# Who Owns The Monkey?

### Task 116 ... Years 4 - 10

#### Summary

A popular task with cards for students to physically manipulate in order to solve a logic problem. Clue cards provide some 'certain' information and enough detail so that missing information can be decided by a process of elimination. The cleverness of the clues and the task name is that nearly all the cards have to be on the grid before the last few cards (including the Monkey card) can be placed. It is not necessary that the problem is solved in one sitting. However, students frequently want to keep working on it until the solution appears.

#### Materials

• 5 cards in each set of houses, cars, drinks, pets, nationalities and clues

#### Content

• problem solving skills

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

These young ladies are trying the problem around the kitchen table. (See Library Kit for more details about Home/School Lending and Maths Around The Kitchen Table.)

Eventually they solved the problem (the Malaysians own the monkey)...

...and given their kitchen table is in The Netherlands they probably increased their English fluency a little too.

Once it is solved, the next question is How did the designer come up with the problem?. The most likely answer is that (s)he came up with the story line, set out the cards and then invented the clues. This realisation suggests the possibility of the students making up a similar problem of their own. They could begin by laying the cards out in any order based on the houses and constructing their own set of clues. This is not an easy exercise. There needs to be just enough clues to make the problem interesting and solvable, but the clues must not conflict. The students would need to draft their clues and trial them on others before 'releasing' them to the public.

For example, Tim Wilson-Brown, at the time a student in Armidale NSW, prepared this alternative set of clues to Who Owns The Monkey.

Note: All left/right references are to your left and right.

 The Moke owners drink soda. The tea drinkers enjoy living to the left of the coffee drinkers. The New Zealanders live to the right of the orange juice drinkers. The Americans loathe living in the plain house and are going to spice it up. The orange juice drinkers live in the middle. The Moke drivers would run over the turtle if they went into the driveway to the left of their house. The antique car owner drinks morning coffee listening to the budgie sing on the left. The French are saving up to buy a bigger sports car than the people on the right. The truck driver drinks tea. The brick house owners wonder why the people on the left painted their house wavy. The crab is to the left of the budgie. The striped house owners deliberately moved next to the wavy house. The Malaysians drink orange juice and live in the wavy house. The Americans wish that the dog to the right of them didn't bark all night. The French live in the striped house.

The solution to this second set of clues is:

 PLAIN STRIPED WAVY BRICK GREY American French Malaysian New Zealand Australian Wine Soda Orange Juice Tea Coffee Turtle Dog Crab Budgie Monkey VW Moke Sports Car Truck Antique Car

Both Monkey puzzles have a unique answer. But it may be more exciting to explore a problem with multiple solutions. More experienced students might like to alter one or other set of clues slightly to create the puzzle Who Might Own The Monkey? which would respond to the mathematician's questions:

• How many solutions are there?
• How do we know when we have found them all?
Alternatively, students could create their own set of cards and clues independent of the materials in the task. Story shells might be:
• Who Owns The Footy Shorts?
• Who's Hobby Is Camping?
• Who Gets The Dessert?
Designing the puzzle, inventing the clues and validating that users find it interesting and challenging is a major project that can simultaneously address mathematics, language and technology outcomes. Can the students design a set of clues which reflect the title in the same sense as the monkey puzzle does, ie: the answer isn't revealed until the end.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

This task is a partner (in terms of content) to Who Lives Where?, Diamonds & Rectangles, Police Line Up and others in the set. Selecting several such tasks can be the source of a Language and Logic menu-based unit.

However, words matter in this task so you might prefer to build a strong literacy component around the language of the card. Consider producing the clues in large form - poster or word processed and projected (you cannot photocopy the card) - to generate discussion. Also consider creating A5 size house, car, pet, drink and nationality cards. Most of these are words so you could just hand write them. The others can be easily created using clip art or photos from the web.

Given there are twenty-five cards involved, in most classes, one card could be assigned to each student while the clues are on public display. Students are then responsible for the placement of their own card while simultaneously being part of the general class debate. The teacher's role is to:

• clarify the problem solving strategies being used
• connect the class struggle to the Working Mathematically process
• highlight the cleverness of the title
• explain that the clue set is both necessary and sufficient for a unique solution
• explore how the designer probably constructed the puzzle
The next phases could be to:
1. Ask students to work in small groups to solve Tim's monkey puzzle, given that you had prepared sufficient small scale material.
2. Challenge the students to create their own puzzle, individually or in teams, as a project for assessment.

A variation on this approach is to write the clues on strips of paper - one clue per strip - and give one strip to each pair. It is the pair's responsibility to make sure there clue is taken into account.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 190, Who Owns The Monkey?, which includes two alternative clue sets, masters for preparing a class set of cards and details for presenting the task as part of a Menu Maths approach. It also suggests further extensions, some of which connect the investigation to the mathematics of selections and arrangements.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Who Owns The Monkey task is an integral part of:

• MWA Space & Logic Years 5 & 6
• MWA Space & Logic Years 7 & 8
This task is also included in the Primary Library Kit. Solutions for tasks in this kit can be found here.