Lesson 1: Tape Diagrams and Equations

Tape Diagrams and Equations

Student Summary

Tape diagrams can help us understand relationships between quantities and how operations describe those relationships.

Tape diagram A, 3 equal parts labeled x, x, x. Total, 21. — A

Tape diagram B, 2 parts, labeled y, 3. Total, 21. — B

Diagram A has 3 parts that add to 21. Each part is labeled with the same letter, so we know the 3 parts are equal. Here are some equations that all represent Diagram A:

$\displaystyle x+x+x=21$

$\displaystyle 3\boldcdot {x}=21$

$\displaystyle x=21\div3$

$\displaystyle x=\frac13\boldcdot {21}$

Notice that the number 3 is in the equations, but it's not written in the diagram. The 3 comes from counting 3 boxes representing 3 equal parts in 21.

Diagram B has 2 parts that add to 21. Here are some equations that all represent Diagram B:

$\displaystyle y+3=21$

$\displaystyle y=21-3$

$\displaystyle 3=21-y$

Visual / Anchor Chart

Standards

Building Toward

6.EE.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = q for cases in which p, q, and x are all nonnegative rational numbers.