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?
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.
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.
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).
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).
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.