Subtraction and division boxes
0
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about completing equations that have brackets, using only numbers 2-12.
Task administration:
This task can be completed with pencil and paper or online.
Level:
4
Curriculum info:
Keywords:
Description of task:
Students complete subtraction and division linear equations with brackets by selecting from a range of numbers.
Answers/responses:
|
Y7 (03/2005) |
||
|
a) |
7,1 or 6,2 or 5,3 or 4,4 (or the reverse of each) |
easy |
|
b) |
12,6 or 11,5 or 10,4 or 9,3 or 8,2 |
moderate |
|
c) |
9,2 or 10,3 or 11,4 or 12,5 |
very difficult |
|
d) |
2,3 or 3,2 |
difficult |
|
e) |
12,3 or 8,2 |
very difficult |
|
f) |
2,6 or 3,9 or 4,12 |
very difficult |
Results are based on a sample of 220 students.
NOTE: Questions a), b) and d) can be solved without knowledge of order of operations (specifically, solving brackets first). Students who get these questions and not other questions correct may not have a full understanding of order of operations.
Diagnostic and formative information:
| Common error | Likely calculation | Likely misconception | |
| b) | 10,6 or 6,2 etc. |
10 - 6 = 4 or 6 - 2 = 4, etc. |
Solves the equation but ignores the "- 2" |
| d) | 6,3 or 4,2 |
6 : 3 = 2 4 : 2 = 2 |
Solves the equation but ignores the "12 :" |
|
c) e) f) |
5,2 or 4,3 or 6,1 (or the reverse of) 2,2 or 1,4 6,2 or 9,3 or 12,4 |
e.g., (17 - 5) - 2 = 10 (20 : 2) : 2 = 5 or (20 : 1) : 4 = 5 e.g., (9 : 3) : 3 = 1 |
Incorrectly uses or ignores the brackets. |
| d) | 6,2 | 12 : 6 : 2 = 2 : 2 | Incorrectly assumes that 2 : 2 = 2. |
|
e) f) |
10,2 3,3 |
20 : (10 : 2) = 5 3 : 3 : 3 = 1 |
Arithmetic error in working out division equation (possibly transposing 20 : 5 = 4 and 20 : 4 = 5). |
| e) | 10,5 (or the reverse of) | 20 - (10 - 5) = 5 | Uses subtraction instead of division and incorrectly uses brackets. |
Next steps:
Students who demonstrated a lack of understanding of order of operations for subtraction, division, and brackets could explore the effects of changing the order in which operations are performed on the result of equations, and develop a general rule to explain the process to use.
Extension:
Students could find all the possible numbers that will work for each equation, and identify the general rule for those two numbers.
Other ARB resources
For similar resources at level 4 involving use of brackets and orders of operations see: Using brackets and Using brackets II.
For similar resources at level 4 involving use of brackets and orders of operations see: Using brackets and Using brackets II.