Algebra Through the Grades

As the National Mathematics Advisory Panel has explained, making Algebra in 8th grade needs to be a top priority. You can read the full report or the highlights at the link above but I would like to delve into what we are doing as a district K-7 in the algebra strand of the N.Y.S. Mathematics Standards.

Students in our district are actively involved in problem solving from the time they begin their schooling at the Kindergarten Center. Students at the Kindergarten Center are using various materials to create patterns of different color shape, and size. As well they are figuring out ways to create, describe and extend patterns.

In first grade students are problem solving, solving scenarios that involve unknown quantities. For example, a problem may read, “Steve has 6 pennies in his pocket. His mother gives him some more, now he has 14. How many pennies did Steve’s mother give him?” A problem like his may require students to model the problem at first before being able to “see the problem.”

Second grade is where we dive into the discussion of symbols including the greater than (>) and less than (<) signs. Students are given opportunities to compare whole numbers up to 100. I would think tha once students were flexible enough with numbers and the symbols that could begin to compare simple expressions using whole numbers.

The greater than and less than symbols are extended to include unit fractions such as 1/2, 1/3, 1/4, etc in third grade. As well, students are describing and extending numeric (addition and subtraction) and geometric patterns.

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As you can see from a previous N.Y.S. Exam, students need to be able to determine the correct number to place in the open sentence to make it true. As students gain more experience, they need to see that a variable can have more than one answer (x²=64) or a set that meets the requirement (x ≤ 33).

Fourth grade sees the introduction of ≠ to the symbols previously introduced as well as comparing decimals. They are also exposed to determining the solution or solutions to > and < type problems. As well, students are asked to analyze and state the rule for input/output boxes as well as tables. This is where students may begin to generalize and state rules algebraically.

During the Post-March time period of 5th grade, students are now learning how to solve algebraic expression. Students should and need to have a fluency with the number facts in order to give their full attention to solving these problems. They are also asked to translate simple verbal expressions into algebraic expressions as well as substituting a number for a variable and solve.

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This is a Part II question from a previous 6th grade state exam. Although students may revisit this concept in 6th grade, it is extremely important to continue to lay the groundwork in 5th grade for students to be able to think algebraically.

At the 6th grade level, students will continue to be exposed to solving problems algebraically but no performing two-step problems as opposed to the one-step problems they saw last year. As well, they are learning how to translate two-step verbal sentences into algebraic expressions.

Seventh grade is the year when teachers and students are solving multi-step equations, one-step inequalities, and evaluating formulas. As well, students are representing a pattern from an equation or table graphically. they are also writing equations to represent functions from a table.

As you can see, concepts and skills build upon one another from kindergarten through seventh grade. I believe by including algebra throughout the grades as well as having a strong foundation in numeracy, students will be prepared for algebra in 8th grade.

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