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Learning Sequences

Target students' misconceptions and help them develop a deeper understanding of important concepts.

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Expressions & Equations

Students build their understanding of expressions and equations by exploring relationships between variables, numbers and operations.

Fractions

Students explore big ideas about fractions using number lines and area models to represent relationships and operations with fractions.

Ratios & Proportions

Students use manipulatives, tables, graphs, and double number lines to explore the relationship between ratios, proportions, slope and scaling.

Statistics & Probability

Students discover how data, statistics, and probability can be used to describe, make predictions and inform decisions about their world.

GRADE LEVEL 6,7

Expressions & Equations

1. What is an Exponent?

This lesson allows students to investigate exponents and learn how to use exponents as a compact way to write expressions involving whole number multiplication.

6.EE.A.2c

7.2.E

GRADE LEVEL 6,7

Expressions & Equations

2. What is a Variable?

In this lesson students evaluate expressions, write expressions that correspond to given situations, and use expressions and formulas to solve problems.

6.EE.A.2
6.EE.A.3

6.5.A
7.14.A

Expressions & Equations

3. Building Expressions

In this lesson students focus on comparing expressions and establish a foundation for the definition of equivalent expressions.

6.EE.A.2
6.EE.A.3
6.EE.A.4

6.13.B
6.5.A

GRADE LEVEL 6,7

Expressions & Equations

4. What is an Equation?

In this lesson students investigate expressions and equations to develop what it means to have a solution to an equation.

6.EE.A.4
6.EE.B.5
6.EE.B.6

7.5.B

GRADE LEVEL 6,7

Expressions & Equations

5. Equations and Operations

In this lesson students investigate the relationship between the solution to an equation and the solution to a new equation formed by adding, subtracting, multiplying, or dividing one or both sides of the original equation by a numerical value.

6.EE.B.6
6.EE.B.7

7.5.A

GRADE LEVEL 6,7

Expressions & Equations

6. Using Structure to Solve Equations

In this lesson students reason about the structure of expressions on either side of an equation as a way to relate the equation to the order of arithmetic operations and use this method to solve equations.

6.EE.B.5
6.EE.B.6
6.EE.B.7
7.EE.B.3
7.EE.B.4

6.10.A
7.11.A

GRADE LEVEL 6,7

Expressions & Equations

7. Visualizing Equations Using Mobiles

In this lesson students explore interactive mobiles for modeling one or more equations. Students are given specific constraints and use solution preserving moves to reinforce the understanding of how equations work.

6.EE.B.5

6.10.B
6.6.C
6.7.C
7.11.B

GRADE LEVEL 6,7

Expressions & Equations

8. Linear Inequalities in One Variable

In this lesson students focus on inequalities and methods of solving them, building on the concept of solution- and order-preserving moves in the context of an inequality.

6.EE.B.5
7.EE.B.4b

6.10.B
7.11.A

GRADE LEVEL 6,7

Expressions & Equations

9. Visualizing Linear Expressions

In this lesson students will use the distributive property to rewrite expressions for a given context in order to make connections between the scenario and the expression(s) that describe it.

6.EE.A.2
7.EE.A.2

6.10.A
7.11.A

GRADE LEVEL 6,7

Expressions & Equations

10. Building Expressions in Two Variables

In this lesson students gain more practice creating equivalent expressions using the properties of multiplication and addition. Students are able to build more complex expressions for the purpose of demonstrating expressions of the second and third degree.

7.EE.A.2

6.7.D

Expressions & Equations

11. Extending Exponents

In this lesson students investigate how patterns in the computations for

$a^n, (ab)^n, (a^m)^n$ that held for positive integer exponents extend naturally to integer exponents.

8.EE.A.1

8.2.C

GRADE LEVEL 6,7,8

Expressions & Equations

12. Solving Equations

In this lesson students draw upon tools learned in previous work and focus on making strategic choices in solving linear equations.

8.EE.C.7

6.10.A
7.11.A
8.8.C

Expressions & Equations

13. Equations of the Form $ax+by = c$

In this lesson students investigate linear equations of the form

$ax+by = c$ . Students use coordinate grids to explore the “trade off” or “exchange” between the values of the two variables in order to maintain the constraint imposed by the constant c.

8.EE.C.8

8.5.I

Expressions & Equations

14. Prop. Relationships to Linear Equations

In this lesson students use previous experience with proportional relationships of the form

$y = kx$ to consider relationships of the form

$y = mx$ and eventually

$y = mx+b$ .

8.EE.B.6

8.5.B

Expressions & Equations

15. Visualizing Systems of Linear Equations

In this lesson students will reason about solutions to systems of equations while modeling the systems on mobiles.

8.EE.C.8

8.9

Expressions & Equations

16. What is a solution to a System of Equations

In this lesson students are introduced to a system of linear equations in two variables and find solutions using balances. Then students investigate graphically systems with a unique solution, no solutions, or infinitely many solutions.

8.EE.C.8

8.9

Expressions & Equations

17. Solving Systems of Equations Algebraically

In this lesson students will investigate pathways for solving systems of linear equations algebraically.

8.EE.C.8

8.9

GRADE LEVEL 6,7

Expressions & Equations

18. Visualizing Quadratic Expressions

In this lesson students manipulate geometric figures to explore equivalent expressions that can be expressed in the form

$x^2 + bx + c$ where

$b$ and

$c$ are positive integers.

7.EE.B.4

6.7.C

Please revise your search criteria. Activities for the topic at the grade level you selected are not available.

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