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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”