options: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Use polynomial identities to solve problems.

Understand the relationship between zeros and factors of polynomials.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand and apply properties of operations and the relationship between addition and subtraction.

Multiply and divide within 100.

Understand properties of multiplication and the relationship between multiplication and division.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Work with radicals and integer exponents.

Understand solving equations as a process of reasoning and explain the reasoning.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Solve systems of equations.

Interpret the structure of expressions.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Work with addition and subtraction equations.

Understand the connections between proportional relationships, lines, and linear equations.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with equal groups of objects to gain foundations for multiplication.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.
problem_activity: Activity
Students solved equations of the form
\(x+p = q\)
and
\(px=q\)
in grade 6, but the equations only involved positive values. This activity bridges their understanding of a solution to an equation as a value that makes the equation true with their understanding of operations involving negative numbers from this unit. This activity builds on the work students have done in this lesson evaluating expressions at different values.
Monitor for students who:
take an arithmetic approach by substituting in values and evaluating. (Does
\(\text-2 \boldcdot (\text-4.5) = \text-9\)
?)
take an algebraic approach by writing an equivalent equation using an inverse operation (If
\(\text-2 \boldcdot x=\text-9\)
, then
\(x=\text-9 \div \text-2\)
.)
Digital
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to a value that makes it true by dragging the answer to the corresponding equation. Be prepared to explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to its solution.
\(\frac12 x=\text-5\)
\(\text-2x=\text-9\)
\(\text-\frac12 x=\frac14\)
\(\text-2x=7\)
\(x+\text-2 = \text-6.5\)
\(\text-2+x=\frac12\)
\(x = \text-4.5\)
\(x = \text-\frac12\)
\(x = \text-10\)
\(x = 4.5\)
\(x = 2 \frac12\)
\(x=\text-3.5\)
Be prepared to explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select an equation for which there is a student who took an arithmetic approach and a student who took an algebraic approach. Ask students to share their reasoning for why a solution is correct. Sequence arithmetic approaches before algebraic approaches. An example of an arithmetic approach: “I know that -3.5 is the solution to
\(\text-2x=7\)
, because I know that
\(\text-2 \boldcdot (\text-3.5)=7\)
. An example of an algebraic approach: “If
\(\text-2x=7\)
, then I know that
\(x=7 \div \text-2\)
.) Record their work, side by side, for all to see. If there are no equations for which students took both approaches, present both approaches anyway. Tell students that either approach is valid, but that in the next unit they will see some more complicated equations for which one approach might be simpler than the other.
Representing, Conversing, Listening: MLR7 Compare and Connect.
Use this routine to support whole-class discussion. Ask students, “What is the same and what is different?” about how they matched the expressions. Connect strategies by showing the different ways operations are used in each approach (e.g., arithmetic method by substituting in values and evaluating; algebraic method by using an inverse operation). Use gestures, and color on the display to highlight these connections. This helps students use mathematical language as they reason about their strategies to evaluate equivalent equations.
Design Principle(s): Maximize meta-awareness; Support sense-making


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