# Seesaw 2: A 3-Act Lesson for 6th Grade Expressions and Equations

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.

# 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.

# I’m on a Mission: Calculus for All!

I’m on a mission.  And I invite you to join me. I’m on a mission to tear calculus down from its ivory tower on the math landscape.  Even if you don’t know calculus, you can still join me because this mission is also for you. Here are a few myths that I would like to dispel on […]

# The Objectives of Objectives, Part Three: Joy

One of the reasons why we teach is because we want our students to experience the JOY of mathematics. Mathematics should be about questioning, wondering, and the joy of discovery…and math classes should leave students wanting to know more math and do more math thinking. We cannot build an appreciation of math through content standards alone. Math classes should be filled with opportunities for students to have voice and a choice. At the very least, they need a voice in making meaning of problems and a choice in how they go about seeking a pathway to a solution.

But sometimes we (or our textbooks) squash all the joy out of a math lesson. We rob them of their right to notice math things, wonder about math ideas, or do messy math stuff. And lessons that focus on “measurable outcomes” with “explicitly defined objectives” often euthanize mathematical curiosity.

# The Objective of Objectives, Part Two: Headache First

Welcome back Math Geeks! I’ve been thinking a lot about the objectives of lesson objectives, and I’m committing to writing a series posts to spark a conversation. I’m curious about how you frame lesson objectives to maximize student thinking, and I invite you to tell me. If you missed my first post about ways to make the learning objective an invitation and not a mandate, I encourage you to check it out here.

Dan Meyer has written extensively about the importance of creating intellectual need in the mathematics classroom. If we are going to ask students to use mathematics to solve problems, we need to let students internalize problems through inquiry and exploration BEFORE we teach them the mathematics. As Dan suggests, if math is the aspirin, then how do we create the headache?

# The Objective of Objectives, Part One: Invite

Why we teach must align with how we teach. In other words, our professional identity (the reasons why we became teachers in the first place) must be congruent with our choices and our practices in the classroom. When purpose and practice are not aligned, both teachers and students waste energy fighting needless friction in the classroom and learning suffers.

One habit where I continue to see a misalignment between purpose and practice centers on how we post, frame, communicate lesson objectives to our students. All teachers want students to be inspired, motivated, engaged, and curious, yet I’ve witnessed a lot of teachers euthanize student intellect by spending the first 5 minutes of a lesson reading aloud and unpacking a lesson objective that is written on the board.

# A Fraction Talk in 4th Grade

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.

# 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.