This task is the first part of the culminating lesson of unit 2 in grade 8, which is about dilations and similarity. (You will need to create a free teacher account to open the link.) It is a variation on the popular “use shadows and similar triangles to determine the height of a tall thing that it is impossible to measure directly.”

# What is an instructional routine?

*By William McCallum and Kate Nowak*

People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She expects a snack, homework time, play time, dinner, some television, a bath, pajamas, a book, and to get tucked into bed. She might have responsibilities, like setting the table for dinner, and engage in predictable dialog along the way, like sharing something that happened at school. She might expect her father to sing her a song. (Over and over and over again, in the case of my daughters—Bill.) The routine makes her comfortable and makes necessary chores go smoothly. Continue reading “What is an instructional routine?”

# Using Math Routines to Build Number Sense in First Grade

By *Allison Van Voy*

When I started teaching four years ago, I had no idea how important number sense was to a student’s math understanding. I was fresh out of college, brand new to teaching, and number sense was not a concept I had learned in my math courses.

Continue reading “Using Math Routines to Build Number Sense in First Grade”

# Sometimes the Real World Is Overrated: The Joy of Silly Applications

*By Charles Larrieu Casias*

One of the cool things about math is that it can provide powerful new ways of seeing the world. Just for fun, I want you to open up this lesson from the grade 8 student text. Take a quick skim. What do you notice? What do you wonder?

When writing this lesson, I was guided by a few key questions:

- To paraphrase Dan Meyer: If I want arithmetic with scientific notation to be the aspirin, then how do I create the headache?
- What are some weird, silly comparisons involving really large numbers?
- Here, towards the end of 8th grade, what should students be doing to transition towards the high school mathematical modeling cycle?

Continue reading “Sometimes the Real World Is Overrated: The Joy of Silly Applications”

# Instructional Materials Matter: Interpreting Remainders in Division

*By Jody Guarino*

We know instructional materials play a key role in student learning experiences but how do we ensure our students are learning from coherent high-quality instructional materials that engage them in critical thinking and provide opportunities to “do math?”

Let’s think about this from the lens of a 4th grade standard, *4.OA.A3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing in for the unknown quantity. Assess the **reasonableness of answers using mental computation and estimation strategies including rounding.* Continue reading “Instructional Materials Matter: Interpreting Remainders in Division”

# 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?**

- “Nothing”
- “Math”
- “The questions on this worksheet”
- “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?**

- Pretend like you didn’t hear the question
- With an eye roll
- “Everything I say is going to be on the test”
- “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.

# 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”