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 dierent

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 dierent 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.