Middle (6-8) Sets of Related Lessons

The IFL offers performance-based assessments (PBAs) that assess students' learning of concepts and practices in specific Sets of Related Lessons. Sets of Related Lessons with associated PBAs are marked with an asterisk (*). Please see here for more information about the mathematics PBAs.

Integers: Equivalent Expressions*Purchasable Online

Grade Level
6

This lesson set provides students with an introduction to the equivalence of expressions and to generating equivalent expressions. Students will:

  • determine when to apply the distributive property and the order of operations;
  • define and evaluate an expression for a variable; and
  • use a variety of strategies and representations to determine equivalence and non-equivalence of expressions and generate equivalent expressions.

Mathematical Content Standards: 6.EE.A.3, 6.EE.A.4

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Solving One-Variable Equations and Inequalities*Purchasable Online

Grade Level
6

This lesson set provides an introduction to one-variable equations and inequalities. The set of lessons allows students to work on writing and solving one-variable equations then transition from equations to inequalities. Students will:

  • translate contexts into one-variable equations and inequalities;
  • determine the meaning of the variable and numbers in an equation as they relate to a context in order to solve problems with equations; and
  • use inverse operations to isolate a variable; or if the variable solution is known, use substitution and evaluation.

Mathematical Content Standards: 6.EE.B.5, 6.EE.B.6, 6.EE.B.7, 6.EE.B.8

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Ratios: A Focus on Part-Part and Part-Whole RelationshipsPurchasable Online

Grade Level
6

Learning to reason proportionally is one of the key mathematical studies of the middle school grades. In this lesson set for grade 6, students use a variety of representations to explore ratio thinking. Students will:

  • examine the meaning of ratio by exploring the composed units and iterations that underlie the multiplicative nature of ratio;
  • understand the distinction between fraction and ratio, and learn that while some ratios can be part-whole relationships, others are part-part relationships;
  • scale ratios up as well as down; and
  • use a variety of representations to solve real-world problems.

Mathematical Content Standards: 6.RP.A.1, 6.RP.A.2, 6.RP.A.3, and 6.RP.A.3.A

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Proportional Relationships Second Edition*Purchasable Online

Grade Level
7

This lesson set provides a study of Proportional Relationships. Students will learn to move from the grade 6 study of ratios and equations of the form px = q to the study of proportional relationships. They combine their previous understanding of the topics of both ratio and equation to examine tests that establish or refute the presence of a proportional relationship between two variables. Students will:

  • develop an understanding of proportional relationships;
  • make and confirm conjectures about tests for proportionality;
  • recognize proportional relationships visually when they are presented in equation or graphic form;
  • recognize proportional relationships in tables and contexts; and
  • articulate how to test for proportional relationships.

Mathematical Content Standards: 7.RP.A.1, 7.RP.A.2, 7.RP.A.2.A, 7.RP.A.2.B, and 7.RP.A.2.C

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Solving Linear Equations in One Variable*Purchasable Online

Grade Level
8

This lesson set provides students with the opportunity to write and solve linear equations in one variable, focusing particular attention on what it means for a value to be in the solution set of a linear equation in one variable. Students will:

  • determine whether or not a value is in the solution set of a linear equation in one variable;
  • use the properties of operations and the properties of equality to solve linear equations in one variable; and
  • classify linear equations as having no solution, a unique solution, or infinitely many solutions.

Mathematical Content Standards: 8.EE.C.7, 8.EE.C.7.A, and 8.EE.C.7.B

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Understanding and Solving Systems of Linear Equations*Purchasable Online

Grade Level
8

This lesson set provides the opportunity for students to extend their previous understanding of linear equations to include systems of linear equations. Students will:

  • analyze what it means to be a solution to a system of equations;
  • solve a system of equations graphically, using a table of values, and algebraically; and
  • develop an understanding of the conditions under which a system that consists of two linear equations has zero, one, or infinitely many solutions.

Mathematical Content Standards: 8.EE.C.8.A and 8.EE.C.8.B

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

Understanding Congruence and Similarity*Purchasable Online

Grade Level
8

This lesson set provides the opportunity for students to explore congruence and similarity as a result of transformations in the plane. Students will:

  • examine the results of reflecting, translating, rotating, and dilating polygons in the plane;
  • recognize which transformations produce congruent figures and which do not;
  • recognize which transformations produce similar figures and which do not; and
  • determine a center of dilation.

Mathematical Content Standards: 8.G.A.1, 8.G.A.1.A, 8.G.A.1.B, 8.G.A.1.C, 8.G.A.2, and 8.G.A.4

Approximately 8-15 days of instruction.

Purchase this teacher manual with 25 student workbooks for $119.00

Purchase the student workbooks for $4.95 each

Purchase the teacher manual (set of related lessons) alone for $65.00

* The IFL offers performance-based assessments (PBAs) that assess students' learning of concepts and practices in this Set of Related Lessons. PBAs come with scoring guides and annotated student work.