Expression Equation Word Wall Cards
Eureka Math² • Grade 7
Module 3 Word Wall: Expressions, Equations & Inequalities
Topic A: Expressions • Card Set 1 of 4
1
Algebraic Expression
Topic A • Vocabulary
Definition
A mathematical phrase built from numbers, variables, and operations (\(+\), \(-\), \(\times\), \(\div\)).
⚠️ Critical Rule: An expression never has an equal sign (\(=\)) or inequality symbol (\(<, >, \le, \ge\)).
Worked Example & Anatomy 3 Terms
4x − 7y + 12
Variables \(x\) and \(y\)
Coefficients \(4\) and \(-7\)
Constant \(+12\)
2
Term • Coefficient • Constant
Parts of an Expression
• Term: A single number, variable, or product of both separated by \(+\) or \(-\).
• Coefficient: The number factor multiplying a variable.
• Constant: A standalone number with fixed value.
Sign Tip: The sign in front belongs to that term! E.g. in \(5 - 3x\), the coefficient is \(-3\).
Expression Breakdown: \(-8a + b - 15\)
| Term | Role / Type | Key Value |
|---|
| \(-8a\) | Variable Term | Coefficient = \(-8\) |
| \(+b\) | Variable Term | Coefficient = \(1\) (invisible 1) |
| \(-15\) | Constant Term | Constant = \(-15\) |
If no number is written in front of a variable, the coefficient is \(1\) (or \(-1\) if negative).
3
Like Terms
Combining Expressions
Definition
Terms that share the same variable(s) raised to the exact same exponent(s). All constants are like terms with each other.
❌ Non-Example: \(3x\) and \(3x^2\) are NOT like terms because their exponents differ (\(1\) vs \(2\)).
Worked Example: Simplify by Combining
Original Expression
\(9x + 6 - 4x + 7\)
Step 1: Group Like Terms
\((9x - 4x)\) + \((6 + 7)\)
Simplified: \(5x + 13\)
Cut along dashed border lines to display on classroom word wall
Eureka Math² Grade 7 • Module 3
Eureka Math² • Grade 7
Module 3 Word Wall: Expressions, Equations & Inequalities
Topic A & B • Card Set 2 of 4
4
Distributive Property
Expanding Expressions
Core Rule
Multiplying a factor outside parentheses by every single term inside:
\(a(b + c) = ab + ac\)
Negative Factor Alert: \(-2(x - 4) = -2x + 8\). Negative times negative equals positive!
Worked Example: Expand \(-3(4x - 5)\) Area Model
Factor
\(4x\)
\(-5\)
\(-3\)
\(-12x\) \((-3 \times 4x)\)
\(+15\) \((-3 \times -5)\)
Expanded Result: \(-12x + 15\)
5
Factoring Expressions
Reverse of Distributing
Definition
Writing an expression as a product of its Greatest Common Factor (GCF) and another expression.
Factoring Steps:
1. Find GCF of coefficients.
2. Divide each term by the GCF.
Worked Example: Factor \(18x - 24\)
Step 1: Greatest Common Factor \(\text{GCF}(18, 24) = 6\)
Step 2: Divide each term by \(6\) \(18x \div 6 = \mathbf{3x}\), \(-24 \div 6 = \mathbf{-4}\)
Factored Form: \(6(3x - 4)\) Check: \(6 \cdot 3x - 6 \cdot 4 = 18x - 24 \checkmark\)
6
Linear Equation
Topic B • Balance Scale
Definition
A mathematical statement declaring that two expressions are equal in value, joined by an equal sign (\(=\)).
The Balance Concept: Both sides of the equal sign must weigh the exact same amount.
Anatomy of an Equation: \(3x + 4 = 19\)
Left Expression \(3x + 4\)
\(=\)
Right Expression \(19\)
When does it balance? If \(x = 5\), then \(3(5) + 4 = 15 + 4 = 19 \checkmark\)
Cut along dashed border lines to display on classroom word wall
Eureka Math² Grade 7 • Module 3
Eureka Math² • Grade 7
Module 3 Word Wall: Expressions, Equations & Inequalities
Topic B: Equations • Card Set 3 of 4
7
Solution of an Equation
True Values
Definition
The specific number value for a variable that makes the equation a true statement when substituted.
