In this lesson students are introduced to equivalent percents and fractions. This is also the first time they are expected to make their own box diagrams to model fraction and percent problems. The central theme of this lesson is having students share their ideas about how they make sense of the problem and how the math relates to the diagram. Students are asked to explain the thinking of others as well as their own thinking to encourage them to make connections between the multiple methods and representations.
In the warm up warm up box diagram to find a fraction students are asked to find 2/5ths of 35, 40% of 35, 3/4ths of 80, and 7/10ths of 60. I provide a partial box diagram for them which they may or may not choose to use. The first one is separated into parts for them, but the rest are left whole. Even if they choose not to use the box diagram it still serves as a visual representation which is helpful in the concept development for fraction and percent of a number. The visual is also really helpful for the ELL students, not just for concept development, but for vocabulary reinforcement and for sharing their ideas visually.
It is really important to spend time making connections between the math and the visual model. There are several questions I ask students in order to get them to make these connections. warm up box diagram to find a fraction notes. After asking the questions I want the class to listen to the different ways in which they respond, so I have them come up and explain. This is a great way to help them make sense of the problem and improve their fraction sense.
Students do their work on individual white boards, but have access to their math family group. A lot of peer instruction and support takes place during white board practice. For the first one or two I let them solve it however they choose. Before I ask them to raise up their boards and show me I make sure they check in with their math family and have them explain how they solved it. On the count of three everyone holds up their boards at the same time so that I can give corrective feedback if necessary and no one can opt out.
20% of 45 25% of 40
After each one I ask who used (Angelina's method) with a box diagram and who used (Mariella's method) by simplifying and then scaling up to the new total? For the next one (60% of 25) I might ask them all to try Angelina's method with a box diagram. I might ask Angelina to join me as I circulate to help out. Then I would ask students to try Mariella's method on the last one (75% of 28). This really encourages students to see each other as resources and to feel that their input in math class is valuable. They also try harder when they are working on ideas that came from their own peers.