Red and black

Red and black

Pencil and paper
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Using this Resource
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Marking Student Responses
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Further Resources
This task is about calculations with negative numbers.

 

Denis has a pack of cards in which each card is either black or red. Each card has a number on it.
The red cards show positive numbers and the black cards show negative numbers.
For example, a red 4 represents 4, but a black 6 represents ⁻6.
 
a)   Denis draws out two cards and multiplies the numbers together.
     Find the answers he gets for each of these combinations of cards.
 
  1st card    ×   2nd card 
=   Answer
 
      i)
 
      ii)
 
      iii)
 
      iv)
Red 3
 
Black 4
 
Black 8
 
Red 6
×   Red 9
 
×   Red 6
 
×   Black 5
 
×   Black 5
=   __________
 
=   __________
 
=   __________
 
=   __________
 
b)   Next Denis draws out three cards. He multiplies the first two and then adds the third.
      Find the answers he gets for each of these combinations of cards.
 
1st card
×   2nd card   
+   3rd card 

=   Answer
 
 
      i)
 
      ii)
 
      iii)
 
      iv)
Red 5
 
Black 6 
 
Black 8
 
Black 3
×   Red 3
 
×   Red 4
 
×   Red 4
 
×   Black 2   
+   Black 4
 
+   Red 10
 
+   Black 5
 
+   Black 7
=   __________
 
=   __________
 
=   __________
 
=   __________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
negative numbers, addition, multiplication
Description of task: 
Students perform calculations using whole numbers and negative numbers.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (09/1999)
a) i)
ii)  
iii)
iv)  		 27
⁻24
40
⁻30		 4 correct – easy  

2-3 correct – very easy
b) i)
ii)  
iii)  
iv)  		 11
⁻14
⁻37
⁻1		 4 correct – moderate  
    
2-3 correct – easy

NOTE: accept answers in which students have used "black" and "red" in place of – and +, e.g., accept "black 24" as being equivalent to ⁻24.
 

Diagnostic and formative information: 
  Common error Likely calculation Likely reason
b) i)  

    ii)  
    iii)  
    iv)  
 ⁻60

⁻240
160  
⁻42
 5 × 3 × ⁻4

⁻6 × 4 × 10
⁻8 × 4 × ⁻5
⁻3 × ⁻2 × ⁻7
 Multiplies instead of adding.  
b) i)  

    ii)  
    iii)  
    iv)  
 19  

34  
⁻27
13  
 5 × 3 + 4  

6 × 4 + 10  
⁻8 × 4 + 5
⁻3 × ⁻2 + 7
 Adds 4 rather than ⁻4.

Multiplies by 6 rather than ⁻6. 
Adds 5 rather than ⁻5.
Adds 7 rather than ⁻7.