# Criss-Cross Numbers

### Task 39 ... Years 2 - 7

#### Summary

This is a hands-on example of Cross Number (cf: Crossword) puzzle. Using the numbered counters makes it easier (and safer?) than a pencil and paper version. The problem is to fill the empty spaces knowing only the numbers in the completed puzzle and a few given digits.

The puzzle is equivalent to completing a crossword with no clues other than the words in the puzzle, a few correctly placed letters and sufficient scrabble tiles to complete all the words.

#### Materials

• Counters numbered as shown in the photo
• Puzzle board

#### Content

• place value
• if-then reasoning
• creating and solving equations #### Iceberg

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

Reasoning is the focus of this task. Encourage students to notice and record their reasoning at each step. The first step is (should be?)...

• Where would you start and why?
...There is only one three digit number with a 3 in the tens column, so 438 is a good choice for the first column.
When done well, the journal entries should provide an extensive record of student thought processes.

One solution is... ...Are there others?

#### Extensions

1. When you have a solution, number your puzzle boxes in the same way as a crossword is numbered. Create equations ('sums') which have the puzzle answers as their answers. Try your equations out on another student.
2. Create your own Criss-Cross Number puzzle. Is it possible to create one with no clues printed on the puzzle, and have a unique solution?
3. Create your own Criss-Cross Number puzzle where the clues are equations.
4. If you haven't noticed already, take a second look at the black squares. If you still don't notice anything, focus attention on just one set of the black squares and rotate the board 90 degrees. The set you are watching moves on, but another set moves in to take its exact place. The task was created by starting with a board that is rotationally symmetric; in this case rotation symmetry of order 4 (why?). Is the board you created above rotationally symmetric? If not, create another puzzle which begins with one of these boards.
5. Calculatng Changes Members can extend the equation making in a cross number and crossword context using a calculator and the activity The Good Oil.

#### 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.

Use the photograph as a guide to making your own printed version of the task in a program like Word. Create the equivalent of the number tiles as a printed sheet which pairs of students cut into the nineteen tiles required. Use the activity to highlight and share the strategies students use to complete the puzzle. Extend the puzzle with challenges such as those above. Consider encouraging the students to make a class set of puzzles. Those which pass agreed criteria could then be published in a more permanent form.

At this stage Criss-Cross Numbers 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 Criss-Cross Number task is an integral part of:

• MWA Number & Computation Years 3 & 4
This task is also included in the Task Centre Kit for Aboriginal Students. 