Get your game on: Three in a row

Article (PDF Available) · October 2015with 318 Reads
Abstract
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. Searching for a simple yet engaging and mathematically meaningful activity to enhance students’ mental computation skills and reinforce explicitly-taught strategies? 3-in-a-row is a series of dice and card games all based around the same principle; placing three of your counters in a row on a hundreds board. The winner of the game is the first player to score three different 3-in-a-rows.
GET YOUR GAME ON
THREE IN A ROW
James Russo
Belgrave Primary School and Monash University
Searching for a simple yet engaging and
mathematically meaningful activity to
enhance students’ mental computation skills
and reinforce explicitly-taught strategies?
3-in-a-row is a series of dice and card
games all based around the same principle;
placing three of your counters in a row on
a hundreds board. The winner of the game
is the first player to score three dierent
3-in-a-rows.
The games have been designed around
this common objective to take advantage
of the fact that students already have some
familiarity with the rules and workings of
the game. There is a version of 3-in-a-row
that covers the following teaching points
related to mental computation:
Count On and Count Back
(3-in-a-row Original)
Doubles and Near doubles
(3-in-a-row Doubles)
Decomposition and ‘recomposition’
(3-in-a-row Friendly Numbers)
Complements to 100
(3-in-a-row Super Rainbow Facts)
Bridging through 10 and
Compensation (3-in-a-row Freestyle)
In addition to building fluency in mental
computation, engaging in the series of
3-in-a-row games exposes students to
number patterns and place value concepts,
as they navigate the 100’s chart. It also
invites students to think strategically and
probabilistically, as, on every turn, students
have to decide whether they should ‘take
the number’ or ‘take a card’.
The series of 3-in-a-row games could
potentially be enjoyed by all students of
primary school age, however they are
primarily of instructional value to students
in Years 1-4.
HOW TO PLAY 3-IN-A-ROW
GAMES
3-in-a-rows can be recorded by placing
three consecutive counters either
horizontally (e.g., 31, 32, 33), vertically (e.g.,
64, 74, 84) or diagonally (36, 45, 54). The
winner of the game is the first player to
score three dierent 3-in-a-rows (note that
a 4-in-a-row only counts as one 3-in-a-
row). All of the games are suitable for 2 or
3 players.
At the beginning of the game, players roll
the dice, and the player with the highest roll
begins the game.
As an alternative to using counters,
consider obtaining 100 charts that are
whiteboard marker friendly.
Only one counter can occupy a given
number square. Consequently, if a player
lands on this number later in the game,
they will miss their turn. It is for this reason
that a player is forced to ‘take a card’ (see
below), if they land on an already occupied
number. If a player takes a card, and this
new number is also already taken, they miss
their turn.
Materials
Dice (various – see below)
Playing cards
100 chart or 120 chart
20 (or more) distinctive counters per
player
The above picture provides an example of
a game of 3-in-a-row Super Rainbow Facts.
PRIME NUMBER: VOLUME 30, NUMBER 4. 2015
PAGE 16
The Blue Player adopted the more
conservative strategy, only ‘taking a card’
on average every three turns. By contrast,
the Red Player’s strategy was high risk,
‘taking a card’ on every turn. The Blue
Player won the game, having scored three
3-in-a-rows (63, 72, 81; 32, 33, 34, 35; 19, 28,
37, 46).
3-IN-A-ROW: ORIGINAL
Mental computation concepts and
strategies
Count on
Count back
Age group
Foundation to Year 2
Dice
20-sided dice
How to play
The first player rolls the dice (e.g., they
roll a 15). The player then has a choice.
They can either place a counter over this
number (15), or take a card. If the card
is black, they add 1 to their number and
place their counter over this new number
(16). If the card is red, they subtract 1 from
their number, and place their counter over
this new number (14). The second player
than has their turn, and follows the same
process.
For an extra challenge
Players add (subtract) 1 to their score if
they draw a number card (Ace to 10),
players add (subtract) 2 to their score in
the draw a picture card (i.e., Jack, Queen,
King, Joker).
3-IN-A-ROW: FRIENDLY
NUMBERS
Mental computation concepts and
strategies
Decomposition and ‘recomposition’
Adding 10 and subtracting 10
Age group
Year 1 to Year 3
Dice
10-sided 10’s dice (10,20,30…100)
10-sided 1’s dice (0,1,2…9)
How to play
The first player rolls the two dice (e.g.,
they roll a 50 and a 7). They have to add
the two numbers together through using
their understanding of decomposition and
‘recomposition’ (i.e., just knowing that 50
and 7 equals 57, because 57 is comprised
of 50 and 7). Adding numbers together
fluently in this way can be referred to as
the Friendly Numbers approach (multiples
of 10 being friendly numbers because they
make addition easy). If students are not
confident applying Friendly Numbers, they
could potentially use Count On to ‘check’
the answer.
The first player can then either place a
counter over this number (57), or take a
card. If the card is black, they add 10 to
their number and place their counter over
this new number (67). If the card is red,
they subtract 10 from their number, and
place their counter over this new number
(47). The second player than has their turn,
and follows the same process.
