Mathematics 7
Items to Support Formative Assessment
Unit 1: The Number System
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add
and subtract rational numbers; represent addition and subtraction on a horizontal or
vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0.
7.NS.A.1a (Pre - Assessment)
The sum of opposite integers is equal to zero (Definition of Additive Inverse). This situation
lends itself to the Act it Out problem solving strategy.
Sample Act it Out Problem:
Julia and Roberto are each holding cards with integers on them. One has a positive integer and
the other has a negative integer. The teacher has put a number line on the floor using tape and
asks Julia and Roberto to stand on the points that represent their numbers. How can they
determine if their numbers are opposites without showing each other their cards?
Source http://teachersites.schoolworld.com/webpages/TAhrens/files/Integers,%20Opposites,%20Absol
ute%20Value.pdf.
Sample answer: They must each determine how far they are from zero. Since they are on
opposite sides of 0, their distances from zero are the same if they are holding cards with opposite
numbers on them.
7.NS.A.1a (Post - Assessment)
1. Take a liberal handful of two-color counters.
2. Place the counters on your desk in a small group.
3. Calculate the value of the pile of your counters, using “zero pairs” to do so.
4. As you work through the calculations, write the algorithm on your paper that represents your
two-color counters. Keep in mind that when you encounter the zero pairs, you should write
them as such, “-4 + 4”.
5. Did the value of your counters equal 0? Did the value of your counters equal something
greater than or less than 0?
6. How many two-color counters might you need to add or subtract from your total to equal 0?
For example:
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The algorithm would reflect -5 white counters +5 blue counters = 0,
plus 1 blue counter = a grand total of +1
(-5+5) +1 = +1
The student would need to add one counter representing -1 to make their total equal 0.
7.NS.A.1a Short Task
Billie and Bobbie are contestants on the game show, We Made Zero. To win, Billie must select
5 jobs from the Job Opportunities table to earn money. Additionally, Bobbie must purchase 30
items from the Purchases table that equals the amount that Billie earned. What is the correct
combination of earnings and spending to win the game? Model this situation on a number line.
Job Opportunities
Task
Time
Rate
Collecting Cans
4 Hours
$ 5.00 per Hour
Washing Cars
5 Hours
$ 8.00 per Hour
Sweeping
6 Hours
$ 10.00 per Hour
Cooking Eggs
8 Hours
$ 13.00 per Hour
Handy Man
9 Hours
$ 20.00 per Hour
Pool Cleaner
10 Hours
$ 15.00 per Hour
Purchases
Item
Quantity
Unit Price
Diet Coke
4- 12 Packs
$ 5.00 per Pack
Tide Pods
6 - 30 Pod Containers
$ 10.00 per Container
Trivia
8 Boxes
$ 5.00 per Box
Rib Eye Steaks
10 2lb Steaks
$ 8.00 per Pound
Golf Balls
8 Boxes
$ 25.00 per Box
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Bath & Body Soap
6 Bottles
$ 5.00 per Bottle
Milk
3 1 Gallon Bottles
$ 4.00 per Gallon
Possible Solution:
Earnings
Task
Time
Rate
Collecting Cans
4 Hours
$ 5.00 per Hour
Washing Cars
5 Hours
$ 8.00 per Hour
Sweeping
6 Hours
$ 10.00 per Hour
Handy Man
9 Hours
$ 20.00 per Hour
Pool Cleaner
10 Hours
$ 15.00 per Hour
20 + 40 + 60 + 180 + 150 = $ 450
Purchases
Item
Quantity
Unit Price
Tide Pods
6 - 30 Pod Containers
$ 10.00 per Container
Rib Eye Steaks
10 2lb Steaks
$ 8.00 per Pound
Golf Balls
8 Boxes
$ 25.00 per Box
Bath & Body Soap
6 Bottles
$ 5.00 per Bottle
Items 6 + 10 + 8 + 6 = 30
Purchases 60 + 160 + 200 + 30 = $ 450
Number Line Model: Students would plot 450 and -450 on the number line to see that these are
opposite integers showing Billie’s earnings ($450) and Bobbie’s purchases (-$450).
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7.NS.A.1a
Point T is shown on the number line below.
Point R is the opposite of Point T. Determine the location of Point R. Explain how you
determined the location of Point R on the number line.
Solution:
Sample Explanation: Since T is 4 units to the left of 0, I placed point R four units to the right of
zero. Point T is at -4, so point R should be placed at 4.
7.NS.A.1a Short Task
Jenny likes to play golf. On average she will normally par each hole. To par a hole you must
take only the number of suggested shots to get the ball in the hole. For example a par 3 hole will
only take 3 shots to get the ball in the hole. At Timbers the first nine holes have four par 3 holes,
three par 4 holes, and two par 5 holes. Below is her score card. What must she shoot for on the
next 4 holes to remain on par?
Jenny’s Score Card:
Hole
1
2
3
4
5
6
7
8
9
Par
5
4
3
3
4
3
4
3
5
Jenny’s Score
7
3
4
3
4
2
3
4
5
6
7
8
9
Possible Solution
Hole
1
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Par
5
4
3
3
4
3
4
3
5
Jenny’s Score
7
3
4
3
4
3
3
2
5
7.NS.A.1a Short Answer
In Fairbanks the temperature at 6:00 AM on Sunday is - 48°F. The weather forecast predicts that
a warming trend will raise the temperature to 0°F. (Have students model using the number line.)

