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Measurement and Area

Unit Plan

Measurement and Area

Objectives

Students will learn about measurement and practice measuring various ways. They will investigate and develop an understanding of area. The relationship between the area of a rectangle and the array model of multiplication will be developed and connected to the formula for finding the area of a rectangle. Students will:

  • distinguish between various units of measure.
  • know the different measureable attributes for linear measure.
  • measure length, area, time, and weight.
  • select the correct measuring tool.

Essential Questions

How precise do measurements and calculations need to be?
In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
When is it is appropriate to estimate versus calculate?
Why does “what” we measure influence “how” we measure?
  • What does it mean to estimate or analyze numerical quantities?
  • When is it appropriate to estimate versus calculate?
  • What makes a tool and/or strategy appropriate for a given task?
  • Why does “what” we measure influence “how” we measure?
  • In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted?
  • How precise do measurements and calculations need to be?

Related Unit and Lesson Plans

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.

  • Interactive Web site measurement using ruler with various difficulty levels

http://www.funbrain.com/measure/index.html

  • Interactive Web site measurement to the nearest centimeter

http://www.hbschool.com/activity/length_strength1_centi/

  • Customary measurement conversion: Concentration Game

http://www.quia.com/cc/65838.html

  • Interactive Web site feet and inches conversion

http://www.aaastudy.com/meaadd_ftin.htm#section2

  • Interactive Web site calculation of area: various levels of difficulty ~ choose area

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

  • Interactive Web site: calculate area of irregular/regular shapes

http://www.shodor.org/interactivate/activities/AreaExplorer/

  • Interactive Web site measuring area with immediate feedback

http://www.studyzone.org/testprep/math4/k/squaresp.cfm

  • Interactive Web site where students can estimate length and area. Various levels of difficulty are available and immediate feedback is given.

http://shodor.org/interactivate/activities/Estimator/

  • Interactive Web site to estimate mass using grams/kilograms. Variety of types of objects measured for mass.

http://www.bbc.co.uk/skillswise/e3/numbers/measuresshapespace/weight/game.shtml

  • Interactive Web site where students choose objects based on mass and units of measure for mass

http://www.studyzone.org/testprep/math4/d/massgram4p.cfm

  • Interactive Web site to explore the concept of capacity

http://pbskids.org/cyberchase/find-it/measurement/

  • Estimating length PDF worksheet

http://www.education.com/files/55101_55200/55172/file_55172.pdf

 

Formative Assessment

  • View

    Multiple-Choice Items:

    1. Which item listed below has an attribute that can be measured in miles?

     

          A         a river

          B         an airplane

          C         a car

          D         swimming pool

     

     

    Use the picture below to answer question 2.

     

     

    1. Use your ruler to determine the length of the candle to the nearest inch.

    A          inches

    B         inches

    C          inches

    D         3 inches

     

     

     

    Use the picture below to answer question 3.

    1. Use your ruler to determine the length of the notepad to the nearest inch?

    A         inches

    B          inches

    C         4 inches

    D         inches

     

    1. Which units would be best to measure the length of time a basketball game is played?

     

    A         days

    B         minutes

    C         seconds

    D         weeks

     

    1. Which area would best be measured in square inches?

    A         area of a bedroom floor

    B         area of Pennsylvania

    C         area of a piece of paper

    D         area of a soccer field

     

    1. Which area would best be measured in square yards?

     

    A         area of a football field

    B         area of Pittsburgh, Pennsylvania

    C         area of a butterfly’s wingspan

    D         area of a poster

     

    1. Which unit of measure would be best to weigh a bicycle?

     

    A         grams

    B         ounces

    C         pounds

    D         tons

     

    1. Which item would most likely weigh about 6 ounces?

     

    A         watermelon

    B         sandwich

    C         puppy

    D         textbook

     

    1. Which object would have the least mass?

     

    A         basketball

    B         baseball

    C         beach ball

    D         tennis ball

     

    Multiple-Choice Answer Key:

    1. A

    2. C

    3. C

    4. B

    5. C

    6. A

    7. C

    8. B

    9. C

     

     

     

    Short-Answer Items:

    1. Sarah measured the length of the pencil to the nearest centimeter as 10 centimeters. Her teacher marked her answer wrong. Explain why the teacher marked the answer wrong and what the measurement of the pencil should be.

     

    1. Ron drew a rectangle that was 7 inches by 10 inches. A picture of Ron’s rectangle is shown below but it is not shown to scale.

     

                What is the area of Ron’s rectangle?              square inches

     

                Show or explain how you found the area of Ron’s rectangle.

    ________________________________________________________________________

    ________________________________________________________________________

    ________________________________________________________________________

    ________________________________________________________________________

     

    1. List three classroom items that are longer than 1 meter.

     

    ____________________________               

    ____________________________

    ____________________________

     

    Short-Answer Key and Scoring Rubrics:

    1. Sarah measured the length of the pencil to the nearest centimeter as 10 centimeters. Her teacher marked her answer wrong. Explain why the teacher marked the answer wrong and what the measurement of the pencil should be.

     

     

    Sarah’s answer was marked wrong because the pencil in the drawing is not lined up with the starting point of the ruler. The pencil starts at 2 cm. The actual measurement of the pencil to the nearest centimeter should be less than 10 cm. To find the length of the pencil, you must subtract 2 cm from 10 cm10 cm − 2 cm = 8 cm. Or you could move the ruler so the pencil starts at the starting point. The length of the pencil is 8 cm long.

     

     

    POINTS

    DESCRIPTION

    2
    • Written explanation is thorough, clear, and supported with specific details and mathematical data.
    • Student shows complete understanding of the mathematics.
    • Answer meets the problem requirements.

    1
    • Written explanation is brief and may not be supported with specific details or mathematical data.
    • Student shows partial understanding of the mathematics.
    • Answer partially meets the problem requirements.

    0
    • Written explanation is brief or missing or is illogical.
    • Student shows no understanding of the mathematics.
    • Answer does not meet the problem requirements.

     

     

    1. Ron drew a rectangle that was 7 inches by 10 inches. A picture of Ron’s rectangle is shown below but it is not shown to scale.

    What is the area of Ron’s rectangle? 70 square inches

     

    Show or explain how you found the area of Ron’s rectangle.

    Answers will vary. Possible explanation: I knew that one row has ten units. I do not have to draw in all the squares. I then ask myself how many rows would I need to fill the space. The
    7 along the side tells me I can fill it with 7 rows. So if each row has 10 squares, I can do repeated addition 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70 square inches. A shortcut would be to multiply 7 × 10 = 70 square inches.

     

    POINTS

    DESCRIPTION

    2
    • Calculation of area is accurate.
    • Written explanation is thorough, clear, and supported with specific details and mathematical data.
    • Student shows complete understanding of the mathematics.
    • Answer meets the problem requirements.

    1
    • Minor error may be present in the calculation of area.
    • Written explanation is brief and is not supported with specific details or mathematical data.
    • Student shows partial understanding of the mathematics.
    • Answer partially meets the problem requirements.

    0
    • Calculation of area is incorrect.
    • Written explanation is brief or missing or is illogical.
    • Student shows no understanding of the mathematics.
    • Answer does not meet the problem requirements.

     

     

    1. List three classroom items that are longer than 1 meter.

    Answers will vary.

     

    Points

    Description

    2
    • All items identified have a length longer than one meter.
    • Student demonstrates thorough understanding of estimating length of familiar objects.
    • Answer meets the problem requirements.

    1
    • Two classroom items identified have a length that is longer than one meter.
    • Student demonstrates partial understanding of estimating length of familiar objects.
    • Answer meets the problem requirements.

    0
    • No more than one classroom item identified has a length that is longer than one meter.
    • Student demonstrates no understanding of estimating length of familiar objects.
    • Answer does not meet the problem requirements.

     

     

    Performance Assessment:

    Materials:

    • large bowl of paperclips (or other object weighing approximately 1 gram)
    • string
    • ruler (with inches and centimeters marked)
    • yardstick
    • white paper
    • square centimeter grid paper (M-4-1-2_Square Centimeter Grid Paper.doc)

    On Your Mark, Get Set, Measure!

    You will visit various stations set up around the room. At each station you must complete a measurement task. You will first need to estimate, then record the measurement in a chart. Decide if you overestimated or underestimated and find the difference. Record any difference in the last column.

    Station

    Estimate

    Actual

    + or −

    Big Foot: Estimate the length of your shoe to the nearest centimeter and record. Then trace the bottom of your shoe on a piece of paper and measure the length to the nearest centimeter.

     

     

    _____ cm

     

     

    _____ cm

     

    overestimated by ___

     

    RIGHT ON!

     

    underestimated by ___

     

    Paper Clip Grab: Estimate how many paperclips you can grab with your left hand and record. Then count how many paperclips you grabbed to determine the mass. Remember that a paperclip weighs approximately one gram.

     

     

    _____ g

     

     

    _____ g

     

    overestimated by ___

     

    RIGHT ON!

