 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            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.   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 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 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 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 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  Session 10, Grades 3-5: Index | Notes | Solutions | Video