Wholes and Parts

By Mathnasium | Added Oct 18, 2012

Add 17 + 18 + 19. Do it quick! If you reached for a scratch sheet to get to the solution of 54, you didn't do it wrong, but here's a different way to think about this question:

First, round each number to the nearest 10 (20 in this case), and add the 20 three times, making a total of 60.

Now, take away 19 from 20 (1), 18 from 20 (2), and 17 from 20 (3). That gives you a total of 6 (1 + 2 + 3).  This 6 represents how much "extra" you added by adding 20 three times instead of just adding 17, 18, and 19.

Finally, take the 6 from 60 and you get 54 as your solution!

Try this:  99 + 99 + 99.

By doing this mentally, we can help children to develop strong numerical fluency skills.

Number Sense is the ability to appreciate the size and scale of numbers, in the context of the question at hand. Three elements establish Number Sense: Counting, Wholes and Parts, and Proportional Thinking. We already discussed Counting. Today, we will focus on Wholes and Parts.

The concept of Wholes and Parts is the backdrop for many mathematical concepts.

A whole that is broken into equal parts creates fractions. 100% of something represents a whole. Many people do not have a clear idea of what a fraction represents nor do they break down the word ‘percent' for what it is: per-CENT-"for each 100." Without a solid understanding of Wholes and Parts, solving word problems becomes very difficult.

Wholes: equal to the sum of its' parts.

Parts: equal to the whole minus the other part(s).

Let's dig deeper, starting with complements. A complement is the amount needed to make a whole complete.  Problem solving comes to the ability to identify the missing part(s) or the complement.

Children should be asked to visualize and answer a question like:

Together we have 10 pieces of candy. You have 7 pieces. How many pieces do I have?  Here, the whole is 10 and one part is 7.  So, the other part is 10 minus 7 (the whole minus the part, you know).

This will help set up their understanding of complements.

Children also need to be introduced to the fraction "half" as being "2 parts the same." Before other fractions are introduced (1/3s, 1/4s...) children need to master questions like:

How much is half of 6? 3? 7? 20? ˝? 99?


Half of what number is 5? 10? 25?

Wholes and Parts creates a strong understanding of the structure of mathematics, eventually building up a child to understand how to solve complex fractions, equations, and word problems.

When dealing with Wholes and Parts, kids really like examples that deal with cookies, sandwiches, or anything they can eat. Try this example:

You have a box of cookies. You get to eat half of them after lunch and half of what you left over after dinner. After dinner, you have 3 cookies left. How many cookies did you start with? The answer is 12.

When a word problem is set up like this, children can often visualize the situation. If visualization doesn't work, have a Plan B (drawing a picture), or C (using physical objects) until the child understands.

For every kid, there is a way to explain every topic in a way that makes sense to them.