After reading Daniil Kharms’s First, Second to a class of eighth graders, I wrote the following on the board: A tall man, an average man, and a short man each walked with different length paces. The tall man walked five meters in five paces. The average man walked two meters in five paces. The short…

In this game, eighth grade students practice writing equations in scientific notation and standard form. The key to learning mathematics is understanding the “why” behind the “how”. HMH Into Math emphasizes the importance of establishing conceptual understanding and reinforces that understanding with procedural practice. The learning model asks students to first develop their reasoning before connecting…

In this game, seventh grade students use angle measures and side lengths of triangles to determine the missing angle measure and to draw the accurate triangle using a protractor. The key to learning mathematics is understanding the “why” behind the “how”. HMH Into Math emphasizes the importance of establishing conceptual understanding and reinforces that understanding with…

In this game, sixth grade students roll number cubes to create a numerical expression that has a value as close as possible to the given number. The key to learning mathematics is understanding the “why” behind the “how”. HMH Into Math emphasizes the importance of establishing conceptual understanding and reinforces that understanding with procedural practice. The…

Overview of Lesson Lessons 1 through 4 focus on understanding the general formula for linear relationships, y = mx + b. In Lesson 1 students work with in-out tables and relate the table values to the formula y = mx + b. They see that b is the starting value (y-value when x is…

In this lesson, children reflect on the idea that when a number less than one is multiplied by a whole number, the answer will be smaller than the starting number. This fact conflicts with the belief of many students that multiplying a number always makes it larger. Materials calculators, 1 for each pair of students…

In their book, Good Questions for Math Teaching, Why Ask Them and What to Ask, Grades 5–8, Lainie Schuster and Nancy Anderson provide a rich collection of questions for teachers to use in math lessons. Asking questions helps make math lessons dynamic and thought provoking and encourages students to make important mathematical connections. The topics…

Annette Raphel taught this lesson to her seventh-grade students in Milton, Massachusetts. The lesson provided a meaningful way for her students to manipulate data, promoted the students’ number sense, and gave them much-needed experience with large numbers. At the end of the lesson, Annette includes a bibliography of children’s books that are useful for other…

Overview of Lesson In this lesson students work on multiple measurement concepts, including measuring length, scale, ratio, and proportion. Students apply all the concepts in an activity that involves enlarging a picture to scale so that it fits on a piece of graph paper. Students must take measurements, determine the ratio they will need to…

Mildred D. Taylor’s Roll of Thunder, Hear My Cry (Puffin, 1991) is the story of a young African American girl, Cassie, and her family living in Mississippi in the 1930s, during which time African Americans were threatened, ridiculed, and burned alive. In this investigation, students are able to develop a more personal understanding of what…

In this introductory lesson on algebraic thinking, students explore several stages of a rocket built with pattern blocks, record the number of blocks for each stage on T-charts, and find rules to describe the pattern. This activity appears in Ann Lawrence and Charlie Hennessy’s new book, Lessons for Algebraic Thinking, Grades 6–8 (Math Solutions Publications,…

Nancy Anderson’s middle school students had prior experience studying ratios and proportions: they were familiar with the concept of a ratio as a comparison of two measures; they had solved problems that required them to determine which two measures to compare and to reason about how they compared; and they had used the process of…

The following lesson is adapted from Len Sparrow and Paul Swan’s Learning Math with Calculators. The book is organized into two sections: the first addresses a broad range of teachers’ questions and concerns about using calculators for teaching math; the second is a collection of classroom-tested activities using calculators, all chosen for the purpose of…

I began by introducing the class to one version of the game Race to One. I explained the rules, “To play this decimal game, you first clear the calculator so that the display reads zero. Then, taking turns, each player adds either one-tenth or two tenths to the total on the display. The winner is…

This lesson is excerpted from Cheryl Rectanus’s new book, So You Have to Teach Math? Sound Advice for Grades 6–8 Teachers (Math Solutions Publications, 2006). The focus of the book isn’t primarily about classroom lessons but rather on responses from a master teacher to questions raised by middle school math teachers. (See a sample in…

Overview of Lesson In this lesson students translate among representations so that their understanding can advance from words to tables to graphs to equations. The concepts are covered in the context of playing a video game where Zombies are zapped to score points and advance a level in the game. Introduce to students the background…

To begin the lesson, I told the class, “Each of you will estimate the weight of each student’s backpack and then we will find the actual weights, using a bathroom scale. We’ll work together to create a graph known as a scatter plot. Then each of you will create and interpret a personal scatter plot…

Instructions 1. Explain to students the importance of estimation in measurement. You might do this by reading the last half of the book Millions to Measure, by David Schwartz (HarperCollins,2003). It contains an engaging description of the metric system and how it works. It also mentions the miscalculation that the U.S. space engineers made…

I began by asking the class who had read Hatchet. A large number of students raised their hands, and Nelson briefly summarized the book. At my request, he stopped at the point when Brian drops his hatchet into the lake. I then presented the following problem to the class: When Brian dropped his hatchet to…

Cathy wrote the following problem on the board: A school has 500 students. If a school bus holds 75 students, is there enough room on one bus for all of the school’s left-handed students? Cathy ﬁrst had the students report on a class graph whether they were right-handed or left-handed. They analyzed the data and…

When I read “Eighteen Flavors” aloud, I asked the class why there was a “sniffle” at the end of the poem. “Because you can’t eat ice cream off the ground!” Lori said. “Does it surprise you that these eighteen scoops would be on the ground?” I asked. “No, because that’s too many for the cone…

After reading A Drop of Water aloud, I drew on the board a large blank four-column table for recording data. I labeled the first column Circle Number and then asked what a diameter of a circle was. Ariella said, “It goes all the way across the circle.” Madison added, “It has to go through the…

Last year Carrie DeFrancisco wanted to celebrate Dr. Seuss’ birthday with her sixth-, seventh-, and eighth-grade students. The students were studying simplifying and evaluating expressions and solving one- and two-step equations. Carrie centered activities on the Dr. Seuss classic Green Eggs and Ham. “As you know, today our school is celebrating Dr. Seuss’ birthday. I…

Asking “good” questions—questions that help students make sense of math—lies at the heart of good math teaching. In Good Questions for Math Teaching: Why Ask Them and What to Ask, Grades 5–8, Lainie Schuster and Nancy Anderson provide teachers with questions across seven math strands. The questions are open-ended and offer opportunities for a range of…