Solving comparison word problems

Question

There are 4 fewer cats than dogs. There are 2 cats. How many dogs are there?

Answer 1

Thinking through the problem:

If there are 4 fewer cats than dogs then that means that to have the same number of cats as dogs, you need to add 4: dogs = cats + 4

Next, if there are only 2 cats then you substitute 2 for cats: dogs = 2 + 4

Then solving: dogs = 4 + 2 = 6

Therefore, there are 6 dogs and 2 cats.

Answer 2

Problem: There are 4 fewer cats than dogs. There are 2 cats. How many dogs are there?"

For young children the "fewer than" language is hard. Does the child understand "less than"? There are 4 less cats than dogs. Compare questions such as how many more or how many less are difficult concepts for a child to visualize so teaching with concrete objects and pictures first will help him or her "see" the relationship.

Try modeling out the concept of more than, less than with pennies. If I have 2 pennies and you have 4 more pennies, how many pennies do you have? I have 2 pennies and you have 6 pennies. 6 is 4 more than 2. Who has more? You do. How many more? 4 Who has less? I do. How many less? 4 less. After the child understands more than and less with pennies.

Switch to pictures, use a simple picture such as a circle for a cookie and repeat. Draw your cookies and the child's cookies in rows so he or she can "compare" to see which is more, which is less and see the "more than" part and the missing "less than" part.

Now, instead of pennies and cookies, can he or she understand the word problem above with cats and dogs. Can she imagine 2 cats? Are there more cats or dogs in this story problem? It says there are less or fewer cats so there are more dogs than cats, right? How many more dogs than cats? 4 more. How many cats are there? 2. What is 4 more than 2? 6. Yes, there are 6 dogs!

You may need to draw a simple picture with cats and dogs if he or she is still in the pictorial stage of learning. Attach numbers to the pictures. Keep the pictures simple so not to distract from the basic math concept. Save detailed drawings for art. :)