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Card Game – Approximate Square Roots

October 4, 2012

In an earlier post I talked about using card games to help solidify basic facts and develop mental math strategies.I have found this effective for my grade 7 class this year and the excitement of the game makes for a fun start to every game.

For grade 8, I wanted to build on the game idea for the fun component but also wanted to make sure that I was addressing concepts in the curriculum. As a result, I was determined to come up with a similar game for developing a better understanding of squares and square roots. I have found that students in middle school do not have a real concept of the impact of squaring a number and that the difference between successive numbers is not the same as the difference between their squares.

The eventual game I came up is played in the following manner:

1) Each person in the class is randomly assigned a number and placed into a double elimination bracket. This provides groups of two to play against each other.

2) Cards are assigned the following values: Joker – 0, Ace – 1, Jack – 11, Queen – 12, King – 13  and numbered cards retain their face value.

3) Opponents split the card deck into two equal parts with each person taking half of the cards.

4) Opponents decide which card will be first and then each  flip over a card.

5) The “value” of the two cards is determined by reading the cards from left to right. For example a 9 and a 1 would be 91, a King and an ace would be 131 and a King and a Jack would be 1311.

6) Each opponent determines two whole numbers the square root of the number showing would lie between. For example in the case of 91 the square root lies between 9 and 10. For 129 the square root lies between 11 and 12. For 49 the answer is 7.

7) Opponents race to state the two numbers. Calculators can be used to verify solutions but not in the initial solution.

8) The person to state the correct answer first wins both cards. In the event of a tie the cards remain on the table and two more cards are drawn with the winner of the round taking all four cards.

9) At the end of the allotted time the person with the most cards goes on to the next round until a victor is crowned for the class.

Some tips that I have found helpful include:

  • One round per day is played so it does not have a major impact on class time. This also allows time for students to practice (some do).
  • Scrap paper and a pencil are very helpful.
  • If the groups are odd then I play with the person who is not actively competing as this gives me some one on one time with the person.
  • Once people start to get eliminated have them play against each other for additional practice.
  • Everyone wants to watch the final.
  • This game is a great way to talk about using the distributive property to improve computational fluency.
5 Comments leave one →
  1. October 13, 2012 5:11 pm

    Great game, Richard, for practicing this skill! Thanks for sharing it.

  2. Ms. Wagner permalink
    October 25, 2012 1:02 am

    Thanks for the idea Richard! I adapted it for my grade 11s… 🙂

  3. October 25, 2012 7:57 am

    Glad you like it. Let me know how you make out with the grade 11 version. It is always nice to get feedback.


  1. A Game for Practicing Simplifying Radicals | Ms. Wagner's Blog
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