This is the second lesson where students use their Can You Make charts to list the equivalent fractions from 1/2 to 1/12, and extend the pattern to add three more equivalent fractions. Although this appears to be a simple lesson, it develops students' understanding of fractions in preparation to go on and add, subtract, multiply and divide fractions in any form – like/unlike denominators, mixed numbers.
This lesson is linked to MP4 - representing the problem in a variety of ways - because the students have already created the chart and are now looking at the chart to find equivalent fractions.
If a student doesn’t have this deep understanding when they leave my room for 6th grade they are going to have a hard time when they are working with formulas and algorithms rather than models.
Ask your students to list the fractions 1/2 to 1/12 down the left side of a page in their math journal or folders – skipping a line in between. Do the same on your board, SMARTBoard or a wall chart. Ask your students to list the equivalent fractions for 1/2. Do the same for 1/3 and 1/4, then ask your students if they see any patterns. When doing this students are looking for patterns and structures in the chart (MP7 and 8). This repeated practice gives students a strong foundation to build more complex and abstract fraction concepts.
They should comment that the "top numbers" increase by one and the "bottom number" is a multiple of the first fraction. I use every opportunity to reinforce the words multiples and factors because it is one thing students get mixed up with. It is also an important place to use, and contextualize the use of, the words numerator and denominator. If your students do not comment about the addition (ex 1/4 + 1/4 = 1/2 where 1/4 + 1/4 equals 2/4 = 1/2. You will need to bring it up. (5.NF.A.1)
We say multiples multiply while factors are a fractured (broken up) number.
Have your students work with a partner to finish the chart. Once they are done have them go back and add the next three equivalent fractions to each row. Again using MP 7 and 8. I've included an example of proficient student work.
Once again, have your students reflect on their learning. Ask, “What did you learn about fractions today?” Also ask reflective questions about their own behavior and/or mathematical thinking, “What would you do differently if you had to do this lesson another time?”