Age problems are the friendly way into algebra: one unknown, a comparison, and sometimes a jump into the future. These free printable word problems ask a child to name the age they do not know and build a sentence around it.
The move these teach is choosing what the letter stands for. Once a child writes down that the younger age is the unknown, the older age is an expression in it — three times as old, or seven years more — and the sentence in the story becomes an equation almost by itself. Naming the right unknown is most of the work.
Why this sheet works
The ones that reach into the future are where it gets interesting, because both ages grow by the same amount. In four years both people are four years older, and holding that steady is the reasoning the problem is really testing — a mistake there is a mistake about time, not about algebra.
How this one works
One question from this sheet, worked through a step at a time.
How old is the cedar tree?
The maple tree has stood 68 years longer than the cedar tree, and is 3 times as old.
3 − 1 = 2
3 − 1 = 2
68 ÷ 2 = 34 years
asked:How old is the cedar tree?
34 years
Read it through once. One is a MULTIPLE of the other, so think in equal PARTS: the smaller one is a single part, and the bigger one is that many parts.
The gap between them is the EXTRA parts — one fewer than the multiple: 3 − 1 = 2 parts of difference.
One part is the smaller age, so divide by the 2 parts: 68 ÷ 2 = 34 years.
Answer the question that was asked — "How old is the cedar tree?" — 34 years.
