Algebra Task Performance
By Hannah Cooper
Overview
 Rationale for algebra in elementary schools
 NCTM and GPS Algebra Standards
 Algebra in everyday
 Equal Sign
 Looking at Patterns and Generalizations
 “Algebrafy”
 Connection to work after graduation
Rationale
 Algebra is included in the elementary
curriculum to help students build a solid
foundation of mathematical skills.
 Because algebra is a part of all other areas of
mathematics, it is important for it to be
included early on.
NCTM Standards for pre-K through
2nd Grade
– To understand patterns, relations – To represent and analyze mathematical
and functions all students in presituations and structures using algebraic
K through grade 2 should be able
symbols all students pre-K through
to:
grade 2 should be able to:
• sort, classify, and order objects
by size, number, and other
properties;
• recognize, describe, and extend
patterns
• analyze how both repeating and
growing patterns are generated.
• illustrate general principles and
properties of operations, such as
commutatively, using specific numbers;
• use concrete, pictorial, and verbal
representations to develop an
understanding of invented and
conventional symbolic notations.
NCTM Standards for 3rd Grade
through 5th Grade
– To understand patterns, relations
and functions all students in
grades 3–5 should be able to:
• describe, extend, and make
generalizations about geometric
and numeric patterns;
• represent and analyze patterns
and functions, using words,
tables, and graphs.
– To represent and analyze mathematical
situations and structures using
algebraic symbols all students grades
3-5 should be able to:
• identify such properties as
commutatively, associativity, and
distributive and use them to compute
with whole numbers;
• represent the idea of a variable as an
unknown quantity using a letter or a
symbol;
• express mathematical relationships
using equations.
GPS Standards for 3rd Grade
– M3A1. Students will use mathematical expressions to
represent relationships between quantities and interpret
given expressions.
• Describe and extend numeric and geometric patterns.
• b. Describe and explain a quantitative relationship represented by a
formula (such as the perimeter of a geometric figure).
• c. Use a symbol, such as □ and Δ, to represent an unknown and find
the value of the unknown in a number sentence.
GPS Standards for 4th Grade
– M4A1. Students will represent and interpret mathematical
relationships in quantitative expressions.
• Understand and apply patterns and rules to describe relationships
and solve problems.
• Represent unknowns using symbols, such as □ and Δ.
• Write and evaluate mathematical expressions using symbols and
different values.
GPS Standards for 5th Grade
– M5A1. Students will represent and interpret the
relationships between quantities algebraically.
• Use variables, such as n or x, for unknown quantities in algebraic
expressions.
• Investigate simple algebraic expressions by substituting numbers
for the unknown.
• Determine that a formula will be reliable regardless of the type of
number (whole numbers or decimals) substituted for the variable.
Algebra into the Daily Routine
 Listening to what students are saying for an
opportunity to extend on a thought about
algebra.
 You only need the resources that you have
available to you.
Confusion of the Equal Sign
 The misconception
 The true meaning – “the same as”
 Understanding the equal sign leads to firm
foundation for understanding equations and
inequalities.
Student Work
Student Work
Student Work
Student Work
Student Work
Table
Grades
K (1)
1 (1)
2 (2)
3 (1)
4 (4)
5 (1)
12
100%
100%
50%
25%
17
50%
100%
50%
100%
7
25%
Finding Patterns
Finding Patterns cont.
 Come up with a conjecture to test.
 Test the conjecture
– True – then you have found the generalization or
pattern
– False – revise the conjecture to try and come up
with a true one
 Write it symbolically.
What it means “Algebrafy” a
problem
 By changing variables of the problem so that it
does not just produce a single number answer
any more.
 Handshake Problem
Bridging the gap:
Arithmetic to Algebra
 Basic math problems to complex equations
 Base-10 blocks to Algebra tiles
Review
 Today we have discussed way we are teaching our elementary students
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algebra.
We looked at what the NCTM and the GPS standards are for including
algebra in the curriculum.
We have talked about ways to incorporate algebra in daily.
We have also discussed why students get confused about the equal sign and
what we as teachers need to do to help them understand the difference.
We discussed the generalization of patterns.
How to “algebrafy” work in the classroom.
And we also talked about the connection between elementary arithmetic
and algebra.
Conclusion
Thank you!
Works Cited
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"3-5 Mathematics Georgia Performance Standards." Georgia Standards. 11 Sept. 2008. Web. 18
July 2011.<https://www.georgiastandards.org/Standards/Georgia%20Performance %20Standards/
Math_3-5_9-11-08_REVISED_4-27-10%5B2%5D.pdf>.
"Algebra." National Council of Teachers of Mathematics. Web. 18 July 2011.
<http://www.nctm.org/standards/content.aspx?id=26853>.
Blanton, Maria L. "Section III." Algebra and the Elementary Classroom: Transforming Thinking,
Transforming Practice. Portsmouth: Heinemann, 2008. 91-120. Heinemann: Publisher of
Professional Resources and Provider of Educational Services for Teachers. Web. 23 July 2011.
<http://www.heinemann.com/shared/onlineresources%5CE00946%5 Cblanton00946Sample.pdf>.
Falkner, Karen P., Linda Levi, and Thomas P. Carpenter. "Children's Understanding of Eqality: A
Foundation for Algebra." (1999): 232-36. Print.
Kaput, James J., and Maria L. Blanton. "Developing Elementary Teachers' "Algebra Eyes and Ears""
(2003): 70-77. Print.
"Lessons for Algebraic Thinking." Xi-Xii. Print.
Mann, Rebecca L. "Balancing Act: The Truth Behind the Equals Sign." (2004): 65-69. Print.