Unit Plan

## Measurement

• Assessment Anchors
• Eligible Content
• Big Ideas
• Measures can be estimated by using known referents.
• Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
• Patterns exhibit relationships that can be extended, described, and generalized.
• Some attributes of objects are measureable, e.g., length, mass, capacity, and can be quantified.
• Two- and three-dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively.
• Concepts
• Classification of figures: Two- and three-dimensional figures
• Perimeter: Units, tools, strategies to measure
• Competencies
• Understand perimeter as a measurable attribute and select appropriate units, strategies, and tools to solve problems involving perimeter.

### Objectives

Students will develop strategies for measuring time, length of time, and length of objects. They will apply measurement strategies to estimate and calculate perimeter and area. Students will:

• identify time to the minute on digital and analog clocks.
• investigate the relationships between time on a clock and time on a calendar.
• relate time on a clock to length of time or elapsed time.
• select and apply appropriate standard and nonstandard units and tools to measure length and width.
• apply concepts of measurement and estimation to select appropriate tools and find perimeter of regular and irregular shapes.
• relate perimeter and area using concrete objects.

#### Essential Questions

• What makes a tool and/or strategy appropriate for a given task?
• How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems?
• Why does “what” we measure influence “how” we measure?
• How can recognizing repetition or regularity assist in solving problems more efficiently?

### Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

• AAA Math, http://www.321know.com/geo.htm, see the learn, practice, play, and explore activities related to perimeter and area.
• Carrie Measures Up by Linda Williams Aber. Kane Press, 2001. A lower-level book that introduces measurement through sizing up everyday objects around the house.
• Game Time! by Stuart J. Murphy. HarperCollins, 2000. A MathStart book to teach time in weeks, days, hours, minutes, and seconds.
• How Big Is a Foot? by Rolf Myller. Yearling, 1991. A book that teaches a king that measurement by his foot and by the foot of the young apprentice result in very different outcomes.
• How Big Is It? A Big Book All About Bigness by Ben Hillman. Scholastic, 2007. A collection of amazing size comparisons to build an understanding of what big really means.
• How Do You Know What Time It Is? by Robert E. Wells. Whitman, 2002. A history of time measurement, including clocks, calendars, and time zones, written specifically for children.
• How Long or How Wide? A Measuring Guide by Brian P. Cleary. First Avenue Editions, 2009. A humorous approach to measuring length and using measuring tools.
• How Tall, How Short, How Far Away? by David Adler and Nancy Tobin. Holiday House, 1999. A book that introduces several measuring systems and presents the need for standard units of measure.
• It’s About Time, Max! and The Long Wait by Kitty Richards. Kane Press, 2000. When a young boy loses his digital watch, he replaces it with an analog watch that he must learn how to read; the partnered story in the book, The Long Wait, tells about estimating time while waiting in line for a thrill ride.
• IXL Math Practice Site, http://www.ixl.com/math/grade/third/, free online practice questions for time, measurement, geometry, and other math concepts.
• Just a Minute! by Jeff Szpirglas. Maple Tree Press, 2009. A fact-filled look at elapsed time of a minute, a day, a month, and a year.
• Keep Your Distance! by Gail Herman. Kane Press, 2001. In the context of sibling rivalry and sharing a room, sisters learn about measurements of distance and time.
• Length (Measuring Up) by Peter Patilla. Belitha Press, 2000. An interesting discussion of measuring systems past and present with examples of unusual lengths.
• Take It to Your Seat Math Centers Grades 3–4 by Jill Norris. Evan-Moor, 2004. Practical ideas for learning centers including perimeter and area.
• Racing Around by Stuart J. Murphy. Steck-Vaughn, 2002. A story of racing around a perimeter.
• Spaghetti and Meatballs for All! by Marilyn Burns. Scholastic, 2008. A delightful way to compare perimeter and area as 32 chairs are arranged and rearranged at a family reunion.
• Super Sand Castle Saturday by Stuart J. Murphy. Steck-Vaughn, 1999. A tale of using nonstandard units of measurement to compare sizes of sand castles.
• Telling Time by Jules Older. Charlesbridge, 2000. A humorous look at what it means to tell time and to learn about smallest units of seconds, minutes, and hours to largest units of weeks, months, years, and more.
• Telling Time, http://www.bbc.co.uk/wales/snapdragon/yesflash/time-1.htm, telling time to the hour.

