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.
![two tape diagrams are shown](../../../../embeds/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBaEVrIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--a38f6c068bc6691881aba084a086216665a03538/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBZzZGMjF6WDIxaGRHaGZkakpmWkdsbmFYUmhiQT09IiwiZXhwIjpudWxsLCJwdXIiOiJ2YXJpYXRpb24ifX0=--9c87e6556271e1d3a3a9dc16b03f00c39ee39775/6.6.A1.Image.Revision.01.png)
1.2 Match Equations and Tape Diagrams
Here are two tape diagrams. Match each equation to one of the tape diagrams.
![two tape diagrams are shown](../../../../embeds/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBaFFrIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--15198c4b64c74206036fe5e5e67f0313d101db65/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBZzZGMjF6WDIxaGRHaGZkakpmWkdsbmFYUmhiQT09IiwiZXhwIjpudWxsLCJwdXIiOiJ2YXJpYXRpb24ifX0=--9c87e6556271e1d3a3a9dc16b03f00c39ee39775/6.6.A1.Image.Revision.05.png)
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.
![two tape diagrams are shown](../../../../embeds/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBaGNmIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--bd65683ff198542b555c679f67e38b976bef4e8e/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBZzZGMjF6WDIxaGRHaGZkakpmWkdsbmFYUmhiQT09IiwiZXhwIjpudWxsLCJwdXIiOiJ2YXJpYXRpb24ifX0=--9c87e6556271e1d3a3a9dc16b03f00c39ee39775/6.6.A2.LessonSummary.png)
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.