TV game show

TV game show

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working with negative numbers.
 
A TV game show gave 10 points for a right answer, but took off 5 points for a wrong answer.
 
a) Part way through the game the scores were:

 
 
i)
 
ii)
Who had the highest score? _____________
 
Who had the lowest score? _____________
 
b)  
Ataria started with a score of 0.
After answering only two questions, she had a score of ⁻10.
How did she get that score?
 
 
 
 
 
c)  
i)
 
 
ii)
 
 
iii)  
Josh is on a score of ⁻5 points.
If he gets the next 4 questions wrong, what will his new score be? __________
 
Wiremu is on a score of 10 points.
If he gets 1 question right and 5 wrong, what will his new score be? __________
 
Tala is on a score of ⁻15 points.
If he gets 4 questions right and 2 wrong, what will his new score be? __________
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
negative numbers, addition, subtraction, multiplication
Description of task: 
Students find the biggest and smallest numbers from a list of positive and negative numbers. They add, subtract and multiply using these numbers.
Curriculum Links: 
This resource can help to identify students' ability to apply additive strategies flexibly to decimals and integers to solve addition and subtraction problems.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 7-8
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y9 (04/1999)
a) i)
ii)		 Ataria
Sarah		 very easy
b)    Explains in some way that she gets both questions wrong. easy
c)   i)  
ii)  
iii)		 ⁻25
⁻5
15		 easy  
moderate  
moderate
Diagnostic and formative information: 
  Common error Likely calculation Likely reason
a) i)
    ii)
c) i)		 Sarah
Josh
25

5 + 4 × 5

 Ignores the negative sign (i.e., works with the absolute value of the number).
c) i)  
    ii)  
    iii)  		 ⁻20
⁻15
30		 4 × ⁻5
10 + (5 × ⁻5)
4 × 10 + 2 × ⁻5		 Ignores the initial score of the person.  
c) iii)  45   15 + 40 – 10  
15 + 4 × 10 + 2 × ⁻5		 Ignores negative sign on initial score of ⁻15.