction, Decimal, Percent CardsFraction, Decimal, Percent Cards100% or Bust100% or Bust

Meeting NormsMeeting Norms

4

oPlease Put Your Cell Phone on Vibrate…

oUse The Rule of Two Feet…

oSide-bar talkingPlease limit talking with other

participants unless group work is under way.oParticipate Actively

Respect and solicit opinions

Community BuildingCommunity Building

Community BuildingCommunity Building

Sit in table groups of 6Sit in table groups of 6– 4 teachers of the same grade level4 teachers of the same grade level– 2 teachers of special education for that grade 2 teachers of special education for that grade

levellevel– Curriculum coaches and others sit at tables Curriculum coaches and others sit at tables

as needed to form the tables of 6as needed to form the tables of 6

Introductions and SharingIntroductions and Sharing

Within group of 6 –

Share with a partner something (an idea or activity) that they have done something with (thought about – read about) from the last meeting.

Introduce person to rest of group tell what they said.

Decide on common theme/pattern for table.

Share out common theme by table

Math ProficiencyMath Proficiency

Doing Math….One more Doing Math….One more problem!problem!

What features of “doing math” does this task (and the others you have done) have?

If students regularly engage in tasks like this, what impact will it have on: their knowledge (concepts and procedures)beliefs about mathematics beliefs about themselves as mathematicians

Mathematics Mathematics ProficiencyProficiencyConceptual Conceptual UnderstandingUnderstanding

Procedural ProficiencyProcedural Proficiency

Strategic CompetenceStrategic Competence

Adaptive ReasoningAdaptive Reasoning

Productive DispositionProductive Disposition

Doing Math….Condominium!Doing Math….Condominium!

With your group share the following:With your group share the following:– What you FIRST tried to solve the problemWhat you FIRST tried to solve the problem– What you EVENTUALLY did that worked (if What you EVENTUALLY did that worked (if

you found a strategy that worked!)you found a strategy that worked!)

Let’s Share Strategies!!Let’s Share Strategies!!

Doing Math….Condominium!Doing Math….Condominium!

Discuss with your Group:Discuss with your Group:– What “interfered” with you being able to solve What “interfered” with you being able to solve

this task?this task?– What “assisted” you as you solved this task?What “assisted” you as you solved this task?– And the $10,000 question…What messages And the $10,000 question…What messages

does this experience give us about what we does this experience give us about what we need to be doing to support students in need to be doing to support students in learning mathematics (including algebra)?learning mathematics (including algebra)?

Mathematics Mathematics ProficiencyProficiencyConceptual Conceptual UnderstandingUnderstanding

Procedural ProficiencyProcedural Proficiency

Strategic CompetenceStrategic Competence

Adaptive ReasoningAdaptive Reasoning

Productive DispositionProductive Disposition

Vocabulary AssessmentVocabulary Assessment

Variable

Inequality

Order of operations

Equation

Ratio

Distributive property

Function

Function

???

???

???

???

Everyone Needs a BreakEveryone Needs a Break

The Toothpick ProblemThe Toothpick Problem

The shapes below are made with The shapes below are made with toothpicks. Look for patterns in the toothpicks. Look for patterns in the

number of toothpicks in the perimeter number of toothpicks in the perimeter of each shape.of each shape.

Use a pattern from the shapes below to determine the perimeter of the 5th shape in the sequence.

Write a rule you can use to determine the perimeter of any shape n.

Four Teacher-friendly Postulates for Four Teacher-friendly Postulates for Thriving in a Sea of Change Thriving in a Sea of Change

(Leinwand)(Leinwand)

1. Select a postulate that holds “square” 1. Select a postulate that holds “square” with your beliefs. with your beliefs. 2. Find someone who has picked the same 2. Find someone who has picked the same

one.one.3. 60 second (each) quick share.3. 60 second (each) quick share.4. Find someone who picked a different one.4. Find someone who picked a different one.5. 60 second (each) quick share.5. 60 second (each) quick share.

Four Teacher-friendly Postulates for Four Teacher-friendly Postulates for Thriving in a Sea of Change Thriving in a Sea of Change

(Leinwand)(Leinwand)

1. Select a postulate that is going “round and 1. Select a postulate that is going “round and round” in your head.round” in your head.

2. Find someone who has picked the same 2. Find someone who has picked the same one.one.

3. 60 second (each) quick share.3. 60 second (each) quick share.4. Find someone who picked a different one.4. Find someone who picked a different one.5. 60 second (each) quick share.5. 60 second (each) quick share.

Two of EverythingTwo of Everything

by Lily Toy Hongby Lily Toy Hong

– Make a table that shows what goes in the pot Make a table that shows what goes in the pot and what comes out.and what comes out.

  – Explain what would happen if you dropped Explain what would happen if you dropped

twenty Jelly Beans in the Pot. twenty Jelly Beans in the Pot.

  – What would happen if you dropped a dozen What would happen if you dropped a dozen

eggs in the pot? eggs in the pot?

– What if 32 sandwiches came out of the pot? What if 32 sandwiches came out of the pot? How many were dropped in?How many were dropped in?

– Will an odd number of items ever come out of Will an odd number of items ever come out of the pot? Why or why not?the pot? Why or why not?

  – Write a rule to describe what happens when Write a rule to describe what happens when

any number of items goes into the pot.any number of items goes into the pot.

PatternsPatterns

Understanding Patterns, Understanding Patterns, Relations, and FunctionsRelations, and Functions

•Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;

•Relate and compare different forms of representation for a relationship;

•Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Understanding Patterns Understanding Patterns Relations, and FunctionsRelations, and Functions

Working with patterns is at the heart of Working with patterns is at the heart of mathematics.mathematics.Exploring repeating patterns in the Exploring repeating patterns in the elementary grades lays the foundation elementary grades lays the foundation for considering growth patterns and for considering growth patterns and number sequences in the middle number sequences in the middle grades.grades.

Experiences in generating growth Experiences in generating growth sequences include:sequences include:

Finding the first few terms of a sequence.Finding the first few terms of a sequence.

Drawing the next shape in a sequence.Drawing the next shape in a sequence.

Describing the shapes with words in such a Describing the shapes with words in such a way that someone who hasn’t seen them will way that someone who hasn’t seen them will be able to duplicate the sequence.be able to duplicate the sequence.

Generalizing and writing a the rule for a Generalizing and writing a the rule for a sequence.sequence.

Compare different ways of arriving at a Compare different ways of arriving at a generalization.generalization.

Exploring PatternsExploring Patterns

Snowball FightSnowball Fight

1.1. Using only half of your paper, quickly Using only half of your paper, quickly draw the first three designs of a linear draw the first three designs of a linear growing pattern. (wait for directions)growing pattern. (wait for directions)

2.2. Add the fourth design.Add the fourth design.

3.3. Write the rule in words.Write the rule in words.

4.4. Write the rule in symbols.Write the rule in symbols.

Wrap UpWrap Up

ReflectionsReflections

Sounding BoardsSounding Boards

Return name tags to the meeting boxReturn name tags to the meeting box