Teaching fractions? Welcome to one of my favorite units!
It all starts with a basic understanding of the concept of fractions. With a firm grasp of the basics, learning fractions becomes a fun and exciting exploration of important math concepts.
(Scroll down for tips on teaching decimals.)
The teaching of fractions begins in third grade, although younger students usually have a solid understanding of “half”. It starts with a developmental approach: what fractions are and what they mean in the daily lives of your students.
For example, “5/8 of a pie is left if somebody has eaten three of the pieces.” Now that means something to kids! They can picture it and understand it.
So let's dig in! Your students will be dividing “wholes” like pros if you follow these basic steps.
Teaching fractions step-by-step
Kids are intimidated by fractions. They look funny to them and fractions don't have much real world meaning in their lives beyond the concept of one-half of something. So we start teaching fractions with a discussion of food.
Students easily grasp that fractions can be expressed as one whole piece of food being shared among family or friends. This helps them understand the concept of fractions: that they are a range of “portions” from zero (nobody is eating) up to one (all pieces of the pie – all portions – are being consumed).
I start my fractions unit with an apple lesson where we cut apples up into halves, fourths, eighths, etc., and they quickly understand that fractions are parts of a whole.
They also get to taste a variety of apples, which they love!
Video tips: how to introduce fractions
The next step in teaching fractions is to compare them so students can figure out (for example) whether 2/3 is less than, greater than or equal to 3/4. To do this, you need a fraction tool, and I'm providing a free one for you here.
My students wear these sheets out! There really is no substitute when when teaching how to compare fractions.
Fractions = Division
Of course, it's not enough to understand the concept of fractions and their relative sizes. Students need to move on to manipulating them and using them in basic operations.
So the next step is to build students' understanding of the equivalency that fractions have with division. A little advance planning will simplify this task immensely.
You see, teachers who begin to teach the concept of division while teaching multiplication will find their jobs much easier when the fractions unit arrives. Why? Because a fraction is actually a mini division problem:
- 1/3 is another way of saying “1 divided by 3”
The first step is showing them the reverse of those math facts they are memorizing when learning multiplication. For example, if they know that 7 x 8 = 56, then students should also understand that 56 ÷ 8 = 7.
The secret is the symbol
The division symbol (÷) is a very important early concept, and teachers should explain to children that the dot separated from another dot by a line is actually representative of a fraction – they are simply replacing those dots with numbers.
After we talk about the division equivalent of multiplication math facts, I show them that 6 ÷ 2 = 3 is actually the same as 6/2 = 3. So they start to become familiar with both division and fraction notation.
As you can see, teaching fractions begins well before we start the fractions unit. Apply these steps and you'll find that your students grasp concepts of fractions much more quickly
Teaching decimals really comes down to teaching kids about money. It's only natural since by fourth grade they are very familiar with money and we usually teach decimals to the hundredths (pennies) place.
Kids naturally understand money, and so it's not difficult to teach them the difference between 1.15 and 5.11.
So let's get started and “make some money!”
To the Left and the Right
The first step in teaching decimals is ensuring that students know that any numbers to the left of the decimal are whole numbers or whole dollars, and this number can be any size.
Anything to the right of the decimal is portions of “one” or portions of a single dollar.
Of course, it's those numbers to the right of the decimal that are the heart of the matter. This is where the understanding of money really comes in handy for building understanding.
I teach that the first place to the right of the decimal point is the dime's place, and stands for some number out of 10. It can be stated as:
“How many dimes do you have out of ten?”
The second place to the right of the decimal point is the “penny's” place, which is:
“How many numbers do you have out of 100?”
“How many pennies do you have out of 100?”
Make sure to point out to students that after 9 pennies (or 9/100) you have a dime and more pennies.
Here's free download of the chart above for you. It prints on legal size (8.5 x 14 inch) paper.
After they've had enough practice with decimals (and Smart board lessons are great for reinforcement), the next step is to write out a variety of them on cards (such as 0.33, 0.5, 0.25) just as we might do with basic fractions (1/3, 1/2, 1/4). Shuffle them and have students lay them out on the floor in order.
The best strategy for students is to put the card with 0.50 (1/2) in the middle and then start going through the process of figuring out the rest.
Teaching decimals must include a knowledge of the equivalency between decimals and fractions. Again, we turn to the subject of money as a basis for building this understanding since basic fractional equivalents can be related to parts of a dollar.
For example, there are 4 quarters in $1, which can be expressed as 1/4 of a dollar or 0.25.
- When reading 1/4, I say both “one-fourth” and “one-quarter” to strengthen that link to money.
Students can easily figure out that 1/2 dollar is 0.50 or fifty cents. They also quickly realize that 1/10 is one dime or 0.10, ten cents. From there they know that a nickel has half the value of a dime so there are twice as many in a dollar: 1/20 which is 0.05 or five cents.
Once students have the money decimals mastered, we break out calculators for the oddballs: 1/3 and 2/3. Doing these mini division problems (i.e. 1 ÷ 3) lets them figure out the different fractional equivalents quickly.
Kids “get” decimals because kids “get” money. Have some fun with it!