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

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!"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?

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PRIME NUMBER: VOLUME 32, NUMBER 2. 2017

!"The Mathematical Association of Victoria