Addo

Years 1 - 7

Summary
This activity begins as addition practice of two numbers from 0 - 10, but becomes an investigative challenge to find the 'best Addo arrangement'. That search involves exploring the number of ways each total of two numbers can be found and the spatial logic of where to place the chosen totals to best effect. The initial game is suitable for threading and the investigative component can extend over several sessions. Addo also works well as a partner with Five Cards, Six Plus and Add Town in younger years and Cribbage in older years.
If you school is a member of Maths300, Addo can be used effectively in conjunction with Lesson 186, Addo, which also supplies software to support the investigation.
Materials

One Poly Plug set for each player

One Poly Plug Frame for each player

Two piles of digit cards numbered 0 - 10 for the teacher

Playing cards A - 10 can be used if one of the royals is also included, by agreement, as zero.

Jumbo size cards, available from games shops, are effective.

Acknowledgement

This activity was developed from suggestions by Charles Lovitt, consultant.

Procedure

Explain that the game is going to use the two piles of cards. Show the cards and explain that each pile has cards with values 0 to 10.

This is an addition game. I take the top card from each pile and you have to add them.

Explain that there is more to learn about the game, but for now you are just going to have a quick practise of this part. Take the top cards and ask for the total. Do this three or four times.

What's the highest total we could make?
What's the lowest?
Can we make any totals in between?
Tell me some.

The next step is for the children to poke out three rows of three from their red board, as in the photo above, and put the poked out plugs in the plastic bag. While they are doing this hand out the Poly Plug Frames.

Now, put your red board on top of the paper. You are going to write numbers in the circles you can see. The numbers will be totals made by adding two numbers from my card piles. You can only write each total once.

Content

addition facts beyond 10
addition facts to 10
complementary addition
data: collecting, recording, displaying
data: describing & comparing with statistics
data: interpretation
decimal calculations
decimal interpretation
mathematical conversation
problem solving
properties of number
recording - written
tallying

Check that the children are clear about what they have to do. Ask them how many totals they have to write.

Okay, slide your board away and write your totals. You can choose any totals you like and put them in any of the nine circles. But remember, you can't use a total twice.

This will take a little while and you might have to hurry some children along. Children slide their red board back when they are done.

Now for the first challenge. I choose cards from my pile. You calculate their total and if it is one of your numbers you put a plug in that gap. Make it have the yellow side up. The aim of the game is to be the first with three in a row horizontally, vertically or diagonally.

Play the game until the first person gets three in a row. Keep a record of the cards you draw as additions (or number pairs) so you can check that the totals under the first person's plugs are correct. Perhaps choose one person to have the special job of being your recorder; but the recorder doesn't play the game.

Well done Mary. You are first, but I think if we kept playing the game everyone would get three in a row. Let's see what happens. Mary you can keep going to see if you can fill all your gaps with yellow plugs.

Continue playing until most have made at least one line of three. Turn to someone who is still waiting for their first three and ask what total they are waiting for. Discuss the cards that could pair up to make it. Repeat this with others and begin a mini-exploration to highlight that some totals can be made in more ways than others.

Try to follow the game through now until everyone makes at least one line of three. Round off by refreshing the discussion about some totals being made in more ways than others and exploring whether it matters which circles you use for which totals.

Now that you understand how to play Addo and you are thinking about which numbers to use and where to put them, our challenge is going to be to find the very best Addo board.

Suggest that a good player would be one who is working like a mathematician to make these decisions.

Threaded Activity

Use the game as a threaded activity for a while now. Say 10 minutes a day, three or four days a week, over two or three weeks. Each time you use it the children will be rehearsing their decisions about which totals should be placed where, and discussing why. You don't have to be the game manager for this. If you have enough card piles, arrange the children into groups of three with one person taking the teacher's role and the other two competing to make the first three in a row. The winner becomes the 'teacher' for that group the next time it is played.

As the activity is continued, ask the children to submit their 'best board' any time they think they have created it. Store these away rather than displaying them.

Thanks Danny. I'll keep that secret until it's time to discover who has the best. You can go on winning with it and if you want to change your 'best board', just give me a new one and I will tear up the old one.

Investigation

When the time is right, make a display of all the 'best boards' and highlight that the time has come to find the best of the best.

We all think we have found the best board and they are certainly all pretty good. But how would a mathematician design an experiment to test which is the best of all? How could we work together, like that mathematician, to see if we can find out.

Explore any ideas the class suggests - there could be some quite interesting ones - and come to an agreement about which method the class will try. Two possible approaches are:

Number of Pairs
It might be argued that the best board is the one that consistently produces three in a line in the least number of draws, each draw being one card from each pile. Players then take anyone's best board and play the game by themselves, keeping track of how many times a number pair is drawn to get the first line of three. Each child runs the experiment an agreed number of times, say 10 or 20, and calculates the average number of pairs.
Play Off
It might be argued that any board which consistently gets three in a line before another one must be better. So, organise an Addo league by pairing players to play eleven games against each other. The boards that wins more of the 11 games in the first round play off in the second and so on until a 'best board' is found.

Congratulate the class on working together so well to find the best of best so far. Suggest that the result might change if there had been time to run more trials. For example, in the Play Off model a board that won 6 to 5 might lose if the experiment went to 21 trials. Suggest that a mathematician might program a computer to simulate the game if they wanted to be more sure.

Round off by comparing the way the children have been working with the process of Working Mathematically.

Extensions

What happens if Addo is played on a Big Toe board still making lines of three?
What happens if Addo is played with cards sets from 0 to 12 or 0 to 20?
What happens if Addo is played on a 4 x 4 board and the aim is to make lines of 4?
Link this activity with Maths300 Lesson 186, Addo,which includes software to extend the challenge.
What happens if the game is Multo instead of Addo? Use Maths300 Lesson 52, Multo, which also has software.

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