*Lesson 1: Introduction to Quadrilaterals (What makes you say that?)
Objective: The purpose is to have students identify the key aspects of various types of quadrilaterals. By varying the quadrilaterals used for the activity, this lesson can be used with students as young as 3rd or 4th grade up through a high school Geometry class. For the purpose of this blog, I will tailor it to 10th grade Geometry class.
Timing: Approximately 45 minutes (can be completed in one class period) with a follow up assessment the next class.
Materials: Pictures of various types of quadrilaterals, including a general quadrilateral, rectangle, square, trapezoid, parallelogram, kite, rhombus. Clipboards or other hard surface students can use to write on during Gallery Walk.
- Introduce students to the Thinking Routine “What makes you say that?” by posting the pictures of the quadrilateral, rectangle, and square at the front of the classroom. Students will be familiar with these shapes from previous math classes. Explain that we are reviewing these shapes as an introduction to the Thinking Routine, “What makes you say that?” and ask students to take a few minutes to jot down some observations about each shape. Students can draw on their prior knowledge of these shapes or just what they can conclude from the pictures.
- Begin a group discussion by having students share some of their observations. As observations are provided, record them on or around the picture with which they are associated. Ask the student the follow-up question “What makes you say that?” Open the question to the class for additional/alternative answers.
- Once students have a feel for listing observations and also asking themselves why they can make that observation, split students into small groups of 3-4. Place the pictures of trapezoids, parallelograms, kites, and rhombuses around the room to create a Gallery Walk. (See The Teacher Toolkit for an introduction to Gallery Walks if you are not familiar. http://www.theteachertoolkit.com/index.php/tool/gallery-walk) Have students spend 2-3 minutes at each picture, making observations about what they see. Let students know they will, once again, be asked “What makes you say that?” for their observations. Groups should start practicing their justifications while noting their observations.
- Repeat step 2, taking observations from groups this time.
Assessment: To start the next class, hand students a quadrilateral as they enter the classroom. Ask students to classify the quadrilateral based off the observations they made last class.
Social Media: This Quadrilaterals Song is a parody of a popular Imagine Dragons song that students will likely recognize. Use it as an opener or closer on the first day, or have it playing while students are classifying their quadrilateral on Day 2.
Lesson 2: Normal Distribution (Headlines)
Objective: Conclude an introduction to the Normal Distribution with the Headlines Thinking Routine to help students focus on key aspects of the distribution. This could be used with a high school statistics class or functions and modeling class.
Timing: 15 minutes at the close of class, with an informal assessment at the start of the next class.
Materials: Markers and paper
Process: Use an activity of your choice to introduce students to the Normal Distribution. For example, this popcorn activity from the American Statistical Association. After the lesson, ask students to write a headline that might appear in a newspaper about the Normal Distribution. It could be a key feature, a tip for using the distribution, etc. Give them a couple minutes to work independently, then ask students to share their headlines with a neighbor or two. As a small group, refine the headlines as needed and then write them on paper to be posted around the room.
Assessment: In the next class period, supply students with a practice problem that utilizes the Normal Distribution. Ask students to work independently or with a neighbor to solve the problem, using the headlines as a reminder of the important aspects. After reviewing the problem, ask students “Which headlines were most useful?” “Are there any you would like to refine or modify?”
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Angie, Oh my! The “Imagine Dragons” rendition of quadrilaterals was stellar and the students would love it… so relevant to your lesson and MTV strategy. The way you executed “What makes you say that?” and “Headlines” will provide rich opportunities for your students to make their thinking visible. The subject matter you tied to the strategies will work wonderfully, as well.
What other sorts of open-ended questions could you use to guide your “What makes you say that?”
Can you think of any sample “headlines” that the students might create (just curious)? I like how you would post the Headlines around the room and then revisit them upon concluding the lesson.
Angie, Using the “what makes you say that” routine as an introductory lesson on to quadrilaterals will serve two purposes. By making them verbally justify their thought process, it reinforces it for them. It also acts as a pre-assessment for the level of knowledge they are bringing to the game, which can help inform your lessons down the road. I really liked the way you used whole-class on a few of the more familiar quadrilaterals as a way to model the process for them. I was wondering if the gallery walk in groups was a quiet walk, or a walk and talk? Will each student make his own observations to be discussed in a group immediately after, or will each group have a discussion and come to agreement while at a particular figure, and then move on? Both methods have their pros and cons, just wondered how you envisioned it. A starter question the next day as assessment is a fantastic idea. I have always been a proponent of a Problem of the Day type activity to start each class, this one ties in to the prior days lesson and gets them back on task to continue that theme right off the bat.
