Introduction: Squaring a number means you multiply the number by itself. It is easy to square small numbers. For example, 7² = 7(7) = 49. Other squares are harder to calculate in your head. Trying to solve 43² would be hard to do in your head. You can find the answer using a pencil and paper or it is easily found using a calculator. In this problem you will learn and use a "trick" to let you solve 43² and some other tough questions in your head.

Problem:

1. Before you learn the "trick", you must know how to and become quick at squaring the numbers between 1 and 9. Find a partner and take turns asking questions such as 5², 2², 9², 4², 1², 8², and so on. Try to give instant answers.
2. Now, here is a "trick" to square numbers between 41 and 59 in your head. In this "trick" 25 and 50 act like "magical" numbers. The two examples below show how the "trick" is used.

   

   On paper, show how the "trick" would be used to solve 56². Show how it would be used to solve 49².

3. Now take turns with your partner posing and answering questions where you square numbers between 41 and 59 in your head. See how quickly you can answer the questions.
4. Write down, in words, the steps of the "trick" shown in the two examples above.
5. Can you use the "trick" to square numbers such as 38² or 66²? Would you have to make any changes to the "trick"? Is it harder to use? Explain.
6. Try to find a "trick" using 25 and 50 as "magical" numbers that helps you multiply any two numbers between 41 and 49. For example, can you find a "trick" that helps you multiply 43(47) in your head. Explain your "trick" and show a few examples of it working.

Materials: pencil, paper, calculator (to check your answers)

Number facts, squares, patterns, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
Yes     No     Optional 
Toward Your Marks?
Yes     No     Optional 

  Hints:

Investigate other number "tricks" that let you square numbers whose last digit is 5 (e.g., 35²) or square numbers close to 100 (e.g., 94²).