Published by CTB/McGraw-Hill LLC. Copyright © 2004 Page 1 Quiz Test 7by Mathematics Assessment Resource Service. All rights reserved.

QuizThis 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.

Steve Marty Zac LizNumber of correct answers 5 4 6 5Number of incorrect answers 4 4 3 1Number of questions not attempted 1 2 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

Seventh Grade – 2004 pg. 5

Student Materials Using Positive and Negative Numbers in Context S-1 © 2012 MARS, Shell Center, University of Nottingham

Temperature Changes 1.

(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.

(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.

The temperature was +3°C at midday.

By evening, the temperature was −5°C.

The temperature was −7°C at midnight.

By the next day, the temperature had risen by 11°C.

Student Materials Using Positive and Negative Numbers in Context S-2 © 2012 MARS, Shell Center, University of Nottingham

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 S-3 © 2012 MARS, Shell Center, University of Nottingham

Temperature Scales

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Student Materials Using Positive and Negative Numbers in Context S-4 © 2012 MARS, Shell Center, University of Nottingham

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 S-5 © 2012 MARS, Shell Center, University of Nottingham

Card Set: City Temperatures

Anchorage

_ _ _ _ _ _ _ _

New York −5°C

Washington

_ _ _ _ _ _ _ _

Fairbanks

_ _ _ _ _ _ _ _

New Orleans +10°C

Honolulu +25°C

Las Vegas +20°C

Detroit

_ _ _ _ _ _ _ _

Student Materials Using Positive and Negative Numbers in Context S-6 © 2012 MARS, Shell Center, University of Nottingham

Card Set: Changes in Temperature

Washington to Las Vegas _ _ _ _ _ _ _ _ _ _____

New Orleans to Las Vegas _ _ _ _ _ _ _ _ _ _____

Honolulu to Anchorage

−35°C

Detroit to Honolulu _ _ _ _ _ _ _ _ _ _____

Anchorage to Washington

+30°C

Washington to New Orleans

−10°C

Anchorage to New York

_ _ _ _ _ _ _ _ _ _____

New York to Detroit

+15°C

Las Vegas to Fairbanks

−45°C

Fairbanks to Honolulu

+50°C

Student Materials Using Positive and Negative Numbers in Context S-7 © 2012 MARS, Shell Center, University of Nottingham

Card Set: Changes in Temperature (Continued)

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _

−5 − (+25) = −30°C _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

−10 − (−25) = +15°C

Student Materials Using Positive and Negative Numbers in Context S-8 © 2012 MARS, Shell Center, University of Nottingham

Temperature Changes (revisited) 1.

(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.

(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.

The temperature was +5°C at midday.

By evening, the temperature was −3°C.

The temperature was −2°C at midnight.

By the next day, the temperature had risen by 9°C.

Student Materials Using Positive and Negative Numbers in Context S-9 © 2012 MARS, Shell Center, University of Nottingham

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:

Using Positive and Negative Numbers in Context Projector Resources

Temperature Changes

P-1

London +13°C

Beijing −5°C

Paris +22°C

Vancouver −11°C

Using Positive and Negative Numbers in Context Projector Resources

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.

P-2

Using Positive and Negative Numbers in Context Projector Resources

More Temperature Changes

P-3

London +8°C

Madrid

_ _ _ _ _ _ _ _ _ _ _

+7°C

−12°C

Berlin

_ _ _ _ _ _ _ _ _ _ _

Tromso −7°C

Tromso

−7°C

London +8°C

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Using Positive and Negative Numbers in Context Projector Resources P-4

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Sixth  Grade   Performance  Test   2012  (c)  Silicon  Valley  Mathematics  Initiative  2011.    To  reproduce  this  document,  permission  must  be  granted  by  the  SVMI  info@svmimac.org    

 

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

-12º

Feb 2

-17º

Feb 3

-8º

Feb 4

10º

Feb 5

2º

Feb 6

-16º

Feb 7

-11º Feb 8

-21º

Feb 9

8º

Feb 10

-13º

Feb 11

5º

Feb 12

13º

Feb 13

-9º

Feb 14

-33º Feb 15

-42º

Feb 16

-27º

Feb 17

-2º

Feb 18

-4º

Feb 19

18º

Feb 20

15º

Feb 21

-3º Feb 22

-18º

Feb 23

-15º

Feb 24

-4º

Feb 25

-28º

Feb 26

-6º

Feb 27

10º

Feb 28

3º  

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.  

       

Performance Task Freezing in Fargo

Sixth  Grade   Performance  Test   2012  (c)  Silicon  Valley  Mathematics  Initiative  2011.    To  reproduce  this  document,  permission  must  be  granted  by  the  SVMI  info@svmimac.org    

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  

©Silicon Valley Mathematics Initiative 2012. To reproduce this document, permission must be granted by the SVMI info@svmimac.org.

20

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

points

section points

1. Gives correct answers: Sunday Feb. 15 and -42 Degrees Fahrenheit 1

1

2. Gives correct answer: -18 (accept 18 degrees colder) Show correct work such as: -33 - -15

1 1

2

3. Gives correct answer: The greatest change was 29º - Feb. 8 and Feb. 9 Gives an explanation such as: Checked other close answers Feb. 16 and 17 (25º) or Feb. 24 and 25 (24º) or Feb. 13 and 14 (24º), etc.

1 1

2

4. Gives correct answer: The coldest average week was Feb. 22 to Feb. 28 Gives an explanation such as: Feb. 1 – 7 average temperature was -7.4º or total -52º 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

1 1

2

5. Gives correct answer: 3.5 Gives an explanation such as: -28 ÷ -8 = 3.5

1 1

2

Total Points 9