BIG SMALL
Lesson 2: Working it out
Australian Curriculum: Mathematics (Year 7)
ACMNA154: Multiply and divide fractions and decimals (using efficient written strategies and digital technologies).
Lesson abstract
Three games each for two players are provided to develop fluency in estimating the results of multiplication and
division by decimals between 0 and 1. They can be used separately or together and can be revisited over time.
One activity is a calculator game, another is a game set in the context of football and the other is in board game
format.
Mathematical purpose (for students)
To develop skill in estimating the results of multiplying and dividing.
Mathematical purpose (for teachers)
Students will develop their estimation skills and consolidate understanding of the effect of multiplication and
division by decimal numbers between 0 and 1. It is important that calculators are used, enabling students to focus
attention on the choice and effect of the operations, rather than the algorithms. The rules of all the games can be
varied to suit students’ different stages of expertise.
Lesson Length
Flexible – games take about 15 minutes each
Vocabulary Encountered
Lesson Materials
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General words related to
multiplication and division
useful.
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scientific calculators (1 per pair)
Student Sheet 1 – Estimo Game Instructions (1 per pair)
Student Sheet 2 – AFL Game Instructions (1 per pair)
Student Sheet 3 – AFL Game Board (1 per pair)
Student Sheet 4 – Build a Bridge Game Instructions (1
per pair)
Student Sheet 5 – Build a Bridge Game Board (1 per
pair)
We value your feedback after this lesson via http://tiny.cc/lesson-feedback
Introduction
This lesson is intended to build on Lesson 1: What is happening? to consolidate learning and to increase fluency.
There are three games that can be used in a sequence or stand-alone. The purpose of the games is to increase skill
in estimation and to consolidate knowledge of the effect of multiplying or dividing by numbers between 0 and 1. A
calculator is used in each game so that the play continues at a good pace, and to keep the students’ attention on
the estimation and the effect of the operation.
Include class discussion about the learning from each game at appropriate points.
Game boards and instructions can be laminated for reuse.
Estimo
Aim: Be the first player to get close enough to the target number using a calculator.
Resources per group of 2 students:
• Student Sheet 1 – Estimo Game Instructions
• calculator
Notes: The game can be adjusted for students with different skill levels by changing the range of answers that are
accepted as a win, and by choosing whether only multiplication is allowed, only division is allowed or both
multiplication and division. The last option makes the game much easier because it can avoid the use of numbers
between 0 and 1 – teachers may decide this level is suitable for some students.
Initially, teachers should guide students in setting up the game (rules 1, 2 and 3 on the game instructions).
AFL
Aim: Score the most points in the football game.
Resources per group of 2 students:
• Student Sheet 2 – AFL Game Instructions
• Student Sheet 3 – AFL Game Board
• counter or coin to be used as the ball (a ‘proper’ ball can be cut from
the instruction sheet)
• calculator
Notes: The game is easily adjusted for different students by choosing whether
only multiplication is allowed, only division is allowed or both multiplication
and division, as for Estimo above.
Build a bridge
Aim: Win a series of the hexagon tiles so that you are the first to build a
bridge across the river.
Resources per group of 2 students:
• Student Sheet 4 – Build a Bridge Game Instructions
• 2 sets of about 20 counters (one colour for each player), or a
pen/pencil per player to colour the tiles
• calculator
Notes:
• To adjust the difficulty, teachers could construct a new tool box and
answer set using fractions (easy or difficult) or simpler non-repeating
decimals (using tenths, hundredths, halves and fifths etc.).
• Students will probably randomly guess to begin with, then start to
plan their path. If planning takes too long, set a time limit for each move.
• There are two duplicate answers on the board (0.6 and 0. 3̇ ) but this
does not substantially affect the game.
2
Estimo Game Instructions
Student S heet 1 – Est imo Game Inst ruc tions
Number of players:
Name:
2
Things your group needs:
•
calculator
How to win:
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Get the calculator to show a number close enough to the target number (within the winning range).
Rules:
1. Select a target number and write this down.
2. Agree on how close you need to get to the target number to win and write this down (e.g. ± 1, ± 0.05).
3. Select either multiplication OR division.
4. Player 1 chooses a start number and enters it into the calculator, then hands calculator to Player 2.
5. Player 2 presses the following buttons on the calculator:
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The multiplication or division button (whichever has been agreed on for this game).
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A number of their choice.
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The equals button.
6. If the answer on the calculator is within the winning range then Player 2 wins; otherwise Player 1 has a
turn repeating the process in step 5.
7. The game continues, alternating players, until there is a winner who gets close enough to the target
number.
As you get better at the game you can make it harder by:
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Choosing a smaller winning range.
Changing the operation.
Thinking of numbers that might make it harder for your opponent.
AFL Game Instructions
Student S heet 2 – A FL Gam e Instr uct ions
Number of players:
Did you know:
2 (the team coaches)
Things your group needs:
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Name:
AFL Game Board
marker/counter for the ball (or ‘ball’ cut from this worksheet)
calculator
The official Sherrin AFL ball
dimensions are a long
circumference of 72cm and a
short circumference of
54cm.
How to win:
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Get the highest score in the time allowed.
Points are won by getting the ball through the posts for goals or behinds.
Rules:
1. Select which direction each team is going (i.e. where the goal is for each team).
2. Choose a team to go first. You will start with the ball in the centre field and the AFL player there has first
kick. The starting number is 50 - put this in your calculator.
3. Choose which AFL player you are trying to kick towards. You will be trying to get a number in the range
shown for that player.
4. Select a number between 0 and 1 by which to multiply or divide the current number showing in the
calculator, and tell your opponent.
5. Use the calculator to find the answer. If the answer is:
• Within the range of the AFL player you are kicking towards - the player on your team marked
(caught) the ball. Move the ball to this player and have another turn using the number now showing
on the calculator.
• Not within range of the AFL player you are kicking towards - your opponent has marked the ball.
Move the ball to these players and your opponent has a turn. Start with the number now showing.
6. After a goal has been scored, play returns to the centre.
Scoring:
1. Taking a shot at goal:
• If you get a result within the goal range you score 6 points.
• If you get a result within the behind range you score 1 point.
• If your result is not within range you score 0 points.
2. Tally your goals and behinds as you play. Add up your score when the allotted time is over.
Team 1
Goals
Tally
Score
Behinds
Team 2
Total
Goals
Behinds
Total
AFL Game Board
Student S heet 3 – A FL Gam e B oar d
Name:
Build a Bridge
Game Instructions
Student S heet 4 – B uild a Br idge Game Instr uct ions
Number of players:
Name:
2
Things your group needs:
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Build a Bridge Game Board
2 sets of about 20 counters (one colour for each player), or a pen/pencil per player to colour your tiles
calculator
How to win:
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Be the first to build a bridge from one side of the river to the other.
Rules:
1. Choose a player to go first. Players take it in turns.
2. Choose a tile that you want to include in your bridge. You will be able to include a tile in your bridge if its
number is the answer to a calculation you nominate.
3. Select two numbers from the tool shed on the game board.
4. State if you are going to multiply or divide your selected numbers.
5. Use the calculator to work out the answer.
6. If the calculation gives the answer on the tile, put your counter on it. This tile cannot be taken from you.
7. Keep playing until one player has built a bridge across the river and so wins, or it is no longer possible for
someone to win. A bridge cannot cross the other player’s bridge. A bridge does not need to be ‘straight’ –
it can twist and turn as long as every piece of the bridge is touching another piece along an edge.
Build a Bridge
Game Board
Student S heet 5 – B uild a Br idge Game Board
Name: