When you were a fifth-grade student sitting in your little desks, you probably did this concept totally differently than it is done today.
You took your mixed numbers, changed them to improper fractions, multiplied them together, and the changed that often times enormous number back into a mixed number. It was a lot of steps, often with large numbers, and mistakes were easy to make. If your understanding of fractions was anything similar to mine, you didn’t have a clue why you were doing those steps.
Nowadays, using a visual model has become the key word, and I love it. I’m not saying the steps are shorter, but the students are not just doing random steps. They are visualizing the problem, and through that, they are understanding the WHY behind the steps. And I, of course, love that.
If you do not have an unpacking the standards in your state, you need to be pulling one from other states. I love North Carolina’s. It really breaks down what needs to be taught and shows how to solve problems using visual representation.
How do you solve a mixed number by a mixed number using a visual model?
It is easy. Take a look at this example provided by North Carolina.
As you can see they are multiplying 2 1/4 by 1 1/3. They began by drawing three wholes across at the top (you will always round up your fraction to the next whole when drawing an array). The colored in 2 wholes, then took the third whole divided it up into fourths and colored in 1/4.
Next. they drew two wholes going down. They only had to draw one, as the first whole was already drawn. They then took the second whole and divided it into thirds and colored in 1/3.
It is important at this point to extend the 1/4 to the bottom of the area, and the 1/3 all the way across. Notice that this divides the box into twelfths. Isn’t that an awesome representation of why we multiply the denominator?
At this point, you have two options. Add up the colored in part of the array. 2 + 2/3 + 1/4 + 1/12 = 3
Or you can have them multiply the numbers like they have done in third and fourth grade when multiplication was taught.
2 x 1 = 2
2 x 1/3= 2/3
1/4 x 1 = 1/4
1/4 x 1/3 = 1/2
2 + 2/3 + 1/4 + 1/12 = 2
The arrays may be a little confusing at first for our precious students. They need time playing with them, and being able to recognize what they are seeing.
I created this FREE game to help students get practice playing with arrays, and learning to see the fractional parts in them.
What you get!
There are four different arrays. Each player should have their own copy of an array, though the array should be the same array that their opponent has. Laminate the boards, provide them with dry erase markers, and the correct game pieces.
How to Play!
I highly recommend playing this game in a small group at the beginning. This FREEBIE has detailed directions, discussion questions, and variations to the game, but is more manageable in a small group setting.
- Player one draws a fraction card and colors in that fraction based on what 1 equals in the array. The first square in the array equal 1 whole. (Example: If the square is a 10×10 and the player draws ½ then the player will color in 50 small squares or 5 rows.) When finished the player put the fraction face down at the bottom of the pile.
- Player two then draws a card and colors in that fraction based on what 1 equals in the array.
- The players continue to take a turn. Whoever fills up the whole array first, wins.
- To make the game more challenging you could have to fill up the array exactly, or if you go over you have to erase that amount instead of add.
Games are a fun way to help children experience and begin to love math. I hope that this game cultivates a love for math in your kiddos.
You’ve Got This
Need some other activities for multiplying mixed numbers by mixed numbers? Try out one of these!
Click HERE to get your freebie.