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CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.

Subject:
Algebra
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Farbizio, Annamaria
Gloag, Andrew
Gloag, Anne
Kramer, Melissa
09/21/2010 Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
11/17/2020 Unrestricted Use
CC BY
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In this task students have to interpret 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.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

This real world task requires students to answer questions about equations for calculating compound interest.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/20/2012 Unrestricted Use
CC BY
Rating

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/24/2012 Unrestricted Use
CC BY
Rating

This task asks students to perform computations involving complex numbers using the given information.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
09/13/2012 Unrestricted Use
CC BY
Rating

The primary purpose of this task is to illustrate certain aspects of the mathematics described in the A.SSE.1. The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

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. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

This task contrasts the usefulness of four equivalent expressions. Students first have to confirm that the given expressions for the radioactive substance are equivalent. Then they have to explain the significance of each expression in the context of the situation.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
02/03/2013 Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Expressions and Equations to 8th graders through a series of 4712 questions and interactive activities aligned to 32 Common Core mathematics skills.

Subject:
Mathematics
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
11/17/2020 Unrestricted Use
CC BY
Rating

This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents, precisely the language being used in standard A-SSE.B.3.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating

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.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC
Rating

Subject:
Mathematics
Provider:
Pearson
02/28/2022 Rating

Equations and Inequalities

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide with whole numbers, fractions, and decimals.
Use the symbols <, >, and =.
Evaluate expressions for specific values of their variables.
Identify when two expressions are equivalent.
Simplify expressions using the distributive property and by combining like terms.
Use ratio and rate reasoning to solve real-world problems.
Order rational numbers.
Represent rational numbers on a number line.

Lesson Flow

In the exploratory lesson, students use a balance scale to find a counterfeit coin that weighs less than the genuine coins. Then continuing with a balance scale, students write mathematical equations and inequalities, identify numbers that are, or are not, solutions to an equation or an inequality, and learn how to use the addition and multiplication properties of equality to solve equations. Students then learn how to use equations to solve word problems, including word problems that can be solved by writing a proportion. Finally, students connect inequalities and their graphs to real-world situations.

Subject:
Mathematics
Algebra
Provider:
Pearson Conditional Remix & Share Permitted
CC BY-NC
Rating

Lesson OverviewStudents solve problems using equations of the form x + p = q and px = q, as well as problems involving proportions.Key ConceptsStudents will extend what they know about writing expressions to writing equations. An equation is a statement that two expressions are equivalent. Students will write two equivalent expressions that represent the same quantity. One expression will be numerical and the other expression will contain a variable.It is important that when students write the equation, they define the variable precisely. For example, n represents the number of minutes Aiko ran, or x represents the number of boxes on the shelf.Students will then solve the equations and thereby solve the problems.Students will solve proportion problems by solving equations. This makes sense because a proportion such as xa=bc is really just an equation of the form xp = q where p=1a and q=bc.Students will also compare their algebraic solutions to an arithmetic solution for the problem. They will see, for example, that a problem that might be solved arithmetically by subtracting 5 from 78 can also be solved algebraically by solving x + 5 = 78, where 5 is subtracted from both sides—a parallel solution to subtracting 5 from 78.Goals and Learning ObjectivesUse equations of the form x + p = q and xp = q to solve problems.Solve proportion problems using equations.ELL: ELLs may have difficulty verbalizing their reasoning, particularly because word problems are highly language dependent. Accommodate ELLs by providing extra time for them to process the information. Note that this problem is a good opportunity for ELLs to develop their literacy skills since it incorporates reading, writing, listening, and speaking skills. Encourage students to challenge each others' ideas and justify their thinking using academic and specialized mathematical language.

Subject:
Algebra
Material Type:
Lesson Plan
Provider:
Pearson
Author: