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Get your game on: Hopping to 100

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This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. ‘Hopping to 100’ is a strategy-based game which exposes students to skip-counting from non-zero starting points. The mathematics in the activity is suitable for students in Years 2, 3 and 4, with more mathematically capable students encouraged to employ their knowledge of multiplication facts and mental strategies for adding two-digit numbers, rather than skip-counting. Upper primary students could also enjoy the game, focusing more on optimal strategy than the specific mathematics involved.
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PRIME NUMBER: VOLUME 31, NUMBER 2. 2016
PAGE 6
OVERVIEW
‘Hopping to 100?’ is a strategy-based
game which exposes students to skip-
counting from non-zero starting points.
The mathematics in the activity is suitable
for students in Years 2, 3 and 4, with
more mathematically capable students
encouraged to employ their knowledge of
multiplication facts and mental strategies
for adding two-digit numbers, rather than
skip-counting. Upper primary students
could also enjoy the game, focussing
more on optimal strategy than the specific
mathematics involved.
The game can be played by two, three or
four players. To begin the game, you need
a deck of playing cards, a 6-sided dice, a
counter for each player and a 120s chart
(preferable) or a 100s chart, which serves
as the game-board. The goal of the game
is to be the closest player to 100 after the
eight rounds have been played
HOW TO PLAY
Each player is dealt eight playing cards: an
ace, two, three, four, five, six and seven and
a jack (representing zero). These are the
players ‘hop cards’ and are displayed face-
up (see Figure 1).
A turn begins by a player rolling the dice.
Each number on the dice represents
a dierent skip-counting sequence or
requires the player to miss a turn:
Rolling 1: Skip counting by 10’s
Rolling 2: Skip counting by 2’s
Rolling 3: Skip counting by 3’s
Rolling 4: Miss a turn
Rolling 5: Skip counting by 5’s
Rolling 6: Miss a turn
After rolling the dice, the player needs to
decide which of their ‘hop cards’ to play.
The value on their hop card designates how
many times they need to skip count. For
example, if they roll a 5, they may choose
to play the 4 ‘hop card’. This would require
the player to move their counter 20 places
on the game-board (i.e., 5, 10, 15, 20). Note
that players need to play a ‘hop card’ even
if they are required to ‘miss a turn’ (i.e., they
have to discard a hop card on every turn).
Once a ‘hop card’ is played, it is returned to
the deck and cannot be used again by that
player in the game.
Players begin at the number 0. As stated
earlier, the goal of the game is to be
the closest player to 100 after the eight
rounds have been played; that is, after all
players have played all their hop cards. It is
important to note that players must play all
eight rounds (i.e., they cannot stop playing
once they have reached 100, or very close
to 100). Consequently, deciding when
to play which ‘hop card’ becomes highly
strategic.
SUPPORTING THE
MATHEMATICS
Encourage students who are confident and
have knowledge of their multiplication facts
(i.e., 2’s, 3’s, 5’s and 10’s) to multiply the
number rolled on the dice by the ‘hop card’
they choose to play, and add this amount to
their game score. These students can use
their knowledge of skip-counting as a back-
up strategy to check their multiplication/
addition. Other students will use their
knowledge of skip-counting sequences
as their primary strategy for moving their
counter along the game board.
In addition, during the subsequent
classroom discussion, the teacher should
encourage students to reflect on, and
share, their various strategies by asking
questions such as:
When did you decide to play your 6
and 7 ‘hop cards’? Why?
When did you decide to play your
0 ‘hop card’ Why? Is there any point
having the zero hop card in the game?
What are some of the dierent ways
you can end up on exactly 100 after
eight rounds?
