MCS Family Maths Night
27th August 2014
Year 5-8 Games Booklet
Stage Focus:
Multiplicative Thinking
Partitioning
Proportional Reasoning
How are games used in a classroom context?
Strategically selected games have become a fantastic tool to engage students with their fellow classmates. Games
allow students to interact with other students, build confidence in their own ability and practise learned skills and
concepts.
Each of the selected games requires a minimum of resources, usually things that can be easily found around the
home (dice, cards, pencil, paper) and can be adjusted to be more challenging as skills and understandings grow.
Apart from motivation, games allow the building of confidence with number facts. For this reason, competitive
games, when some players more often lose, are not recommended.
Games are not a substitute for understanding the meanings of the operations. However, the experience of playing
games in small groups has the additional advantage of developing social skills.
Decimal Maze
The aim of the game is to have the smallest number on your calculator when the game ends.
Resources Required
• Maze board
• Two calculators
• One playing piece (counter) per pair
Both players enter 100 on their calculator and the counter is placed on the START.
• Player A chooses to move the counter along a single line segment and performs the
operation on their calculator.
• Player B moves the counter from its new position along a single line segment (but not
back along the line segment their opponent has just used) and performs this operation on
their calculator.
• The game continues with each player in turn moving the counter and performing the
operation that is on the line segment they have just passed.
• The calculator is not cleared between turns.
• The game ends when one player reaches the FINISH and the winner is the player with
the smallest number on their calculator.
Alternatively you could choose to end the game after a certain time has elapsed and the
player with the smaller number at that point is the winner.
Learning Outcomes and Related Concepts
•
•
Operating with decimals
To dispel the misconception that multiplication always increases the value of numbers and
division always makes them smaller.
How can we extend the learning?
• Changing the aim to the largest number wins, or nearest to a particular number e.g. 127.6
• Playing with three players
• Letting each player have their own counter
• Not allowing any segments to be retraced. The game ends when the finish is reached or there are no further moves
possible
• Removing the word ‘finish’ and asking players to keep moving around the game board until the time is up.
Broken Calculator
The aim of the game is to use combinations of numbers and multiplication to create numbers.
Resources Required
•
•
•
Calculator
Pencil
Paper
Instructions
You have a calculator and the only buttons that work are: 3, 5, 0, X and = Could you make the number 81 appear on
the screen?
•
•
•
Try using larger numbers: 225; 150; 405 and 450
Try rewriting the aim and changing ‘the only keys that work’
Increase the number of broken digit keys and use more difficult numbers.
Learning Outcomes and Related Concepts
•
•
•
Operating with multiplication
Place value
Factors
How can we extend the learning?
This activity focuses on extending the use of factors to multiply, using a ‘broken calculator’.
Each person has a calculator, with which to work out the calculations below. There is only one obstacle. They must
pretend that the entry key for digit 1 is broken along with the addition and subtraction keys and cannot be used. The
digit 1 can appear in the display.
Sample ‘broken calculator’ calculations:
Broken Keys
Calculation
Answer
1, +, 1, +, 1, +, 1, +, 1, +, 1, +, 1, +, 1, +, -
12 × 3
12 × 12
16 × 32
16 × 22
18 × 223
16 × 18
120 × 81
111 × 101
36
144
512
Alternative
Calculation
4×3×3
4×3×4×3
2 × 8 × 32
(3 × 37) × (5 × 20.2)
Alternative
Calculation
6×2×3
2×6×3×4
8 × 64
Colour in Fractions
The aim of the game is to form common, proper and improper fractions and represent these on the
fraction wall, attempting to colour in the whole board game in as few turns as possible.
Resources Required
•
•
•
Fraction Wall
Dice
Coloured Pencils
Instructions
•
•
•
•
•
Students have a dice that create fractions up to twelfths and a fraction wall. They colour in sections
of the wall that correspond to the fractions that they roll with the dice.
Players in turn throw both dice.
They make a fraction with the first die being the numerator.
Each horizontal strip on the game board is one whole. So this game board is equivalent to six
wholes or six.
Students then colour the equivalent of the fraction shown. For example, if they throw 2 and */4,
then they can colour in:
2
4
•
•
•
of one line or
4
8
of one line or
2
combination that is the same as 4.
1
of one line and
4
2
8
of or another or any other
A “brick” within the wall cannot be cut to make the required fraction.
