Quiz
This problem gives you the chance to:
• interpret a table of data
• compare results of calculations
Steve, Marty, Zac, and Liz take part in a quiz.
The quiz consists of ten questions.
Here are their results.
Number of correct answers
Number of incorrect answers
Number of questions not attempted
Steve
5
4
1
Marty
4
4
2
Zac
6
3
1
Liz
5
1
4
A correct answer scores 3 points.
An incorrect answer scores minus 2 points.
A question not attempted scores 0 points.
This is how Steve works out his total score:
5 x 3 = 15 points, 4 x -2 = -8 points, and 1 x 0 = 0 points = 7 points
1. Who scores the most points?
Show how you figured it out.
2. One of the rules is changed.
A question not attempted scores minus 1 point.
Who scores the most points?
Show how you figured it out.
8
Published by CTB/McGraw-Hill LLC. Copyright © 2004
by Mathematics Assessment Resource Service. All rights reserved.
Page 1
Quiz
Test 7
Seventh Grade – 2004
pg.
5
Temperature Changes
1.
The temperature was +3°C at midday.
By evening, the temperature was −5°C.
(a) Some of the calculations below show how to figure out the temperature change.
Circle any that apply.
3−5
3 + (−5)
(−5) − 3
(−5) + 3
(b) What was the change in temperature? Explain your answer.
2.
The temperature was −7°C at midnight.
By the next day, the temperature had risen by 11°C.
(a) Some of these calculations show how to figure out the temperature the next day.
Circle any that apply.
7 − 11
11 + (−7)
(−11) − (−7)
(−7) + 11
(b) What was the temperature the next day? Explain your answer.
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-1
3. Here is a calculation:
5 − (−11)
(a) Figure out the answer to the calculation:
(b) Which of these story questions fits the calculation? Circle any that apply.
A
It was extremely cold at midnight.
During the morning, the temperature rose by 5°C.
By midday, it had reached -11°C.
What was the temperature at midnight?
B
The temperature at midnight was −11°C.
By midday, the temperature was 5°C.
What was the temperature change?
C
At midday, the temperature was 5°C.
The temperature then fell by 11°C.
What was the final temperature?
Explain your answer:
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-2
Temperature Scales
Student Materials
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Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-3
Card Set: Introduction to Negative Numbers
London
+13°C
Paris
+20°C
Vancouver
−11°C
Beijing
−5°C
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-4
Card Set: City Temperatures
Anchorage
New York
−5°C
_______ _
Washington
Fairbanks
_______ _
_______ _
New Orleans
Honolulu
+10°C
+25°C
Las Vegas
Detroit
+20°C
Student Materials
_______ _
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-5
Card Set: Changes in Temperature
Washington to Las Vegas
_________
_____
New Orleans to Las Vegas
_________
Washington to New Orleans
_____
Honolulu to Anchorage
−10°C
Anchorage to New York
_________
New York to Detroit
+15°C
−35°C
Detroit to Honolulu
_________
Las Vegas to Fairbanks
_____
Anchorage to Washington
−45°C
Fairbanks to Honolulu
+30°C
Student Materials
_____
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
+50°C
S-6
Card Set: Changes in Temperature (Continued)
_______________
_______________
−5 − (+25) = −30°C
−10 − (−25) = +15°C
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-7
Temperature Changes (revisited)
1.
The temperature was +5°C at midday.
By evening, the temperature was −3°C.
(a) Some of these calculations show how to figure out the temperature change.
Circle any that apply.
5−3
−3 − (+5)
−5−3
(−5) + 3
(b) What was the change in temperature? Explain your answer.
2.
The temperature was −2°C at midnight.
By the next day, the temperature had risen by 9°C.
(a) Some of these calculations show how to figure out the temperature the next
day.
Circle any that apply.
−2 − 9
9 + (−2)
(−9) − (−2)
(−2) + 9
(b) What was the temperature the next day? Explain your answer.
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-8
3.
Here is a calculation:
9 − (−4)
(a) Figure out the answer to the calculation:
(b) Which of these story questions fits the calculation?
Circle any that apply.
A
At midday, the temperature was 9°C.
The temperature then fell by 4°C.
What was the final temperature?
B
At midnight, the temperature was −4°C.
By next morning, the temperature was 9°C.
What was the change in temperature?
C
It was extremely cold at midnight.
During the morning, the temperature rose by 9°C.
