Achi Chance Game
Achi is a strategy game from Ghana and is a more advanced form of noughts and crosses. Players take turns putting their markers on a 3x3 board, with the aim of trying to get three in a row. While playing, students will be required (unconsciously) to collect data and make predictions based on probability, to develop their own strategy for winning.
These reflective strategies (“If I do this, then they will do that.”) develop Mathematical thinking and problem solving.
Engage your students in a discussion using questions like:
- “Was there a pattern that you observed when winning?”
- “Did you change how you played after learning how the game worked?”
- “Does it make a difference who goes first? Do you play differently if you go second?”
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Learning goals
- We are learning to identify outcomes of familiar events using ‘likely’, ‘unlikely’, ‘certain’ or ‘impossible’.
- We are learning to identify outcomes of familiar events using everyday language.
- We are learning to collect, record, compare and discuss data displayed in various ways.
- We are learning to collect data by asking questions to make simple inferences.
- We are learning to collect data using surveys, sort data into categories and display data in lists and tables.
- We are learning to gather data and record observations to answer a question.
- We are learning to identify and describe possible outcomes by conducting chance experiments.
- We are learning to identify and describe possible outcomes by conducting chance experiments.
- We are learning to describe possible everyday events, order their chances of occurring and determine independent or dependent events.
- We are learning to identify everyday events where one cannot happen if the other happens, e.g. weather cannot be dry and wet at the same time.
Curriculum alignment
AC9M1ST01
9
Acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols
AC9M3P01
9
Identify practical activities and everyday events involving chance; describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ explaining reasoning
AC9M4P01
9
Describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events
AC9M2ST01
9
Acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables
AC9M3P02
9
Conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation
ACMSP048
8.4
Identify a question of interest based on one categorical variable. Gather data relevant to the question
ACMSP093
8.4
Identify everyday events where one cannot happen if the other happens
ACMSP067
8.4
Conduct Probability (Chance) experiments, identify and describe possible outcomes and recognise variation in results
ACMSP047
8.4
Identify practical activities and everyday events that involve Probability (Chance). Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’
ACMSP262
8.4
Choose simple questions and gather responses and make simple inferences
ACMSP024
8.4
Identify outcomes of familiar events involving Probability (Chance) and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’
MA1-1WM
old
Describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols
MA2-19SP
old
Describes and compares chance events in social and experimental contexts
MA2-3WM
old
Checks the accuracy of a statement and explains the reasoning used
MA2-1WM
old
Uses appropriate terminology to describe, and symbols to represent, mathematical ideas
MA1-2WM
old
Uses objects, diagrams and technology to explore mathematical problems
MA1-17SP
old
Gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results
MA1-3WM
old
Supports conclusions by explaining or demonstrating how answers were obtained
MA1-18SP
old
Recognises and describes the element of chance in everyday events
MA2-CHAN-01
new
Records and compares the results of chance experiments
MA1-DATA-01
new
Gathers and organises data, displays data in lists, tables and picture graphs
MA1-DATA-02
new
Reasons about representations of data to describe and interpret the results
MA1-CHAN-01
new
Recognises and describes the element of chance in everyday events
VCMSP125
Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’
VCMSP147
Conduct chance experiments, identify and describe possible outcomes and recognise variation in results
VCMSP127
Collect, check and classify data
VCMSP126
Identify a question of interest based on one categorical variable. Gather data relevant to the question
VCMSP100
Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’
VCMSP175
Describe possible everyday events and order their chances of occurring
VCMSP176
Identify everyday events where one cannot happen if the other happens
VCMSP177
Identify events where the chance of one will not be affected by the occurrence of the other
VCMSP101
Choose simple questions and gather responses
Australian Curriculum covers QLD / SA / WA / NT / TAS / ACT.
Differentiation
Modifications
Have students begin by playing noughts and crosses and talking through different strategies for that game, before introducing Achi.
Extensions
Instead of four pieces for each player, you can reduce the number of markers to three, making a game known as ‘Three Men’s Morris’ or ‘Nine Holes’.
Teach it your way
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