Dividing a number into equal-size groups with remainders is the main focus of Stuart J. Murphy’s book Divide and Ride (Harper Trophy, 1997). In this story, eleven friends go to a carnival. When they must get into groups of two to ride the roller coaster, groups of three for the satellite wheel, and groups of…

It’s important to make connections among the different areas of mathematics, and this lesson presents an addition problem in a geometric context that is appropriate for third graders. The problem also is good for supporting mental computation and for giving children experience with a math problem that has more than one solution. The idea for…

Estimation Jar is excerpted from Susan Scharton’s book, Teaching Number Sense, Grade 2 (Math Solutions Publications, 2005), part of a three-book series for grades K, 1, and 2 that focuses on the critical role number sense plays in students’ math learning. This lesson is one in a series of estimation activities that Susan includes in…

Lessons for Introducing Multiplication, Grade 3 is a revision that replaces Multiplication, Grade 3, the Math By All Means unit I wrote in 1991 that has been used by more than 85,000 teachers. Over the years since I wrote the original unit, I’ve learned a good deal more about teaching multiplication to third graders from…

This excerpt is from the introductory lesson in Maryann Wickett, Susan Ohanian, and Marilyn Burns’s book, Teaching Arithmetic: Lessons for Introducing Division, Grades 3–4 (Math Solutions Publications, 2002). This book is a revision of the popular Math By All Means unit Division, Grades 3–4, and this lesson is one of the new additions. The context…

I prepared a baggie for each pair of children, each with one hundred identical objects such as cubes, milk jug lids, pennies, beans, tiles, and so on. For several days, the children used these materials to build different-size arrays. For instance, I’d ask them to build a row of four, six times, and walk around…

In this lesson, students explore halves, looking for patterns between numerators and denominators. Maryann Wickett created this simple yet powerful fractions lesson and then built on it, doing an activity from Marilyn Burns’s Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4–5 (Math Solutions Publications, 2001). My-third grade students had experience using fraction kits to informally…

Overview of Lesson This lesson is a math variation of the popular 20 questions game. The teacher chooses a secret number on the 1–100 chart. Students ask 20 questions to try to ascertain the secret number. Students mark their 1–100 charts to keep a visual record of information they have gathered and to see the…

In this lesson, excerpted from Maryann Wickett and Marilyn Burns’s new book, Teaching Arithmetic: Lessons for Extending Place Value, Grade 3 (Math Solutions Publications, 2005), children use base ten blocks to cement their understanding of how ones, tens, and hundreds relate to our number system. Before class, I gathered the base ten blocks and enough…

Bruce Goldstone’s book Ten Friends (Henry Holt, 2001) uses rhymes and illustrations to suggest different ways to invite ten friends to tea. At the back, he lists all of the ways to represent ten using two addends, three addends, and so on up to ten addends. Marilyn Burns read the story to second graders and…

As part of their classroom routine, Bonnie Tank and Lynne Zolli regularly ask children to figure out answers to questions like “How many more?,”“How many less?,” and “What’s the difference?” The Game of More provides a context for asking these questions. This card game gives children practice with basic facts and with adding and subtracting…

When I ﬁrst saw a copy of It All Adds Up!, by Australian teacher Penny Skinner, I began reading it eagerly. I was searching for ways to teach arithmetic with the same excitement I had for the other areas of the math curriculum. In the introduction, Penny explains that her book explores teaching strategies for…

We’re excited about our newest Math Solutions publication, Getting Your Math Message Out to Parents, by Nancy Litton. Nancy is a classroom teacher with almost thirty years of experience as well as a Math Solutions instructor. She’s thought a great deal about how to bridge the gap between home and school and knows that teachers…

This game gives children practice with adding and subtracting ones and tens. Using a special die, two 0–99 charts, and two markers, children play in pairs. During the course of a game, they calculate between 20 and 30 addition and subtraction problems. The Game of Tens and Ones appears in Maryann Wickett and Marilyn Burns’s…

Hand Spans uses a measurement activity to give students experience with the grouping model of division and practice with rulers and tape measures. The students measure their hand span and the length of their arm, and then figure out how many of their hand span lengths are in their arm length. This lesson appears in…

Second grade students use 3-digit numbers and their understanding of place value in this game. 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…

Along with teaching students how to use ordered pairs of numbers as coordinates to plot points, this lesson gives students background understanding about our system of graphing and helps them see how axes — intersecting perpendicular number lines — make it possible to locate points anywhere on a plane. The activity appears in Maryann Wickett,…

In this partner game, third grade students use their multiplication foundation to solve for the area of rectangles. 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…

A Lesson with Second Graders by Linda Dacey and Rebeka Eston Salemi All teachers have students with a range of mathematical abilities and understandings in their classrooms. In this lesson on estimation and measurement, the teacher differentiates three aspects of the curriculum—content, process, and products. This lesson is excerpted from Math for All: Differentiating Instruction,…

This lesson is from Marilyn Burns’s book Teaching Arithmetic: Lessons for Introducing Multiplication, Grade 3 (Math Solutions Publications, 2001), a revision of the Math By All Means: Multiplication, Grade 3 unit she wrote in 1991. This book presents five completely new whole-class lessons plus five new lessons in the Additional Activities section. Also, four children’s…

The need to interpret data accurately looms large in today’s world. By modeling ways to gather, represent, and interpret data, teachers can make young children feel more comfortable in this arena; children can then do these activities independently. Categorical Data Collection appears in the “December” chapter of Nancy Litton’s new book, Second-Grade Math: A Month-to-Month…

Each two-page spread in Cheryl Nathan and Lisa McCourt’s book The Long and Short of It (BridgeWater Books, 1998) shows two animals and compares the size of some part common to both of them by comparing each part to an everyday object. For example, the chameleon’s tongue is described as being “longer than a fire…

In Blue Balliett’s novel Chasing Vermeer (Scholastic, 2005), Petra and Calder, the main characters, are in the same class but barely know each other. Their friendship grows, however, and they work together to recover a stolen painting—a valuable Vermeer. Pentominoes are included in the clues they need to decode. Maryann Wickett uses this book as a…

Children are surrounded by things containing numbers — license plates, addresses, room numbers, shoe sizes, signs, even telephone numbers. One way that students can develop number sense is to think about the numbers they encounter in the everyday world. This lesson by Bonnie Tank and Lynne Zolli provides a playful experience with numbers that are…

A Lesson for Third Graders by Maryann Wickett and Marilyn Burns This lesson is excerpted from Maryann Wickett and Marilyn Burns’s new book, Teaching Arithmetic: Lessons for Extending Place Value, Grade 3 (Math Solutions Publications, 2005). Children’s understanding of place value is key to their arithmetic success with larger numbers, and this book is important…

Students beneﬁt from repeated practice with addition and subtraction throughout the year. In her book, Third-Grade Math: A Month-to-Month Guide (Math Solutions Publications, 2003), Suzy Ronfeldt provides a midyear perspective on providing practice, suggesting fresh approaches to computing with larger numbers that are suitable for older students as well. The problems are useful not only…

Amanda Bean loves to count anything and everything. But sometimes she just can’t count fast enough. Her teacher tries to convince her that multiplying might help, but Amanda will have none of it—until she has an amazing dream about free-wheeling sheep on bicycles, speed-knitting grandmas, and who knows how many long-sleeved sweaters. Only then does…

The metric system is particularly easy to work with since its units relate to each other in the same way that units in place value relate to each other: powers of ten. This activity helps make that connection for students. Here students compare centimeter cubes, decimeter rods, and meter sticks and find all the ways…

This lesson appears in Bonnie Tank and Lynne Zolli’s new book, Teaching Arithmetic: Lessons for Addition and Subtraction, Grades 2–3 (Math Solutions Publications, 2001). Based on Rolf Myller’s book How Big Is a Foot?, this lesson gives children experience with comparing quantities in the context of measuring a variety of lengths. Partners measure, record, and…

Vocabulary instruction is a large part of geometry instruction throughout the elementary grades. To learn geometric terms and their meanings, students need opportunities to interact with and use the language of geometry. In this lesson, Maryann Wickett used the experience of making tangrams as an opportunity to help a class of third graders expand their…

Algebra Content Standards • Create numeric patterns that involve whole-number operations. (3-3.1) • Apply procedures to find missing numbers in numeric patterns that involve whole-number operations. (3-3.2) • Illustrate situations that show change over time as increasing. (3-3.4) Lesson Process Standards • Generate descriptions and mathematical statements about relationships. (3-1.4) …

This activity, Looking at Data, is excerpted from Mini-lessons for Math Practice, Grades 3–5, by Rusty Bresser and Caren Holtzman (Math Solutions Publications, 2006). The book presents ideas for providing opportunities for students to practice the things they have learned, with practice defined broadly to include understanding as well as skill. In this instance, students…

Dana Islas is a Math Solutions consultant, kindergarten teacher at Pueblo Gardens Elementary School in Tucson, Arizona, recipient of the Presidential Award for Excellence in Mathematics and Science Teaching, and author of the multimedia resource How to Assess While You Teach Math: Formative Assessment Practices and Lessons, Grades K–2. Overview of Lesson This lesson is…