Explore Circumference and Diameter

Est. Class Sessions: 4

Mathematical Standards

5.OA.B: Analyze patterns and relationships. (5.OA.B.3)
5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions.(5.NF.A.1)
5.NBT.A: Understand the place value system. (5.NBT.A.1)

Standards for Mathematical Practice

MP1.: Make sense of problems and persevere in solving them.
MP2.: Reason quantitatively.
MP3.: Construct viable arguments and critique the reasoning of others.
MP4.: Model with mathematics.
MP5.: Use appropriate tools strategically.
MP6.: Attend to precision.
MP7.: Look for and make use of structure.
MP8.: Look for and express regularity in repeated reasoning.

Students explore the relationship between the circumference and the diameter of circles, record their measurements in a data table, plot them on a graph, and analyze their results. Students find that the circumference of a circle is about three times its diameter and equal to π times the diameter.

Content in this Lesson

Identifying the parts of a circle [E5].
Investigating the relationship between circumference and diameter.
Representing the relationship between variables as a ratio [E2].
Defining π as the ratio of circumference to diameter of a circle.
Finding and expressing the relationship between the circumference and the diameter of circles: C = π × D.
Finding equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables) [E3].
Using ratios and proportions to solve problems [E4].
Measuring the circumference of a circle to the nearest tenth of a centimeter [E8].
Representing the variables and procedures of an investigation in a drawing [E9].
Collecting and organizing data into a table and line graph to represent the relationship between variables [E10].
Making point graphs and drawing best-fit lines to represent ratios and proportional relationships [E11].
Using patterns in tables and line graphs to make predictions and solve problems [E12].
Knowing the problem [MPE1].
Using labels [MPE6].

Daily Practice and Problems W–DD

W. Multiplying Fractions

X. Recycle Problem Solving

Y. Area Problem

Z. Multiplying Decimals

AA. Plot a Shape

BB. Play Fractions Digits Game

CC. Smallest to Largest

DD. Different Densities

Materials for Students

		Daily Practice and Problems	Lesson	Homework	Assessment
Student Books	Student Guide		Explore Circumference and Diameter Pages 551–558	Explore Circumference and Diameter Homework section Pages 553–555	Explore Circumference and Diameter Lab Homework section Pages 553–555 Explore Circumference and Diameter Check-In: Questions 20–26 Pages 557–558
Student Books	Student Activity Book			Going around in Circles Page 445
Teacher Resources	Teacher Guide - digital	DPP Item W DPP Item X DPP Item Y DPP Item Z DPP Item AA DPP Item BB DPP Item CC DPP Item DD Centimeter Grid Paper	Three-Trial Data Table Centimeter Grid Paper	Home Practice Part 6	Explore Circumference and Diameter Lab Feedback Box Explore Circumference and Diameter Check-In: Questions 20–26 Feedback Box DPP Item X Recycle Problem Solving DPP Item DD Different Densities Gluing It Down optional

Supplies for Student Pairs

glue
string that will not stretch
scissors
circular objects such as cans and lids of various sizes
centimeter ruler
calculator
adding machine tape, optional

Materials for the Teacher

Display of circle diagram on first page of Explore Circumference and Diameter (Student Guide) Page 551
Display of Three-Trial Data Table Master (Teacher Guide)
Display of Centimeter Grid Paper (Teacher Guide)
Math Facts Class Record

Materials Preparation

Collect Circular Objects. Collect about 45 lids of various sizes, so that each student pair has three to measure. Gather together a good selection of other small, medium, and large circular objects for students to measure. For example, small objects like spools of thread or Life Savers® rolls; medium objects—soup cans or duct tape rolls; and large objects–coffee cans or paper towel rolls. Ask students to bring these or similar circular objects to school.

Assessment in this Lesson

Assessment	Expectation Assessed	Math Practices Expectation Assessed
Explore Circumference and Diameter Lab Student Guide Pages 553–555 and corresponding Feedback Box Teacher Guide - digital	E5. Identify the parts of a circle. E8. Measure the circumference of a circle to the nearest tenth of a centimeter. E9. Represent the variables and procedures of an investigation in a drawing. E10. Collect and organize data into a table and line graph to represent the relationship between variables. E11. Make point graphs and draw best-fit lines to represent ratios and proportional relationships. E12. Use patterns in tables and line graphs to make predictions and solve problems.
Explore Circumference and Diameter Check-In: Questions 20–26 Student Guide Pages 557–558 with corresponding Feedback Box Teacher Guide - digital	E2. Represent the relationship between variables as a ratio. E3. Find equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables). E4. Use ratios and proportions to solve problems. E12. Use patterns in tables and line graphs to make predictions and solve problems.	MPE1. Know the problem. I read the problem carefully. I know the questions to answer and what information is important. MPE6. Use labels. I use labels to show what number mean.
DPP Item X Recycle Problem Solving Teacher Guide - digital	E1. Represent ratios with words and as fractions. E2. Represent the relationship between variables as a ratio. E3. Find equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables). E4. Use ratios and proportions to solve problems.
DPP Item DD Different Densities Teacher Guide - digital	E4. Use ratios and proportions to solve problems.