Making Algebraic Connections Math Science Partnership Grant Funded by the United States Department of Education through the Kentucky Department of Education

Fraction, Decimal, Percent Cards 100% or Bust

Meeting Norms 4 o Please Put Your Cell Phone on Vibrate… o Use The Rule of Two Feet… o Side-bar talking Please limit talking with other participants unless group work is under way. o Participate Actively Respect and solicit opinions

Community Building

Sit in table groups of 6 Sit in table groups of 6 –4 teachers of the same grade level –2 teachers of special education for that grade level –Curriculum coaches and others sit at tables as needed to form the tables of 6

Introductions 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 Proficiency

Doing Math….One more 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 Proficiency Conceptual Understanding Procedural Proficiency Strategic Competence Adaptive Reasoning Productive Disposition

Doing Math….Condominium! With your group share the following: –What you FIRST tried to solve the problem –What you EVENTUALLY did that worked (if you found a strategy that worked!) Let’s Share Strategies!!

Doing Math….Condominium! Discuss with your Group: –What “interfered” with you being able to solve this task? –What “assisted” you as you solved this task? –And the $10,000 question…What messages does this experience give us about what we need to be doing to support students in learning mathematics (including algebra)?

Mathematics Proficiency Conceptual Understanding Procedural Proficiency Strategic Competence Adaptive Reasoning Productive Disposition

Vocabulary Assessment Variable Inequality Order of operations Equation Ratio Distributive property Function ???

Everyone Needs a Break

The Toothpick Problem The shapes below are made with toothpicks. Look for patterns in the number of toothpicks in the perimeter of each shape.

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

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

Four Teacher-friendly Postulates for Thriving in a Sea of Change (Leinwand) 1. Select a postulate that holds “square” with your beliefs. with your beliefs. 2. Find someone who has picked the same one second (each) quick share. 4. Find someone who picked a different one second (each) quick share.

Four Teacher-friendly Postulates for Thriving in a Sea of Change (Leinwand) 1. Select a postulate that is going “round and round” in your head. 2. Find someone who has picked the same one second (each) quick share. 4. Find someone who picked a different one second (each) quick share.

Two of Everything by Lily Toy Hong

–Make a table that shows what goes in the pot and what comes out. –Explain what would happen if you dropped twenty Jelly Beans in the Pot. –What would happen if you dropped a dozen eggs in the pot?

–What if 32 sandwiches came out of the pot? How many were dropped in? –Will an odd number of items ever come out of the pot? Why or why not? – Write a rule to describe what happens when any number of items goes into the pot.

Patterns

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

Experiences in generating growth sequences include: Finding the first few terms of a sequence. Drawing the next shape in a sequence. Describing the shapes with words in such a way that someone who hasn’t seen them will be able to duplicate the sequence. Generalizing and writing a the rule for a sequence. Compare different ways of arriving at a generalization.

Exploring Patterns

Snowball Fight 1. Using only half of your paper, quickly draw the first three designs of a linear growing pattern. (wait for directions) 2. Add the fourth design. 3. Write the rule in words. 4. Write the rule in symbols.

Wrap Up Reflections Sounding Boards Return name tags to the meeting box