In 5th grade, students need to develop their fraction fluency and apply fraction models with addition and subtraction of fractions with unlike denominators. This lesson is just step one in developing this fluency. Today, students look for equivalency patterns using fraction circle models or MP7 - look for and make use of structure.
There are some materials required for this lesson such as fraction circles. If you don't have the plastic circles you can print paper copies. I've included fraction circle templates in the lesson.
It is important to model your thinking during this lesson, especially because students will mix up the Can You Make column with the actual models drawn in the rows. The first row takes time but if you have started with my Parts of a Whole: Modeling Fractions & Creating a Portfolio lesson your students should have practice with drawing the models.
This lessons strength is in MP7 - look for and make use of structure where students look for patterns and express regularity in repeated reasoning MP8.
For this part of the lesson I put a blank Can You Make page under my document camera so the students can see what I am doing step by step.
I keep my finger pointing to 1 on the left side and get out a one whole piece from the fraction circles and ask, “Can you make one whole with a one whole piece?” pointing to the top of the column where it says With Wholes. I get out another one whole fraction circle and place it over the one whole.
This seems obvious but I’ve found that for my students who are visual spatial or English Language Learners the modeling and express regularity in repeated reasoning is important (MP8). I continue by keeping my finger on the number 1 and ask, “Can you make one whole with halves" – and point to the With Halves. I also take two one-half pieces and place them over the one-whole and explain why and label the illustration with 2/2. It takes 2 one-half pieces to cover the whole. I continue this way until we get to 7ths because we do not have manipulatives for 1/7th (I have found out they are not made because 1/7, 1/9 and 1/11 are not commonly used.) It is a great place to see if your students are following the repeated reasoning of every fractional shape fitting into the one-whole with exactly the number of pieces in the numerator as the denominator.
If you don't have plastic fraction circles, you can use this fraction circle template.
So, as you're repeating but with different fractions the students should be doing the reasoning themselves (because this is looking for and making use of structure)- and when you call on them it is a great time to check student understanding. Listen for the mistakes and the thinking that supports the errors, not the correct answers. I mentally take a note or jot down on a sticky note who makes the mistake, and I make sure to follow up with them later. This could just mean listening to their answers later in the lesson or having a conversation.
As you continue on a pattern emerges with factors of a number, odd and even numbers, etc (MP7). Once the chart is completed, it really does go fast once the pattern is found that if the denominator is bigger than the fraction piece it cannot be made, have a conversation with your students about what the chart tells them. (MP7 – look for and make use of structure) In this student work you can see how they filled out the chart.
By this point in the year I have established an end of lesson routine for my students. Once they have filled out a chart, students have to write 3-5 facts on the back. The number is dependent on the student. Each student knows their work expectation (3, 4 or 5 responses). I’ve established the more the better, but if the student is not there yet they will be and it is a goal to work towards. The more the better could also mean a student has written half a page on 3 things and not short answers to 5. I also ask my student to reflect on their thinking skills and behavior in one or two sentences by asking “Can you now see fractions in your mind?” and simply “ How was your behavior during the lesson?”