Statistics and Probability 14_Guided and Independent Investigations
(Year 4) ACMSP092, ACMSP093, ACMSP094, NSW MA2 19SP
Order chance, chance affecting chance.
GUIDED AND INDEPENDENT INVESTIGATION
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative
assessment data for both the child and the teacher. ‘Doing’ mathematics is not enough and is not a good indicator of
understanding.
Children investigate and explain independently over many lessons at just beyond their current level of understanding, informing
both themselves and the teacher of their current level of understanding. It is during independent investigation that deep understanding and
metalanguage develops.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop resilience and deep understanding, If children knew
what it was they were doing, it would be called learning.
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Use chance
words and order
chance events.
Discuss chance
affecting chance
outcomes.

In pairs, children use chance word cards or chance event cards to consider events with the given likelihood, or to match the
likelihood to certain events. Children place the event or chance cards into order from most to least likely.

In pairs, students roll a dice or spin a spinner. Children explain that for each roll/spin, only one outcome is possible. Children
roll two dice or spin a spinner multiple times and discuss that the outcome of each roll/spin does not affect the other
dice/spin.
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1
Play chance
games.

In pairs, children play chance games, for example, Snakes and Ladders, Bingo. Children use the language of chance as they
play to make predictions, for example, I predict I am unlikely to roll a six / I am likely to go down the snake / I am more likely
to win.
Make predictions
based on dice
roll.

In pairs, children take turns to roll a standard die. Child 1 gets a point if a 1, 2, or 3 is rolled. Child 2 gets a point if 4, 5, or 6 is
rolled. Children decide on the number of turns. Children discuss the likelihood of each child winning.
Make predictions
based on roll of
two dice.

In pairs, children take turns to roll two standard six-sided dice. Irrespective of who rolls the dice, Player 1 wins a point if the
difference between the numbers on the dice is 0, 1 or 2; Player 2 wins a point if the difference is 3, 4 or 5. The child with
more points after 10 rolls is the winner. Children discuss if each child had equal chance of winning, or if one child had more
or less chance of winning.
Investigate die
with different
numbers of
faces.

In pairs, children have dice with different numbers of faces, for example, 3-sided dice, 4-sided dice, 10-sided dice, 12-sided
dice etc. They identify the possible outcomes from 1 roll of the die. They determine whether the occurrence of one outcome
affects the chance of another outcome occurring in one roll. They roll the die to prove it.
Investigate
multiple die with
the same number
of faces.

In pairs, children have 2, 3 or 4 dice with the same numbers of faces, for example, 3-sided dice, 4-sided dice, 10-sided dice,
12-sided dice etc. They identify the possible outcomes on each die from rolling 2 dice, or 3 dice, or 4 dice. They determine
whether the occurrence of one outcome on one dice affects the chance of outcome occurring on other die / dice. They roll
multiple dice / one die multiple times to prove it.
Investigate
outcomes from 1
coin toss.

In pairs, children have coins. They identify the possible outcomes from 1 toss of the coin. They determine whether the
occurrence of one outcome affects the chance of another outcome occurring in one toss. They toss one coin to prove it.
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Email: [email protected]
Twitter: @learn4teach
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2
Investigate
outcomes from
multiple coin
toss.
Identify
outcomes from
spinning a
spinner once.
Identify
outcomes from
spinning a
spinner multiple
times.

In pairs, children have coins. They identify the possible outcomes on each coin from tossing 2 coins, or 3 coins, or 4 coins.
They determine whether the occurrence of one outcome on one coin affects the chance of outcome occurring on other
coins. They toss multiple coins / one coin multiple times to prove it.

In pairs, children have / construct spinners with different numbers of segments (either actual spinners or amendable
computer generated spinners). They identify the possible outcomes from 1 spin of the arrow. They determine whether the
occurrence of one outcome affects the chance of another outcome occurring in one spin. They spin the arrow to prove it.

In pairs, children have / construct spinners with different numbers of segments (either actual spinners or amendable
computer generated spinners). They identify the possible outcomes from spinning 2 times, or 3 times, or 4 times. They
determine whether the occurrence of one outcome on one spin affects the chance of outcome occurring on other spin / s.
They spin multiple arrows / the arrow multiple times to prove it.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Select chance event cards or chance word cards.
Determine the likelihood of the chance event or name an event with the likelihood named on the
chance card.
Place the chance event cards and chance words in order of likelihood
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Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Select a die or spinner.
Roll one die or spin the arrow once.
Explain that one number cannot be rolled / spun if another number is rolled / spun.
Select 2 dice or 1 spinner.
Roll both dice or spin the arrow two times.
Explain that the chance of one outcome occurring on one die / spin is not affected by the
occurrence of another outcome on the other dice / spin.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Play chance games, for example, Snakes and Ladders, Bingo.
Use the language of chance as you play to make predictions, for example, I predict I am unlikely to
roll a six / I am likely to go down the snake / I am more likely to win.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Take turns to roll a standard die.
Child 1 gets a point if a 1, 2, or 3 is rolled.
Child 2 gets a point if 4, 5, or 6 is rolled.
Decide on the number of turns.
Discuss the likelihood of each child winning.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Take turns to roll two standard six-sided dice.
Player 1 wins a point if the difference between the numbers on the dice is 0, 1 or 2; Player 2 wins a
point if the difference is 3, 4 or 5.
The child with more points after 10 rolls is the winner.
Discuss if each child had equal chance of winning, or if one child had more or less chance of
winning.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Have dice with different numbers of faces, for example, 3-sided dice, 4-sided dice, 10-sided dice,
12-sided dice etc.
Identify the possible outcomes from 1 roll of the die.
Determine whether the occurrence of one outcome affects the chance of another outcome
occurring in one roll.
Roll the die to prove it.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Have 2, 3 or 4 dice with the same numbers of faces, for example, 3-sided dice, 4-sided dice, 10sided dice, 12-sided dice etc.
Identify the possible outcomes on each die from rolling 2 dice, or 3 dice, or 4 dice.
Determine whether the occurrence of one outcome on one dice affects the chance of outcome
occurring on other die / dice.
They roll multiple dice / one die multiple times to prove it.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Have coins.
Identify the possible outcomes from 1 toss of the coin.
Determine whether the occurrence of one outcome affects the chance of another outcome
occurring in one toss.
Toss one coin to prove it.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
St with a friend.
Have more than 1 coin.
Identify the possible outcomes on each coin from tossing 2 coins, or 3 coins, or 4 coins.
Determine whether the occurrence of one outcome on one coin affects the chance of outcome
occurring on other coins.
Toss multiple coins / one coin multiple times to prove it.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Children sit in pairs.
Have spinners with different numbers of segments (either actual spinners or amendable computer
generated spinners).
Identify the possible outcomes from 1 spin of the arrow.
Determine whether the occurrence of one outcome affects the chance of another outcome
occurring in one spin.
Spin the arrow to prove it.
http://www.alearningplace.com.au
Investigating Chance of Events Occurring When another Event Occurs
STATISTICS (DATA) AND PROBABILITY (CHANCE) 14 Order chance of familiar everyday events occurring from most likely to least likely,
identify everyday events where one cannot happen if the other happens, identify events where chance of one occurring not affected by
occurrence of other
Sit with a friend.
Have spinners with different numbers of segments (either actual spinners or amendable computer
generated spinners).
Identify the possible outcomes from spinning 2 times, or 3 times, or 4 times.
Determine whether the occurrence of one outcome on one spin affects the chance of outcome
occurring on other spin / s.
Spin multiple arrows / the arrow multiple times to prove it.
http://www.alearningplace.com.au
Ellen wins a prize in a
competition in which she
has half of the tickets.
Donald wins a prize in a
competition in which he
has all of the tickets.
Sally wins a prize in a
competition in which she
has no tickets.
It will be sunny
tomorrow.
A bus will drive past in
the next hour.
Lilly chooses a red apple
from a bag with 8 red
apples and 5 green
apples.
Harry will roll a 6 with a
standard six-sided die.
Alice will roll a 1, 2, 3, 4, 5
or 6 with a standard sixsided die.
Fred buys a carton of eggs The arrow will stop on red The arrow will stop on red
from a furniture store.
on this spinner.
on this spinner.
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The arrow will stop on
red on this spinner.
never
equal chance
no chance
possible
always
probable
impossible
certain
likely
unlikely
more likely
50 - 50
maybe
might
very likely
very unlikely
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