Lesson 1
Tape Diagrams and Equations
Let's see how tape diagrams and equations can show relationships between amounts.
Problem 1
Here is an equation: \(x + 4 = 17\)
 Draw a tape diagram to represent the equation.
 Which part of the diagram shows the quantity \(x\)? What about 4? What about 17?
 How does the diagram show that \(x+4\) has the same value as 17?
Problem 2
Diego is trying to find the value of \(x\) in \(5 \boldcdot x = 35\). He draws this diagram but is not certain how to proceed.
 Complete the tape diagram so it represents the equation \(5 \boldcdot x = 35\).
 Find the value of \(x\).
Problem 3
Match each equation to one of the two tape diagrams.
 \(x + 3 = 9\)
 \(3 \boldcdot x = 9\)
 \(9=3 \boldcdot x\)
 \(3+x=9\)
 \(x = 9  3\)
 \(x = 9 \div 3\)
 \(x + x+ x = 9\)
Problem 4
For each equation, draw a tape diagram and find the unknown value.

\(x+9=16\)

\(4 \boldcdot x = 28\)
Problem 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.
Problem 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.
Problem 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.