This lesson focuses on skills practice to clear up some common mistakes and misunderstandings. I expect confusion in three different areas. Many students simply need reminders that the percent is a fraction out of a total of 100. Many will have trouble when they need to simplify a fraction first before scaling it up to 100 and others will still be thinking additively. In this lesson students rely on their math family groups for peer instruction. I find they develop much better understanding when they can help and get help from each other. This is especially helpful so that ELL students can use their primary language to connect to prior knowledge.
This warm up Warm up writing percents.docx asks students to convert fractions to percents. Two need to be scaled up, one needs to be simplified, and one needs both. Early on I expect students to forget about the definition of percent and to need clarification when writing fractions as percents that their target denominator is 100. I usually just need to ask them "percent means what?" and that is enough. If it is not then I can follow up with "so, what do we want the denominator to be?", "can we make that happen?"
Many students also have trouble converting fractions to percents when they first need to be simplified. When I intervene here I want to encourage students to "try it and see". I start by asking why they think someone might get stuck with problems like 18/30 = ?%. I expect them to say that 30 doesn't go into 100 or you can't scale 30 up to 100. I tell them that when I get stuck one thing I look for is any math that I know how to do and ask them if they see any math they can do with 18/30. When they say they could simplify I ask if we know for sure that will help. When they say no I ask what we should do until someone suggests to try it and see. Once they simplify to 6/10 they can "see" the next step. It is really important to recognize that the brain needs to "see" clues in order to know what steps to take next.
A handful of students who struggle with multiplication will still have confusion over adding to scale up. With a ratio, for example, of 3/5 you can add to scale up the numbers but can't choose which numbers to add; the ratio tells you the numbers (3 & 5) to add repeatedly. This works fine for smaller amounts, 6/10, 9/15, etc., but not for scaling up to larger numbers like percents. I continue to try to connect this thinking to multiplying by asking how many times would we have to add on repeatedly to get from 5 to 100 (for example)? Part of this discussion must include that it is more efficient to multiply. I do not discuss this until the idea comes from a student.
In the videos for this section you will see students share their thinking, ask each other questions, explain each other's work, and make corrections. I love letting their ideas lead the discussion because they take more ownership and pride in their learning.
Students work on individual white boards, but they can work collaboratively for peer instruction. Everyone shows me their answers at once so that I can give them corrective feedback if necessary and no one can opt out.
I start with fractions that can be scaled up in one step like 13/20 and 2/5. They may need reminders that the target denominator is 100 simply by asking what percent means. If they get these easily I move on to some that can be simplified like 9/300 and 44/200. Then I move on to the fractions that need to be simplified then scaled up like 28/40 and 6/15. This process really helps many of my students practice their multiplication, as a lot of them still struggle with their facts.
If some students really need more practice with one type, but others are ready to move on I give them a choice between two to complete. When given the choice many will try to do both. This gives me time to work with students who are struggling with one type of problem.