If the Temperature rises an average of 16° a day, how many days will it take to get to 0?
3 days

If the temperature starts at -48°F on Sunday and rises 15° on Monday, 25° on Tuesday
and 10° on Wednesday, what must the temperature rise or fall on Thursday to reach 0?
Fall 2 degrees (-2)
7.NS.A.1a Short Answer
Have you ever ridden the Tower of Terror? The Chang Family is riding the Tower of Terror in
Disney’s Hollywood Studios. They get on the ride for the first time and it takes them up the 21st
floor and opens up to the grand view of the theme park. The second time they get on the ride, it
opens up to the 42nd floor. The third and final time on the ride, it opens to the 18th floor.
There are frequent drops on the ride where you are taken up and then dropped several times.
Here is a record of their time on the Tower of Terror.

First time on the ride: They go up to the 21st floor, down 7 floors, up 5 floors, down 2
floors, and up 4 floors. What floor did they end up on? 21st floor

Second time on the ride: They go up to the 42nd floor, down 15 floors, up 10 floors,
down 5 floors, and up 10 floors. What floor did they end up on? 42nd floor

Third time on the ride: They go up to the 18th floor, down 9 floors, up 5 floors, down 6
floors, and up 10 floors. What floor did they end up on? 18th floor
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7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add
and subtract rational numbers; represent addition and subtraction on a horizontal or
vertical number line diagram.
b. Understand p + q as the number located a distance from p, in the positive or negative
direction depending on whether q is positive or negative. Show that a number and its
opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by
describing real-world contexts.
7.NS.A.1b (Pre - Assessment)
Write 3 or 4 number sentences, using addition or subtraction, that equal 0.
Then, use the red/yellow counter chips to prove that your number sentence equals 0.
Why do they equal 0?
Possible Solution:
5 + (-5) = 0
4 + (-4) = 0
-6 + 6 = 0
Example for 5 + (-5):
Example for 4 + (-4):
Example for -6 + 6:
All of the above sentences equal zero because a number and its opposite equal zero. In addition,
when you use the chips and create zero pairs with no chips left over, the value is zero.
Website resource - http://www.basic-mathematics.com/modeling-integers.html
7.NS.A.1b (Post - Assessment)
Michael is trying to play par golf for today (Par golf equals a score of “0” for the day. For
example, if a golf course suggests that it would take 72 strokes to finish a round of 18 holes of
golf, and it takes exactly 72 for him/her to do so, then he/she played “par golf.” This would
result in a score of “0.” Also, if it takes 80 strokes to finish a round, this would result in a final
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
score of +8, or “8 over par.” Likewise, finishing in 70 strokes would result in an overall score of
-2, or “2 under par.” Individual scores for each hole are also calculated the same way, based on
their suggested strokes.
Calculate what Michael would need to score on the 9th hole of golf in order to play par golf
(total score of 0) for Holes 1-9, if his score card for the first 8 holes is as follows:
Hole 1
Hole 2
Hole 3
Hole 4
Hole 5
Hole 6
Hole 7
Hole 8
Hole 9
-1
0
-2
+4
-2
+5
-2
+2
??
Now, fill in the blanks on Michael’s score card for Holes 10-18, so that his final score for these
holes is par. What could his possible scores be for Holes 11, 15 and 18?
Hole
10
Hole
11
Hole
12
Hole
13
Hole
14
Hole
15
Hole
16
Hole
17
Hole
18
-2
??
+1
0
+3
??
-1
+4
??
Based on the scores that you wrote for Holes 11, 15 and 18, calculate Michael’s overall score for
Holes 1-18. Did he play par golf today?
Answers: Hole 9: -4 to have a total score of 0 by end of Hole 9
Answers will vary for Holes 10-18. The total shown is +5, so the three numbers would have to
add to -5.
7.NS.A.1b Short Answer
You are keeping the statistics for Saturday’s football game. The shorthand you developed is
simple, an arrow right is a gain, an arrow left is a loss, and the number that follows the arrow
represents the yardage.

