Understand and use variables in a symbolic way
Gain practice in solving for a variable using given numbers
Magic Square handout
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.
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:
"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:
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.
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?
(handout adapted from Prentice Hall Mathematics, 6th Grade Edition, 2000)
Discuss problems and answers.
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
Students create their own