     

    underestimated by ___

    Take It in Stride: Estimate the length of your stride to the nearest inch and record. Your stride is the length between the back of your front foot to the tip of your back foot. Have a partner cut a piece of string that distance. Measure the length of your stride to the nearest  inch.

     

     

    _____ in.

     

     

    _____ in.

     

    overestimated by ___

     

    RIGHT ON!

     

    underestimated by ___

    Give Me a Hand: Estimate the area of your hand when your fingers are all touching to the nearest square centimeter and record. Then trace your hand (with your fingers touching) on a piece of centimeter grid paper. Determine the area to the nearest centimeter.

     

     

    _____ sq cm

     

     

    _____ sq cm

     

     

    overestimated by ___

     

    RIGHT ON!

     

    underestimated by ___

    On the Line: On a piece of paper draw a straight line that you think measures  inches. Do NOT use a ruler. Then measure the line to the nearest  inch.

     

     

     in.

     

     

    _____ in.

     

     

    overestimated by ___

     

    RIGHT ON!

     

    underestimated by ___

     

     

     

    1) Using your chart, what observations can you make about how you estimated these measurements? Explain. ___________________________________________________

    ________________________________________________________________________

    ________________________________________________________________________

     

    2) Identify a real-world situation where you would need to find an actual measurement and explain why.

    ________________________________________________________________________

    ________________________________________________________________________

     

    3) Identify a real-world situation where it would be appropriate to find an estimated measurement and explain why.

    ________________________________________________________________________

    ________________________________________________________________________

     

    4) What are two units of measure for length that are not listed in the chart? _____________

    ________________________________________________________________________

     

    5) Pick one of the units of measure listed in the chart, and identify one object that you could measure using that unit.

     

    ________________________________________________________________________

     

    6) What are two units of measure for mass that are not listed in the chart? _____________

    ________________________________________________________________________

     

    7) Pick one of the units of measure listed in the chart, and identify one object that you could measure using that unit.

     

    ________________________________________________________________________

     

     

     

    Performance Assessment Answer Key:

     

    Answers will vary for the chart.

     

    1) Using your chart, what observations can you make about how you estimated these measurements? Explain.

    Answers will vary. Students may notice that they overestimated with one unit of measure and underestimated with another unit of measure. Students may mention that they have a good understanding of inches but not necessarily of centimeters.

     

    2) Identify a real-world situation where you would need to find an actual measurement and explain why.

    Answers will vary. If you need to measure the length of the foundation of a house, you want an accurate measurement so that the house is stable and the walls can be properly built.

     

    3) Identify a real-world situation where it would be appropriate to find an estimated measurement and explain why.

    Answers will vary, e.g., If you need to determine if you have enough material.

     

    4) What are two units of measure for length that are not listed in the chart?

    Answers will vary. Two examples of units of measure are feet and miles.

     

    5) Pick one of the units of measure listed in the chart, and identify one object that you could measure using that unit. Answers will vary. With feet, you could measure the length a car.

     

    6) What are two units of measure for mass that are not listed in the chart?

    Answers will vary. Two examples of units of measure are pounds and tons.

     

    7) Pick one of the units of measure listed in the chart, and identify one object that you could measure using that unit.

    Answers will vary. With pounds, you could measure the weight of a large bag of dog food.

     

     

     

    Performance Assessment Scoring Rubric:

     

    Points

    Description

    4
    • Displays advanced understanding of the questions, mathematical concepts, and processes related to measurement.
    • Uses refined mathematical reasoning when estimating measurements.
    • Provides thorough and clear written explanations.
    • Meets all assessment requirements with accuracy and thoroughness.

    3
    • Displays good understanding of the questions, mathematical concepts, and processes related to measurement.
    • Uses effective mathematical reasoning when estimating measurements.
    • Provides clear written explanations.
    • Meets or attempts all assessment requirements with no major mathematical errors.

    2
    • Displays partial understanding of the questions, mathematical concepts, and processes related to measurement.
    • Uses some mathematical reasoning when estimating measurements.
    • Provides written explanations but they lack some detail.
    • Partially meets the assessment requirements with a few minor mathematical errors or one major mathematical error.

    1
    • Displays little understanding of the questions, mathematical concepts, and processes related to measurement.
    • Shows limited evidence of mathematical reasoning when estimating measurements.
    • Provides written explanations but they are incomplete and lack detail.
    • Does not meet several of the assessment requirements.
    • Makes several major errors.

    0
    • Displays no understanding of the questions, mathematical concepts, and processes related to measurement.
    • Provides estimations which are more like random guesses.
    • Does not provide written explanations or explanations are illogical.
    • Does not attempt or does not finish a substantial portion of the assessment requirement.

     

Final 05/10/2013
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