By midday, the temperature was −4°C.
What was the temperature at midnight?
Explain your answer:
Student Materials
Using Positive and Negative Numbers in Context
© 2012 MARS, Shell Center, University of Nottingham
S-9
Temperature Changes
London
+13°C
Beijing
−5°C
Paris
+22°C
Vancouver
−11°C
Projector Resources
Using Positive and Negative Numbers in Context
P-1
Instructions for Working Together
1.  Take turns to place cards.
2.  When it is your turn, connect two City Temperature
cards using a Changes in Temperature arrow card.
–  Figure out any missing temperatures.
–  Explain your calculations.
3.  If others in your group disagree, they should explain
why. Then figure out the answer together.
4.  When you have reached an agreement, write your
solution in the box on the card.
Projector Resources
Using Positive and Negative Numbers in Context
P-2
More Temperature Changes
London
+8°C
Berlin
___________
Tromso
−7°C
Projector Resources
+7°C
Madrid
___________
−12°C
____________________
Using Positive and Negative Numbers in Context
Tromso
−7°C
London
+8°C
P-3
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Projector Resources
Using Positive and Negative Numbers in Context
P-4
Performance Task
Freezing in Fargo
The chart indicates the daily lowest temperature for each day of February in Fargo, ND. Temperatures are in Fahrenheit. Sunday Monday Tuesday Wednesday Thursday Friday Saturday Feb 1
Feb 2
Feb 3
Feb 4
Feb 5
Feb 6
Feb 7
-12º
Feb 8
-17º
-8º
10º
2º
-16º
-11º
Feb 9
Feb 10
Feb 11
Feb 12
Feb 13
Feb 14
-21º
8º
-13º
5º
13º
-9º
-33º
Feb 15
Feb 16
Feb 17
Feb 18
Feb 19
Feb 20
Feb 21
-42º
-27º
-2º
18º
15º
-3º
Feb 22
Feb 23
Feb 24
Feb 26
Feb 27
Feb 28
-18º
-15º
-4º
-6º
10º
3º
-4º
Feb 25
-28º
1. Which date recorded the lowest daily temperature in the month? ___________ What was the temperature? __________ Degrees Fahrenheit. 2. What is the difference in temperature between Saturday Feb. 14 and Monday Feb. 23? ______________. Show how you determined your answer. Sixth Grade Performance Test 2012 (c) Silicon Valley Mathematics Initiative 2011. To reproduce this document, permission must be granted by the SVMI [email protected] 3. What is the greatest change in temperature between two consecutive days? Show how you figured it out. 4. Which week (Sunday – Saturday) recorded the average lowest temperature for the month? _________________. Justify your answers. 5. How many times colder is Wednesday Feb. 25 than Tuesday Feb. 3? ________ Explain. 9 Sixth Grade Performance Test 2012 (c) Silicon Valley Mathematics Initiative 2011. To reproduce this document, permission must be granted by the SVMI [email protected] Freezing in Fargo
Rubric
The core elements of performance required by this task are:
• modelling a situation using integers.
• understanding and performing operations on integers.
• finding the mean using integers.
Based on these, credit for specific aspects of performance should be assigned as follows
1.
Gives correct answers: Sunday Feb. 15 and -42 Degrees Fahrenheit
points
section
points
1
1
2.
Gives correct answer: -18 (accept 18 degrees colder)
1
Show correct work such as:
3.
-33 - -15
1
Gives correct answer: The greatest change was 29º - Feb. 8 and Feb. 9
1
2
Gives an explanation such as:
4.
Checked other close answers Feb. 16 and 17 (25º) or Feb. 24 and 25 (24º) or
Feb. 13 and 14 (24º), etc.
1
Gives correct answer: The coldest average week was Feb. 22 to Feb. 28
1
2
Gives an explanation such as:
Feb. 1 – 7 average temperature was -7.4º or total -52º
1
Feb. 8 – 14 average temperature was -7.1º or total -50º
Feb. 15 – 21 average temperature was -6.4º or total -45º
Feb. 22 – 28 average temperature was -8.3º or total -58
5.
2
Gives correct answer: 3.5
1
Gives an explanation such as:
-28 ÷ -8 = 3.5
1
Total Points
©Silicon Valley Mathematics Initiative 2012. To reproduce this document, permission must be granted by the
SVMI [email protected].
2
9
20