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Learning Math Home
Measurement Session 10, Grades 3-5: Classroom Case Studies
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
Glossary
measurement Site Map
Session 10 Materials:
Notes
Solutions
Video

Session 10, Part C:
Problems That Illustrate Measurement Reasoning (55 minutes)

In this part, you'll look at several problems that are appropriate for students in grades 3-5. For each problem, answer the questions below. If time allows, obtain the necessary materials and solve the problems.

 Questions to Answer:

a. 

What is the measurement content in the problem? What are the big ideas that you want students to consider and understand?

b. 

What prior knowledge is required? What later content does it prepare students for?

c. 

How does the content in this problem relate to the mathematical ideas in this course?

d. 

What other questions might extend students' thinking about the problem?

e. 

What other instructional activities or problems might you use in conjunction with this one to further your content goals?

Problem C1

Solution  

Take 24 square tiles. Make all the rectangles that have an area of 24 square units. Record the dimensions of each rectangle. What do you notice about the relationship of the length and width of a rectangle to its area? How are the dimensions of the rectangles related to their areas? Write a rule for finding the area of any rectangle given its length and width.


 

Problem C2

Solution  

Examine the following measurements collected by students:

Names

Circumference
of Flagpole

Length of Math Book

Carlos and Pam

58 cm

29 cm

Linda and Jen

56 cm

29.5 cm

Yoji and Pete

57.5 cm

28.8 cm

Why aren't the measurements the same? What affects precision?


 

Problem C3

Solution  

Cut out the net of a box with dimensions of 4 by 6 by 2 from centimeter grid paper. Without folding the net into a box, predict how many centimeter cubes will fit into the box when folded. Then connect two centimeter cubes together to form a 1-by-1-by-2 package. How many 1-by-1-by-2 packages fit into the box? What strategies did you use to predict how many centimeter cubes and how many 1-by-1-by-2 packages fit into the box? Check your answers by filling the box with cubes. Finally, generalize an approach to determining the number of cubes in a box. Note 4


 

Problem C4

Solution  

Use geometry software such as Geometer's Sketchpad for this problem. If geometry software is not available, collect pictures or models of the different types of triangles and measure the angles with a protractor.

Use the software to measure the angles in each of the triangles in the table. Find the sum of the angles of the triangle. Record your findings.

Type of Triangle

Measure
A

Measure
B

Measure
C

Sum

Right Triangle

Equilateral Triangle

Isosceles Triangle

Acute Triangle

Obtuse Triangle

What patterns do you notice about the sum of the angles in a triangle? Create a few more triangles and find the angle sum for each of them. Do you think these patterns will hold for all triangles? Why or why not?


Next > Homework

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