• View

# Multiple-Choice Items:

Use the clock below for question 1.

1. What is the time shown on the clock?
1. 8:50
2. 9:17
3. 9:43
4. 10:43

1. Anna started piano practice at 5:16. Which clock shows 5:16?

1. Caleb started reading at the time shown on the first clock. Caleb stopped reading at the time shown on the second clock.

How many minutes did Caleb spend reading?

1. 10 minutes
2. 15 minutes
3. 25 minutes
4. 45 minutes

Use the picture below for question 4.

1. What is the perimeter of the rectangle?
1. 7 units
2. 11 units
3. 18 units
4. 22 units

Use the rectangle below for question 5.

1. What is the perimeter of the rectangle?
1. 7 units
2. 11 units
3. 12 units
4. 14 units

Use the rectangle below for question 6.

1. Which shows the area and perimeter of the rectangle?
1. Area = 15 square units, Perimeter = 26 units
2. Area = 26 square units, Perimeter = 26 units
3. Area = 26 square units, Perimeter = 30 units
4. Area = 15 square units, Perimeter = 13 units

Use the rectangle below for question 7.

1. Which sentence is true?
1. The perimeter is less than the area.
2. The perimeter is greater than the area.
3. The perimeter is 16 units, and the area is 16 square units.
4. The perimeter is 16 square units, and the area is 16 units.

Use the rectangle below for questions 8 and 9.

1. What is the perimeter of the rectangle?
1. 24 units
2. 30 units
3. 34 units
4. 36 units
1. What is the area of the rectangle?
1. 24 square units
2. 30 square units
3. 34 square units
4. 36 square units

1. C

2. A

3. C

4. D

5. D

6. C

7. C

8. B

9. D

1. When it is 13 minutes before 4 o’clock, what time is it? Explain how you know. Make a drawing to show your work.

1. How is measuring the length, in feet, of a room on a measuring tape different from measuring the length using your own feet?

1. If a rectangular sidewalk is 1 meter wide and 10 meters long, are the perimeter and area of the sidewalk the same? Explain and draw a picture to show how you know.

# Short-Answer Key and Scoring Rubric:

10. When it is 13 minutes before 4 o’clock, what time is it? Explain how you know. Make a drawing to show your work.

Explanations will vary.

The time is 3:47, and the drawing should show an analog clock that is set to a close approximation of 3:47. The hour hand on the clock should be drawn between 3 and 4, but closer to the 4.

The visual representation may show arrows to count back from the 12 by fives and then 3 more minutes to indicate 13 minutes before the hour. Written explanations are likely to describe the counting back process. Some students may count back to 15 minutes before the hour and then move clockwise 2 minutes forward.

11. How is measuring the length, in feet, of a room on a measuring tape different from measuring the length using your own feet?

Explanations should point out that measuring by a child’s foot will result in a very different total than measuring feet by a standard measuring tape. If a student walks the length of the room and counts his/her steps, the result will probably be a number less than the number of linear feet. If a student measures the length by walking heel-to-toe or using shoes, the unit of measurement is likely shorter than a foot, so the total number of units will be greater.

12. If a rectangular sidewalk is 1 meter wide and 10 meters long, are the perimeter and area of the sidewalk the same? Explain and draw a picture to show how you know.

Explanations will vary.

The perimeter and area of this rectangle will not be the same. The minimal drawing will show a rectangle that is 10 squares long and 1 square wide.

The visual representation may show beans, Xs, or numbers to mark each line segment as a unit of perimeter around the outside of the figure. Likewise, the squares inside the rectangle may show some method used for counting such as circles, shading, or numbers. Written explanations should indicate an understanding that perimeter refers to the units around the figure (22 units) and area refers to the square units inside the figure (10 square units).