For an extra challenge
Players add (subtract) 10 to their score
if they draw a number card (Ace to 10),
players add (subtract) 20 to their score in
the draw a picture card (i.e., Jack, Queen,
King, Joker).
3-IN-A-ROW: DOUBLES
Mental computation concepts and
strategies
Doubles
Near Doubles
Age group
Year 1 to Year 4
Dice
10-sided dice (Grade 1 to 2) OR
20-sided dice (Grades 2 to 4)
How to play
The first player rolls the dice (e.g., they
roll a 15). They then have to double the
number they rolled (15 + 15 = 30). The
player then has a choice. They can either
place a counter over this number (30), or
take a card. If the card is black, they add
1 to their number and place their counter
over this new number (31). If the card is
red, they subtract 1 from their number, and
place their counter over this new number
(29).
The second player than has their turn, and
follows the same process.
For an extra challenge
Players add (subtract) 1 to their score if
they draw a number card (Ace to 10),
players add (subtract) 2 to their score in
the draw a picture card (i.e., Jack, Queen,
King, Joker).
3-IN-A-ROW: SUPER
RAINBOW FACTS
Mental computation concepts and
strategies
Complements to 100 (referred to as
‘super rainbow facts’)
Decomposition and ‘recomposition’
Age group
Year 2 to Year 4
Dice
10-sided 10’s dice (10,20,30…100)
10-sided 1’s dice (0,1,2…9)
How to play
The first player rolls the two dice (e.g.,
they roll a 50 and a 7). They have to add
the two numbers together through using
their understanding of decomposition and
‘recomposition’ (i.e., just knowing that 50
and 7 equals 57, because 57 is comprised
of 50 and 7). Adding numbers together
fluently in this way can be referred to as
the Friendly Numbers approach (multiples
of 10 being friendly numbers because they
make addition easy).
PRIME NUMBER: VOLUME 30, NUMBER 4. 2015
PAGE 17
card from their number, and place their
counter over this new number. For example,
a red 8 would involve subtracting 8 from
their original number. All picture cards are
worth 9. This is to promote the use of the
compensation strategy (e.g., 57 + 9 = 57 +
10 – 1) and to enable more 3-in-a-rows.
For an extra challenge
Rather than play with a 10-sided 10’s dice
and a 10-sided 1’s dice, students play with
two 10-sided 1’s dice. Then, instead of
adding up the total amount rolled, students
have to multiply the two numbers they roll
together. For example, if a student rolled
a 3 and an 8, their total would be 24. They
then have the option of taking this number
or ‘taking a card’ as described above.
The player can then either place a counter
over this number (57), or take a card. If
the card is black, they get the original
number (57) and the numbers complement
to 100, which is termed its ‘super rainbow
buddy’ (43). If the card is red, the player
misses their turn (i.e., they do not get any
numbers). The second player than has their
turn, and follows the same process.
For an extra challenge
If using a 120’s board, have players
practice complements to 120, rather than
complements to 100.
3-IN-A-ROW: FREESTYLE
Mental computation concepts and
strategies
Bridging through 10
(e.g., 53 + 8 = 53 + 7 + 1)
Compensation
(e.g., 53 + 8 = 53 + 10 -2)
Decomposition and ‘recomposition’
Age group
Year 2 to Year 4
Dice
10-sided 10’s dice (10,20,30…100)
10-sided 1’s dice (0,1,2…9)
How to play
The first player rolls the two dice (e.g.,
they roll a 50 and a 7). They have to add
the two numbers together through using
their understanding of decomposition and
‘recomposition’ (i.e., just knowing that 50
and 7 equals 57, because 57 is comprised
of 50 and 7). Adding numbers together
fluently in this way can be referred to as
the Friendly Numbers approach (multiples
of 10 being friendly numbers because they
make addition easy).
The first player can then either place a
counter over this number (57), or take a
card. If the card is black, they add the face
value of the card to their number and place
their counter over this new number. For
example, a black 8 would involve adding
8 to their original number. If the card is
red, they subtract the face value of their
PRIME NUMBER: VOLUME 30, NUMBER 4. 2015
GET YOUR GAME ON
THREE IN A ROW (CONT)
PAGE 18
A game of 3-in-a-row Friendly Numbers. Blue won the game, and finished with four 3-in-a-rows
(61, 72, 83; 52, 62, 72; 43, 52, 61; 46, 56, 66, 76) – a result of getting 52 on the final turn.
  • Article
    Full-text available
    Mathematical games are widely used in the primary classroom; however, not all games are equally valuable. How might teachers decide which specific games to introduce? The authors present five principles of educationally-rich games to support teachers to address this issue.
  • Article
    Full-text available
    This article considers how a simple board game, Snakes and Ladders, can be used to teach a rich variety of number concepts from Foundation to Year 4, through subtle modifications of game rules and student instructions. One modification in particular offers a powerful means of attempting to move students on from count-on to using more efficient mental computation strategies.
This research doesn't cite any other publications.