The Great Divide: A Mathematical Marathon

Purpose

This is an activity based on the picture book The Great Divide: A Mathematical Marathon

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Specific Learning Outcomes

Students will be able to demonstrate an understanding of halving even sets within the context of dividing by two.  

Students will be able to model the concept of remainder of one, when halving odd numbers.

Description of Mathematics

When an even number set is divided in half it creates two equal sized sets. When an odd numbered set is divided in half it creates two equal sized sets and a remainder of one.

Required Resource Materials
The Great Divide: A Mathematical Marathon by Dayle Ann Dodds

Counting materials

Large sheets of paper

Activity

Split A-parts

This activity is based on the picture book The Great Divide: A Mathematical Marathon

Author: Dayle Ann Dodds
Illustrator: Tracy Mitchell
Publisher: Candlewick Press (1999)
ISBN: 978-0-7636-1592-5

Summary:
Eighty participants start out on a cross country race that sees their numbers divided in half at various points in the race until eventually only 1 racer crosses the finish line.

Lesson Sequence:

  1. Prior to reading, revisit the concept of halving with the group. Through various contexts ask the students to model the dividing of a set of objects into two equal parts: the halves. Explore with them what happens when halving a number that is even and what happens when a number is odd. Discuss the idea of “remainder”.
  2. Share the book with students linking to the context of cross-country racing. Draw students’ attention to how the 80 participants are grouped into 10 teams on pages 3-4. Watch how the teams divide during the book. Also engage students in a discussion about how the author deals with the division of 5. Model the story by running a race with your class dividing them into two groups at various points, asking half to sit down each time until you are left with 1. When you have remainders of one ask them to stand but remain with the sitting group that has to stop.
  3. The next day re-read the story with your students while tracking the divisions on a large sheet of paper, on the whiteboard, or in a modeling book. Create a map of the race showing the division of the race groups with a flowchart. Talk about the group of riders dividing and splitting apart into two equal groups.
  4. Ask the students in pairs or small groups to select a number between 20 and 100 for their cross-country race. This will be the number of racers. They then create a story map like a flow chart showing what barriers their racers encounter and what numbers they get when they split apart into halves. They can keep track of the divisions with a set of dots in their book or small materials.
    How will you deal with the remainder of one when you have to split an odd number in half?
    What will happen to the one racer?
    How will your race end- will two people cross the finish line together (tie) or will only one cross?
  5. Ask students to present their Split A-part stories to the class explaining how they knew a number was odd or even and how they dealt with the remainders when they occurred.

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