Unit 7 Rational Numbers — Unit Plan

State whether you agree with each of the following statements. Explain your reasoning.

1. A temperature of 35 degrees Fahrenheit is as cold as a temperature of -35 degrees Fahrenheit.
2. A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.
3. A city that has an elevation of -17 meters is closer to sea level than a city that has an elevation of -40 meters.

1. Plot a point on the number line to represent the value -3.2.

   

2. What is the opposite of -3.2? 

3. What is the opposite of the opposite of -3.2?

The elevation of Death Valley, California, is -282 feet. The elevation of Tallahassee, Florida, is 203 feet. The elevation of Westmorland, California, is -157 feet.

1. Label each point on the number line with the name of the city whose elevation is represented by the point.

   

2. Use the symbol < or > to compare the elevations of Death Valley and Tallahassee.

3. Use the symbol < or > to compare the elevations of Death Valley and Westmorland.

1. Place these numbers in order from least to greatest:

   $\frac{16}{5}$

   -3

   6

   3.1

   -2.5

   $\frac14$

   $\text-\frac{3}{4}$

   $\text-\frac{3}{8}$

2. Write a sentence to compare the two points shown on the number line.

   

The table shows records of the money-related activities of an event planner over the period of a week.

1. For which items did the event planner receive money?
2. What does the number -147.95 mean in this context?
3. Did the event planner receive more or spend more money on May 5? Explain your reasoning. 

1. Write a number that has the same value as each expression:

   1. $|5|$

   2. $|\text-12.9|$

2. Write a number that has a value less than $|4.7|$.
3. Write a number that has a value greater than $|\text-2.6|$.

Mark each statement as true or false, and explain your reasoning.

1. $\text-5 < 3$
2. $\text-5 > 3$
3. $|\text-5| < 3$
4. $|\text-5| > 3$

Andre looks at a box of paper clips. He says: “I think the number of paper clips in the box is less than 1,000.”

Lin also looks at the box. She says: “I think the number of paper clips in the box is more than 500.”

1. Write an inequality to show Andre's statement, using $p$ for the number of paper clips.
2. Write another inequality to show Lin's statement, also using $p$ for the number of paper clips.
3. Do you think both Lin and Andre would agree that there could be 487 paperclips in the box? Explain your reasoning.
4. Do you think both Lin and Andre would agree that there could be 742 paperclips in the box? Explain your reasoning.

1. 1. Select all numbers that are solutions to the inequality $w<1$.

      5

      -5

      0

      0.9

      -1.3
   2. Draw a number line to represent this inequality.
2. 1. Write an inequality for which 3, -4, 0, and 2,300 are solutions.
   2. How many total solutions are there to your inequality?

1. Lin says that the inequalities $h >150$ and $h <160$ describe her height in centimeters. What do the inequalities tell us about her height?
2. Andre notices that he is a little taller than Lin but is shorter than their math teacher, who is 164 centimeters tall. Write two inequalities to describe Andre's height. Let $a$ be Andre's height in centimeters.

3. Select all heights in centimeters that could be Andre's height. If you get stuck, consider drawing a number line to help you.

   1. 150
   2. 154.5
   3. 160
   4. 162.5
   5. 164

Here are the scores for landing an arrow in the different regions of the archery target.

• A: 10 points
• B: 8 points
• C: 6 points
• D: 4 points
• E: 2 points

1. Andre shot three arrows and they landed at $(\text-5, 4),\, (\text-8, 7)$ and $(1, 6)$. What is his total score? Explain or show your reasoning.
2. Jada shot an arrow and scored 10 points. She shot a second arrow that landed directly below the first one but scored only 2 points. Name two coordinates that could be the landing points of her two arrows.

1. Plot points that represent the data. Be sure to label the axes.

   

2. In the town of New Haven, CT, the temperature at midnight was $1.2^\circ \text{C}$. Plot and label this point.
3. Which town was warmer at midnight, Princeton or New Haven? How many degrees warmer was it?
4. If the point $(3, \text-2.5)$ were also plotted on the diagram, what would it mean?

1. Plot the following points in the coordinate plane, and connect them in the order listed to create a polygon.

   $A~(1, 3)$

   ​​​​​​$B~(3, 3)$

   $C~(3, \text-2)$

   $D~(\text-2, \text-2)$

   $E~(\text-2, 0)$

   $F~(0, 0)$

   $G~(0, 2)$

   $H~(1, 2)$

   $I~(1, 3)$

   

2. Find the perimeter of the polygon.

1. What is the greatest common factor of 24 and 64? Explain or show your reasoning.

2. In your own words, what is the greatest common factor of two whole numbers? How can you find it?

1. What is the least common multiple of 6 and 9? Explain or show your reasoning.
2. In your own words, what is the least common multiple of two whole numbers? How can you find it?

For each problem, tell whether finding the answer requires finding a greatest common factor or a least common multiple. You do not need to solve the problems.

1. Elena has 20 apples and 35 crackers. She wants to make as many snack bags as possible that each contain the same combination of apples and crackers. What is the largest number of snack bags she can make?

2. A string of lights flashes two colors—red every 5 seconds and blue every 3 seconds. How long before both lights flash at the same time?

3. A florist orders sunflowers every 6 days and daisies every 4 days. On which day will she order both kinds of flowers on the same day?