Welcome back math geeks!
I love teaching young students about data and statistics. And I enjoy finding ways to make data and statistics matter more to young students. But I’m troubled by two curriculum practices about how we teach students to think about data and statistics, especially at the K-6 level. This post is Part 2. In my first post, I wrote about how data is often represented to students in heavily scaffolded textbook pages that rob students of the opportunity to purposely engage in thinking, wondering, and discourse…and a solution to this practice. (If you missed Part 1, click here.)
In this post, I’ll outline another troubling practice and my attempt to help to teachers work around this obstacle.
I conducted a lesson study with some elementary teachers. We used Dan Meyer’s engaging lesson called Sugar Packets to get students talking about an interesting problem, sharing their thinking, showing what they know about division strategies. Dan has the lesson listed as 6th grade ratio and proportional reasoning activity, but we found this problem to be suitable for both 3rd and 4th graders and possibly as a review for 5th graders. There is a remainder in the solution. And we found that this lesson works best if students haven’t had many opportunities to learn about remainders. It’s a wonderful introduction to thinking about the contextual and mathematic meaning for the remainder. (If you teach 3rd grade, I think you’ll find that your students will dig it! Don’t let the remainder spook you off!)
This lesson addresses many of the Operation and Algebraic Thinking standards for 3rd and 4th grade. It is also a rich opportunity for students to reason abstractly and quantitatively and to communicate their reasoning with each other.
So, give it a read and give it a go! Let us know what you learn. Let’s get better together.
How do we invite 6th (and 7th) grade students to authentically engage with an equation in a way that invites students (1) to appreciate how the structure of an equation models a context and (2) to dive deeper in to the meaning of the relationships between variables?
Instead of teaching students how to use the properties of equality to solve “one-step” equations first (which is like using a bazooka to kill a cockroach by the way), I’m wondering if there’s a way to start the exploration of equation solving by inviting students to experience the dynamic relationship between variables first.
Here’s my thinking on one way to do that. I’d love to hear your thoughts so we can get better together.
Have you seen the amazing visuals over at www.fractiontalks.com? They’re ideal for any teacher looking to get all students, regardless of ability levels, talking about equivalent fractions (4.NF.1), comparing the value of fractions (4.NF.2), and expressing mathematical reasoning. This activity could also work for 3rd grade students that are exploring fraction equivalence (3.NF.3). We used one of images to introduce 1/2 as a benchmark fraction to some 4th grade students. We learned a lot and the students did too! We’d like to share our learning with you.