This post is going to give you some good visuals on teaching students to multiply fractions. Yes, I know that it is MUCH easier to just say, “reduce diagonally and multiply straight across.” Sometimes it is easier that way, but what do students really learn about the number sense of it all? Is it good enough to just tell them the steps and let them be? I don’t think so. Not to mention the fact that my students LOVE to color, cut, paste, move things around, what-have-you. It makes math fun and much more interesting.
Here is a little pictorial lesson on how to multiply fractions.
First of all, you need this nice little worksheet that I made for you….click here or on the picture to get the download.
Let’s look at the problem 1/3 X 3/4:
Using the grid I just gave you and a colored pencil, make an array. First, you are going to draw a line horizontally to represent the 1/3. The line should be three squares long and you should shade in one of the three squares. Then you are going to make a line vertically to represent the 3/4. It should be four squares long, and you should shade in three of those four squares. Your picture should look something like this…….
Looking at that grid, you can see that three out of the twelve squares are shaded, making 1/3 X 3/4 = 3/12. From this point, your students should realize that they need to simplify this answer.
Now you can show them that multiplying fractions is commutative. They can multiply in any order. Let’s look at 3/4 X 1/3
Your horizontal line should be four squares long and shade in three of those four squares. Your vertical line should be three squares long and shade in one of those three squares. You should have three of the twelve squares shaded. Here is a picture of what that should look like……
Here is another problem… 2/5 X 3/4
Your horizontal line should now be five squares long, with two squares shaded. Your vertical line should be four squares long with three squares shaded down, but now shading two columns to stay with the two of the 2/5. Your graph should look like this……
You should have six out of the twenty shaded, or 2/5 X 3/4 = 6/20.
In order to show them again that fraction multiplication is commutative, you can show them 3/4 X 2/5 is the same. It should look like this……
After students see the pictorial representation, you can start to show them the repeated addition or remind them how to find the area of rectangles in order to go from the pictorial representation to just doing the computation.
The following are some games that I have made to help reinforce multiplying fractions. If you follow my blog at all, then you know that I am not a big fan of giving homework, but instead playing fun games and activities at the end of the class or beginning of the next.
The first activity I have for fraction multiplication is a “partner find” type of a game. Students are each given a card with a problem on it. They must work their problem, and then go around the room to other students and work their problems. They continue until they’ve found all of the problems or until time is up. By making sure that each student’s answer is correct on the initial problem, students are able to check their answer with each partner.