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.
A friend and I were reflecting over a beer at Twitter Math Camp in July about how to get more elementary teachers to attend this amazing conference. (Click here to know more!)
He’s an inspirational colleague with a background in special education at the elementary and middle school level. We were talking about content knowledge. He said, “My ability to teach math has always been limited by my lack of content knowledge beyond middle school.” After pondering a beat, I replied, “Me too.” Knowing my teaching experience, he leaned back with a skeptical smirk and looked askance at me. I continued…
Imagine a football team operating like a faculty at a school site.
Players (teachers) gather at the beginning of the season (school year) for some team-building and some pep talk (fall PD) about goals and visions for improvement from their coach (principal).
The players then study a playbook (curriculum) and some plays (instructional strategies) and maybe they practice them. Maybe they don’t. Once the season starts, they hardly ever observe each other run drills (routines). They definitely don’t scrimmage together. The coach may walk around once or twice, check some boxes on a list, and give that feedback to a player, but rarely does the coach model techniques or facilitate collaboration and discussion between players.
The players practice all year for one single game (student testing) that they don’t even believe is worth playing but everyone makes them prepare for it anyway because how else could we measure our effectiveness except through standardized test data. The players won’t find out until 4 months later how they did and how they compared to other teams (schools) in the league (district). Except by then, the offseason has happened, players have shifted teams, new playbooks have been adopted, perhaps new coaching has been hired, and it’s time to start the whole process again.
The season concludes without any player ever watching another player play.
How stupid is that?
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.
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.
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.
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 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.
The clothesline is a simple low-tech visual and effective manipulative at fostering student engagement, using student arguments and reasoning to structure classroom discourse, exposing student misconceptions, and helping students attend to precision.
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 4th grade classrooms using the clothesline to encourage students to develop strategies on how to plot and compare values of fractions on a number line (4.NF.1, 4.NF.2). However, this lesson particular pathway is appropriate for 4th-9th grade students depending on their learning needs.
I hope that there are other 6th (and 7th) grade teachers out there that might find this analysis useful if they are looking for ways to increase student engagement, thinking, and discourse around percents, fractions, and proportional reasoning standards. This engaging learning opportunity can be used at the beginning of a unit as an inquiry-based exploration and pre-assessment. It can also be used as a way of assessing student learning in the middle or the end of a unit. It’s a low-floor opportunity that allows for students at all levels to participate. It also allows for rich discussion and sense-making because solutions can be reached via multiple strategies.