Adapting Curriculum For Students to Know, Use and Enjoy Fractions

By Melissa Greenwald

You know it is time for a change when half of the students in class are lost by the third lesson of a new unit.

I teach third grade in a charter school in Philadelphia. We use Go Math! and each year I have followed Chapter 8: Understand Fractions, exactly as written. In the first lesson, students name equal parts in pictures such as halves, thirds, and fourths, and then move into finding equal shares. By the third day, when we discuss unit fractions, I feel like I have already lost about half of my students. Despite this, I usually trudge along and move into the fourth lesson where students are asked to identify the shaded fraction of different shapes. By the end of the lesson, my students typically have learned the rote skill of counting the number of shaded and total pieces in order to write the fraction. This becomes incredibly evident when we move to putting fractions on a number line and problematic when problem solving with fractions. Continue reading “Adapting Curriculum For Students to Know, Use and Enjoy Fractions”

Learning Goals and Learning Targets

By Jennifer Wilson

One of your students is asked, “What are you learning about today in class?”

How does your student respond?

  1. “Nothing”
  2. “Math”
  3. “The questions on this worksheet”
  4. “Deciding if two figures are congruent”

During class, one of your students asks you, “Is this going to be on the test?”

How do you respond?

  1. Pretend like you didn’t hear the question
  2. With an eye roll
  3. “Everything I say is going to be on the test”
  4. “Let’s see how what we’re doing is connected to today’s learning goals”

We know from years of math education research that establishing and sharing learning goals are important for both teachers and students. Even so, we don’t always agree with when and how they should be shared.

Continue reading “Learning Goals and Learning Targets”

Warm-up Routines With a Purpose

By Kristin Gray

As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have great, accessible problems but also create opportunities for students to openly share their ideas with others. It only makes sense that when I learned about routines that encouraged students to share the many ways they were thinking about math such as Number Talks, Notice and Wonder, and Which One Doesn’t Belong?, I was quick to go back to the classroom and try them with my students. It didn’t matter which unit we were in or lesson I had planned for that day, I plopped them in whenever and wherever I could because I was so curious to hear what students would say. Continue reading “Warm-up Routines With a Purpose”

Adapting Problems to Elicit Student Thinking

By Jody Guarino

As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical understandings for the class.

First, I need a task that will make student thinking visible. Here’s a task from Illustrative Mathematics, Peyton’s Books.

Peyton had 16 books to take on his trip. He lost some. Now he has 7 books. How many books did Peyton lose?   

Continue reading “Adapting Problems to Elicit Student Thinking”

A Fraction Unit Does Not Always Begin With Lesson 1

By Jared Gilman

As I sat down at my local coffee shop to plan my upcoming 5th grade unit on fractions, a wave of dread spread across my body. I started having flashbacks to last winter, when my students’ frustrations with fractions led to daily meltdowns. Looking back at my lesson plans, I noticed how many reteaching lessons I was forced to add into the middle of my unit. I recalled the painstaking hours of scouring YouTube for videos on the “easiest tricks” and “fastest shortcuts” for adding and subtracting fractions. “My students just didn’t get it,” I thought at the time. This year would be different, I told myself as I gulped down my large iced coffee.

Continue reading “A Fraction Unit Does Not Always Begin With Lesson 1”

Why is the graph of a linear function a straight line?

By William McCallum

In my last post I wrote about the following standard, and mentioned that I could write a whole blog post about the first comma.

8.F.A.3. Interpret the equation $y = mx + b$ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function $A = s^2$ giving the area of a square as a function of its side length is not linear because its graph contains the points $(1,1)$, $(2,4)$ and $(3,9)$, which are not on a straight line.

Continue reading “Why is the graph of a linear function a straight line?”

Why We Don’t Cross Multiply

By Kate Nowak
(co-authored with Kristin Gray)

“Ultimately, the goal of this unit is to prepare students to make sense of situations involving equivalent ratios and solve problems flexibly and strategically, rather than to rely on a procedure (such as “set up a proportion and cross multiply”) without an understanding of the underlying mathematics.”
Illustrative Mathematics 6–8 Math, grade 6, unit 2, lesson 12

Continue reading “Why We Don’t Cross Multiply”

The Illustrative Mathematics Team Reflect on the 5 Practices

The entire Illustrative Mathematics team spends a lot of time reading about teaching and learning. Most recently, we have been reading—some of us rereading—and reflecting on the 5 Practices for Orchestrating Productive Mathematics Discussions by Mary Kay Stein and Margaret Schwan Smith. Members of the team were asked to reflect on the following two questions to share with the Illustrative Mathematics community:

  • What idea stood out to you when reading the 5 Practices for Orchestrating Productive Mathematics Discussions?
  • Why do you feel this idea is important?

Continue reading “The Illustrative Mathematics Team Reflect on the 5 Practices”

Using the 5 Practices with Instructional Routines

By Robin Moore

As a coach, how can I help teachers structure their lesson-planning in order for students to unpack their mathematical understandings?

This question is always at the forefront of my mind as I reflect on my work as an instructional coach. Most times, I walk into classroom after classroom witnessing teachers working harder than the students. To be clear, the students are all on task and working on the mathematical concepts presented to them with little to no behavior problems. The biggest challenge for teachers is attempting to differentiate for the range of learners in the classroom. To address this challenge, teachers have implemented a math workshop format. In this format, teachers communicate the learning objectives for the lesson and present a scaffolded mini-lesson where they gradually lead students through problem-based activities to ensure each student’s success. While the activities are problem-based, something authentic is missing and many would say that the work does not appear rigorous for all students. From a coaching lens, I wonder when and where learning is happening and who is unpacking it.   Continue reading “Using the 5 Practices with Instructional Routines”

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