GET YOUR GAME ON: HOPPING TO 100
James Russo, Belgrave South Primary School and
April Contaoi, Monash University
Figure 1. Beginning a game of ‘Hopping to 100’
PRIME NUMBER: VOLUME 31, NUMBER 2. 2016
PAGE 7
Figure 2: Victory is sweet, as Mika finishes the game closest to 100
EXAMPLE OF A GAME
Jasmyn (Year 4), Sunny (Year 4) and Mika
(Year 3) began a game of ‘Hopping to
100?’. Jasmyn and Mika are using the more
sophisticated multiply and add approach,
whilst Sunny is employing skip-counting.
1. Jasmyn rolled a 4 (miss a turn) and
discarded her 3 ‘hop card’. Her counter
remained on 0. Sunny rolled a 5 and
decided to play her 5 ‘hop card’. She
moved her counter to 25 ( ‘5, 10, 15,
20, 25’). Mika rolled a 6 (miss a turn),
and played her 7 ‘hop card’. Her
counter remained on 0.
2. Jasmyn rolled a 1 (representing
skip-counting by 10s) and decided to
use her 7 ‘hop card’. She moved her
counter to 70 (7 × 10 = 70). Sunny
rolled a 2 and decided to use her 2
‘hop card’. She moved her counter
to 29 (’27, 29’). Mika rolled another 6
(miss a turn), and played her 1 ‘hop
card’. Her counter remained on 0.
3. Jasmyn rolled a 5 and decided to
play her 4 ‘hop card’. She moved her
counter to 90 (5 × 4 = 20; 70 + 20 =
90). Sunny rolled a 3 and decided to
play her 7 ‘hop card’. She moved her
counter to 50 (’32, 35, 38, 41, 44, 47,
50). Mika rolled a 3, and played her 3
‘hop card’. She moved her counter to
9 (3 × 3 = 9).
4. Jasmyn rolled a 6 (miss a turn) and
discarded her 6 ‘hop card’. Her counter
remained on 90. Sunny rolled a 3 and
decided to play her 3 ‘hop card’. She
moved her counter to 59 (’53, 56,
59’). Mika rolled a 4 (miss a turn) and
played her 2 ‘hop card’. Her counter
remained on 9.
5. Jasmyn rolled a 5 and decided to
play her Jack ‘hop card’ (representing
zero). Her counter remained on 90
(5 × 0 = 0; 90 + 0 = 90). Sunny rolled
a 2 and decided to play her 6 ‘hop
card’. She moved her counter to 71
(’61, 63, 65, 67, 69, 71’). Mika rolled a
1 (representing skip-counting by 10s)
and decided to play her 5 ‘hop card’.
She moved her counter to 59 (5 × 10 =
50; 9 + 50 = 59).
6. Jasmyn rolled a 3 and decided to
play her 2 ‘hop card’. She moved her
counter to 96 (3 × 2 = 6; 90 + 6 = 96).
Sunny rolled a 6 (miss a turn) and
decided to play her 1 ‘hop card’. Her
counter remained on 71. Mika rolled a
1 (representing skip-counting by 10s)
and decided to play her 4 ‘hop card’.
She moved her counter to 99 (4 × 10 =
40; 59 + 40 = 99).
7. Jasmyn rolled a 1 (‘representing
skip-counting by 10’s) and decided to
play her 1 ‘hop card’. She moved her
counter to 106 (10 × 1 = 10; 96 + 10 =
106). Sunny rolled a 5 and decided to
play her ‘4’ hop card. She moved her
counter to 91 (‘76, 81, 86, 91’). Mika
rolled a 5 and decided to play her Jack
‘hop card’ (representing zero). Her
counter remained on 99 (5 × 0 = 0; 99
+ 0 = 99).
8. Jasmyn rolled a 2 and played her
last ‘hop card’, a 5. She moved her
counter to 116 (5 × 2 = 10; 106 + 10 =
116). Sunny rolled a 3 and played her
last ‘hop card’, the Jack (representing
zero). Her counter remained on 91.
Mika rolled a 6 (miss a turn), and
played her last ‘hop card’, a 6. Her
counter remained on 99.
9. Mika is the winner of the game. She is
closer to 100 (1 away), than Sunny (9
away) or Jasmyn (16 away).
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