When students first start learning equation solving, you want them to get a feeling for how to balance equations by using opposite operations. For example, in one-step equations if the original operation is addition, you’ll use subtraction to solve the equation.
Write the following operations and numbers on flash cards so they are large and visible from a distance. These operations and numbers will now be your number soup: – 5, + 3, – 7, + 5, + 9, -2 (some of these numbers will be used more than once)
Write one of these equations on the board (see poster) and ask students which of the numbers from the “soup” of numbers will help them solve for the variable in that equation.
Ask them to tell you why they picked a particular operation with its companion number out of the soup.
At this stage, you only want them to think about what operations and numbers they will need to form zero pairs and balance the other side of the equation as they are forming those pairs. Don’t have them do any equation solving, but instead concentrate on what’s needed to solve a one-step equation with addition or subtraction.
If students have not yet learned negative numbers, you can alter the equations accordingly.
This activity is a continuation of the Part 1 activity. After you have been working with one-step equations with addition and subtraction for a while it’s time to turn your attention to one-step equations that require multiplication or division to solve.
These are more difficult for students because they need to understand that division by 2 is the same as multiplication by ½.
Once again, prepare some operations and numbers for your “soup.”
For example, the equations on this poster will require:
÷ – 3 (or multiplication by – 1/3)
÷ – 2 ( or multiplication by – 1/2)
÷ 12 (or multiplication by 1/12)
÷ 5 (or multiplication by 1/5)
x 6
x (– 3)
x (4/3)
Ask them to tell you why they picked a particular operation with its companion number out of the soup.
The key takeaway here is to make sure that students develop a facility for switching back and forth from division to multiplication by the reciprocal.
Students may be frustrated by the fact that they can figure out that 12 = 72/6 and why do they need equation solving anyway? Make sure they understand that they are learning techniques to serve them when they are asked to solve more complex equations. This is only the beginning in the land of equation solving!