Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Teacher Background Information:
Linear Context Examples
Many of the real contexts for negative numbers are linear. In addition, the number line provides a good tool for learning the operations and relate well to what
the students have done with whole number and fraction operations. See www.mathgoodies.com/lessons/vol5/intro_integers.html for a good introduction to
integers on a number line.
Temperature. The “number line” measuring temperature is vertical. This context demonstrating negative integers may be the most familiar to
students, as they have either experienced temperatures below zero or know about temperatures at the North or South Pole. A good starting
activity for students is finding where various temperatures belong on a thermometer. For example, a thermometer marked in increments of five
degrees, and students are asked to place on the number line the following temperatures from a week in North Dakota: 8°, -2°, -12°, 4°, -8°. Ask
students to order the temperatures from the coldest to the warmest (least to greatest). Temperatures as a context have the advantage that you can
also use fractional and decimal values.
Altitude. Another vertical number-line model, altitude, is also a good context for integers. The altitudes of sites below sea level are negative, such
as the town of Dead Sea, Israel (with an altitude of –1371 feet), and Badwater, California, in Death Valley (which has an altitude of –282 feet).
Positive values for altitude include Mount McKinley (the tallest mountain in North America) at 20,322 feet. Students can order the altitudes of
various places around the world (data easily found through a Google search on the Web).
Process Standards to Emphasize with Instruction of 6.NS.3:
6.PS.1: Make sense of problems and persevere in solving them.
6.PS.2: Reason abstractly and quantitatively.
6.PS.4: Model with mathematics.
6.PS.5: Use appropriate tools strategically.
6.PS.7: Look for and make use of structures.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Lesson Plans/Print Activities:
Web-based Practice:


Indiana Math Connects: Study Guide and Intervention Workbook, pages
35-36.
Indiana Math Connects: Skills Practice Workbook, pages 18-19.

http://www.mathsisfun.com/algebra/compare-numbers-1010.html Online Game

http://www.mathsisfun.com/flash.php?path=%2Fmeasure/images
/thermometer.swf&w=750&h=525&col=%23FFFFFF&title=Interacti
ve+Thermometer Interactive Thermometer

https://www.engageny.org/resource/grade-6-mathematics-module-3topic-b-overview EngageNY Module 3 Topic B Overview

https://www.engageny.org/resource/grade-6-mathematics-module-3topic-b-lesson-7 EngageNY Lessons 7-10

http://www.mathsisfun.com/numbers/ordering-game.php
Ordering Game

Georgia Department of Education Learning Task


https://www.illustrativemathematics.org/contentstandards/6/NS/C/7/tasks Illustrative Mathematics Tasks
http://www.virtualnerd.com/common-core/grade-6/6_NSnumber-system/C/5/positive-negative-number-definitions Video
lessons


https://learnzillion.com/lessonsets/138-interpret-statements-ofinequality-and-write-interpret-and-explain-statements-of-order-forrational-numbers Learnzillion videos Interpret statements of inequality
and write , interpret, and explain statements of order for rational numbers
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thnegative-number-topic/cc-6th-comparing-negativenumbers/e/ordering-rational-numbers Khan Academy Ordering
rational numbers

