Illuminations: Magnificent Measurement

Magnificent Measurement

The Area of Things ...

Students have opportunities to recognize and use the attributes of length and area using non-standard units.

Learning Objectives
 
Students will:
  • recognize the attributes of length and volume
  • measure area using nonstandard units
  • measure with multiple copies of units of the same size, such as clips laid end to end

Materials
 
Blue construction paper
Glue sticks
Cotton balls
Chart paper
Book: It Looked Like Spilt Milk, by Charles G. Shaw
Yarn (one 12” piece for each child)
Pencils
12-inch rulers

Instructional Plan

Gather students so they may see the book and hear you read aloud the story It Looked Like Spilt Milk, by Charles G. Shaw. This story uses the natural movement of what seems to be a cloud to create many different shapes (i.e. a squirrel, a tree, and a bird). After reading the story, explain that students will make their own pictures using a piece of yarn and cotton balls.

Introduce the concept of measuring area using nonstandard units by showing students how to create regions, predicting how many cotton balls are required to fill the region, filling the regions with cotton balls, and counting the number of cotton balls required to fill the region. Glue the cotton balls into place and label the picture with the total number of cotton balls used. This numerical label gives students a mental picture of area and helps them understand the concept of measuring area.

Give each student a 12-inch piece of yarn and a ruler for “checking” the length of yarn.

 

 

After each child has checked the length, give each student one sheet of blue construction paper. Model how the two ends of the yarn must touch to create a picture. Depending on other concepts that need to be reinforced, you may suggest to some students that they create simple geometric shapes for their pictures. For very young students, you might want to tie the ends of the yarn together to make this step easier. However, be sure that the yarn is no longer than 12 inches for this age group too, so that they will be able to count the number of cotton balls needed to cover the region.

Ask students to draw a region on the blue construction paper. Assist students in gluing their yarn along the outline they created (making a “trail” with glue and then placing the yarn on top often makes this task easier for younger students). Have students first predict and record how many cotton balls it will take to cover the inside of their shape, then place the cotton balls inside their figure so that the entire area is covered. Students need to glue, count, and record once their cotton balls are in place. When this activity is completed, students will have made a picture made of yarn as well as recorded estimates of and counted the number of cotton balls used.

Create a bulletin board using various regions filled with cotton balls. Label each with the number of cotton balls required to fill the area. Students could create additional examples of area while working in the math center.

Questions for Students
 

What is the area of a figure?

How can we figure out the area using these cotton balls?

Could we use beans to figure out the area of our shapes?

Would using beans and cotton balls give us the same answer? Why?

What other objects could we use to figure the area of these regions? (This helps students recognize the relationship between measuring tools and the object to be measured.)

If you had to teach this lesson to another student or your parents, what would you tell them and what directions would you give them?

Assessment Options
 
  1. At this stage of the unit, it is important to know whether students can accurately measure area using nonstandard units. Checking students’ pictures and their calculations of area using cotton balls will provide assessment of the students’ understanding or lack of understanding of this concept and their ability to apply the concept.
  2. Using the Class Notes Recording Sheet, you might collect data and document information about the following:
    • How accurately did students define area?
    • How accurately did students predict the number of cotton balls required to fill their region?
    • Can students transfer this knowledge to other area-related problems?
    • Can students calculate area using other nonstandard units?
  3. For the class bulletin board, students could add descriptive writings or stories about the shapes they created.

Teacher Reflection
 
  • Is there another piece of literature that would be useful for teaching area?
  • Which students demonstrated an understanding of area in the pictures they created? Which students need more practice with area?
  • What would I do differently the next time I teach this lesson? Why?
  • Would it be more beneficial to complete a class picture calculating
    area prior to providing individual practice?

NCTM Standards and Expectations
 
Measurement Pre-K-2
  1. Recognize the attributes of length, volume, weight, area, and time.
  2. Understand how to measure using nonstandard and standard units.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity
More and Better Mathematics for All Students
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