Understanding the Properties

SD Counts

Ground Rules

Honor private think time Be prepared for sessions, everyone

should have something to contribute Listen carefully to take in another

participant’s ideas Cell phones off or on vibrate Start and end each session on time Take care of your needs

Problem-solving Activity

Pattern Block Equations First do this individually Then share with a partner Large group sharing

Understanding the Properties of Arithmetic

In order to understand relational thinking and how students are thinking about and using number relationships, it is necessary for students to have a good understanding of the basic properties of number operations.

Article job descriptions

Choose a card at your table. This will be your assigned task. Good way to have a different person do different work 1 recorder 2 reporter 3 time keeper and material person

Take out the article“Understanding the Properties of Arithmetic”

With your group of three, reflect on the parts that you highlighted as you read. This should be information that either you didn’t know or information that reinforced what you did know

At the end of the 20 minutes discuss key ideas with the large group

Create a poster of the property that you were given

Each poster will have Kid friendly definition Visual model Number statement Variable statement

Use the article to help you complete your posterYour group will have 35 minutes to complete

Gallery Walk to see the different representations

NEED TO GET GRAPHIC ORGANIZER

Please Remember

It is not necessarily important that the students know the property names, but more important that they understand each one of them.

Properties Matching Game

In your group of three take turns matching the number sentences to the properties.

Great way to individually access as you are walking around.

You can see instantly which properties the students are struggling with

10 minutes

View DVD 2.9 Distributive Property

8 x 6 = (6 x 6) + (2 x 6) We will stop after the child solves

the first two problems. What problem might you pose next to

this child? What benefits were there to using such

large numbers in these problems? 15 minutes

Let’s talk about the order of operations

Mathematical ConventionThis is information that you just TELL your

students, as they will never explore and discover this process

Please (parenthesis) excuse (exponent) my (multiplication OR division from left to right) Dear Aunt Sally (add or subtract from left to right)

Good idea to write in your math journal

Do this activity individually at your table

1 + 20 x (6 + 2) / 2 = 1 + 20 x 8 / 2 = 1 + 160 / 2 = 1 + 80 = What was the common answer 5 minutes

Order of Operations Square Puzzle

With your group of three solve this puzzle

Again, another assessment you can use to see what they understand after you have worked with order of operations

10 minutes

Accountability Piece

Read “Motivating Activities That Lead to Algebra”

-be prepared to share activity with the rest of the group

*Group 1 The Constant Sum Grid

*Group 2 Fibonacci Sequence *Group 3 Predict Your Age

*Group 4 Target 21-prepare and teach games to rest of class

Stop

If time is short stop here and have them read the article for the accountability piece.

Early Algebra

Participants will explore introducing children to algebraic notation and procedures for enriching student understanding of important mathematical ideas

Big Ideas of Early Algebra Concepts

Take out the handout “Big Ideas of Algebra Concepts” Will read and discuss

Early Algebra

In Grades K-3, the following concepts of Algebra must be covered and covered well Equality Relational thinking Basic number properties

Caged Mice

Work with your tableChoose a different jobIdentify all of the combination of mice

in a cage that you would findBe ready to prove to me how you know

you have found all of the combinations

Be ready to discuss the different ways to record your answers

The Caged Mice Problem

Ricky has 7 pet mice. He keeps them in two cages. One cage is red and the other is blue. Show all the ways that 7 mice can be in two cages.

What are you looking for when students do this problem?

Do they have an organized way to make sure they have all of the combinations?

Does anyone know the number of combinations there would be for “n” mice and how do you know?

What would the number sentence look like for this combination?

www.pasd.wednet.edu-good website to find early algebra problems in context

Early Algebra Number Sentences

Solve the problems using ONLY your understanding of equality, relational thinking, basic number properties and mathematician’s rules. NO FORMAL ALGEBRA

Solve the way your 2nd-5th grade students would solve

Number Sentence

What can we put in for s and t so that this number sentence is true?

S + t = 8 Read page 70-71

Teachers must work with a lot of sentences helping students understand letters as variables

Number Sentence

What if I have 2 letters that are the same?

S + S = 10Read page 72

Mathematicians Rule-If variables are the

same the number’s used are the same.

Solving Equations

Once students have learned the rule for dealing with number sentences with repeated variables, they can attempt to solve number sentences that challenge their mathematical thinking.

d + d – 5 = 13 Read Page 73

The goal is giving students these types of number sentences is not to teach student efficient ways to solve algebra equations; it is to engage them in thinking flexibly about number operations and relations

Watch video clip 4.1

Watch video clip 4.2

K + K + 13 = k + 20

Watch video clip 4.3

E + e + e = e + 24

Watch video clip 4.4

4 x 48 = p + p

Accountability Piece

Work with properties in your classroom-student example

Play Operations Game in classroom Operations Square Game Article-”Algebraic Problem Solving

in the Primary Grades”