Scaffolding a Math Problem:

Solving for a Single Variable

The Problem

Pete and Bryan are cousins. Bryan is three times older than Pete. If the sum of the age of the cousins is 36, how old are Pete and Bryan?

Step #1

Step #1

Bryan is three times as old as Pete, but Pete’s age is unknown. Since it’s an unknown, let’s use x to represent Pete’s age.

If Pete is x, and Bryan is three times as old as Pete, which picture best represents their ages?

Bryan

Pete = x

Bryan

Pete = x

Oops, Try Again

Hint: How many kids Pete’s age would it take to equal the age of Bryan?

Return to Step #1

CORRECT!

Return to the problem.

Scaffolding a Problem

Pete and Bryan are cousins. Bryan is three times older than Pete. If the sum of the age of the cousins is 36, how old are Pete and Bryan?

Step #2Bryan = 3x

Pete = x

Step #2

If the sum of the age of the cousins is 36, how can we write that as an equation.

Bryan = 3 x

Pete = x

3x + x = 36

x = 3x + 36

3x = x + 36

Oops, Try Again

Hint: If the sum is 36, what do we need to add together to make 36?

Return to the problem.

CORRECT!

Return to the problem.

Step 3

Pete and Bryan are cousins. Bryan is three times older than Pete. If the sum of the age of the cousins is 36, how old are Pete and Bryan?

3x + x = 36

Now that you have converted the word problem to an equation, you can solve for x. If you need help, return to one of the your guided practice options.

Sum

The sum is the total when two or more numbers are added together.

1 + 1 = 2

2 is the SUM of 1 + 1.

Return to the problem.

Times

In math, “times” is another way of saying multiply.

So three times one can also be written as 3 x 1.

Return to the problem.

Unknown

In math, the unknown is the number we are trying to determine in order to solve a problem.

For example, if a + 1 = 3, a is the unknown.

Return to the problem.

Equation

An equation is a mathematical statement where sets of numbers and/or unknowns are connected by an equals sign.

7 + 3 = 10 is an equation.

Return to the problem.