Sixth Grade
Math Prep: Session 4
Note to Teachers:
This lesson will focus on rational numbers. Students will be required to:
 Compare/order positive and negative numbers
 Find and explain absolute value in real world contexts
 Solve real world problems by graphing points in all four quadrants of
the coordinate plane
The session should be split up as such:
 Part 1- 20 minutes straight computation
 Part 2- 40 minutes problem solving
In problem solving sections, have students read the problems, think
carefully about each, and underline important math facts and information. When
students are finished, go over the correct answers, while providing explanations as
to why the problem would be solved with a particular method.
Grade 6 Lesson 4: Rational Numbers
Part I: Computation
Order each set of integers on a number line.
Find the absolute value.
Compare the pairs of integers using the <, >, or = symbols.
Part II: Problem Solving
1. One of the thermometers below shows -3°C and the other shows -7°C.
_________
________
Part A: Label each thermometer with its correct temperature.
Part B: Which is the colder temperature? How much colder?
______________________________________________________________________________
______________________________________________________________________________
Part C: Write an inequality to show the relationship between the temperatures and explain how
the model shows this relationship.
______________________________________________________________________________
2. The elevation of Mount Washington in New Hampshire is 6,288 feet. This means that Mount
Washington is 6,288 feet above sea level. The elevation of Death Valley is -282 feet. What
does an elevation of -282 feet mean?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Mark an X on the number line that shows the location of the opposite of Point A.
4. Which number on the number line is the same distance from both Point A and Point B?
Show or explain how you found your answer.
5. If the point (3,-5) is reflected across the x-axis, what are the coordinates of the new point?
Show or explain how you found your answer. You may use the coordinate plane below to help
you find the answer.
6. Look at the table below:
State
Connecticut
Maine
Massachusetts
New Hampshire
Rhode Island
Vermont
Record Low
temperature (°F)
-32
-48
-35
-47
-25
-50
Which state had the coldest temperature? Show or explain how you found your answer.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. Which number has the greatest absolute value? Explain your answer.
15, -34, -27, 28
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
8. A whale is swimming at a depth of -25 feet. A submarine is located at a depth of -40 feet.
Sea level is 0 feet. Which is deeper, the whale or the submarine?
Show or explain how you know your answer is correct.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
9. Look at the coordinate plane below:
Part A: Points A, B and C are the vertices of a rectangle. What are the coordinates of the
missing vertex of the rectangle?_____________________________________________
Part B: What is the distance between points A and B?____________________________
10. A train leaves Tooele, Utah at 9:00 am traveling east to Salt Lake City, Utah.
The distance is 34 miles. At the same time and speed a train leaves Park City,
Utah traveling west to Salt Lake City, Utah. The distance is 33 miles.
Part A: Place a dot on 0 representing Salt Lake City and label.
Part B: Place dots on the number line to represent Tooele and Park City and label.
Part C: Distance of Tooele to Salt Lake is_______.
Distance of Park City to Salt Lake is_______.
Distance from Tooele to Park City is_______.
11. The slide at the water park is 12 ft high. The pool is 6 ft deep. The distance from the bottom
of the slide to the surface of the pool water is 2 ft.
Part A: Label 0 as the bottom of the slide on your number line.
Part B: Label the top of the slide and the bottom of the pool on the number line.
Part C: Distance from the bottom of the pool to the bottom of the slide is_______.
Part D: Distance from the top of the slide to the bottom of the slide is_______.
Part E: Distance from the top of the slide to the bottom of the pool is_______.
12. Freezing point is 0˚C and boiling point is 100˚C. On February 1, 1985 the record coldest
temperature measured in Utah at Peter’s Sink was -56 ˚C. On July 5, 1985 the record hottest
temperature measured in Utah in St. George was 47 ˚C.
Part A: Label the four temperatures on your number line.
Part B: The difference between the highest and lowest temperature marked on your
number line is_______.
Part C: The difference between the hottest and coldest temperatures in Utah on record
is_______.
Part D: The difference between Utah’s hottest temperature and the boiling point
is_______.
13. Write the integer that would represent the following scenarios:
A:
A 4 dollar a day increase in pay_________
B:
5 feet below the surface_________
C:
An elevator rises 10 floors_________
D:
A coupon for 5 dollars off___________
E:
A 75 dollar deduction from your bank account_________
14. What inequality does this number show? Write your inequality starting with x.
______________________________________________________________
15. What inequality does this number show? Write your inequality starting with x.
______________________________________________________________
16. What inequality does this number show? Write your inequality starting with x.
______________________________________________________________
17. Write which quadrant on the coordinate graph each point is in.
A: (3, -4)_________________
B: (-4, 5) _________________
C: (7, 5) _________________
D: (-5, -6) _________________
18. Use the map below to answer the following questions.
Part A: What is at point (-3, -4)?______________________
Part B: What is at point (4, -4)?_______________________
Part C: What is the distance between these two locations?_________