Lesson 1
Tape Diagrams and Equations
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?
Solution
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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.
![Tape diagram. 5 equal parts labeled x, x, x, x, x.](https://cms-im.s3.amazonaws.com/4VGXNLeBYZUek9zDvoTh36ig?response-content-disposition=inline%3B%20filename%3D%226-6.6.A1.PP.Rev.Image.0707.png%22%3B%20filename%2A%3DUTF-8%27%276-6.6.A1.PP.Rev.Image.0707.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000927Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=218917e6a0d8e8d9962d8112d008014bfc73e416387688fd02ebd9fd4dce6fb2)
- Complete the tape diagram so it represents the equation \(5 \boldcdot x = 35\).
- Find the value of \(x\).
Solution
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Problem 3
Match each equation to one of the two tape diagrams.
- \(x + 3 = 9\)
- \(3 \boldcdot x = 9\)
- \(9=3 \boldcdot x\)
- \(3+x=9\)
- \(x = 9 - 3\)
- \(x = 9 \div 3\)
- \(x + x+ x = 9\)
![Two tape diagrams, A and B. A, 3 equal parts labeled, x. Total, 9. B, 2 parts labeled x and 3. Total, 9.](https://cms-im.s3.amazonaws.com/GH9DyQppzsfn3ziFDhzassX3?response-content-disposition=inline%3B%20filename%3D%226-6.6.A1.PP.Rev.Image.0303.png%22%3B%20filename%2A%3DUTF-8%27%276-6.6.A1.PP.Rev.Image.0303.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000927Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4af6a3761fdf4896c8efb1ee3337152a57a567d056df28ad881e30394ed1030a)
Solution
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Problem 4
For each equation, draw a tape diagram and find the unknown value.
-
\(x+9=16\)
-
\(4 \boldcdot x = 28\)
Solution
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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.
Solution
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(From Unit 3, Lesson 20.)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.
Solution
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(From Unit 2, Lesson 23.)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.
![A double number line.](https://cms-im.s3.amazonaws.com/k9aNYe3EkGX3VZoQmLExzLXM?response-content-disposition=inline%3B%20filename%3D%226-6.3.D.PP_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D.PP_Image_1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000927Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f218cbdd5af5e8d2e7b2c18433641076a507ebad4d119f4358a1dd4ca759edf9)
Solution
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(From Unit 2, Lesson 20.)