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Interpreting Inequalities: IM 7.6.16
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1. Lesson 7.6.16
- IM 7.6.16 Lesson: Interpreting Inequalities
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2. Practice 7.6.16
- IM 7.6.16 Practice: Interpreting Inequalities
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Interpreting Inequalities: IM 7.6.16
IM 6 – 8 Math, GeoGebra Classroom Activities, Aug 10, 2020
“Interpreting Inequalities” from IM Grade 7 by Open Up Resources and Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 license.
Table of Contents
- Lesson 7.6.16
- IM 7.6.16 Lesson: Interpreting Inequalities
- Practice 7.6.16
- IM 7.6.16 Practice: Interpreting Inequalities
IM 7.6.16 Lesson: Interpreting Inequalities
For each inequality, find the value or values of x that make it true.
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Choose the inequality that best matches each given situation.
The Garden Club is planting fruit trees in their school’s garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need pound fertilizer each.
Explain why you chose that equation.
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The Chemistry Club is experimenting with different mixtures of water with a certain chemical (sodium polyacrylate) to make fake snow. To make each mixture, the students start with some amount of water, and then add of that amount of the chemical, and then 9 more grams of the chemical. The chemical is expensive, so there can’t be more than a certain number of grams of the chemical in any one mixture.
Explain why you chose that equation.
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The Hiking Club is on a hike down a cliff. They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute.
Explain why you chose that equation.
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The Science Club is researching boiling points. They learn that at high altitudes, water boils at lower temperatures. At sea level, water boils at . With each increase of 500 feet in elevation, the boiling point of water is lowered by about .
Explain why you chose that equation.
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Your teacher will assign your group one of the situations from the last task. Create a visual display about your situation. In your display:
- Explain what the variable and each part of the inequality represent
- Write a question that can be answered by the solution to the inequality
- Show how you solved the inequality
- Explain what the solution means in terms of the situation
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Your teacher will assign your group one of the situations from the last task. Create a visual display about your situation with the criteria above.
{3, 4, 5, 6} is a set of four consecutive integers whose sum is 18.
How many sets of three consecutive integers are there whose sum is between 51 and 60? Can you be sure you’ve found them all? Explain or show your reasoning.
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How many sets of four consecutive integers are there whose sum is between 59 and 82? Can you be sure you’ve found them all? Explain or show your reasoning.
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IM 7.6.16 Practice: Interpreting Inequalities
Priya looks at the inequality and says “I subtract a number from 12 and want a result that is bigger than 5. That means that the solutions should be values of that are smaller than something.”
Do you agree with Priya? Explain your reasoning and include solutions to the inequality in your explanation.
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When a store had sold of the shirts that were on display, they brought out another 30 from the stockroom. The store likes to keep at least 150 shirts on display. The manager wrote the inequality to describe the situation.
Explain what means in the inequality.
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Solve the inequality the manager wrote:
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Explain what the solution means in the context of the situation.
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You know is a number less than 4. Select all the inequalities that must be true.
Here is an unbalanced hanger.
If you knew each circle weighed 6 grams, what would that tell you about the weight of each triangle? Explain your reasoning.Font sizeFont size
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If you knew each triangle weighed 3 grams, what would that tell you about the weight of each circle? Explain your reasoning.
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Match each sentence with the inequality that could represent the situation.
Han got $2 from Clare, but still has less than $20.
Mai spent $2 and has less than $20.
If Tyler had twice the amount of money he has, he would have less than $20.
If Priya had half the money she has, she would have less than $20.
At a skateboard shop:
The price tag on a shirt says $12.58. Sales tax is 7.5% of the price. How much will you pay for the shirt?
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The store buys a helmet for $19.00 and sells it for $31.50. What percentage was the markup?
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The shop pays workers $14.25 per hour plus 5.5% commission. If someone works 18 hours and sells $250 worth of merchandise, what is the total amount of their paycheck for this pay period? Explain your reasoning.
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