Introducing Division

Introduction

This post includes a variety of resources (books, websites, lesson plans, games, printables, etc.) that can be used to introduce basic division concepts to students and aid them in committing the basic division facts (dividends to 144) to memory. The target grade level is third grade since these skills are first introduced at this level.  However, many of these resources could and perhaps should be used at the fourth and fifth grade levels to reinforce basic division skills, which are the basis for so many other higher-level math concepts.

FIVE BOOKS for INTRODUCING SIMPLE DIVISION

The Great Divide, written by Dayle Ann Dodds and illustrated by Tracy Mitchell: Using a cross-country race as a plot line, Dodds demonstrates how dividing by two decreases the contenders in the race to the finish.  Eighty contestants start out on bikes in ten groups of eight but when half pop tires, only forty continue.  Forty becomes twenty, twenty becomes ten, and ten becomes five, at which point one contestant has to stop with a rock in her shoe and only four move on.  Though the plot is minimal, a surprise ending, likable characters, and fun illustrations keep children engaged while getting the mathematical concepts across.

Divide and Ride, written by Stuart Murphy and illustrated by George Ulrich: Murphy's book introduces division as eleven children sort themselves into smaller groups in order to go on different rides at a carnival.  Mathematical vocabulary such as "per", "divide", and "left over" is used throughout to introduce the concepts of "groups of", "sets of", and remainders.  The children in the story are racially diverse and even young children can relate to the idea of going to an amusement park and begin to see the patterns that emerge as the book continues.

How Hungry Are You, written by Donna Jo Napoli and Richard Tchen and illustrated by Amy Walrod: In the same vein as Pat Hutchins classic, The Doorbell Rang, Napoli and Tchen's book is a great introduction to simple division and the difficulties that can arise when sharing.  A rabbit and a frog decide to have a picnic.  Along the way, they meet up with a variety of other creatures who share in the food (creating the need to redivide) and contribute more food.  The story presents a great opportunity for reader's theater as the entire tale is told through dialogue of the various characters identified by rebus-like headshots at the beginning of each line.

A Remainder of One, written by Elinor J. Pinczes and illustrated by Bonnie MacKain: An army of 25 insects line up in multiple arrays in an attempt to create a formation that doesn't leave anyone out.  Rhyming text and simple illustrations combine to present the basis for a clear understanding of remainders and the use of arrays in division problems.

One Hungry Cat, written by Joanne Rocklin and Marilyn Burns and illustrated by Rowan Barnes-Murphy: A hungry cat bakes 12 cookies and invites over two friends to share them, but each time he divides the cookies into equal shares, he gets hungry, gobbles them up, and has to bake something else. Throughout the story, subtle math problems arise.   For example, how does one divide eight cookies onto three plates, or cut a square cake into three equal pieces? Answers to the problems are presented in the back of the book along with suggested activities for reinforcing the math lesson.  The cartoon illustrations add to the fun and kids will enjoy the slapstick while they figure out the math.

ADDITIONAL BOOKS FREQUENTLY REFERENCED

Everybody Wins, written by Sheila Bruce and illustrated by Paige Billin-Frye:  When Oscar and Emmy both contribute box tops for a contest and agree to split the prize of 100 frozen pizzas, they learn valuable lessons about how to divide and the costs and rewards of friendship.  As the book continues, so does the sharing as friends practice dividing other things among their classmates.  Additional activities to support the lessons in the book are listed on the inside back cover.

Division, written by Sheila Cato and illustrated by Sami Sweeten: Less of a story and more of a straight up math lesson, this book effectively uses authentic math problems to teach division.  A group of ethnically diverse children present a series of division problems using everyday examples that get progressively more difficult.  Equations are used to reflect the original word problem and the explanations are thorough and concise, building on prior knowledge.  Boxed areas provide further information and offer more practice equations, while colorful cartoons break up the text and illustrate the answers.

The Doorbell Rang, written and illustrated by Pat Hutchins: Pat Hutchins uses a dozen cookies to illustrate the partitive model of division as more and more children have to share the same batch of cookies. Two children are delighted when their mother bakes a tray of a dozen cookies and they find that by dividing them equally each can have six. But the doorbell rings repeatedly, friends arrive and the cookies must be re-divided again and again. When each child's share is down to one, a surprise visit from Grandma brings dozens more cookies for the elated multiracial children to share.

17 Kings and 42 Elephants, written by Margaret Mahy and illustrated by Patricia MacCarthy: As 17 kings and 42 elephants make their way through the jungle, they encounter a variety of animals from crocodiles and tigers to hippopotomums and baboonsters.  Though the book has no formal plot and uses words both sensible and nonsensical, it holds great appeal to children because of the rollicking rhymes, joyous adventure, and beautiful illustrations.  From a mathematical perspective, the book can be used as a springboard for a division problem with remainders as students figure out how many elephants each king has if the kings share the elephants equally.

One Hundred Hungry Ants, written by Elinor J. Pinces and illustrated by Bonnie MacKain:  Rhymed verse is used to tell this whimsical story of 100 hungry ants setting out in one long line for a picnic.  When the littlest ant announces that the line is moving too slowly and suggests 2 lines of 50, followed by 4 lines of 25, 5 lines of 20, and 10 lines of 10 to speed things up.  By the time the ants reach the picnic, the food is all gone but students will have gained valuable background knowledge about both multiplication and division.

WEBSITES FOR REINFORCING BASIC DIVISION FACTS

Divider Machine: Students attempt to answer basic division facts and obtain a score of 100 without making any mistakes by selecting the appropriate level of difficulty.

Division Derby: Choose from a series of racecar themed multiplication and division games for single or multi-players focused on basic facts.

Flashcards: Students can use this site to generate their own division flashcards by entering the highest level of quotients they are interested in working with.  The site also has a variety of division games for students to choose from to support their learning process.

Math Magician: Great site for building automaticity with basic division facts.  Answer 20 division facts in a minute or less and earn a certificate.

Mystery at the Peculiar Zoo: Students read and use the clues in a poem along with multiplication and division skills to figure out how many animals were stolen by the Zoo Bandit.  If you like this story, additional mysteries are available through this scholastic site as well.

ADDITIONAL TEACHER RESOURCES

Basic Division Facts Differentiated Learning Pack: This Scholastic resource, while worksheet driven, does provide a good opportunity for differentiating activities for students who are reading below, on, or above grade level.

Lesson Idea for Introducing Division: In this activity, students are placed in groups of five or six and provided with 30 pieces of dry pasta and a paper plate for each child.  Students are asked to share the pasta equally and talk about their results.

Dividing with Bricks: This worksheet is a simple way to support the development of division concepts while children divide sets of bricks (or any cubes) into towers.

All About Division Smartboard Lesson: This Smartboard Lesson provides an introduction to the math concept of division and provides students with the opportunity to practice dividing by 3's, 4's. and 5's.