In the previous lesson (Accurate Reporting) students had to determine if several different statements accurately reported the results of a survey. They discussed in small groups to make their decisions. This lesson highlights some of the ideas that came out of those small group discussions. I specifically chose the statements that caused the most disagreement. This allows students to share the evolution of their thinking to focus on what might have been confusing and what changed their minds. I chose the ones that students were the most mistaken about, because my students know that learning from mistakes is what makes you smarter. One of the biggest roadblocks to perseverance is the fear of making mistakes. I have tried to instill in my students that mistakes are to be explored not hidden.
Strips of paper with statements Exploring confusing statement pairs.docx are placed at each table group of 3 or 4 in an envelope labeled with the question "can they both be true?". This activity follows one from a previous lesson (Accurate Reporting) in which students had to decide whether several statements accurate reporting.docx accurately reported the information from a given survey. The pairs I chose were the statements that were the most hotly debated. As students are deciding I circulate to encourage them to convince each other and show some math. Many times they will discuss the math without showing it to which I respond "it sounds like you need to show some math".
As I listen to the discussions I do not correct any mistakes, but I will try to help them catch them. I may ask if anyone in the group is doubtful or needs more convincing or if they can show some math to back up their decision. I may encourage them to examine the context. It is helpful to ask them to define the terms and explain what the numbers represent, count, or compare. Sometimes just reflecting back to them what they said is enough to help them hear their mistake. If the mistake persists I am pretty sure the class will catch it when the group presents their decision to them.
In this section I have the groups present their decision to whole class. Before they share their thoughts I put their two statements under the document camera and let the whole class make a quick assessment and discuss it in their math family groups for a minute or two. I will also ask if anyone had the exact same statements. If a group has the same statements I will let them know that they will be listening for two things.
This is a good way to engage students in critiquing arguments (mp3).
When one group is presenting I allow them to do so from their seats while I try to model their thinking on the board or one or more of the members can come up and present to the class. When they are done I ask the class if anyone has anything to add or ask. This is when students might present additional evidence for why they agree or disagree with the group.
Because I find it hard to follow another person's thinking and I really want my students to make sense of each other's reasoning I like to ask questions that invite elaboration and clarification:
I think these types of questions help students fill in the blanks, connect the dots, and use more and more precise language.
For larger classes with more groups to present there may not be time for a wrap up, but this is one Lady bug spots.docx that helps students learn to write different statements using ratios or percent. If we don't get a chance to fully explore the ideas I may bring it back as a warm up again later.
Students are asked to write a statement that correctly reports the results of a scientific study that found 40 lady bugs with spots and 10 without spots. Lady bug spots possible responses.docx