I am not sure how exciting this lesson is, but I believe the idea beats the run of the mill take notes-practice on a worksheet. It gives students opportunities to notice patterns on their own, a chance to share and discuss those ideas as well as consider ideas from their classmates.
I appreicate Math Equals Love Walk the Plank Wednesday post and will definitely use some of her ideas with the “why” we do this.
My goal is for my students to be able to determine if expressions are equivalent, so I am beginning with a simple card matching task. As students enter the room, they will receive a card with a radical expression either simplified or not (similar to set A). As we begin class, they will be asked to find their match…without verbal communication…while I post attendance, etc. They will come to me with their match and I will confirm if they are correct. Yes, I will allow calculators. I know, not too high level on the thinking scale.
I will have several sets of cards similar to those they matched. Each group will then be asked to complete an open-card sort. This simply means, I do not give them any direction on how to sort their cards. The only stipulation is they are ready to explain why they chose to sort them as they did. When the timer goes off, we will share sorts (both volunteers and any I find that are interesting to me).
Part C, I will have concept attainment cards placed around the room. Each card will contain examples of radical expressions labeled simplified and expressions labeled not simplified. Students will carousel to different cards, noticing patterns, trying to develop their own rules. After a set time, they will do a quick pair-share to summarize their findings before we have a whole class discussion.
Hopefully their ‘rules’ will encompass all we need to know, but if not, I can always use their ideas to lead us to our goal.
We will create a set of notes for our INBs. Part of their HW will be a LHP assignment to give examples of expressions that are simplfied and not simplified from their earlier carousel work. Ideally, they would create their own expressions.
If students need practice with skills, an idea from a workshop several years ago…on a page of say 30 problems, I pick 5 I want them to do, then they pick another 5 or 10, whatever I/they feel is necessary. By giving them this option, I have more success getting them complete the practice. I would much rather have 10 complete than 30 incomplete or not even attempted.
An idea for formative assessment…return to card sort from Part B. They should sort into groups of simplified/not, even match up equivalent expressions. One person stays with the sorts, while others go to different groups to peer assess.
Possible written assessment questions, a) give a bank of expressions to match equivalents, noting simplified terms; b) given a simplified expression, create an unsimplified, equivalence.
This is a very generic layout, but I can use the sequence with whatever level of Algebra I am working with.
I will post again when I have sets of cards completed.
Feedback to move forward, ideas for improvements are welcomed.
Pam Wilson, NBCT
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough