Goal
Understand and use variables in a symbolic way

Objective
Gain practice in solving for a variable using given numbers

Materials
Magic Square handout

Time
About an hour of direct instruction to explain the concept of magic squares. Students use the rest of the week to practice solving existing magic squares and experiment with making their own.

Activities
Students are individually presented with magic squares in which variables appear. They replace the variable with a number that creates an equal sum, whether one adds the numbers horizontally, vertically, or diagonally. Students complete handouts that provide practice in finding the value for the missing variables:


 

Handout

"A magic square is an arrangement of numbers in a square in which the rows, columns, and diagonals each have the same sum. A magic square is shown below:
 

7
 

2
 

1
 

5
 



 

8
 

4
 

To find the missing values in a magic square first identify a row, column, or diagonal in which all the values appear. The sum of the completed diagonal in the magic square shown above can be represented by the numerical expression 8 + 5 + 2. A numerical expression contains only numbers and mathematical symbols.

1. What is the sum of each row, column, and diagonal of the magic square shown above? (answer: 15)
 

You can represent the missing value in each square by a variable, as shown below. A variable is a symbol, usually a letter, that stands for a number.


 

a
 

7
 

2
 

1
 

5
 

b
 

8
 

c
 

4
 


 

2. Name the variables in the magic square. (answer: a,b,c)

The variable expression a + 7 + 2 represents the sum of the entries in the first row. A variable expression is an expression that contains at least one variable.

3. What is the value of a? (answer: 6)

(handout adapted from Prentice Hall Mathematics, 6th Grade Edition, 2000)


 

Closure
Discuss problems and answers.

Assessment
In having each student complete problems from the handouts, the teacher will be able to monitor whether or not students are able to apply the vocabulary to the manipulation of symbols.

Extensions
Students create their own magic square

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