Use the scoring rubric below for questions 10–12.

 Points Description 2 The written and visual explanation is thorough and clear, and supported with specific details and mathematical data. The student response shows complete understanding of the mathematics. The student response meets the requirements of the problem. 1 The written and visual explanation is brief and is not supported with specific details or mathematical data. The student response shows partial understanding of the mathematics. The student response partially meets the requirements of the problem. 0 The written or visual explanation is brief or missing or is illogical. The student response shows no understanding of the mathematics. The student response does not meet the requirements of the problem.

# Performance Assessment:

You invite 30 people to a party. You send invitations for a party on Saturday. The invitation shows when the party will begin and end. Then you will draw a picture to show how many tables you will need.

Part 1:Write the invitation with a date and the time to begin and end. Use a calendar to find a date that is on a Saturday. Write the times to have a 2-hour party.

Part 2: Draw a picture to show the tables you need to seat exactly 30 people. Use more than 1

table. The tables can be squares, rectangles, or some of both. Every table must be full.

Also draw a bean, a circle, or an X to show where the chairs will sit. Be sure there is a chair for every unit around every table.

# Performance Assessment key:

Many of the answers will vary based on the current month and year, the tables students choose, and student thinking.

Look for mathematically sound, logical, and reasonable thought processes in student answers.

Part 1: Check a current calendar to make sure the date listed on the invitation is indeed a Saturday. The beginning time of the party should specify a logical time to begin a dinner party, but clarify whether students consider dinner to be an afternoon or evening meal prior to any discussion of whether the time is logical. Students who specify A.M. or P.M. on the invitation indicate an understanding beyond the expectation of this lesson. The ending time of the party must name a time exactly 2 hours from the start.

Part 2: There are various ways to draw and arrange tables to seat exactly 30 guests. Make sure students have drawn 30 circles or Xs to indicate where 30 people will sit. Any unit indicating a blank at the table, including the ends, means that the student did not fulfill the requirements of the task or misunderstood part of the task.

Following are a few ways the tables and 30 chairs could be arranged successfully:

• 3 tables that are each 4 units long and 1 unit wide
• 1 table that is 7 by 1 and 1 table that is 6 by 1
• 5 tables that are 2 units by 1 unit
• many other arrangements are possible

Arrangements that do not meet the criteria:

• 1 table that is 14 units long and 1 unit wide (correct perimeter, but does not fill the requirement to use more than 1 table)
• 2 tables of equal size (cannot seat 15 people at each rectangular table, as each would have a blank unit)
• 8 square tables for 4 (result would leave 2 blank units somewhere)

# Performance Assessment Scoring Rubric:

 Points Description 4 Understanding of the concepts of time and perimeter is clearly evident. Student uses effective strategies to get accurate and reasonable answers. Student clearly shows logical thinking and the steps used to arrive at conclusions. Explanations are clear and supported with specific details and mathematical data. Accurate answers are shown for the invitation and the tables. 3 Understanding of the concepts of time and perimeter is evident. Student uses appropriate strategies to arrive at reasonable answers. Student shows thinking and some steps used to arrive at conclusions. Explanations have some details and mathematical data. Minor errors in computation may result in arrangements that are close. 2 Limited understanding of the concepts of time and perimeter is evident. Student uses strategies that may be ineffective or inaccurate. Steps show some evidence of understanding of how to identify perimeter. Explanations may not be developed with detail or may be difficult to follow. Student may arrive at an answer using flawed reasoning. 1 Lack of understanding of the concepts of time and/or perimeter is evident. Attempts are made to solve the problem, but student is unable to work through steps to arrive at reasonable answers. Information from the problem is not used correctly. Explanation is limited and may contain incorrect reasoning. 0 Complete lack of understanding of the concepts of time and perimeter is evident. No attempts are made to solve the problem. Student shows no understanding of the questions. No explanation is given.
Final 4/12/13