Water level

Water level

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about calculations with negative numbers.
 
 
 
 
 
 
Tide Gauge (measurement in millimetres)

The tide gauge shows the water level is currently +5 mm.

 

a)
What will the water level be if it falls from this level by:
 
 
 
 
i)
 
ii)
 
iii)
 
 
 
5 mm?
 
10 mm?
 
20 mm?
  
New Water Level
 
__________
 
__________
 
__________
 
 
b)
 
What is the difference in water level from:
 
 
i)
 
ii)
 
iii)
 
–5 mm to 5 mm?
 
–5 mm to 10 mm?
 
–15 mm to 15 mm?
 
__________
 
__________
 
__________
 
 
c)
 
How many millimetres from 5 mm below the zero mark to:
 
  i)
 
ii)		 10 mm below the zero mark?
 
40 mm above the zero mark?		 __________
 
__________
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
negative numbers, scale, number lines
Description of task: 
Students answer questions involving negative numbers about rising and falling water levels.
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
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y6 (11/1996)

Y7 (11/1996)
a) i)
ii)
iii)		 0 mm
⁻5 mm
⁻15 mm		 difficult moderate
b) i)
ii)
iii)		 10 mm
15 mm
30 mm		 difficult moderate
c) i)
ii)		 5 mm
45 mm		 very difficult difficult
Diagnostic and formative information: 
  Common error Likely miscalculation Likely misconception
a) ⁻5, ⁻10, ⁻20
positive answers		 0 – 5 = ⁻5 etc
                    -------		 Calculation from "0" on scale
Doesn't recognise importance of "–" sign.
c)  i)
     ii)		 15
35		 10 – ⁻5
40 – 5		 Confusion between above zero and below zero.