Dr Paul Swan’s
Maths Games
Check Sheets, Recording Sheets and
Teacher’s Notes
Pack B
• Coin Collector
• Fraction Action
• Get In Shape
• Stop The Clock
WRITTEN BY DR PAUL SWAN
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CONTENTS
Coin Collector
Teacher’s Notes
2-4
Fraction Action
Check Sheet
Teacher’s Notes
5
6,7
Get In Shape
Check Sheets
Recording Sheets
Teacher’s Notes
8-10
11,12
13
Stop The Clock
Check Sheets
Recording Sheet
Teacher’s Notes
14-16
17
18
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Coin Collector
TEACHER’S NOTES 1/3
Aim
Students need to collect money to reach the highest total to win the game. When students first play the
game they aim to collect as many coins as possible. Later they realise that you may collect less coins if the
coins are of a higher value.
The alternative route at the bottom right of the board was added after the initial trialling of the game to
emphasise this idea and to encourage some risk taking. The alterative route allows the students to collect
gold coins, however, they run the risk of landing on the ‘halve your money’ spot.
Extra Materials
You will need a collection of mixed coins. The coins may be kept in a container and one player – the
designated banker – should be placed in charge of monitoring money that is taken from the bank. Later
if exchanges are allowed the banker should carefully monitor the exchanges, that is, ten 10c coins are
exchanged to $1.
If players are expected to keep a running record of the game each player will need to create a table to
record the money they collect or give back each turn and the running total.
Money
In
50c
Money
Out
Running
Total
50c
20c
70c
$1
$1.70
10c
$1.80
Halve
90c
Prior Knowledge
Students need to recognise coins and be able to write their values in symbols.
Students need to be able to count a collection of coins (same denomination, mixed denominations).
Language
Include a variety of words; bank account, bank balance, coins, notes, purse, wallet.
See pp. 16 & 17 of Swan, P., & Marshall, L. (2009). Money Matters: A teachers handbook for developing money
concepts. Perth: RIC Publications.
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Coin Collector
TEACHER’S NOTES 2/3
The symbol for cents in Australia is a lower case ‘c’. The symbol for Australian dollars is an upper case ‘S’,
with a single vertical line through it $. When writing amounts of money there is no space between the
number and the cents symbol, that is 20c, NOT 20 c.You never mix the symbols eg $1.50c
Some Strategies For Working With Money
Students may need help when they first encounter the following.
Double Your Money
Some students will not be sure how to “double their money”. Use coins to explain some ways of doubling
the money. For example, if a player has collected $2, $1, $1, 50c, 20c, 20c, 10c and 10c ($5.30) that player
may simply collect/match the same number of coins and then count them ($10.60). Ideally the students
would exchange the coins for the least number of coins before counting.
Some students may perform the calculation mentally, doubling the money ($5.30) in two parts, double 30c
to make 60c and double $5 to make $10 – total to make $10.60
Halve Your Money
It is impossible to halve 5c using actual coins so if a students has collected an amount such as $2.65
instruct the student(s) to forget about the 5c and halve the $2.60. Some students may be able to calculate
half of $2.60 but may experience trouble with $5.70. If a student cannot calculate half of $2.60 mentally or
on paper a student may exchange coins so there are an even number of coins. For example, $2, 20c, 20c,
20c, becomes $1, $1, 10c, 10c, 10c, 10c, 10c, 10c. Now one of the dollar coins and three of the 10c coins
may be returned to the bank. If a student had $2, 50c and 10c, then some different exchanges would need
to take place in order to halve the coins.
Give $1 To Each Other Player
Should a player not have enough money to pay, then a loan may be arranged from the ‘bank’. A record
should be kept and the loan paid back as soon as possible. This would provide an opportunity to discuss
the payment on interest and the need to pay back borrowed money in a timely manner.
Include strategies for counting mixed sets of coins:
•
Group coins of the same denomination together and count each group
•
Exchange groups of coins for equivalent coins of higher denominations.
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Coin Collector
TEACHER’S NOTES 3/3
Assessment
Observe how the students count their coins (if using coins)
•
Do they separate the coins and then add coins of like denominations?
•
Do they touch each coin as they count?
•
Do they count to milestones such as $1?
Observe how they double or halve their collection of coins
If students are encouraged to write down how much money they collect each turn and keep a cumulative
total these calculations may be checked. One student “the banker” can check each time a calculation is
made using a calculator. Note that some students can become a little confused when a calculator shows
1.5 instead of 1.50.
