# 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.

## 1.1Which Diagram is Which?

Here are two diagrams. One represents . The other represents . Which is which? Label the length of each diagram.

Draw a diagram that represents each equation.

## 1.2Match Equations and Tape Diagrams

Here are two tape diagrams. Match each equation to one of the tape diagrams.

## 1.3Draw Diagrams for Equations

For each equation, draw a diagram and find the value of the unknown that makes the equation true.

1.

### 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.
Which path leads to the treasure?

## 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

1. Here is an equation:

1. Draw a tape diagram to represent the equation.
1. Which part of the diagram shows the quantity ? What about 4? What about 17?
1. How does the diagram show that has the same value as 17?
2. Diego is trying to find the value of in . He draws this diagram but is not certain how to proceed.

1. Complete the tape diagram so it represents the equation .
2. Find the value of .
3. For each equation, draw a tape diagram and find the unknown value.

4. Match each equation to one of the two tape diagrams.

5. 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.

6. 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.

7. 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.