Algebra Task Performance

1. Algebra Task Performance By Hannah Cooper

2. 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

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. Student Work

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15. Student Work

16. Table

17. Finding Patterns

18. 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.

19. 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

20. Bridging the gap:Arithmetic to Algebra Basic math problems to complex equations Base-10 blocks to Algebra tiles

21. 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.

22. Conclusion Thank you!

23. 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.