Lesson 1Tape Diagrams and Equations
Let's see how tape diagrams and equations can show relationships between amounts.
Learning Targets:
 I can tell whether or not an equation could represent a tape diagram.
 I can use a tape diagram to represent a situation.
1.1 Which Diagram is Which?
Here are two diagrams. One represents . The other represents . Which is which? Label the length of each diagram.
1.2 Match Equations and Tape Diagrams
Here are two tape diagrams. Match each equation to one of the tape diagrams.
1.3 Draw Diagrams for Equations
For each equation, draw a diagram and find the value of the unknown that makes the equation true.
Are you ready for more?
You are walking down a road, seeking treasure. The road branches off into three paths. A guard stands in each path. You know that only one of the guards is telling the truth, and the other two are lying. Here is what they say:
 Guard 1: The treasure lies down this path.
 Guard 2: No treasure lies down this path; seek elsewhere.
 Guard 3: The first guard is lying.
Lesson 1 Summary
Tape diagrams can help us understand relationships between quantities and how operations describe those relationships.
Diagram A has 3 parts that add to 21. Each part is labeled with the same letter, so we know the three parts are equal. Here are some equations that all represent diagram A:
Notice that the number 3 is not seen in the diagram; the 3 comes from counting 3 boxes representing 3 equal parts in 21.
We can use the diagram or any of the equations to reason that the value of is 7.
Diagram B has 2 parts that add to 21. Here are some equations that all represent diagram B:
We can use the diagram or any of the equations to reason that the value of is 18.
Lesson 1 Practice Problems

Here is an equation:
 Draw a tape diagram to represent the equation.
 Which part of the diagram shows the quantity ? What about 4? What about 17?
 How does the diagram show that has the same value as 17?

Diego is trying to find the value of in . He draws this diagram but is not certain how to proceed.
 Complete the tape diagram so it represents the equation .
 Find the value of .

For each equation, draw a tape diagram and find the unknown value.

Match each equation to one of the two tape diagrams.

A shopper paid $2.52 for 4.5 pounds of potatoes, $7.75 for 2.5 pounds of broccoli, and $2.45 for 2.5 pounds of pears. What is the unit price of each item she bought? Show your reasoning.

A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? Show your reasoning.

The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of milk has 25% of the recommended daily allowance of calcium. How many milligrams of calcium are in a cup of milk? If you get stuck, consider using the double number line.