“We’re Gonna Need a Different Denominator”

Check out this compeling video from Andrew Stadel. What do you notice? What do you wonder? How can this be used to teach students about adding fractions?

I conducted a lesson study about fractions with some 5th grade teachers.  We used Andrew’s elegantly simple lesson called Black Box 2 to get students talking about adding fractions with unlike denominators.  This task is ideal for introducing the intellectual need for finding a common denominator before adding fractions procedurally.  Student discourse is rich and meaningful and lively.  Give it a read.  You won’t be disappointed.

Making Data and Stats Matter More in K-6, Part 2

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.

How Much Sugar in a Soda? A 3rd/4th Grade Division Problem

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.

Making Desmos Elementary

For the past few weeks, I’ve had the fun opportunity to write for the Global Math Department newsletter.  Haven’t heard of the Global Math Department?  It’s great tool to find out what’s going on in the online math world about math teaching and watch professional development webinars.  Check the site out here and read about some of the fine folks that coordinate the work here.

In the last newsletter, Bridget Dunbar (@BridgetDunbar), Anna Bornstein (@Borschtwithanna), and I (@mathgeek76) wrote separately about the importance of grade level teachers sharing and learning from teachers at other grade levels.  Teachers of all levels have a lot to learn from each other.  You can find the complete newsletter here.  (If you sign up, you’ll get weekly newsletters straight to your inbox!)

Here’s what I wrote about using Desmos as an instructional tool in the elementary classroom.  While historically used by secondary teachers, several elementary teachers are creating a lot of useful stuff.  Give it a read.  Share your thinking.  And I invited you to a call to action.

Punch-A-Bunch: A 3-Act Math Lesson on Probability

Welcome back math geeks!  I need your help making a lesson better.
I love Price is Right because many of the games require contestants to make predictions.  This often involves estimating prices of products.  But sometimes contestants have to make choices of a different nature, and these choices are ripe opportunities to think about probability and expected value.  And I love when a fruitful 3-Act Math opportunity presents itself.  (I’ve written about one before here.)

The example I want to share now doesn’t seem to fit a 3-Act format.  Maybe that’s because it’s not truly a 3-Act Math lesson.  But I don’t know what else to call it.  I’m curious about your thoughts on how to make it better. 

Some questions I’m asking: 

Is it too clunky? 
What grade levels will find this lesson useful? 
What concepts/standards does it best target? 
What opportunities did I miss? 
What extensions can be made?

I’m inviting your feedback in the comment section.  Thanks for helping me get better!

Making Data and Stats Matter More in K-6, Part 1

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.  There are two curriculum practices that trouble me about how we teach students to think about data and statistics, especially at the K-6 level.  In this post, I’ll outline one of these troubling practices and my attempt to help to teachers work around this obstacle.

Numberless Word Problem 3: Data Exploration in 2nd Grade

I worked with a team of amazing 2nd grade teachers this week as a part of an ongoing lesson study. They were in the latter chapters of their curriculum where the Measurement and Data content is often stuffed away as an afterthought because they aren’t “Focus Standards.”

And it’s a drag too because there’s so many rich opportunities for meaningful student discourse about data. That is, if it’s done right. Most textbooks suck all the life out of the content. Students need to understand that data tells a story; it has contextual meaning that is both cohesive and incomplete. Students need to learn how to ask questions about data and to learn to identify information gaps. In other words, students need to learn to be active mathematical agents rather than passive mathematical consumers.

We’d like to share with you what we learned about using Numberless Data Problems and crafting an open investigation into bar graphs that is engaging for all students. As always, feedback welcome. Let’s get better together.

Numberless Word Problem 2: Data Exploration in 1st Grade

Have you seen the amazing visuals over at Number Talk Images? These pictures are ideal for any teacher looking to get all students talking about numbers and mathematical reasoning, regardless of ability levels. We used this image as a number talk to launch a lesson that focused on first grade students making statements about a data display. Inspired by the work by Brian Bushart and Regina Payne, we used a numberless word problem approach to build and structure discourse about a data display.

I hope that there are other 1st (and 2nd) grade teachers out there that might find this analysis useful if they are looking for strategies to get students talking about their mathematical thinking. We wanted students to produce mathematical thinking, not just consume it. Here’s what we created.

A Fraction Talk in 3rd Grade

Have you seen the amazing visuals over at www.fractiontalks.com? They’re ideal for any teacher looking to get all students talking about fractions and mathematical reasoning, regardless of ability levels. We used one of the images to introduce fractions to some 3rd grade students. We learned a lot and the students did too! We’d like to share our learning with you.

Clothesline Math Fun 2 (6th Grade)

Clothesline math activities are fun for teachers and students! I encourage you to try them out for yourself. To help guide your thinking, I’m writing up what I’ve learned from my experiences using the clothesline as the backbone of some lesson inquiries I’ve conducted.

This write-up is about my experiences in three 6th grade classrooms using the clothesline to encourage students to develop strategies on how to solve equations and reason about the value of expressions. We addressed many of the 6.EE standards. However, this particular lesson pathway is appropriate for 6th-9th grade students depending on their learning needs.