Using Fact Families to Solve Problems with Unknowns
First, here is a fact family using addition and subtraction with whole
numbers. If the number sentence is 5 + 3 = 8, make a triangle, putting
the number that is the SUM on the top of the triangle.
8
5
3
Using the number sentence and the figure you can write the fact
family as follows:
5+3=8
3+5=8
8–5=3
8–3=5
The same process can be used with fractions. Because addition and
subtraction are inverse operations, they “undo” each other and are part
of the same family. When you are given a problem with an unknown, say
N, you would put the N in the correct corner of the triangle (the top
position, or either of the bottom corners) and then decide which fact
family sentence would help you solve the problem.
- N=
N
The fact families are:
N
+ =
+N=
-N=
- =N
In this case, you would choose the last math sentence to help
you find the answer. You want the one that has N by itself.
x
=N
N
Multiplication and division fact families are similar since multiplying and
dividing are inverse operations, they also “undo” each other. The fact
families for the above example are:
x
=N
x
=N
N
=
N
=