Decimal Maze
Task Description
This activity helps students to develop number sense of the
four key operators (+ - x ÷) when applied to decimals, in an
engaging and thought-provoking board game.
Students play in pairs taking turns moving a single counter
around a maze board. They each start with the number 100
and are given a choice of moves to make with associated
mathematical functions to perform on the number (using a
calculator). A separate running total is maintained on each
student's calculator throughout the game. The player with the
highest number when the counter reaches the finish is the
winner. In playing this game, the common misconception
that multiplying always makes a number bigger and dividing
always makes it smaller is challenged. It brings into play
estimation skills, ICT skills and involves development of strategies to ensure the opponent
ends up with a lower score.
Materials
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Decimal Maze Game Board & Instructions
A four-function calculator per player
One counter per pair
Key Mathematical Concepts
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Estimation of division, multiplication, addition and subtraction of decimal numbers
mentally.
Multiplication and division by a number less than one.
Using the Activity
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Introductory whole group discussion – revising how to add, subtract, multiply and
divide decimal numbers using a calculator.
Initial explanation of the game rules may include a brief demonstration of how to play
if necessary. Students should be encouraged to estimate the possible moves prior to
choosing which move they will make.
Playing the game.
Debrief of the game. This can include reflection, discussion or sharing the successful
strategies used. What did students discover about dividing, multiplying, adding or
subtracting a decimal number? Were there any patterns in this? The teacher could
pose the question "what will happen if you divide by a number less than 1 (e.g. 0.9)?"
to prompt further thought if necessary. This can be a good moment to
establish/discuss multiplying and dividing by numbers larger and smaller than one.
Play the game again to consolidate ideas learned (this can be done during the same
session or returned to later).
Decimal Maze
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The game takes approximately 10 minutes to play.
Prerequisite Knowledge
Students should be familiar with decimal numbers, and have some understanding of how
to add, subtract, multiply and divide them. Students should also be competent using a
four-function calculator.
Links to VELS
Dimension
Working Mathematically
(Level 2)
Number (Level 3)
Number (Level 3.75)
Number (Level 4)
Standard
They use place value to enter and read displayed numbers on
a calculator… they use a four-function calculator… to check
the accuracy of mental and written estimations.
They estimate the results of computations and recognise
whether these are likely to be over-estimates or underestimates.
Recognition that multiplication can either enlarge or reduce
the magnitude of a number (multiplication by fractions or
decimals).
They add, subtract, and multiply fractions and decimals (to
two decimal places) … They use estimates for computations
and apply criteria to determine if estimates are reasonable or
not.
Assessment
When evidencing knowledge at VELS level 3.75, students will be able to explain that
multiplying by a number less than one results in a smaller number, whilst multiplying by a
number greater than one results in a larger number, and that the converse is true for
division. Students will apply this knowledge to develop effective strategies to achieve a
large number at the end of the game.
Students will also be able to successfully use a four-function calculator for this activity.
Teacher Advice
Some teachers in the trial suggested that a session on calculator use prior to the activity
could be useful. Some teachers also found the discussions within the classroom were
critical to the success of using this activity as a learning tool for decimal division and
multiplication.
Some teachers found drawing diagrams of division by decimals (e.g. 6 ÷ 0.5), and using
language like ‘how many halves are there in 6?’ was needed to help students understand
the concepts.
Decimal Maze
Potential Student Difficulties
In the trial, some students were unfamiliar with how to use a calculator, and others keyed
in the wrong information.
Some students found the concepts of decimal division and multiplication difficult in the
trial.
Feedback
87% of the 85 students who trialled this activity reported that they learned some new
mathematics as a direct result. One student described it as an ‘easy way to learn and it
was fun’.
Most student feedback demonstrated a clear understanding of the key mathematical
concepts investigated throughout this task.
All teachers in the trial reported that their lessons had gone well and that their set goals
had been met.
Decimal Maze
Student Work Samples
Example 1
Provides evidence of student working at VELS Level 3.75
This student has identified that dividing by 0.9 results in the largest increase in a number
on the game board. The concept that multiply and divide are inverse functions has been
clearly understood, and that both multiplying and dividing can enlarge or reduce a
number.
Decimal Maze
Student Work Samples
Example 2
Does not provide evidence of student working at VELS Level 3.75
This student is not comfortable with decimal places, and has incorrectly computed division
by a number less than 1. He/she considers that dividing and subtracting will always make
a number smaller, and did not recognise the significance of the observation that
multiplying by a number less than 1 reduced the value.
Decimal Maze
Student Work Samples
Example 3
Provides evidence of student working at VELS Level 3.75
This student has clearly identified that multiply and divide are inverse functions. He/she
understands that multiplying does not always increase a number, and dividing does not
always decrease it.