If exchanging is allowed (see variation below) then observe how students exchange coins, for example ten
20c coins exchanged to $2. When totalling the amount collected allow exchanging to take place where
various coins are traded for larger coins, for example, 6 x 5c coins and 2 x 10c coins may be traded for a
50c coin.
Differentiating The Curriculum
Initially students might be given coins to literally collect as they move around the board. Later the students
can be encouraged to write down the amounts they collect and keep a cumulative total.
Variations
Allow students to go to the Bank and back home again (They will need to ignore the green arrow on the
return trip). This will increase the time taken to play the game and the amount of money collected.
Start at the Bank with a set amount of money (eg $10 or $20) and subtract amounts until reaching home.
The player who has spent the least, that is, the player with the most money left is the winner.
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FRACTION ACTION
CHECK SHEET
Equivalent fractions are shown in the order they appear on the track.
Spinner
1/3
1/4
1/5
1/8
1/10
2/3
3/4
4/5
5/8
1/2
3/9
3/12
2/10
3/24
5/50
10/15
9/12
12/15
25/40
4/8
2/6
2/8
5/25
2/16
3/30
4/6
6/8
8/10
20/32
50/100
33/99
4/16
4/20
6/48
2/20
8/12
12/16
24/30
15/24
15/30
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6/18
5/20
7/35
4/32
6/60
12/18
15/20
28/35
30/48
5/10
Fraction Action
TEACHER’S NOTES 1/2
Aim
To identify and match equivalent fractions
Prior Knowledge
Students will need to recognise unit fractions and other proper fractions in different (equivalent) forms, eg
1/2 = 2/4 = 3/6.
Prior to playing the game students will need to be given the opportunity to partition rectangular regions
(1 one) into equal-sized parts. For example 3 fifths may be shown as:
Where possible link the region model, fraction name and symbol 3/5.
The same idea may be extended to more than 1 one (2 ones) to link 1 3/4 (a mixed numeral) and 7/4 (an
improper fraction)
Renaming fractions 1 and 3 fourths, 1 3/4, and 7/4 may then be extended to equivalent fractions, that is, 3/5
is the same as 6/10 , 9/15 and so on. Later links to decimals may be made – 0.6
Paper folding may be used to help students understand that two fractions are equivalent. A rectangle may
be folded in fourths. If three of the equal parts are shaded the fraction 3 fourths is depicted.
Folding the rectangle in two lengthwise, creates the equivalent fraction 6 eighths.
You can fold the paper in half again to show 12 sixteenths, however care should be taken that students are
not given the impression that doubling is required. It is a good idea to begin with another piece of paper
folded and shaded to show 3 fourths and then fold it in three lengthwise to show 9 twelfths.
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Fraction Action
TEACHER’S NOTES 2/2
The idea of renaming fractions (or equivalent fractions), will be used later when comparing fractions and
when adding and subtracting fractions.
Language
Equivalent fractions: Fractions that name the same number.
Numerator: The number above the fraction line (vinculum). Tells how many of the named fraction are
being considered.
Denominator: The number bellow the fraction line that indicates the fraction name.
A unit fraction: a fraction where the numerator is one
A proper fraction: a fraction where the numerator is smaller than the denominator, eg 2/5
An improper fraction: where the numerator is larger the denominator eg 5/3
Assessment
One player takes on the role of judge (checker) and uses the check sheet to monitor the moves made by
each of the players.
Pose the task of showing that two fractions (from the playing board) are equivalent using a diagram, paper
folding or manipulative materials. For example, prove that 1/2 and 3/6 are equivalent fractions.
Differentiation/Variation
Two different spinners – one based on shaded rectangular regions and one involving numbers are provided.
