Creating Fraction Bars for Visual Math
Lesson 6 of 8
Objective: The students will be able to add and subtract fractions with unlike denominators by replacing the fractions with equivalent fractions so as to produce an equivalent sum.
There is some prep work for this lesson. Each student needs 5 3/18 pieces of construction paper - each a different color. If you are using 12 x 18 paper you will be able to cut 4 strips out of each one. You will also need a pair of scissors and a pencil for each student. This creates the appropriate tools (MP5) to use with this lesson.
I do lessons with step-by-step assembly, such as this one, in silence because it reinforces non-verbal communication -- the students have to watch me for the instructions.
Fractions need a huge visual basis for students to be able to understand adding, subtracting, multiplying and dividing with unlike denominators and mixed numbers. There are short-cuts or tricks and the formulas to be taught but when they only know the formula, and forget it, they will not be able to figure out the problem using reasoning. This is the basis or prep for NF2. There are no word problems in this lesson as in NF2 but it is critical prep for the word problems because it develops reasoning skills and students practice their "verbal" reasoning which comes before writeen reasoning. This lesson also is prep for NF3, 4 and 5.
I have already cut 3' x 18" strips of paper out five different colors so each student has one in each color. I am all about having my students organize and take charge -This time I gave the first and last table the stack of colored strips and told them to make sure each one at their table has one of each color and pass it on to the next table. Bringing the leftovers to the front of the room - I had cut extra because there is always someone who makes a mistake in cutting and with this lesson they must have the pieces cut into the correct sizes to do equivalent fractions.
You can see from the video Cutting Fraction Bars all of this is done in silence. This time it went smoothly, but if it is your first time having your class follow you silently it will not be silent! They are going to want answers and will probably ask them out loud. It's okay - they are following along and asking inquisitive questions.
Here is how we cut the strips:
1 - left whole
2nd - cut into 1/2s
3rd - cut into 1/4ths
4th - cut into 1/8ths
5th - cut into 1/16ths
This also is a wonderful lesson on multiplying fractions (NF.B.5). After students finish cutting, we put them into an array with the one whole at the top and the 1/16ths at the bottom. I had a student notice that each row was doubled or multiplied by 2. If you don't have a student who recognizes this, ask your students to look for a multiplication pattern (5.NF.A.2).
After students have assembled the display of fraction bars, I ask them to write down as many ways as they can to represent one whole, using their fraction pieces. This reviews and/or introduces that fractions with different denominators can make up one-whole. When we get ready to add/subtract fractions with unlike denominators this gives students a concrete (visualization) reference (5.NF.A.1).
I start my year with "The Brain is a Pattern Seeking Device" and we look for patterns everywhere. My students continue looking for patterns in everything we do so I had one say "Hey look each fraction is broken into two smaller pieces!" They were pointing out 1/2 breaks into two 1/4 pieces, 1/4 breaks into two 1/8th pieces, etc.
For this lesson, I ask my students what did they notice about the fraction bars that is similar to fraction circles. I do this to reinforce that fraction manipulatives can be different shapes and sizes. I am looking for answers that relate to the equivalence of the benchmark fraction. 1/4 and 1/4 always equals one half even if it is in the fraction circle or bar. I want students to see that the "shape" of our fraction model isn't the "big idea" of these lessons. That's why I start this unit using students as examples to represent fractions, then fraction circles, and now fraction bars - giving students as many visual representations as possible.
The next reflection question I ask is, "When you were creating equivalent fractions to one-whole what did you notice about the denominators?" Students answer with statements such as, "I usually had to use all even number denominators to create the one-whole." "The denominators could all be different numbers and each fraction bar was a different size."
My last question always ties to personal collaboration skills. I ask, "What did you do if you didn't understand what you needed to do or missed some instructions." I want students to be looking for answers themselves. One of my reasons for doing this lesson silently is for students to look around to figure out what to do, and to help each other, silently. There are some great examples in the video of students looking to other students for instructions.
I always want students to ask another student for help before they ask me and this reinforces them finding the solution themselves. I have found students, and my own children at this age, will ask for help before they need to. They could figure out how to problem solve on their own if they took the time.