Transcript February 29, 2008

Algebraic Thinking
December 8th, 2010
SD Counts Cohort
Platte, SD
Roxane Dyk
What has happened since the last time we
met, either inside/outside your classroom?
• Share activities you created
• Equality/relational thinking/operations
Do this Activity
(Order of Operations)
• 1 + 20 x (6 + 2) / 2 =
• 1 + 20 x 8 / 2 =
• 1 + 160 / 2 =
• 1 + 80 =
Comic
Excuses
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Ten Commandments of Math
10 Excuses for Not Doing Homework
Algebra Definitions
Math Books for Sale
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
• During Marie’s birthday party, Marie thinks
about the ages of her parents and herself.
Marie says, “Hey, Mom and Dad, together
your ages add up to 100 years!” Her dad is
surprised, “You are right,” he says, “and
your age and mine total 64 years.” Marie
replies, “And my age and Mom’s total 58.”
How old are Mom, Dad and Marie?
• Explain how you got your answer
Outcomes for today’s session
• Celebrate 50 Years of Life
• Review equality, relational thinking,
operations
• Begin to understand concepts of early
algebra
Early Algebra
• In grades K-3 these are the concepts of
Algebra that need to be covered and
covered well
– Equality
– Relational thinking
– Basic number properties
Equality
Relational Thinking
• Pull out the handout in your packets
• Revisit “Big Ideas”
• What are/have you been doing in your
classroom to “foster” these concepts?
– Talk to your neighbor
• What did you find out about your students
relational thinking skills?
– Talk to your neighbor
• How have you continued to address each item?
Video Clip 1.6 Equality
Title 6-Chapter 1
• This is a teacher working with a group of
students
• Listen to what the teacher does before she
allows the students to explain.
• Pay attention to the questions the teacher
asks
• What did you notice?
Video Clip 2.5 Relational Thinking
Title 11-Title 1
• Watch to the type of problem the teacher
poses and listen to the students explain
Properties in Math
We must take the time to make
sure our students know and
understand
Big Ideas of “Early Algebra”
• These are ideas that you want to know
and understand about teaching algebra
concepts in elementary school
• Read the handout individually
• Talk to your table and discuss what you
believe each idea is representing
Early Algebra Concepts
#1-This will depend on your instructional materials.
Does your series have
-specific algebra units-taught
in isolation
-concepts embedded
-no algebra at all
Problem-solving situations
• #2
- Good examples are hard to find if you
don’t have them in your book. Once
you find good examples; just change
the numbers
*Sample Algebraic Sense Problems
How do we approach “algebra”
• #3
– “Today we are going to use what we know
about numbers”
NOT
– “Today we are doing algebra”
• Tell them they were just doing algebra when they
are finished
Box to Variables
#4
Moving away from the
Mathematical Convention
• Because of the “mathematician's rule”..
When the same variable appears more
than one time in a number sentence, the
variable must be replaced by the same
number throughout the number sentence.
Caged Mice
• Work with your table
• Number yourselves of 1-2-3 (see posted
job descriptions)
• Identify all of the combinations 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
• 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 these two cages.
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?
• Title III book has more activities that go
with finding combinations
Early Algebra Number Sentences
• We are going to work through some early
algebra number sentences.
• Work with a partner to solve these
problems using ONLY your understanding
of equality, relational thinking, basic
number properties and mathematician’s
rules. NO FORMAL ALGEBRA
• Solve these problems the way 2nd-6th
graders would solve.
Number Sentence
What can we put in for s and t so that this number sentence
is true:
s+t=8
You must work with a lot of sentences helping your
students understand letters as variables.
Read Page 71
Number Sentence
What if I have 2 letters that are the same?
s + s=10
Mathematician’s Rule-if variables are the same the number’s used are the
same
Read Page 72
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.
The goal in giving students these types of number
sentences is not to teach students efficient ways to solve
algebra equations; it is to engage them in thinking
flexibly about number operations and relations.
d + d – 5 = 13
Read Page 73
Lets watch some students solve
equations….
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Video 4.1-4th grader-2’42”
Video 4.2-4th grader-1’51”
Video 4.3-4th grader-’39”
Video 4.4-4th grader-’51”
Challenge Problems
• Page 77
• Think about the different ways students
will use their understanding of equality,
relational thinking, basis number
properties and the mathematician’s rule to
solve these problems
Article
• “Algebraic Problem-Solving in the Primary
Grades”
• Read individually
• Share with your partner
• Share large group
Next meeting
• January 18th 8:30-3:30
• Conjectures and Justification