CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Discover the rules for keeping it balanced. Collect stars by playing the game!

This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

This is course material published for a secondary Math 1 course. Authors of this work are: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius and updated from the original work in 2013 in partnership with the Utah State Office of Education.

Unit 7: Rational Numbers
Lesson 10: Interpreting Inequalities

In this final lesson on inequalities, students explore situations in which some of the solutions to inequalities do not make sense in the situation’s context. Students learn to think carefully about a situation’s constraints when coming up with reasonable solutions to an inequality. Students also see that inequalities can represent a comparison of two or more unknown quantities.

In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities.

Following a profile of fashion designer and Project Runway winner Chloe Dao, students are prompted to alter garment designs, using their sense of style combined with their math skills to hit target price points. Algebra concepts explored include: linear relationships; rates (percents), ratios, and proportions; using multiple representations; algebraic and numeric expressions, equations, and inequalities. Please click the Display SPL link below to view. This resource is part of the Math at the Core: Middle School Collection. Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied to the world of fashion, challenging them to use algebraic concepts and reasoning to modify garments and meet target price points.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

The Mathematics Vision Project (MVP) curriculum has been developed to realize the vision and goals of the New Core Standards of Mathematics. The Comprehensive Mathematics Instruction (CMI) framework is an integral part of the materials. You can read more about the CMI framework in the Utah Mathematics Teacher Journal. (UCTM, 2009)

Unit 7: Rational Numbers
Lesson 9: Solutions of Inequalities

In this lesson, students consider situations where there might be more than one condition. Students have already learned “solution to an equation” to mean a value of the variable that makes the equation true. Here, they learn a similar definition about inequalities: a solution to an inequality is a value of the variable that makes the inequality true. But while the equations students solved in the last unit generally had one solution, the inequalities they solve in this unit have many, sometimes infinitely many, solutions.

Constraints in real-world situations reduce the range of possible solutions. Students reason abstractly by using inequalities or graphs of inequalities to represent those situations and interpreting the solutions, (MP2). Students think carefully about whether to include boundary values as solutions of inequalities in various contexts.

Unit 7: Rational Numbers
Lesson 8: Writing and Graphing Inequalities

In extending their concept of numbers to all rational numbers, students began writing inequality statements that compared two numbers. In this lesson, students extend their work with inequality statements by considering comparisons with an unknown quantity. These quantities, represented by variables, often describe real-world situations, and their value is usually constrained by minimum or maximum allowable values. Students represent these situations with inequality statements and reason about possible values that make them true (MP2). As there are often many, even infinite, possibilities for the value of the variable that satisfy the constraint, students use the number line as a helpful tool to show all the possible values.

The activities in this lesson present students with two types of scenarios. When the variable represents a measurement, the possible values can usually be any number within the range satisfied by the constraint. When the variable represents a count of people or objects, the possible values are restricted to whole numbers within the range. Students also consider whether the constraint itself is included or excluded in the set of possible values, and learn how to indicate this result on the number line representation.

After writing inequality statements to represent situations, students test values to see if they make the statement true.