I really liked the Headline routine for Normal Distribution. There seems to be an unwritten consensus that using Headlines with topics that can be somewhat overwhelming is the right tool for the job. I particularly was taken with two parts of it. The first was when you allowed the students the opportunity to take their headline and work with another student to refine it. Getting a peers perspective is a good tool. The second part was when you asked the students to identify which of the Headlines displayed on the walls helped them the most. This indicated that there was no one headline that was “correct”. Each student has their own support needs and it will vary.
I enjoyed reading through your lessons, thanks.
Thanks, Chris! I’m glad you enjoyed the post. You brought up some great points that I hadn’t thought about. For me, the initial appeal of using “What makes you say that?” with quadrilaterals was the parallels between verbally justifying their observations and the process of constructing/writing proofs, which can be extremely challenging for many students. Through the discussions and probing questions in the activity, students would get exposure to what qualifies as “proof” vs. where they need to explain more and dig deeper. You’re correct that it will reinforce concepts, too, and I hadn’t even considered the advantage it would provide from the teacher perspective in terms of pre-assessment. That was one of Ritchart, Church, and Morrison’s arguments for making thinking visible – it allows teachers to see where students are, what misconceptions need cleared up, etc. You are very right!
As for the gallery walk, I was envisioning walk and talk, having students discuss in their small groups as they are touring the pictures. The idea of requiring students to make their own observations through a silent walk is definitely appealing, but I worry about missing “just in time” teachable moments from peer-to-peer. If students can discuss their thoughts and questions in the moment, I think they may have more discussion and debate while it’s fresh in their mind. The conversation may progress further than it would in a post-walk report. It would be interesting to try it both ways and see if there’s a noticeable difference in the results.
I really appreciate the feedback and question!
I like that you use the “What Makes You Say That?” process twice, once as a full class and once again in smaller groups/individually. Especially in this is new thinking strategy for your class, it will be so valuable for the students to hear their classmates’ ideas to both broaden and narrow their observations as needed.
The two questions you listed at the end of your Normal Distribution lesson are incredible: “Which headlines were most useful?” “Are there any you would like to refine or modify?” The opportunity for students to compare where their understanding was before the practice problem to after is a great idea. What do you mean by “refine the headlines as needed”? Will this be done on a case-by-case basis?
Thank you for the feedback! Repeating the “What makes you say that?” process was intended as an illustration and practice session, since it would be a new thinking strategy. (At least, this is the first lesson plan I’ve written that uses it!) Hearing classmates ideas is a definite perk, as well. I had envisioned that hearing others’ ideas would help them understand the actual steps of the process, but hadn’t thought about the advantage of it helping them hone their observations. And, a great point that the honing could go either way, both broadening and narrowing their focus!
In my head, the Headline revision process would be somewhat consensus-based. As students make suggestions for how a particular headline was helpful or what it might need to be more helpful, the class can discuss the pros and cons of making changes. The end result may be that an edit is made to a particular headline, or possibly that another headline, a companion headline, is created to supplement the existing one.
Several years ago, I used what I called a “Knowledge Wall” in my classroom, which was basically a bulletin board that was designated as a place where students could hang small post-it notes with key facts, formulas, concepts, etc. on it. During quizzes and exams, students could go up to the wall (leaving their test, pencils, etc. at their desk) and peruse the wall for a formula they were unsure of or a concept or example that might be helpful in resolving a problem they were stuck on. (This was an idea that came from PEAK training, https://www.peaklearningsystems.com/, in my second year of teaching. They made compelling arguments for the motivation of having access to information when a student needs it and is, therefore, motivated to learn it, as well as the memorization advantages it can offer by requiring students to commit the concept to memory for the trek from the Knowledge Wall to their desk.) With all students allowed to add information to the wall, it could become messy quickly, though. So a couple times a month, a small group of students were asked to go through and organize the information on the wall (i.e. – removing duplicate information, updating misconceptions that had been clarified or fixing inaccurate or incomplete ideas, making information as concise as possible, etc.) A similar process could probably be used with the Headlines, as well, if they will be posted for an extended period and/or covering numerous topics.
Hi! I really enjoyed your Lesson 1: Introduction to Quadrilaterals. I think that the “what makes you say that?” thinking routine can be quite simple but also challenging. I can see students, or I can picture myself, struggling to come up with very many descriptions for the quadrilaterals so this question would really make me think about digging deeper. If students do struggle with filling in enough information will you intervene in any way? I’ve been struggling to come up with an assessment for my lesson plans, so I thought yours for this lesson was great! I also thought your video to go along with this lesson was fantastic! What a fun way to get students to engage and understand the lesson through something they are familiar with.