Lesson 6

Rolling Along in Centimeters

Est. Class Sessions: 3–4
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Mathematical Standards

2.NBT.A
Understand place value. (2.NBT.A.4)
2.MD.A
Measure and estimate lengths in standard units. (2.MD.A.1, 2.MD.A.2)
2.MD.D
Represent and interpret data.(2.MD.D.9, 2.MD.D.10)

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.

The Adventure Book story, "Mine Is the Best: The Challenge," sets the context for a TIMS Laboratory Method investigation in which students measure the length toy cars roll. After collecting and recording data for three rolls, students find the median distance rolled then graph and analyze their data.

Content in this Lesson

  • Identifying and maintaining fixed variables to set up a lab.
  • Identifying the median of three numbers.
  • Recognizing the role of fixed (controlled) variables in an investigation.
  • Using words and symbols (e.g., <, >, =) to show comparisons of quantities [E1].
  • Using and applying place value concepts and comparative language to compare and order lengths (e.g., shorter, longer, shortest, longest) [E2].
  • Solving word problems (e.g., compare) involving length [E3].
  • Using a meterstick to measure length in centimeters [E6].
  • Making a table and bar graph to find information about a data set [E8].
  • Reading a table and bar graph to find information about a data set [E9].
  • Using a table and bar graph to solve problems about a data set [E10].
  • Adding and subtracting multidigit numbers.
  • Finding a strategy and appropriate tools to solve a problem [MPE2].
  • Explaining solutions so others understand one's thinking [MPE5].
  • Using labels to show what numbers mean [MPE6].
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Book

Student Activity Book

Teacher Resources

Teacher Guide - digital

Supplies for Students

crayon or colored pencil

Supplies for Student Groups

2 metersticks
ramp (board that can be used as an inclined plane)
4 blocks or books to elevate each ramp
4 toy vehicles
masking tape or small self-adhesive notes

Materials for the Teacher

Display of data table in the Rolling Along in Centimeters (Student Activity Book) Page 210
Display of graph in the Rolling Along in Centimeters (Student Activity Book) Page 211
Display of first page of John's Data (Student Activity Book) Page 215
Display of Math Practices (Student Activity Book) Reference
Display of John's Data Feedback Boxes (Student Activity Book) Pages 218–219
Unit 4 Assessment Record
Unit 4 Individual Assessment Records
Math Facts Class Record
chart paper

Materials Preparation

Gather a Collection of Cars. Have each student bring one toy car to school prior to the lab. To avoid disappointment, tell students to refrain from bringing very small cars. Cars larger than 3 inches are most suitable, as smaller cars often do not roll well for the required distance. Tell students cars will be tested to be sure they are "good rollers." Cars should be tested prior to beginning the lab, as they should roll straight for at least 50 centimeters beyond the bottom of the ramp. You may want to have extra cars on hand for students whose vehicles don't fit the criteria. Have students put their names on their cars so they can be returned at the end of the investigation.

TIMS Tip

This lab can successfully be done with a variety of wheeled toys. You may choose to have students bring a variety of wheeled toys that fit the necessary criteria or make the decision to use only cars or a variety of toys together as a class.

Prepare One Ramp for Each Student Group. Gather a minimum of one ramp of at least 20 inches in length and 3–5 blocks or books to elevate the ramp for each group of four students as shown in Figure 1. A level ramp surface without cracks or bumps is required. Metal bookshelves or ¼-inch plywood work well. Determine an appropriate height for the ramps based on the cars you will use. This will require some experimenting prior to the lab. Mark a starting line near the top of each ramp with a piece of masking tape. Adjust the height and starting line by using blocks or books so that cars roll at least 50, but not farther than 200, centimeters beyond the end of the ramp. Make sure the incline is not too steep. If the cars roll too far, the measurements will be difficult for students to graph.

image

Figure 1: Preparing ramps

Identify an Appropriate Space. Identify an area where teams of students can set up their ramps. A level surface without cracks or bumps is required. If you have space constraints, make arrangements for students to have access to an area in the hallway, the gym, or an outside space for setting up ramps and conducting the investigation.

TIMS Tip

This investigation provides a good opportunity to involve parents in math class. Parent volunteers can help set up ramps, manage larger spaces, and check that distances are recorded correctly during data collection.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed
Rolling Along in Centimeters
Observe Data Collection
Teacher Guide - digital
E6. 
Measure length using nonstandard (palms, footprints) and standard (centimeters, meters, inches, feet, yards) units.
E7. 
Select and use appropriate measuring units (e.g., centimeters, meters, yards, inches, feet).
Rolling Along in Centimeters
Check-In: Question 6
Student Activity Book
Page 211
E8. 
Make a table, bar graph, and line plot to find information about a data set.
John's Data
Check-In: Questions 3–10
with Feedback Boxes
Student Activity Book
Pages 215–219
E1. 
Use words and symbols (e.g., <, >, =) to show comparisons of quantities (e.g., lengths).
E2. 
Use and apply place value concepts and comparative language to compare and order lengths (e.g., shorter, longer, shortest, longest).
E3. 
Solve word problems (e.g., compare) involving length.
E9. 
Read a table, bar graph, and line plot to find information about a data set.
E10. 
Use a table, bar graph, and line plot to solve problems about a data set.
MPE2. 
Find a strategy. I choose good tools and an efficient strategy for solving the problem.
MPE5. 
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.
MPE6. 
Use labels. I use labels to show what numbers mean.
DPP Item M
Addition Facts Quiz: Group E
Teacher Guide - digital
E11. 
Use math fact strategies to add (direct modeling, counting strategies, reasoning from known facts) for the facts in Group E (5 + 7, 8 + 4, 8 + 5, 9 + 3, 9 + 4, 9 + 5, 10 + 1, 10 + 2, 10 + 3).
E12. 
Determine the unknown number in an addition or subtraction sentence relating three whole numbers for the facts in Group E.