## Thursday, 16 October 2014

### Tarsia Puzzle Squares and Square Roots

We came across these puzzles a few years ago. The premise is that you have a bunch of questions and matching answers. Students have cards that have either an answer or question on the edge. They then have to match up the edges that have the pairs of questions and answers and eventually it will make a shape. In this case the activity is matching up perfect squares and square roots.
We found these puzzles originally on the Mr Barton Maths site under the Tarsia Jigsaw Page. The nice thing here is the Tarsia software can be downloaded here (click the green button to download - unfortunately it is Windows only) and you can edit or create your own puzzles. So this puzzle was one of our creations. There are even banks of hundreds of already created puzzles on the site (just scroll down on the Tarsia page and look for the smiley faces for zipped files). These are great puzzles to pull out when you want to break up a long class or have 10 min at the beginning or end of a class to fill.

• Gr7NS - represent perfect squares and square roots, using a variety of tools
• Gr8NS - estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not

Tarsia Card Prep work: There are two downloads (three if you include the actual Tarsia file). The actual cards for the puzzle and the answer card. The cards for the puzzle come on 2-4 sheets (there are different styles of puzzles) and each triangle needs to be cut out (see image tot the right). We have found that if you have several sets of the same puzzle (say if students do it in groups of 3) then it is best to copy each set in a different colour. That way it is harder to get the sets mixed up and easier for clean up after (ie you only need to check if there are 18 cards of each colour). We find that the cards last longer if you laminate them first then cut them.

1. This activity can be done in groups or individually and can take about 5-10 min depending on the student.
2. Hand students the entire set and ask them to match up the numbers written as a square root and its answer.
3. In this case the finished puzzle looks like a diamond.
• Note: this puzzle is a little tricky since all the numbers on the outside edge are not perfect squares and thus have no match. Also there are numbers that appear twice like 16 since it is the root of 256 and has a root of 4

• Square Root Tarsia Cards (pdf)
• Square Root Tarsia Solution (pdf)
• Square Root Tarsia Editable (xjsw)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks