Math Background

Lesson: Estimating and Measuring Amounts
Introducing the Concept

In this lesson, students explore nonstandard and standard units of measurement. They will learn why some nonstandard units are unreliable, while standard units, whose lengths remain constant, are useful.

Materials: Houghton Mifflin Math, Pupil Edition; ten crayons; centimeter ruler (Learning Tool 24 in the Learning Tools Folder) for each group of students

Preparation: Organize crayons in groups of 10 according to length. The crayons in each group should be about the same length (for example, one group of 10 new crayons; one group of 10 used crayons, each about 5 centimeters long; and so on). Distribute the crayons and math books. Cut out or have students cut out the centimeter rulers.

Prerequisite Skills and Concepts: Students should understand the concept of measurement and know that a centimeter is a unit of linear measurement.

  • Say: We're going to use crayons to measure the length of our math books.
    Point to the spine of a math book when you say length of our math books.
  • Say: Line up the end of one crayon with one end of the book.
    Observe students to ensure that they understand this instruction, or demonstrate it for them.
  • Say: Now place more crayons end-to-end alongside your math book.
    As students are working, point out to them that the last crayon may extend somewhat beyond the end of the book or fall just short of the end of the book.
  • Ask: About what is the length of your math book?
    Have a volunteer from each group respond. Encourage students to include the unit of measurement in their response (for example, Our math book is about 6 crayons long.) Record student responses on the board.
  • Ask: Why did each group come up with a different length?
    Elicit from students that the crayons each group used are different lengths.
  • Pass out the centimeter rulers.
  • Ask: What unit of measurement is shown on the ruler? (centimeter) How long is the ruler? (30 centimeters)
  • Say: Let's measure the length of our math books in centimeters. Line up the end of the ruler with the end of your math book.
    Make sure that students line up the correct end of the ruler with the math book.
  • Ask: About what is the length of your math book? (about 28 centimeters) Did everyone come up with the same length when we used centimeters as the unit of measurement?
    Each group should have found that the length of the math book is about 28 centimeters.
  • Ask: Why do you think we use units of measurement such as centimeters to measure length rather than units of measurement such as crayons?
    Students should conclude that units such as centimeters are always the same length and units such as crayons may vary in length.
  • Give students the opportunity to measure several objects so they gain proficiency in using a centimeter ruler.

Houghton Mifflin Math Grade 3