Get your game on: Place that number

Article (PDF Available) · April 2017with 208 Reads
Abstract
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. Place that number is a whole class activity that builds student understanding of place value and magnitude, as well as estimation skills and overall number sense. Working cooperatively as a class, the objective is to accurately mark as many numbers as possible on a number-line. Place that number can be differentiated for students from Foundation to Year 6 by including fewer or more place value slots.
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GET YOUR GAME ON!
PLACE THAT NUMBER
INTRODUCTION
Place that number is a whole class activity
that builds student understanding of place
value and magnitude, as well as estimation
skills and overall number sense. Working
cooperatively as a class, the objective
is to accurately mark as many numbers
as possible on a number-line. Place that
number can be dierentiated for students
from Foundation to Year 6 by including
fewer or more place value slots (see
modifying the game).
GAME PLAY
The game as it is currently described is
suitable for students in Years 1 and 2. Play
begins by the teacher (or gamekeeper)
ruling a large number-line (0-100) on a
whiteboard and a smaller number-line on
a notepad. Students are allocated two
10-sided dice (0-9), corresponding to the
number of place value slots in play for the
game.
A student volunteer rolls the dice and
constructs a two-digit number, such that
one dice represents the tens and the other
dice represents the ones. For example,
rolling a 6 and an 8 would allow the student
to construct either the number 68 or the
number 86. After consulting with the
rest of the class, the student then marks
approximately where their number belongs
on the number-line. However, importantly,
the student is not allowed to record the
actual number. On the smaller number-
line, the teacher replicates the student’s
estimate, while also recording the actual
number. In this way, the teacher is able
to keep track of whether the number-line
constructed by students is consistent.
Play continues, with students placing
numbers until the teacher indicates an error
has been made, whereupon the quantity
of numbers correctly placed is counted,
representing the class’ score for that game.
Although memory is an important aspect
of the game, students will generally achieve
higher scores the more accurately they
estimate the position of the number. After
the activity, the teacher should fill in all the
James Russo, Wilandra Rise Primary School and Monash University
numbers associated with the respective
marks on the number line. This facilitates
opportunities for students to reflect on the
number line they constructed.
SUPPORTING THE
MATHEMATICS
Some students will attempt to count
along the number line. This strategy
generally does not work and tends
to result in students placing small
numbers too far along the line. The
superior strategy is to estimate, and
use fractional concepts as benchmarks
(e.g., half way along the line should be
50, three-quarters should be 75). The
game, therefore, rewards a flexible,
relativistic approach to the number
line, rather than attempts at ‘exact’
counting.
It is important to emphasise that the
student group is working together as
a team. It is expected that there will
be much discussion and conjecture
throughout the game, as students
attempt to work out the most
appropriate spot on the number line to
mark their number.
After the game, get the team to
evaluate their performance. Ask what
they could have done dierently. For
example, were two particular numbers
placed too close together, or too far
apart? Were any specific numbers
placed in an inappropriate position,
making the rest of the game very
dicult? If so, which numbers?
There are also important strategic
aspects of the game which reinforce
some of the key mathematical
concepts, particularly estimation.
Firstly, students may choose to
take maximum advantage of
the pre-existing benchmarks
available (e.g., 0 and 100) when
constructing their number
line. For example, if an astute
student rolls a zero and another
number, they will often choose to
construct a single-digit number
(i.e., place the zero in the tens
column), as these numbers
can always be placed ‘close to
zero’ and are generally easy
for students to recall, which is
important later in the game.
Figure 1. Students work as a team to place 15 numbers on their number line.
PRIME NUMBER: VOLUME 32, NUMBER 2. 2017
PAGE 4
!"The Mathematical Association of Victoria
Secondly, students may
attempt to construct additional
benchmark numbers to aid with
future decision making. For
example, let us assume that, early
in the game, a student rolls two
dice which can be constructed to
create a number that is very close
to 50 (e.g., a 5 and a 1). It might
be advisable for the student to
create this number (51), rather
than its inverse (15), as this
number can be placed half-way
along the line and be used as a
benchmark for the rest of the
game.
MODIFYING THE GAME
Construct a number-line with other
orders of magnitude and vary the
number of ten-sided dice in play
accordingly.
Foundation students: Consider playing
with one dice and getting students to place
numbers on a number line ranging from 0
to 10.
Years 2 and 3: Three dice and a number
line ranging from 0 to 1000.
Years 3 and 4: Four dice and a number line
ranging from 0 to 10,000.
Years 4 and 5: Six dice and a number line
ranging from 0 to 1,000,000.
Years 5 and 6: Three dice, with students
having to construct decimal numbers, with
one dice representing the tenths column,
once dice representing the hundredths
column, and one dice representing the
thousandths column. Students would place
numbers on a number line ranging from 0
to 1.
Set a target score for the class (e.g.,
10 numbers correct, 15 numbers
correct). Alternatively, keep a record
of the classes’ eorts and encourage
the class to beat their previous record.
I find that including some form of
whole-of-class reward (e.g., eating
lunch outside) for either reaching their
target or beating their record further
energises the game.
Split the class into two groups, and
see which group can record the most
numbers before making an error.
For older students, consider playing
in smaller groups and having students
play the role of games-keeper.
For older students, consider exploring
the order of fractional numbers
through playing with modified dice,
and getting students to place numbers
on a number line from 0 to 1.
Figure 2. Does 36 go here?
PAGE 5
PRIME NUMBER: VOLUME 32, NUMBER 2. 2017
!"The Mathematical Association of Victoria
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