Two Equations for Each Relationship: IM 7.2.5
[url=https://im.kendallhunt.com/MS/teachers/2/2/5/preparation.html]“Two Equations for Each Relationship”[/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 7.2.5
- IM 7.2.5 Lesson: Two Equations for Each Relationship
- Practice 7.2.5
- IM 7.2.5 Practice: Two Equations for Each Relationship
IM 7.2.5 Lesson: Two Equations for Each Relationship
Here are the second and fourth figures in a pattern.
What do you think the first and third figures in the pattern look like?
Describe the 10th figure in the pattern.
There are 100 centimeters (cm) in every meter (m). Complete the table.
There are 100 centimeters (cm) in every meter (m). Complete the table.
For each table, find the constant of proportionality.[br]
What is the relationship between these constants of proportionality?[br]
For each table, write an equation for the proportional relationship. Let [math]x[/math] represent a length measured in meters and [math]y[/math] represent the same length measured in centimeters.
Compare the two equations you wrote for the two different tables. What do you notice?
How many cubic centimeters are there in a cubic meter?
How do you convert cubic centimeters to cubic meters?
How do you convert cubic meters to cubic centimeters?
It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let [math]w[/math] be the number of gallons of water in the cooler after [math]t[/math] minutes.[br][br]Which of the following equations represent the relationship between [math]w[/math] and [math]t[/math]? Select [b]all[/b] that apply.
What does 1.6 tell you about the situation?
What does 0.625 tell you about the situation?
Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of [math]w[/math] and [math]t[/math] when it takes 3 minutes to fill the cooler with 1 gallon of water.
Was the cooler filling faster before or after Priya changed the rate of water flow? [i]Explain [/i]how you know.
At an aquarium, a shrimp is fed [math]\frac{1}{5}[/math]gram of food each feeding and is fed 3 times each day. [br][br]How much food does a shrimp get fed in one day?
At an aquarium, a shrimp is fed ⅕ gram of food each feeding and is fed 3 times each day. Complete the table to show how many grams of food the shrimp is fed over different numbers of days.
What is the constant of proportionality? What does it tell us about the situation?
If we switched the columns in the table, what would be the constant of proportionality? Explainyour reasoning.[br]
Use [math]d[/math] for number of days and [math]f[/math] for amount of food in grams that a shrimp eats to write [i]two[/i] equations that represent the relationship between [math]d[/math] and [math]f[/math].
If a tank has 10 shrimp in it, how much food is added to the tank each day?
If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.
IM 7.2.5 Practice: Two Equations for Each Relationship
The table represents the relationship between a length measured in meters and the same length measured in kilometers. Complete the table.
Write an equation for converting the number of meters to kilometers. Use [math]x[/math] for number of meters and [math]y[/math] for number of kilometers.[br]
Concrete building blocks weigh 28 pounds each. Using [math]b[/math] for the number of concrete blocks and [math]w[/math] for the weight, write two equations that relate the two variables. One equation should begin with [math]w=[/math] and the other should begin with [math]b=[/math].
[size=150]A store sells rope by the meter. The equation [math]p=0.8L[/math] represents the price [math]p[/math] (in dollars) of a piece of nylon rope that is [math]L[/math] meters long.[/size][br][br]How much does the nylon rope cost per meter?
How long is a piece of nylon rope that costs $1.00?
The table represents a proportional relationship. 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[/img][/center][br]Find the constant of proportionality and write an equation to represent the relationship.[br][list][*]constant of proportionality: __________[/*][*]Equation: [math]y=[/math] ________[/*][/list]
On a map of Chicago, 1 cm represents 100 m. Select [b]all [/b]statements that express the same scale.