Reasoning about Equations and Tape Diagrams Part 1: IM 7.6.4
[url=https://im.kendallhunt.com/MS/teachers/2/6/4/preparation.html]“Reasoning about Equations and Tape Diagrams (Part 1)”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.6.4
- IM 7.6.4 Lesson: Reasoning about Equations and Tape Diagrams (Part 1)
- Practice 7.6.4
- IM 7.6.4 Practice: Reasoning about Equations and Tape Diagrams (Part 1)
IM 7.6.4 Lesson: Reasoning about Equations and Tape Diagrams (Part 1)
Find a solution to each the equation without writing anything down.
[math]x+1=5[/math]
[math]2\left(x+1\right)=10[/math]
[math]3\left(x+1\right)=15[/math]
[math]500=100\left(x+1\right)[/math]
Draw a tape diagram to represent each situation. For some of the situations, you need to decide what to represent with a variable.
Diego has 7 packs of markers. Each pack has x markers in it. After Lin gives him 9 more markers, he has a total of 30 markers.
Elena is cutting a 30-foot piece of ribbon for a craft project. She cuts off 7 feet, and then cuts the remaining piece into 9 equal lengths of x feet each.
A construction manager weighs a bundle of 9 identical bricks and a 7-pound concrete block. The bundle weighs 30 pounds.
A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30.
Andre bakes 9 pans of brownies. He donates 7 pans to the school bake sale and keeps the rest to divide equally among his class of 30 students.
Each situation in the previous activity is represented by one of the equations.
Match the situation to an equation:[br]Diego has 7 packs of markers. Each pack has x markers in it. After Lin gives him 9 more markers, he has a total of 30 markers.[br]
Find the solution. Use your diagrams to help you reason.[br]
What does the solution tell you about the situation?[br]
Match the situation to an equation:[br]Elena is cutting a 30-foot piece of ribbon for a craft project. She cuts off 7 feet, and then cuts the remaining piece into 9 equal lengths of x feet each.[br]
Find the solution. Use your diagrams to help you reason.[br]
What does the solution tell you about the situation?[br]
Match the situation to an equation:[br]A construction manager weighs a bundle of 9 identical bricks and a 7-pound concrete block. The bundle weighs 30 pounds. [br]
Find the solution. Use your diagrams to help you reason.[br]
What does the solution tell you about the situation?[br]
Match the situation to an equation:[br]A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30.[br]
Find the solution. Use your diagrams to help you reason.[br]
What does the solution tell you about the situation?[br]
Match the situation to an equation:[br]Andre bakes 9 pans of brownies. He donates 7 pans to the school bake sale and keeps the rest to divide equally among his class of 30 students. [br]
Find the solution. Use your diagrams to help you reason.[br]
What does the solution tell you about the situation?[br]
While in New York City, is it a better deal for a group of friends to take a taxi or the subway to get from the Empire State Building to the Metropolitan Museum of Art? Explain your reasoning.
IM 7.6.4 Practice: Reasoning about Equations and Tape Diagrams (Part 1)
Draw a square with side length 7 cm.
Predict the perimeter and the length of the diagonal of the square.
Using the app above, measure the perimeter and the length of the diagonal of the square. Record the measurements below.
Describe how close the predictions and measurements are.
Find the products.
[math]\left(100\right)\cdot\left(-0.09\right)[/math]
[math]\left(-7\right)\cdot\left(-1.1\right)[/math]
[math]\left(-7.3\right)\cdot\left(5\right)[/math]
[math]\left(-0.2\right)\cdot\left(-0.3\right)[/math]
A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show.
Decide which equation represents this story:[br]
What does [math]x[/math] represent in this situation?
Find the solution to the equation you picked above. Explain or show your reasoning.
What does the solution tell you about its situation?
Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.
Decide which equation represents this story:
What does [math]x[/math] represent in this situation?
Find the solution to the equation you picked above. Explain or show your reasoning.
What does the solution tell you about its situation?
Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames.
Decide which equation represents this story:[br]
What does [math]x[/math] represent in this situation?
Find the solution to the equation you picked above. Explain or show your reasoning.
What does the solution tell you about its situation?
Here is a diagram and its corresponding equation.
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[/img] [math]6x+11=21[/math][br][br]Find the solution to the equation and explain your reasoning.
Plot these points on the coordinate plane: A=(3, 2), B=(7.5, 2), C=(7.5, -2.5), D=(3, -2)
What is the vertical difference between [math]D[/math] and [math]A[/math]?
Write an expression that represents the vertical distance between [math]B[/math] and [math]C[/math].