If a player is unable to use their turn, they ‘pass’.
The first player who colours in their whole wall is the winner.
Learning Outcomes and Concepts
•
•
•
Understanding of equivalence
Appropriate use of fractional language
Subtraction and addition of fractions
A discussion of strategies:
After playing the game, we often ask students to consider questions such as:
• If you played the game tomorrow, what would you do differently?
• If you were giving hints to a younger sibling before they played the game for the first time,
what would you say?
Fractions ‘Multo’
The aim of the game is to be the first to cover four numbers in a row (horizontally, vertically, or diagonally)
Resources Required
• An activity sheet for each student
• Two dice (one standard six-sided die and one with fractions
• Counters
1 1 1 1 1 1
, , , , ,
2 3 4 5 6 8
)
Instructions
The students play this game in pairs or in small groups.
• Each person has their own game board (see the activity sheet for Fraction ‘Multo’)
• The aim of the game is to be the first to cover four numbers in a row (horizontally, vertically or diagonally)
• To begin, each person must prepare their own game board by recording one number in each box on their grid.
• Each number is taken from the list of numbers provided in the table at the top of the activity sheet. No number
should be repeated. This means seven numbers from the list will be left off each grid.
• Each person takes it in turns to throw the pair of dice.
• The whole number and fraction are then multiplied and the result or an equivalent number is covered with a
transparent counter on the board of the person who threw the dice. For example if
will
3
cover
5
1
6
on their own game board. If they were to throw and 4
2
then
3
1
5
and 3 are thrown the student
would be covered.
• If the number which is called does not exist on their board (and neither does its equivalent), or the number has
already been covered, then that student misses a turn.
• The play then continues with the next person and so on.
Learning Outcomes and Related Concepts
•
•
•
Multiplying fractions with whole numbers
Determining equivalent, improper fractions and mixed numbers
It is possible to determine the likelihood of rolling certain numbers and form opinions about the
‘best’ game board
How can we extend the learning?
•
•
Change the dice to ten-sided dice (e.g., 0 — 9 and ignore the zero; or 1 — 10) and generate the list of possible
results and play the game again. Possibly use a larger grid.
Consider the probability of each result occurring. Also, pose the question: “Having done this how might you
change your board to improve your chance of winning?”
Fractions ‘Multo’ Game Board
Player 1
1
8
5
8
1
6
5
6
Player 2
1
5
1
4
1
3
1
2
1
2
3
13
1
2
5
1
1
2
2
3
1
1
4
3
4
3
8
3
5
13
22
15
2
1
1
4
5
Bargain Buy
The aim of this activity is to provide students with an understanding of proportional reasoning, that they can then
apply to day-to-day activities like grocery shopping.
Resources Required
•
•
•
Pens/pencils
List of shopping items
Paper
Instructions
Students are provided with a list of various shopping items.
Example: You are shopping for washing powder and your favourite brand is on special. As shown, there are two
different possibilities. For one kilogram of this powder you would pay $4 but for 1.5 kilograms you would pay $6.79.
Which is the better buy?
Students are to record their thinking and share their strategies.
Learning Outcomes and Related Concepts
•
•
•
•
Apply operations in practical contexts
Operating with decimals
Looking at ratio and proportional reasoning
Apply the four operations to solve problems
How can we extend the learning?
• Appling skills to real life situations, such as working out ‘best buys’ when shopping
• Comparing three or more shopping items
Other examples to try:
Mushrooms: $12.99 per kilo, or bulk-buy 2.5kgs for $30
T-Bone Steak: $17.50 per kilo, or bulk-buy 2kg for $37
Wonder White Bread: $3.80 each, or any 2 for $6
Thins Chips 175g: $3.14 each, or 4 for $10
Explain your reasoning:
Target Number
Aim: To use any mathematical process to create a target total.
Resources Required:
• Playing cards, pencil and paper
Instructions:
• Each player draws two cards to make a target number for his or her opponent (e.g. if you draw a 3
and 5 then you could make a target of 53, 35, 8, etc.)
• Players are then dealt 5 cards each and need to use as many of their cards (numbers) as possible to
create the target number using any mathematical process.
• These processes could include any or all of the four mathematical operations, but also square roots,
brackets, etc. Each card can only be used once.
• Players get points for the number of cards used of their 5, i.e. if you use 3 you get three points.
• Whoever has the most points after 3 turns, wins.
