Estimating Square Roots Games & Activities

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Even challenging square roots can be estimated if you know how. To give students practice in this process, why not try out a few of these activities and games?

Estimating Square Roots Games and Activities

To many people, a square root is nothing but a button on a calculator. You press it, and you get your answer. But finding even difficult square roots is possible through estimation. If you know the square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81), and you know the numbers you have to square to get them (1, 2, 3, 4, 5, 6, 7, 8, 9), you can figure out the square root of a number by comparing the number to its position in that list.

For example, you know that the square root of a number between 25 and 36 will be between 5 and 6. By looking at where it is positioned in that range, we can estimate square roots; however, this process takes practice. Let's take a look at a few ideas for games and activities that students can use to practice estimating square roots.

Closest Estimate Game

In this game, students compete to come up with the closest estimate for a square root. Have students work in pairs, and give each pair a set of index cards containing various numbers. Students must reveal one of the cards, and each student writes their estimate for the square root of that number on a separate, hidden card. They each reveal their answers at the same time. The student who is closest to the correct answer (listed on the back of each card, or checked using a calculator) wins a point.

This continues until the entire pack of cards is completed, and the student with the most points is declared the winner. If every pack of cards is different, students can pass the decks around the class to get even more practice.

Square Root Pairs

In this game, have students work in pairs and give them a set of index cards that contain both square root questions and answers. Students must lay the cards out, randomly and facedown, in a grid (for example, you could give them 36 cards to place in a 6 x 6 grid). Then, they take turns to turn over two cards of their choice. If those two cards match - a square number (for example, 36) and its square root (in this case, 6) - they keep the pair of cards and gain a point. If the two cards don't match, they turn them back over again.

This continues until all the pairs have been found. The student who has the most pairs wins the game.

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