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.

Clothesline Math Fun 1 (4th Grade)

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.

Two Engaging Proportional Reasoning Tasks

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.

A Bright Idea for 2nd Grade Addition Strategies

It’s my hope that there are other elementary teachers out there that might find this analysis useful if they want to use this compelling and fun lesson by Graham Fletcher in their classrooms to engage their students in exploring addition strategies with regrouping (2.NBT.5, 2.NBT.6, 2.NBT.9). This engaging lesson is very open in the middle. Students have a wide variety of addition strategies they can use including concrete models (base-10 blocks, place value discs, etc) and abstract strategies (arrow method, decomposing, bar method, etc).

Using Tile Problems to Introduce Fractions and Create Intellectual Need

I had a chance to use Steve Wyborny’s tile images as a part of a 3rd grade lesson inquiry. The tile problems are an effective tool to engage students in discourse about their mathematical reasoning. Furthermore, it allows teachers to identify student misconceptions about partitioning and calculating area. These misconceptions often prevent students from understanding how to use the area model to reason about fractions (3.NF.1).

Knotty Rope 3-Act: Introducing Division in 3rd Grade

This lesson write-up is for teachers who want to engage their students in exploring division reasoning and problem solving strategies (3.OA.2, 3.OA.3 and 3.OA.7). It’s appropriate to use before and/or after students have explored division and allows for many different conceptual approaches to a solution including using repeated subtraction or repeated addition, equal groups with or without manipulatives, number lines, arrays, bar models, and multiplication or division equations to model a real world problem.

This write-up contains a lesson pathway with specific questions/moves to consider, analysis of the opportunities for student learning, and other wisdoms and insights we learned from teaching this lesson as a part of a lesson inquiry.

Give it a try with your own students. And then tell me how it went. Let’s make it better together.

Array-Bow of Skittles and Multiplication Strategies

This lesson write-up is for teaching a two-digit by two-digit multiplication 3-Act Math lesson where students estimate the number of Skittles in a jar before using information and math to find a more accurate estimate. It uses Graham Fletcher’s Array-Bow lesson and while it addresses standard 4.NBT.5, it’s appropriate for 4th and 5th grade students of all levels. The write-up contains a lesson pathway with specific questions/moves to consider, analysis of the opportunities for student learning, and other wisdoms and insights we learned from teaching this lesson as a part of a lesson inquiry.

Give it a try with your own students. And then tell me how it went. Let’s make it better together.