Multiplication Scramble
Aim: To fill every space on the scramble grid.
Resources Required:
• game board, playing cards
Instructions:
• Each player turns over two cards and multiplies them.
• Players write their product in the appropriate space on their board.
• The first player to fill all the spaces wins.
Game Board
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-100
Player 1
Player 2
What’s my Equation?
Aim: use the numbers from 1 – 10 to identify the equations for the products listed.
Resources Required:
• pencil
• paper
Instructions:
• Use each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, in any order, once, to find the equations for the
following products:
15
8
8
42
90
Biggest Product
Aim: To cover more spaces on the game board than your partner.
Resources Required:
• pencil
• game board, dice, playing cards.
Instructions:
• Pick up a playing card and roll the dice.
• Multiply the two numbers together and cover the number that matches the product.
• Whoever has covered the most spaces when all spaces have been filled, wins.
Cover Up Game Board
5
10
15
20
25
30
35
40
45
3
6
9
12
15
18
21
24
27
4
2
1
8
4
2
12
6
3
16
8
4
20
10
5
24
12
6
28
14
7
32
16
8
36
18
9
On-line Resources
National Library of Virtual Manipulative (http://nlvm.usu.edu/)
This is a great resource for a wide variety of mathematical activities. It is set out in such a way that it is easy to
navigate to appropriate activities for the level of the student and mathematical subject area. Some of the
activities to note are:
• “Base Blocks” for addition and subtraction of whole numbers, decimal fractions and non-base ten
numbers (e.g binary numbers)
• “Circle” activities to practise logic and addition skills with positive and negative integers, and decimal
fractions.
• “Color Chips” to develop an understanding of subtraction of negative numbers
• “Fractions” manipulatives for picturing, comparing and multiplying fractions
• “Factor Tree” to identify prime factors, highest common factors and lowest common multiples of
numbers
• “Geoboard” for learning the relationships between shape, perimeter and area
Maths is Fun (http://www.mathsisfun.com/)
This site has a wealth of information on working in all aspects of mathematics and a number of interactive
activities to reinforce concepts. One that we use in class with the interactive whiteboard is:
• Number ordering game (http://www.mathsisfun.com/numbers/ordering-game.php).
Sheppard Software – We make learning fun http://www.sheppardsoftware.com/math.htm
There are lots of games at multiple levels on this website. Many of them are good for individual practice of
concepts that students already have an understanding of, but need more practice with. There are also some
good tutorials, if you want a reminder or a different explanation about a concept discussed in class.
• “Matching Math” http://www.sheppardsoftware.com/mathgames/matching/AdditionX.htm
This has a timed and relaxed (untimed) mode. It involves adding numbers to a missing number to a
specific sum.
TRANSUM – maThs, softwaRe, teAchers, educatioNal, Schools, stUdents, nuMeracy
http://www.transum.org/Software/SW/Starter_of_the_day/index.htm
Every day they post a problem of the day (called the starter of the day), which often combines a wide range of
concepts and skills in real-world situations. They keep past problems on the website too, so you can go and
look at them as well.
Time (Duration)
• http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/timetables/index.htm
•
http://au.ixl.com/math/year-5/add-and-subtract-mixed-time-units
Decimals
• http://www.echalk.co.uk/Maths/PrimaryNationalStrategy_Yr6/DfESMathsActivitiesforyear6/longjump.html
•
http://www.decimalsquares.com/dsGames/games/speedway.html
•
http://www.xpmath.com/forums/arcade.php?do=play&gameid=24
Times tables
• http://www.mathsisfun.com/timestable.html
•
http://www.shodor.org/interactivate/activities/ArithmeticQuiz/
•
http://tablestest.com/
•
http://www.wmnet.org.uk/resources/gordon/Hit%20the%20button%20v9.swf
•
http://www.maths-games.org/times-tables-games.html
Probability
• https://fuse.education.vic.gov.au/content/574be7cd-d985-44ab-9db4-313f80c10fb4/p/index.html
•
https://fuse.education.vic.gov.au/content/eaa98d6a-cb2c-4ad2-bd62-e95ff9e7b2ba/p/index.html
•
https://fuse.education.vic.gov.au/content/26aed168-490c-4256-ba1c-a8ca8a2f5efc/p/index.html
Fractions
• http://resources.woodlands-junior.kent.sch.uk/maths/fractions/index.htm