Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Number:**MAFS.912.A-SSE.1

**Title:**Interpret the structure of expressions. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**912

**Domain-Subdomain:**Algebra: Seeing Structure in Expressions

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

## Unit/Lesson Sequence

## Student Resources

## Original Student Tutorials

Learn how to use multistep factoring to factor quadratics in this interactive tutorial.

This is part 5 in a five-part series. Click below to open the other tutorials in this series.

- Part 1:
**The Diamond Game: Factoring Quadratics when***a*= 1 - Part 2:
**Factoring Polynomials Using Special Cases** - Part 3:
**Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method** - Part 4:
**Factoring Polynomials when***a*Does Not Equal 1: Snowflake Method - Part 5: Multistep Factoring: Quadratics (current tutorial)

Type: Original Student Tutorial

Learn to factor quadratic trinomials when the coefficient *a* does not equal 1 by using the Snowflake Method in this interactive tutorial.

This is part 4 in a five-part series. Click below to open the other tutorials in this series.

- Part 1:
**The Diamond Game: Factoring Quadratics when***a*= 1 - Part 2:
**Factoring Polynomials Using Special Cases** - Part 3:
**Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method** - Part 4: Factoring Polynomials when
*a*Does Not Equal 1: Snowflake Method (Current Tutorial) - Part 5:
**Multistep Factoring: Quadratics**

Type: Original Student Tutorial

Learn how to factor quadratic polynomials when the leading coefficient (*a*) is not 1 by using the box method in this interactive tutorial.

This is part 3 in a five-part series. Click below to open the other tutorials in this series.

- Part 1:
**The Diamond Game: Factoring Quadratics when***a*= 1 - Part 2:
**Factoring Polynomials Using Special Cases** - Part 3: Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method (Current Tutorial)
- Part 4:
**Factoring Polynomials when***a*Does Not Equal 1: Snowflake Method - Part 5:
**Multistep Factoring: Quadratics**

Type: Original Student Tutorial

Learn how to factor quadratics when the coefficient *a* = 1 using the diamond method in this game show-themed, interactive tutorial.

This is part 1 in a five-part series. Click below to open the other tutorials in this series.

- Part 1: The Diamond Game: Factoring Quadratics when
*a*= 1 (Current Tutorial) - Part 2:
**Factoring Polynomials Using Special Cases** - Part 3:
**Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method** - Part 4:
**Factoring Polynomials when***a*Does Not Equal 1: Snowflake Method - Part 5:
**Multistep Factoring: Quadratics**

Type: Original Student Tutorial

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

Type: Original Student Tutorial

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Learn how to factor quadratic polynomials that follow special cases, difference of squares and perfect square trinomials, in this interactive tutorial.

This is part 2 in a five-part series. Click below to open the other tutorials in this series.

- Part 1:
**The Diamond Game: Factoring Quadratics when***a*= 1 - Part 2: Factoring Polynomials Using Special Cases (Current Tutorial)
- Part 3:
**Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method** - Part 4:
**Factoring Polynomials when***a*Does Not Equal 1: Snowflake Method - Part 5:
**Multistep Factoring: Quadratics**

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students explore the structure of the operation *s*/(v*n*). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of *n*, then dividing the result of that operation into *s*.

Type: Problem-Solving Task

Solving this problem with algebra requires factoring a particular cubic equation (the difference of two cubes) as well as a quadratic equation. An alternative solution using prime numbers and arithmetic is presented.

Type: Problem-Solving Task

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. Students must understand the need to transform the factored form of the quadratic expression (a product of sums) into a sum of products in order to easily see *a*, the coefficient of the x^{2} term; *k*, the leading coefficient of the *x* term; and *n*, the constant term.

Type: Problem-Solving Task

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

Type: Problem-Solving Task

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Type: Problem-Solving Task

## Parent Resources

## Perspectives Video: Professional/Enthusiast

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students explore the structure of the operation *s*/(v*n*). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of *n*, then dividing the result of that operation into *s*.

Type: Problem-Solving Task

Solving this problem with algebra requires factoring a particular cubic equation (the difference of two cubes) as well as a quadratic equation. An alternative solution using prime numbers and arithmetic is presented.

Type: Problem-Solving Task

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. Students must understand the need to transform the factored form of the quadratic expression (a product of sums) into a sum of products in order to easily see *a*, the coefficient of the x^{2} term; *k*, the leading coefficient of the *x* term; and *n*, the constant term.

Type: Problem-Solving Task

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

Type: Problem-Solving Task

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Type: Problem-Solving Task