Write an expression that will show the total yards for the first four plays of the game.
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4 + 1 + 6 -3
or 4 + 1 + 6 + (-3)

What was the total yardage gained or lost for the first four plays of the game?
8 yards gained
7.NS.A.1b Short Answer
For your 7th birthday Aunt Hilda purchased 1 share of Under Armour stock for you. Each year
on your birthday you sit down and calculate the total money lost or gained for the stock over the
previous four quarters. Last year the stock gained $10.00 for the first quarter, gained $ 3.00 for
the second quarter, lost $ 6.00 for the third quarter, and gained $ 2.00 for the fourth quarter.

Write an expression that will show the total amount gained or lost for the year.
10 + 3 - 6 + 2
or 10 + 3 + (-6) + 2

What was the total amount gained or lost for the year?
$9.00

The stock share started the year at $ 116.00. Using the gain or loss from the prior
question, how much was the stock worth at the end of the year?
$116.00 + $ 9.00 = $125.00
7.NS.A.1b Short Answer
The temperature of a mixture was 12°Celsius at the start of the experiment. After four hours the
temperature decreased 25°. What is the current temperature of the mixture?
12 + (-25) = -13°Celsius
7.NS.A.1b Short Answer
For homework Pam had to list some of the possible signed outcomes for adding two
integers. She developed the list below.
1. Positive + Positive = Positive
2. Positive + Positive = Negative
3. Negative + Positive = Positive
4. Negative + Positive = Negative
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5. Positive + Negative = Positive
6. Positive + Negative = Negative
Look at the list. Write Always, Sometimes, or Never next to each statement to indicate if the
statement it always true, sometimes true, or never true. If the statement is sometimes true, justify
by providing a counterexample.
1. Positive + Positive = Positive
Always
2. Positive + Positive = Negative Never
3. Negative + Positive = Positive Sometimes;
4. Negative + Positive = Negative Sometimes;
5. Positive + Negative = Positive Sometimes;
6. Positive + Negative = Negative Sometimes;
Cex. -7 + 3 = -4
Cex. -7 + 12 = 5
Cex. 3 + -8 = -5
Cex. 9 + -5 = 4
7.NS.A.1b Short Answer
Scores over Par in Golf Tournaments are recorded as positive integers. Scores under Par in Golf
Tournaments are recorded as negative integers. Even Par is recorded as a 0. The golfer with the
lowest total score is the winner. The table below shows four finishers in the 2011 PGA
Championship Rounds.
Player
Round 1
Round 2
Round 3
Round 4
Pamela Putter
0
-4
2
-1
Donna Driver
3
0
-5
-3
Wilma Wood
-7
2
0
-1
Patty Pitcher
1
-2
-3
0

Find the final score for Pamela Putter.
0 + (-4) + 2 + ( -1) = -3

Find the final score for Wilma Wood.
-7 + 2 + 0 + ( -1) = -6

Find the final score for Patty Pitcher.
1 + (-2) + (-3) + 0 = -4

Find the final score for Donna Driver.
3 + 0 + (-5) + ( -3) = -5
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
Based upon these scores, who would be the winner of the tournament? Explain your
reasoning.
Wilma Wood would be the winner because her score of -6 is the lowest score. She is 6
under par.
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.