A third spinner, where the fraction names are written in words may be downloaded and used. (See next
page)
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GET IN SHAPE
CHECK SHEET - A
Shape
Best Name
Family of Shapes
Equilateral Triangle
(Regular)
Triangles
Regular Pentagon
(Convex)
Pentagons
Regular Octagon
(Convex)
Octagons
Irregular Hexagon
(Concave)
Hexagons
Rectangle
(Oblong)
Quadrilaterals
Trapezium
(Isosceles Trapezium)
Quadrilaterals
Scalene Triangle
(Right angle)
Triangles
Regular Hexagon
(Convex)
Hexagons
Equilateral Triangle
(Regular)
Triangles
Irregular Pentagon
(Concave)
Pentagons
Scalene Triangle
(Obtuse angle)
Triangles
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GET IN SHAPE
CHECK SHEET - B
Shape
Best Name
Family of Shapes
Irregular Octagon
(Concave)
Octagons
Square
(Regular Quadrilateral)
Quadrilaterals
Irregular Pentagon
(Concave)
Pentagons
Isosceles Triangle
(Right angle)
Triangles
Regular Hexagon
(Convex)
Hexagons
Trapezium
Quadrilaterals
Isosceles Triangle
Triangles
Square
(Not Diamond)
Quadrilaterals
Irregular Hexagon
(Concave)
Hexagons
Regular Pentagon
Pentagons
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GET IN SHAPE
CHECK SHEET - C
Shape
Best Name
Family of Shapes
Parallelogram
Quadrilaterals
Regular Octagon
Octagons
Scalene Triangle
(Right angle)
Triangles
Rhombus
(Not Diamond)
Quadrilaterals
Isosceles Triangle
Triangles
Kite
Quadrilaterals
Irregular Octagon
(Concave)
Octagons
Irregular Hexagon
(Concave)
Hexagons
Irregular Pentagon
Pentagons
Scalene Triangle
(Obtuse)
Triangles
Rectangle
(Oblong)
Quadrilaterals
Irregular Octagon
(Concave)
Octagons
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GET IN SHAPE
RECORDING SHEET A (one per player)
Name: ______________________
SHAPE
REGULAR NAME
Date: ____________________
PICTURE
IRREGULAR NAME
TRIANGLE
QUADRILATERAL
PENTAGON
HEXAGON
OCTAGON
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PICTURE
GET IN SHAPE
RECORDING SHEET B
Date: ____________________
Correctly name the shape and draw it.
Player 1:________________________
Player 2:________________________
Player 3:________________________
Player 4:________________________
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Get In Shape
TEACHER’S NOTES
Aim
To collect various combinations of shapes; in the first instance a regular and irregular version of each
shape.
Prior Knowledge
The students will need to know the names and properties of the different types of triangles, quadrilaterals,
pentagons, hexagons and octagons and be able to recognise them in different orientations. These are listed
on the check sheets that accompany the game.
This game is designed to help students recognise shapes other than the stereotypical regular versions of shapes.
Students will also need to recognise shapes shown in different orientations. Some students refer to triangles
and upside down triangles when the triangle is shown with the vertex facing down.
Language
To gain the most from playing the game students will need to understand the properties of shapes like
triangles and quadrilaterals and how they impact on the name of the shape. For example triangles may be
named by:
•
side length
•
angle size,
•
or both.
Note that the only regular triangle is the equilateral triangle, where all sides are equal (the same length and
the angles are all the same size (60°). The only regular quadrilateral is a square.
Concave shapes: those that cave inwards.
Convex shapes: those that curve outwards. Both are featured on the board. The star shape below is an
example of a concave octagon
Assessment
One player is designated as the Gym Instructor and uses the Get in Shape check sheets to monitor
progress in the game.
The recording sheet may be collected after the game.
Variations
Instead of focusing on regular and irregular shapes students could be instructed that they need to collect
one of each type of triangle (or quadrilateral) and one of each type of other shape.
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STOP THE CLOCK
CHECK SHEET - A
Digital
Analogue
10
1:15
11 12 1
4
8
4
10
6
4
10
6
10
6
4:30
10
6
4:55
9
8
6
3
10
4:40
5
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6
5
11 12 1
9
2
3
4
8
7
14
2
4
8
2
3
5
11 12 1
7
4
6
9
5
11 12 1
7
3
4
8
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
4:10
2
9
2
3
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
3:35
2
9
2
3
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
2:50
6
2
3
10
3:40
5
9
2
3
6
11 12 1
7
9
10
2:10
3:20
5
11 12 1
7
2:30
10
4
8
6
3
8
2
3
2
4
7
9
10
2:05
6
11 12 1
9
5
11 12 1
7
1:25
3:10
3
10
1:50
10
4
8
Analogue
2
9
7
1:40
Digital
6
5
STOP THE CLOCK
CHECK SHEET - B
