By Hannah Cooper

Algebra Task Performance

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 and functions all students in pre-K through 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.

– To represent and analyze mathematical situations and structures using algebraic symbols all students pre-K through grade 2 should be able to:

• 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 12 17 7

K (1) 100%    1 (1) 100%    2 (2) 50% 50%  3 (1)   100%  4 (4) 25% 50% 25%5 (1)   100%  

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 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

¨ "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.