A Step by Step Guide to Introducing Fractions
Fractions are a huge part of third grade. According to Common Core they are supposed to be introduced in second grade, but, if your school is like mine, sometimes that just doesn't happen. I totally get it. There is a lot of math curriculum in second grade, and fractions can be overwhelming - for the teachers and the students.
Fractions don't have to be overwhelming. If we start with concepts kids already understand, we can build from there to get to the complicated stuff.
For example, every kid has shared a candy bar (or a pizza, or a birthday cake, etc...). So, let's start there. Bring in a candy bar - a KitKat would be great because it is already partitioned into four equal pieces. Talk to the kids about the fact that you are holding one candy bar and ask them how many pieces are in the candy bar. Take time with this conversation. Talk about how many kids could share this candy bar. Which is more, one part or three parts? If you can swing it, buy many different candy bars and talk about how you could partition these. There are so many good fractions conversations you could have based on a little candy bar math.
The goal of the candy bar conversation is just to get your kids comfortable with the idea of partitioning a whole into equal parts. Next, you want to make sure they know the difference between equal parts and unequal parts.
You can use cut out paper shapes or drawings to explore the idea of equal parts. Either way, have several examples of shapes partitioned into equal parts and shapes partitioned into unequal parts. Ask the kids what equal means. Ask them to explain how they know a shape is partitioned in equal parts vs. unequal parts. This is a very simple idea, but it is one that you want to be sure your students understand. For more practice, give students a set of cards with shapes partitioned into equal and unequal pieces and have them sort them.
Once students understand the difference between equal and unequal pieces, it is time to introduce the word "fraction." Explain that whole that are broken up into equal pieces are called fractions. Fractions have different names depending on the number of equal pieces in one whole. Next, you introduce the terms halves, thirds, fourths, fifths, sixths, and eighths. You can add more, or break the list up into smaller pieces depending on the needs of your students.
Collect items that are already partitioned into equal pieces. Paper will be fine, but real life objects are even better. For example, Legos, a football field, a quilt with square blocks, a pizza, a birthday cake, and an ice cube tray are all partitioned into parts. Give the fraction name for each example you show the class, or ask for volunteers. You could follow this up with another sorting activity or give the kids a worksheet to practice naming fractions based on the number of equal parts in each whole.
The next step is to have kids start writing fractions to match shaded parts of a whole. Again, I would start with real world examples. The easiest thing to work with here is pizza because everyone has eaten pizza. I would actually cut out paper pizzas for this lesson, so you can take away pieces of pizza. Tell the kids that you ordered a pizza. Show them the paper pizza. This is a great time to review equal pieces and fraction names. Next, tell the class that you ate 3 of the pieces of pizza. Write the number three on the board. You can then draw the fraction line (it is called a vinculum). As you draw the line, tell the kids that it means "out of". The bottom number is how many pieces there are in one whole. I would always make sure I said, "out of one whole," because later the students will work with more than one whole, but the denominator won't change. If you consistently emphasize the one whole early in your teaching there will be fewer misunderstandings later. Finish the fraction by writing the 8 (or however many pieces you have total in your pizza) below the fraction line.
I find that this part of fractions is actually pretty easy for kids. You can have them practice by matching fractions and pictures or by completing a worksheet.
If you are teaching third grade, this will be a great time to introduce the vocabulary words numerator and denominator. If you are teaching first or second grade, I wouldn't use these vocabulary words yet. Wait for the kids to be very comfortable using fractions first.
The last step in introducing fractions is to define unit fractions. Unit fractions are the building blocks we use to make bigger fractions. We build bigger fractions by adding unit fractions together. First, make sure kids understand that a unit fraction is one part of a whole. Show the class cards with blank partitioned wholes. Then, color in one part of the whole. Write the matching fraction on the board. Kids will soon see that the numerator for unit fractions is always one. Don't tell them this. Wait for them to see it on their own. You can give kids a worksheet to practice naming unit fractions.
When you are sure that your students understand the concept of a unit fraction, it is time to use unit fractions to build bigger fractions. Plastic fraction strips are perfect for this lesson because they are each labeled as unit fractions. Line up several matching unit fraction strip pieces such as three pieces labeled 1/4. Model adding the three pieces together using a number bond or a tape diagram. Ask your students what the total will be if you add all three pieces together. You may get some misconceptions here, but this is a great time to deal with them. Do enough examples that your students see that the denominator always stays the same. They will remember this fact much better if you don't tell them, but they discover it on their own.
For independent practice students can roll a dice to get a number. Then, they can pull out that many fraction strip pieces (all with the same denominator) and write an addition sentence to match the fraction strips. You can also give them a worksheet that requires them to write addition sentences to match a picture of a given fraction.
After these lessons, your students should have a strong understanding of fractions. You can then build on this understanding by introducing number lines, comparing fractions, and equivalent fractions.