Always Check: Substitute your answer back into the original equation to verify both sides match!
Testing Solutions: \(2x - 3 = 11\)
Test \(x = 5\)
\(2(5) - 3 \stackrel{?}{=} 11\)
\(10 - 3 = 7 \ne 11\)
❌ Not a Solution
Test \(x = 7\)
\(2(7) - 3 \stackrel{?}{=} 11\)
\(14 - 3 = 11 \checkmark\)
✔ Is the Solution!
A linear equation in one variable has exactly one unique solution.
8
Inverse Operations
Properties of Equality
Definition
Operations that undo each other. Applying the same inverse operation to both sides keeps the equation balanced.
Golden Rule: Whatever you do to one side of the equation, you must do to the other side!
Inverse Operation Pairs
Addition \(+ a\)
Subtraction \(- a\)
Multiplication \(\times a\)
Division \(\div a\)
Example: To isolate \(x\) in \(x + 9 = 21\), use inverse operation \(- 9\) on both sides: \(x = 12\).
9
Two-Step Equation
Solving Strategy
Standard Algorithm
An equation requiring two inverse operations to isolate the variable.
Reverse Order of Operations (SADMEP):
1. Undo Addition/Subtraction
2. Undo Multiplication/Division
Worked Example: Solve \(4x - 7 = 25\)
Step 1: Undo Subtraction Add \(7\) to both sides
\(4x - 7 + 7 = 25 + 7\)
\(4x = 32\)
Step 2: Undo Multiplication Divide both sides by \(4\)
\(\frac{4x}{4} = \frac{32}{4}\)
\(x = 8\)
Check: \(4(8) - 7 = 32 - 7 = 25 \checkmark\)
Cut along dashed border lines to display on classroom word wall
Eureka Math² Grade 7 • Module 3
Eureka Math² • Grade 7
Module 3 Word Wall: Expressions, Equations & Inequalities
Topic C: Inequalities • Card Set 4 of 4
10
Inequality Symbols
Comparison Symbols
Definition
A mathematical sentence comparing two quantities using symbols of inequality rather than an equal sign.
Circle Rule on Number Line:
• Open Circle \(\circ\) = Not Included (\(<\) or \(>\))
• Closed Dot \(\bullet\) = Included (\(\le\) or \(\ge\))
Symbol Quick Reference
| Symbol | Meaning & Keywords | Circle Type |
|---|
| \(<\) | Less than, fewer than | Open \(\circ\) |
| \(>\) | Greater than, more than | Open \(\circ\) |
| \(\le\) | Less than or equal to, at most, maximum | Solid \(\bullet\) |
| \(\ge\) | Greater than or equal to, at least, minimum | Solid \(\bullet\) |
Watch out: "at least" means \(\ge\) (minimum) and "at most" means \(\le\) (maximum).
11
Solution Set & Graphing
Number Line Models
Definition
The set of all values that make an inequality true. Because there are infinite solutions, we display them as a shaded ray on a number line.
Test Point Tip: Test a number like \(0\) in your inequality. If it makes it true, shade towards \(0\)!
Graphing Worked Examples
Graph 1: \(x \ge -1\) Solid dot at \(-1\), shade right
-3 -2 -1 0 1 2
Graph 2: \(x < 2\) Open circle at \(2\), shade left
-1 0 1 2 3
12
Inequality Reversal Rule
Crucial Grade 7 Rule
Golden Rule of Inequalities
When you multiply or divide both sides by a negative number, you MUST FLIP the inequality symbol!
Why does it flip? \(2 < 5\), but multiplying by \(-1\) gives \(-2 > -5\). Order reverses on the negative side of zero!
Worked Example: Solve \(-3x + 5 \le 26\)
Step 1: Subtract 5 Subtract \(5\) from both sides
\(-3x \le 21\)
Step 2: Divide by \(-3\) & FLIP! Symbol changes \(\le \longrightarrow \ge\)
\(\frac{-3x}{-3} \ge \frac{21}{-3}\)
Solution: \(x \ge -7\) Check with \(x = 0\): \(-3(0) + 5 \le 26 \implies 5 \le 26 \checkmark\) (True!)
Cut along dashed border lines to display on classroom word wall
Eureka Math² Grade 7 • Module 3
