052 Multo: Better than Bingo!
Multo is a game using multiplication facts to complete a row, column, diagonal or corners of an individually designed game grid. The design of the grid becomes more sophisticated as students consider probabilities of outcomes in order to achieve an optimum result.
The accompanying software is essential. It allows students to compete against each other, and to run multiple trials to test the effectiveness of different grid designs.
- Lesson notes (pdf includes the lesson, pedagogical pointers, information on the software, and practical hints)
- One set of Multo cards (supplied as a pdf)
- One page of Multo grids for each student/group (supplied as pdf)
- Multo: Which one wins? Assessment item, as many as required (supplied as pdf; optional)
- Multo software
- Links to the Australian Curriculum
You will need one set of Multo cards. There are 100 cards, each with a multiplication question. The cards start from 0 x 0 and finish at 9 x 9.
Each student or group will need a page of Multo grids. They enter 16 numbers which could be answers. No numbers can be repeated.
Shuffle the cards, then draw them one at a time, saying the question aloud.
If students have the correct answer on their grid, they cross it off.
Multo is either:
- Four in a row horizontally
- Four in a row vertically
- Four in a row diagonally
- All four corners
Model a game
Explain the rules.
Put a prepared four by four answer grid on the board. A prepared grid has the advantage of avoiding 'impossible' answers (e.g. 13) so that students will have to discover this themselves.
Play one game together as a class. This is an important first step: physically modelling the game before moving to the computer simulations.
Use a variety of ways to call out the questions e.g.
- "six multiplied by nine"
- "four threes"
- "seven by two"
- "five lots of eight".
You may wish to show the cards as well.
Show students the three answer grids (Juli, Steve and Charles) prepared from the software.
With the students working in small groups, ask: "What do you notice? What do you wonder about?" At this stage, do not seek answers to the questions, but encourage observations.
Ask each individual/group to construct an answer grid. Don’t give the students too much time; learning will happen even if the grid is ‘thrown together’.
Teachers have said that the lesson will fail if hints are provided. For example, do not say “You need to use a zero.”
Play a game
When there is a call of "Multo!", check the winning grid and share it with the class.
(Some teachers like to keep playing the game even after a winner has emerged. Groups that already have a Multo can continue to play using a different coloured marker.)
Return to the three grids from the software and say "Do you think that some grids are better than others. Why?" You may need some prompting questions.
- What is the lowest number you can use? Why?
- What is the highest number you can use? Why?
- Are there any numbers you would never use? Why?
Introduce the software and play some games
This is the time to introduce the software Play a game of Multo.
Using one of the prepared grids, have students play a few games so that they can see that the software performs the game the same way as it was played in class. Note that the game pauses until a correct answer is entered.
Students may also observe patterns (for example, the number of times zero comes up as an answer).
The winning grid
"[Students' names] grid won because it achieved Multo with the fewest number of multiplication questions. Let's look at this grid more closely. What do you notice?"
Discuss the features of the grid.
Ask students to use the software to play a few games of the winning grid against their own grid. Share the results and discuss.
Always a winner?
Ask the question "Because [students' names] grid was a winner in our first game, does it mean that it will always be a winner? How could we find out?"
Students should be able to see that the more times the game is played, the better the test of the grid.
“How many games do you think we would need to play?”
At this point, introduce the software Comparing grids: Many games.
Students can see how this works by running various numbers of trials on the prepared (or their own) grids.
Discuss the different ways that the computer expresses the results.
Challenge: Who can design the best (winning) Multo grid?
As each group is designing their grid, ask them to justify their choices and placement by annotating the grid. You may need some prompting questions.
- What are the best numbers to use? Why?
- How often does each number occur? Why?
- Where are the best places to put the numbers? Why?
If students are still stuck, direct them to the software page Build a multiplication table. Further assistance can be found in the software at How often does each number occur?
Wrap it up
Students can test their grids multiple times, making refinements.
Discussion about the best grid to choose can rage for weeks, and times tables become the ‘flavour of the month’!
Which one wins?
Hand out copies of Multo: Which one wins?
Encourage students to discuss their methods of ranking the grids, then record their choices and reasons. Report to the class. Then test them!
Your own challenge
Students can create their own investigations. For example:
- What is the worst possible grid?
- Can you construct a grid that takes an average of 30 cards drawn to win?
- Can you make a grid that wins only half the time?
How many trials do you need to be confident of the outcome? 50? 500? 1000? 100 000?
Examine the variation in the outcomes.
Laminating the cards is a good idea. Alternatively, the cards can be printed onto sticky labels and stuck onto cards.
Show the four possible ways of winning on a grid(s) on the board.
Keep track of the questions by placing the cards in order, so that you can check back when a Multo is declared.
You can project the three answer grids, or have hard copies to hand out.