https://learnzillion.com/lesson_plans/5095-locate-rational-numbersusing-a-number-line#fndtn-lesson Learnzillion Locate rational numbers
using a number line
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Teacher Background Information:
As with any new topic or type of number, it is important to start with familiar contexts so that students can use prior knowledge to build meaning. With
integers, students often get confused as to which number is bigger or which direction they are moving so having context is particularly important.
As students learn to compare they can use the contexts to ground their thinking.
Quantity Contexts Examples:
Golf Scores. In golf, scores are often written in relationship to a number considered par for the course. So if par is 70 for the course, a golfer who ends the day
at 67 has a score of -3 , or 3 strokes under par. Consider a player in a four-day tournament with day-end scores of +5, -2, -3, +1. What would be his or her final
result for the tournament? How did you think about it? You could match up the positive and the negatives (in this case, +5 with -2 and -3 to get a net result of 0),
and then see what is left (in this case, +1). The notion that opposites (5 and -5) equal zero is a big idea in the teaching of integers. You can post a mixed-up
leaderboard of golf scores and ask students to order the players from first through tenth place. Emphasize that first place is the lowest score—and therefore the
smallest number.
Money: Payments and Deposits. Suppose that you have a bank account. At any time, your records show how many dollars are in your account. The difference
between the payments and deposit totals tells the amount of money in the account. If there is more deposited than paid out, the account has a positive
balance, or “in the black.” If there are more payments than deposits, the account is in debt, showing a negative cash value, or is “in the red.” This is a good
context for exploring addition and subtraction of integers.Net worth is a similar way to look at integers (assets and debts). Considering the net worth of famous
people can engage students in making sense of integers.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
1) Andréa and Marta are testing three different coolers to see which keeps the coldest temperature. They placed a bag of ice in each cooler, closed the coolers,
and then measured the air temperature inside each after 90 minutes. The temperatures are recorded in the table below:
Cooler
Temperature (ᵒC)
A
−2.91
B
5.7
C
−4.3
Marta wrote the following inequality statement about the temperatures:
̶ 4.3 < ̶ 2.91 < 5.7
Andréa claims that Marta made a mistake in her statement and that the inequality statement should be written as:
̶ 2.91 < ̶ 4.3 < 5.7
a) Is either student correct? Explain. Yes, Marta is correct. ̶ 4.3°C is colder than ̶ 2.91°C so it has a smaller temperature reading.
b) The students want to find a cooler that keeps the temperature inside the cooler more than 3 degrees below the freezing point of water (0°C) after 90
minutes. Indicate which of the tested coolers meets this goal and explain why. Only Cooler C meets the requirements since ̶ 4.3 is colder than 3 degrees
below 0.
[www.engageny.org]
2) Mary manages a company that has been hired to flatten a plot of land. She took several elevation samples from the land and recorded those elevations
below:
Elevation Sample
A
B
C
D
E
F
Elevation
826.5
830.2
832.0
831.1
825.8
827.1
(feet above sea level)
a. The landowner wants the land flat and at the same level as the road that passes in front of it. The road’s elevation is 830 feet above sea level. Describe
in words how elevation samples B, C, and E compare to the elevation of the road. Sample B is two-tenths of a foot above the level of the road. Sample C
is 2 feet above the level of the road. Sample E is 4.2 feet below the level of the road.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
b. The table below shows how some other elevation samples compare to the level of the road: [www.engageny.org]
Elevation Sample
Elevation
(from the road)
G
H
I
J
K
L
3.1
−0.5
2.2
1.3
−4.5
−0.9
Write the values in the table in order from least to greatest. ̶ 4.5 < ̶ 0.9 < ̶ 0.5 < 1.3 < 2.2 < 3.1
_________< _________ < _________ < _________ < _________ < _________
3. Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a computer program. Mr. Kindle receives a daily email that updates
him on all his transactions from the previous day. This morning, his email read as follows: [www.engageny.org]
Good morning, Mr. Kindle,
Yesterday’s investment activity included a loss of $800, a gain of $960, and another gain of $230. Log in now to see your current balance.
a) Write an integer to represent each gain and loss.
Description
Integer Representation
Indianapolis Public Schools
Loss of $800
̶ 800
Gain of $960
+ 960
Gain of $230
+ 230
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
b) Mr. Kindle noticed that an error had been made on his account. The “loss of $800” should have been a “gain of $800.” Locate and label both points that
represent “a loss of $800” and “a gain of $800” on the number line below. Describe the relationship of these two numbers, when zero represents no
change (gain or loss). Check students’ number lines for correct labeling of intervals and plotting of points. The two numbers are opposites.
[www.engageny.org]
4)
4 5
2
3
,
, ̶
, and ̶
on the number line. Check students’ number lines for accuracy.
3 4
3
4
b. For each of the following, state which inequality is true. Use the number line diagram to help explain your answers.
4
5
4
5
i. Is
>
, or is
<
? The first inequality is true.
3
4
3
4
2
3
2
3
ii. Is ̶
> ̶
, or is ̶
< ̶
? The first inequality is true.
3
4
3
4
3
5
5
3
3
c. Is ̶
or
closer to 0? Explain how you know. ̶
is closer to 0.
to the left of 0 is closer than
to the right of 0.
4
4
4
4
4
[modified from www.illustrativemathematics.org]
a. Plot the numbers
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
(SBAC)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
(Readiness I)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
(Readiness II)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
6.NS.3
Standard: 6.NS.3 Compare and order rational numbers and plot them on a number line. Write interpret, and explain statements or order for rational numbers
in real-world contexts.
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction