by Linda Schulman Dacey and Rebeka Eston Kindergarten is an important beginning. It can be the positive start of a child’s lifelong exploration of mathematical ideas or it can lay the first stones in what can become an impenetrable wall between “real math” and “school math.” In Growing Mathematical Ideas in Kindergarten, Linda and Rebeka…

Teachers typically are comfortable leading classroom discussions when teaching literature or providing social studies instruction. They value these discussions and rely on them to support students’ learning. However, many teachers aren’t as comfortable making use of classroom discussions for mathematics instruction. In Classroom Discussions: Using Math Talk to Help Students Learn, Grades 1–6 (Math Solutions…

All too often young children fail to remember the names of pattern block shapes. Over the years, Kristin Garrison has found that if teachers don’t give students frequent opportunities to use pattern block names and become familiar with the attributes of the shapes, when handling pattern blocks after they leave kindergarten and first grade, they…

In this lesson, students hear the story How Many Feet in the Bed? by Diane Johnston Hamm, and predict how many feet are in the bed as, one after another, family members hop into Mom and Dad’s big bed on a Sunday morning. This book helps young children develop algebraic thinking skills by having them…

Sara Fanelli’s My Map Book (HarperCollins, 1995) is filled with maps of things that are of importance in a child’s life—“Map of My Day,” “Map of My Neighborhood,” “Map of My Face,” and more. In this lesson, excerpted from Jamee Petersen’s Math and Nonfiction, Grade K–2 (Math Solutions Publications, 2004), second-grade students draw maps of…

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 their understanding to concepts and skills. HMH Into Math is more than just a solution,…

First grade students practice adding and subtracting by tens in this hundred chart 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 their…

A Lesson for First and Second Graders by Chris Confer This whole-class lesson is adapted from the Math By All Means replacement unit Geometry, Grades 1–2, written by Chris Confer. By folding a square of paper in several predetermined ways, children investigate and record the different shapes they can make. This activity gives children valuable…

A Geometry Lesson Overview In this lesson, students learn to identify and describe polygons and compare and contrast them with figures that are not polygons. Prior to the lesson, students are introduced to vocabulary words that they will need to use as they learn about polygons. Students are taught various sentence frames and use the…

Before taking my class for a leaf-collecting walk, I distributed 9-by-12-inch drawing paper and asked the children each to draw a picture of a tree. “Don’t put any leaves on your tree,” I said. “We’ll collect leaves on the playground and you’ll arrange those on your trees.” Before we went outside, I gave one…

by Linda Schulman Dacey and Rebeka Eston Kindergarten is an important beginning. It can be the positive start of a child’s lifelong exploration of mathematical ideas or it can lay the first stones in what can become an impenetrable wall between “real math” and “school math.” In Growing Mathematical Ideas in Kindergarten, Linda and Rebeka…

A Lesson for First Graders by Chris Confer When children use mathematics to solve real-world problems, they learn that mathematics is not just something to do for the teacher’s sake, but it offers them important tools to shape their world. In this lesson, which appears in Chris Confer’s new book Teaching Number Sense, Grade 1…

Open-ended problems can make for excellent post-assessment. Wondering how you can design effective post-assessment tasks for your students? This lesson gives a four-step plan, including a K–2 sample task and corresponding authentic student responses. The lesson is adapted from Math for All: Differentiating Instruction, Grades K–2, by Linda Dacey and Rebeka Eston Salemi. Visit www.mathsolutions.com…

A Lesson for First and Second Graders By Jamee Petersen Miriam Schlein’s More than One (New York: Greenwillow, 1996) introduces the concept that one unit can be made up of more than one thing. One pair is always two, one week is seven days, but one family can be two, three, or more people. Here,…

by Rosemarie Dyer Rosemarie Dyer has taught for almost 30 years, primarily in kindergarten and first grade. She taught this activity, in which children collect information about the doors in the school, to her first-grade class in the Warren Consolidated School District, located in suburban Detroit. The lesson gives the children experience recording, organizing, and…

A Lesson for Kindergartners by Chris Confer In this lesson, excerpted from Chris Confer’s new book Teaching Number Sense, Kindergarten (Math Solutions Publications, 2005), children learn that numbers are used for different purposes. They search for numbers in their school, draw pictures of things that have numbers, discuss how numbers help people, as well as talk to adults in…

A Lesson for Kindergartners and First and Second Graders by Linda Dacey and Rebeka Eston The collection and display of data are important to our lives, and through their own investigations, young children begin to understand how they can find and communicate information in data, charts, and graphs. In the following excerpt from Show and Tell: Representing…

A Lesson with Kindergartners and First and Second Graders by Rusty Bresser and Caren Holtzman The concepts of more, less, and the same are basic relationships contributing to the overall concept of number. In this activity, students gain experience with these concepts and are also asked to think about part-part-whole relationships. (For example, students see that…

by Ann Carlyle Children need a good deal of practice counting objects. Second language learners especially need many opportunities to deal with words such as more, less, fewer, most, least, fewest, some, in order, and equal. Working with Counting Cups can be repeated from time to time throughout the year to reinforce children’s counting, ordering,…

by Ann Carlyle Ann Carlyle, recent recipient of the George Polya Memorial Award from the California Mathematics Council, has been teaching kindergarten through sixth grade in Goleta, California, for the past 34 years. As a Math Solutions consultant, she often receives letters from course participants asking her for specific help with their math instruction. The…

by Lisa Rogers Audrey Wood’s book Quick as a Cricket (Child’s Play, 1982) uses rhymes and beautiful illustrations to take children on a joyful celebration of self-awareness. The book features a boy who compares himself to a variety of animals—“loud as a lion,” “quiet as a clam,” “tough as a rhino,” and “gentle as a…

Rusty Bresser, Kathy Melanese, and Christine Sphar Alison Williams’s second-grade class has the full range of English language learners (ELLs), from beginning to advanced, including a few native English speakers. Native languages spoken by the students include English, Vietnamese, Spanish, Somali, and Laotian. Alison knows that ELLs typically experience difficulty understanding and therefore solving math…

A Lesson for Grades K–1 by Dana Islas Materials • The children’s rhyming story Five Little Speckled Frogs, by Nikki Smith (Nikki Smith Books, 2006) • Cubes, 5 per student Overview of Lesson In the delightful rhyme Five Little Speckled Frogs, five frogs sitting on a log gulp bugs and jump into a pool one…

Overview In this game, students roll a die and place that number of counters on a double ten-frame in an eﬀort to reach 20 ﬁrst. This game builds students’ understanding of landmark numbers, speciﬁcally ten and twenty. Through the use of two colors of counters, students decompose the number twenty and use number strings…

by Ann Carlyle Ann Carlyle, a Math Solutions Inservice consultant, has been an elementary teacher in Goleta, California, for more than 30 years. She is the 1993 Presidential Award winner for Excellence in Mathematics Teaching and the 2000 recipient of the George Polya Memorial Award from the California Mathematics Council. Farmer’s Math grew out of…

by Lynn Sherman Lynn Sherman is a teacher candidate at York University in Toronto, Ontario, where she recently taught a geometry class based on The Greedy Triangle, by Marilyn Burns (Scholastic, 1994), to a class of second graders. She gave the story an added dimension with the creation of her Greedy Triangle “prop.” We’re sure…

by Vicki Bachman The end of the school year is both an exhilarating and a challenging time. Unless you’re in a year-round school, everyone is getting excited about the summer vacation ahead. Getting—and holding—the children’s attention requires planning, flexibility, and energy. A balance of novelty, familiar routines, and physical activity—customized to your class and personal…

by Stephanie Sheffield Stephanie Sheffield begins this lesson in her first-grade classroom by reading aloud Ann Jonas’s book Splash! Each page shows what is above and below the water of a young girl’s backyard pond. This girl narrates the story about animals jumping into and out of the pond and continually asks the reader, “How many are…

by Dana Islas Overview of Lesson Mary Wore Her Red Dress and Harry Wore His Green Sneakers is a favorite book to share with students at the beginning of the school year. In the book, animals in assorted brightly colored clothes assemble for their friend Katy’s grand birthday gala. After reading the book, students look…

by Andrea Holmes Andrea Holmes knew that the kindergarten children in Mrs. Fisher’s class had had numerous opportunities to listen to and engage with counting books. She also knew that additional practice allows children to continually think about numbers from one to ten and provides a glimpse of the problem- solving strategies children rely upon…

by Jamee Petersen Understanding the concept of scale is not easy for young children, but Steve Jenkins’s book Big and Little (Houghton Mifflin, 1996) can help. The illustrations in the book show animals at the same scale, making it easy to compare their sizes visually. In this lesson, Jamee Petersen uses the book to introduce…

by Leyani von Rotz and Marilyn Burns Learning the meaning of the less than, greater than, and equals signs is important to children’s numerical and algebraic understanding. In this lesson, first-grade children use the symbols >, <, and = to compare numbers. This activity appears in Leyani von Rotz and Marilyn Burns’s new book, Lessons…

Jane Crawford Overview of Lesson This lesson is appropriate for children who recognize coins and have been introduced to coin values. Follow the instructions in the lesson that allow different levels of ability to participate. Many children can relate to Alexander’s quandary in the book Alexander, Who Used to Be Rich Last Sunday. Feeling rich…

Pour your bag of buttons onto a plate so that everyone can easily see them. Hold up a button and discuss the article of clothing that it might have been attached to. Hold up another button and call attention to the ways in which the buttons are alike and different.

A Lesson with First Graders by Leyani von Rotz and Marilyn Burns Building, extending, and describing growth patterns is an important aspect of developing children’s algebraic thinking. In this lesson, children investigate caterpillars that grow, record on a T-chart, and then extend the pattern. The activity appears in Leyani von Rotz and Marilyn Burns’s new…

by Vicki Bachman In this activity, children build and then determine the height of Cuisenaire rod towers. Students build a tower with a partner, decide the measurement tool to use, measure their tower, and then in a whole-class discussion make comparisons between the towers. Rod Towers is excerpted from Vicki Bachman’s new book, Sizing Up…

by Stephanie Sheffield Many first-grade children have learned to count by twos, at least up to ten. Some have learned the chant“ Two, four, six, eight, who do we appreciate.” And some know that when things are the same, we often say that they are “even.” However, most first graders have not thought about the…

by Rusty Bresser and Caren Holtzman The lesson is excerpted from Minilessons for Math Practice, Grades K–2, by Rusty Bresser and Caren Holtzman (Math Solutions Publications, 2006). The book provides engaging, quick activities to help students practice math concepts, skills, and processes in a variety of problem-solving contexts throughout the day. This sample offers two…

by Rusty Bresser and Caren Holtzman In this activity, students guess a secret number from within a range of numbers and keep refining their guesses based on whether the teacher tells them the secret number is greater or lesser than their guesses. Guess My Number, which appears in Rusty Bresser and Caren Holtzman’s Minilessons for…

A Lesson for Kindergartners and First Graders by Kristin Garrison All too often young children fail to remember the names of pattern block shapes. Over the years, Kristin Garrison has found that if teachers don’t give students frequent opportunities to use pattern block names and become familiar with the attributes of the shapes, when handling…

A Lesson for Kindergartners By Marilyn Burns Dayle Ann Dodds wrote that she developed the idea for her book The Shape of Things (Candlewick, 1994) to help children see “how a few simple shapes make up a lot of things we have in the world.” After reading the book to a kindergarten class, Leyani von…