In this Grade 6 Illustrative Mathematics lesson from Unit 6: Expressions and Equations, students learn to represent and solve one-variable equations using tape diagrams and balanced-hanger diagrams. Students practice matching equivalent equations such as 4 + x = 12 and 4 · x = 12 to their corresponding diagrams, reinforcing how different equation forms can describe the same relationship between quantities. By drawing diagrams and reasoning about unknown values, students build foundational skills for solving equations in one variable.
Section 1
Modeling Equations with Tape Diagrams
A tape diagram, or bar model, is a visual representation of an equation. The total length of the tape represents the value on one side of the equation, while the segments of the tape represent the terms on the other side. This model helps to visualize the relationship between the parts and the whole in an equation.
Section 2
The Truth Value of an Equation
An equation is a statement that two mathematical expressions are equal. This statement can be either true (if the values on both sides of the equal sign are the same) or false (if the values are different). For an equation with a variable, the equation is true only for specific values of that variable, which are called solutions.
Think of an equation as a question: "Are the two sides really equal?" If they are, the equation is true. If they are not, the equation is false. When an equation includes a variable, solving the equation means finding the specific value for the variable that makes the equation a true statement.
Section 3
Introduction: Modeling Equations with Balanced Hangers
A balanced hanger represents an equation where the total weight on the left side is equal to the total weight on the right side.
If the left side has weight and the right side has weight , the balanced hanger represents the equation .
Section 4
Basic Operations for Two-Step Equations
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Section 1
Modeling Equations with Tape Diagrams
A tape diagram, or bar model, is a visual representation of an equation. The total length of the tape represents the value on one side of the equation, while the segments of the tape represent the terms on the other side. This model helps to visualize the relationship between the parts and the whole in an equation.
Section 2
The Truth Value of an Equation
An equation is a statement that two mathematical expressions are equal. This statement can be either true (if the values on both sides of the equal sign are the same) or false (if the values are different). For an equation with a variable, the equation is true only for specific values of that variable, which are called solutions.
Think of an equation as a question: "Are the two sides really equal?" If they are, the equation is true. If they are not, the equation is false. When an equation includes a variable, solving the equation means finding the specific value for the variable that makes the equation a true statement.
Section 3
Introduction: Modeling Equations with Balanced Hangers
A balanced hanger represents an equation where the total weight on the left side is equal to the total weight on the right side.
If the left side has weight and the right side has weight , the balanced hanger represents the equation .
Section 4
Basic Operations for Two-Step Equations
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter