Who Lives Where?

Task 110 ... Years 2 - 8

Summary

Mathematicians have ways of knowing. Learning to work like a mathematician is learning these ways of knowing. This problem requires reasoning skills independent of any text-book-like skills, so is open to a wide range of students. If-then reasoning is called on significantly in this challenge in two ways. If this is true ... then this must also be true and If this is true ... then this cannot be true.

Materials

• 9 cards showing family names, children's names and cars
• 1 sorting board

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.

One approach to Who Lives Where? is Guess, Check & Correct.

Let's try putting the Papadopoulos family here and see if the other clues work.
Students will soon realise that guesses can be influenced by stated or implied information in the clues. For example:
1. Clue 1 tells us that the Nguyen and Papadopoulos families must be in either 1 & 3, or 3 & 5, but it doesn't explain which way around in each case. But that means there are only four possible placements.
2. Clue 6 tells us Kim is definitely a girl. However this fact combined with Clue 3 alone does not necessarily imply that Kim lives in House 3. There may be other families without boys and Chris and Sam are names used for boys or girls.
3. Clue 4 tells us that Sam is definitely not in the Jackson family.
Encourage students to dig deeper into the clues in this sort of way:

 NUMBER 1 NUMBER 3 NUMBER 5 Papadopoulos Nguyen Jackson Sam Kim Chris Ford Falcon Holden Commodore Mazda 323

The iceberg of the task flows from asking students how they think the task was designed in the first place.

What came first? The clues?
It is more likely that the designer first thought of the story shell, then laid out the grid, then thought up the clues.
Would you like to try making up one of your own?
Not as easy as it might sound but a worthy project which will need to involve testing on others before the result becomes part of the class set.

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 the more complex 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. Then use your Maths Mat folded to be 4 rows of 3 as the grid. Some children carry signs representing the cards in the task and sit in the grid where they are told. The remaining children instruct based on their interpretation of the public clues.

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 their clue is taken into account.

At this stage, Who Lives Where? does not have a matching lesson on Maths300.

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 Lives Where? task is an integral part of:

• MWA Space & Logic Years 3 & 4
This task is also included in the Primary Library Kit. Solutions for tasks in this kit can be found here.