Writing percents & defining our terms
Lesson 8 of 16
Objective: SWBAT convert a fraction into a percent by both simplifying and scaling up.
This lesson relies on peer instruction in small groups of 3 or 4 for intervention. We are focused on details and attention to precision. The teacher's role is to ensure that students are sharing their work with each others, asking each other questions, and providing peer instruction when necessary. It is really hard for students to take a risk and share their ideas when they are not sure they are right. This is especially true for ELL students. They feel much lower risk when they share ideas in small groups of their peers. They are also more likely to ask questions and not fear exposing their deficiencies. When students do share a mistake with the whole class it is imperative that the teacher treat the mistake as normal and as a learning opportunity. I like to point out all the correct thinking involved and highlight what the class is going to get to learn that they would not otherwise have learned had this mistake not been shared. I like to say things like "Shay has discovered exactly what is so difficult about this, can anyone else see why this can be tricky?" This shines a positive light on the mistake which encourages students to persevere.
Going over the homework
When a good portion of the class is struggling with something new I like to spend a little more time going over the homework homework writing percents 1.docx. I give them some time to take a look at and give feedback on their partners' work. This is when I expect students to engage in some peer instruction to help remediate and intervene in a non threatening and non judgmental environment. This also tends to surface common concerns and questions that need to be addressed with the whole class.
I expect students may have difficulties for a couple of reasons. homework writing percents 1 review notes.docx One is that they may forget the definition of percent as "out of 100" and that their target denominator is 100. Even more so, I think students will struggle with the fractions that do not simplify to or scale up to 100 in one step. Many of my students give up if they don't "see" the answer, or the path to the answer right away. My goal is to get them to "try something" and see if it helps them. Many times they will qualify their work by saying "I'm not sure if it's right", or "It's probably wrong", or "I'm only guessing". In this case I point out how courageous they are for sharing their ideas with us when they aren't sure! I also point out that this is not guessing, but thinking, which is their brains way of telling them what to try. This positive framing goes a long way to improving their efforts. It also shows ELL and special ed students that they are not the only ones struggling.
This warm up Warm up writing percents 2.docx is similar to the one from the previous lesson (Writing percents). It asks students to write the given fractions as a percent. The important aspect of this warm up is that the students do all the explaining and showing, not the teacher. Pay attention to who is doing most of the talking. Before asking students to share ideas with the class I give them a little time to practice it with their math family groups first. This is very supportive to ELL students who may need a little help from their peers to express their ideas in English.
If a students goes to the board to show the work but doesn't explain it I ask another student to explain it for them. Again, I ask the class to take a moment to look at the work and to try to figure out how and why it works. Then I ask if someone will explain it. This is a good way to get them to learn to critique the work of others, which helps them build arguments as well as helps them provide better peer instruction.
Students work on individual white boards, but have access to each other for help. I encourage the peer instruction by asking them to check in with their "family" before I ask them to show me their boards. As I circulate I look for two things.
Today I want them to practice with the multiple step problems. The one's for which they need to both simplify and scale up, like 14/20 and 6/15.
I look for students who are not getting started and seem stuck and I look for groups that have different answers on their boards. I may ask everyone at that group to put their boards in the middle of their group so that everyone can take a look and see each other's work. I may point out that I see a disagreement they need to work out if they have different answers. I may point out that they did the problem differently and to check and see if that is okay. This can help them see connections between multiple methods. I may tell a student who is stuck to take a look at someone else's board and ask them what they did. Sometimes a students will shout out that they are finished to which I respond that he/she is not finished until he/she has checked in with each of his/her math brothers and sisters. This encourages peer instruction and is a great way to engage them in argumentation.
In one of the two videos you will see students checking in with his partner's automatically. One of the videos shows a student who notices that her partner has a different answer than she has. She points it out and explains why she thinks it is wrong, but ends up changing her mind when the other student explains what he did. You can also hear another student talking about their method. This level of peer interaction really supercharges the learning environment by making everybody a teacher.