Transcript Understanding Properties 08

Understanding the Properties
SD Counts
Ground Rules
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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
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Pattern Block Equations
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First do this individually
Then share with a partner
Large group sharing
Understanding the Properties of Arithmetic
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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
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Choose a card at your table. This
will be your assigned task. Good
way to have a different person do
different work
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1 recorder
2 reporter
3 time keeper and material person
Take out the article
“Understanding the Properties of Arithmetic”
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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
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Each poster will have
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Kid friendly definition
Visual model
Number statement
Variable statement
Use the article to help you complete your poster
Your 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
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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
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8 x 6 = (6 x 6) + (2 x 6)
We will stop after the child solves
the first two problems.
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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 Convention
This is information that you just TELL your
students, as they will never explore and
discover this process
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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
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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
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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
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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
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If time is short stop here and have
them read the article for the
accountability piece.
Early Algebra
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Participants will explore introducing
children to algebraic notation and
procedures for enriching student
understanding of important
mathematical ideas
Big Ideas of Early Algebra Concepts
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Take out the handout “Big Ideas of
Algebra Concepts”
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Will read and discuss
Early Algebra
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In Grades K-3, the following
concepts of Algebra must be
covered and covered well
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Equality
Relational thinking
Basic number properties
Caged Mice
Work with your table
Choose a different job
Identify all of the combination of mice
in a cage that you would find
Be 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
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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?
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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
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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
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What can we put in for s and t so
that this number sentence is true?
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S+t=8
Read page 70-71
Teachers must work with a lot of sentences
helping students understand letters as
variables
Number Sentence
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What if I have 2 letters that are the
same?
S + S = 10
Read page 72
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Mathematicians Rule-If variables
are the same the number’s used are
the same.
Solving Equations
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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
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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
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K + K + 13 = k + 20
Watch video clip 4.3
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E + e + e = e + 24
Watch video clip 4.4
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4 x 48 = p + p
Accountability Piece
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Work with properties in your
classroom-student example
Play Operations Game in classroom
Operations Square Game
Article-”Algebraic Problem Solving in
the Primary Grades”