Easy or harder subtractions

Easy or harder subtractions

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Overview
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This task is about subtraction. 

Here are two subtraction problems.

Once you have completed them, select which was harder for you to do, and explain why.

Question

a) Mere had $76 in her bank account.

    She spent $24.

    How much did she have left in her account?

    • $52

    • $53

    • $62

    • $100

Question

b) Alicia had $54. She paid $36 for some computer games.

    How much did Alicia have left?

    • $12

    • $18

    • $19

    • $22

    • $28

Question

c) Which of the two questions did you find harder?

    • I think that  $76 - $24 was harder.

    • I think that $54 - $36 was harder.

    • I think that they are just as hard as each other.

Question 1Change answer

d) Explain your answer to question c).

  • I think that  $76 - $24 was harder.

  • I think that $54 - $36 was harder.

  • I think that they are just as hard as each other.

Task administration: 
This task can be completed with pen and paper or online (with SOME auto marking).
Levels:
2, 3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
subtraction, money
Description of task: 
Students select the answer for two subtraction problems, select which one they thought was easier, and explain their reasons for this.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, set 5
Additive thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y4 (11/2013)
a) 52 very easy
b) 18 easy
c)  12 students said that 54 - 36 was harder.
   2 student said that 76 - 24 was harder.
  16 students said they were both equally hard or easy		  
d) 4 students commented about the "Won't go" error
   - "Because taking 6 away from 4 is harder because I have to go below a tidy number."
   - "Because you have to go less than zero."
1 student commented that "It was harder because it was a bigger number."
1 student commented that "I had to do more subtracting."
2 student made general comments on their strategy:
  - "I subtracted the tens and the ones."
  - "I used a simple stagegy (sic)." [They got Q2 wrong]
There was little information in the remaining written responses.		  

Based on a sample of 30 Y4 students

Diagnostic and formative information: 
Student strategies
Student results in the trial utilised the following addition and subtraction strategies:
  • Partitioning using rounding and compensation to jump through tidy numbers or Partitioning by rounding one number to a tidy number then compensation. (Year 6, Number Framework Stage 6).
  • Place value partitioning one number into hundreds, tens and ones then adding it on to the other in parts. (Year 5, Number Framework Stage 6).
  • Place value partitioning using tens and ones with correct compensation consistently (Year 4, Number Framework Stage 5 – Early Additive).
  • Place value partitioning using tens and ones with incorrect compensation (Year 3, Number Framework Stage 5 – Early Additive).
  • The student recognises the role of tens and ones but cannot use them to compensate or cross the tens boundary correctly.
  • Using just counting-back strategies (Year 2, Number Framework Stage 4 – Advanced Counting).
 
  Common errors Likely reasons Next steps
a)
b)		 50, 51 or 53, 54
17 or 19		 Uses counting back. Explore subtracting back through ten with simple numbers
e.g., 14 - 4 = 10; 10 – 2 = 8
b) 22 Uses subtraction but takes away the bigger digit from the smaller. Get students to try similar subtractions where the strategy does not work (e.g., 65 - 57, which should be single digit).
Get students to show their working on the number line
b) 28 Crosses the tens boundary without "renaming" . Explore renaming using money ($10 and $1 notes).

  1. Firstly take off 3 $10s.
  2. Then substituting 10 $1 for $10
  3. Then take 8 lots $1 away from 14 lots of $1

This demonstrates a correct "renaming" of $10 as 10 lots of $1.