Digital
Analogue
10
5:40
11 12 1
4
8
4
10
6
4
10
6
10
6
8:50
10
6
8:15
9
8
6
3
10
8:10
5
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6
5
11 12 1
9
2
3
4
8
7
15
2
4
8
2
3
5
11 12 1
7
4
6
9
5
11 12 1
7
3
4
8
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
8:30
2
9
2
3
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
7:30
2
9
2
3
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
6:15
6
2
3
10
7:15
5
9
2
3
6
11 12 1
7
9
10
6:05
7:35
5
11 12 1
7
6:45
10
4
8
6
3
8
2
3
2
4
7
9
10
6:25
6
11 12 1
9
5
11 12 1
7
5:30
7:20
3
10
5:50
10
4
8
Analogue
2
9
7
5:20
Digital
6
5
STOP THE CLOCK
CHECK SHEET - C
Digital
Analogue
10
9:15
11 12 1
4
8
4
10
6
4
10
6
7
10
6
12:15
10
6
12:45
9
8
6
3
10
12:55
5
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6
5
11 12 1
9
2
3
4
8
7
16
2
4
8
2
3
5
11 12 1
7
4
6
9
5
11 12 1
7
3
4
8
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
3
2
9
2
4
6
5
11 12 1
7
9
8
4
8
5
11 12 1
2
3
10
12:30
5
9
2
3
6
11 12 1
7
9
8
4
8
5
11 12 1
7
3
10
11:20
2
9
2
3
6
5
11 12 1
7
9
8
4
8
5
11 12 1
7
10:10
6
2
3
10
11:15
5
9
2
3
6
11 12 1
7
9
10
10:20
11:10
5
11 12 1
7
10:55
10
4
8
6
3
8
2
3
2
4
7
9
10
10:45
6
11 12 1
9
5
11 12 1
7
9:50
11:35
3
10
9:25
10
4
8
Analogue
2
9
7
9:40
Digital
6
5
STOP THE CLOCK
RECORDING SHEET
Name: ______________________
Date:____________________
The winner is the first player to record a time for each hour of the clock.
Once you have landed on at least one time for each hour you call out “Stop the clock”.
Digital
1:
Analogue
10
11 12 1
8
10
8
9:
4
10
6
4
8
10
6
9
3
6
5
11 12 1
9
2
3
4
8
7
5
2
4
8
2
4
8
5
9
10
12:
6
11 12 1
7
3
6
8
5
11 12 1
7
3
2
11:
2
4
10
3
5
11 12 1
7
9
6
9
5
11 12 1
7
3
10
10:
2
4
8
2
3
6
11 12 1
7
9
8
4
5
9
5
11 12 1
7
6:
10
3
2
3
8
2
4
5
11 12 1
7
9
6
9
5
11 12 1
6
3
4
8
10
8:
2
9
2
4
8
10
10
11 12 1
7
3
6
Analogue
5
9
10
5:
6
11 12 1
7
4:
7:
3
4
7
3:
2
9
7
2:
Digital
6
5
This recording sheet is designed to be used with the “Stop The Clock”. It may be freely copied in schools that have purchased
the game for the purpose of recording the progress of the game.
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Stop The Clock
TEACHER’S NOTES
Aim
To collect a time for each hour 1 – 12.
Prior Knowledge
Students will need to be able to read time on analogue and digital clocks in 5 minute intervals.
Students will need to recognise analogue time as depicted on different types of clocks, eg Roman numerals.
Different clock faces have been deliberately used throughout the board.
Language
Students need to be taught that time may be read in different forms. For example, 9:15 may be read as
‘nine fifteen’ or quarter past nine. Likewise 9:25 may be read as ‘nine twenty five’ or twenty-five minutes
past nine. Some students experience confusion when reading times such as 9:40 which may be read as
‘nine forty’ or ‘twenty to ten’ as one statement involves focusing on nine, the other ten.
When ‘reading’ an analogue clock remember to point out that the hour hand moves as well as the minute
hand, that is at half past eight the hour hand should be half way between eight and nine. The minute hand
will be pointing at six. Use a geared clock to demonstrate this.
Various time related phrases are featured on the board such as ‘wasting time’, ‘time flies’, ‘no time to
waste’. Time related phrases may be discussed along with their meaning. For example, what does it mean
to ‘save time’?
Note that when writing digital time a colon should be used to separate the hour and minutes, that is 9:15
rather than 9.15
Assessment
One player takes on the role of checker and is given three check sheets so that players may be monitored
while playing the game. Each player is given a recording sheet. These recording sheets may be collected and
marked.
Most students will have little trouble reading digital clocks, however they may experience difficultly when
reading analogue clock faces, especially those that use Roman numerals or show only the 12, 3, 6 and 9
positions. Watch for any students struggling with this. Students need to read aloud the clock time for the
spot on which they land.
As mentioned earlier times such as 9:40 tend to cause difficulty. Listen as students state times such as this.
Watch for any students who land on ‘Wait a minute’. This is the only cell on the board that involves timing
an event for a set period. Students will need to look at the classroom clock or use a stopwatch or sand
timer to measure one minute.
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OTHER GAMES BY
DR PAUL SWAN
Pack A
Division Decision
Pitstop
Space Race - Addition
Treasure Trove
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