Distance and Measurement
Distance and Measurement
Objectives
In this unit, students will examine distance and other measurements. Students will:
- study distance via multiple approaches.
- examine estimation versus exact.
- convert between Metric units.
- convert between Customary units.
- apply understanding of distance and conversion of measurements.
Essential Questions
- In what realms does distance appear throughout mathematics?
- How does distance relate to other mathematical topics?
- How can distance and conversion of distance and other measurements be applied to real-world problems?
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.
- How Hot Is the Sun?
http://coolcosmos.ipac.caltech.edu/cosmic_kids/AskKids/suntemp.shtml
- The Nearest Star
http://heasarc.gsfc.nasa.gov/docs/cosmic/nearest_star_info.html
- Circumference of a circle
http://www.mathgoodies.com/lessons/vol2/circumference.html
http://www.nctm.org/standards/content.aspx?id=26770
Formative Assessment
-
View
Multiple-Choice Items:
1. Which of the following is the correct measurement for the line segment?
A
1.5 cm
B
2.5 cm
C
3.7 cm
D
4.4 cm
2. Which represents approximately 30% of the distance around a circle with a radius of 7 feet?
A
13
B
21
C
42
D
44
3. Which is the correct perimeter of a rectangle with coordinates: (−5, 8), (5, 8), (5, −8), (−5, −8)?
A
12
B
22
C
48
D
52
4. How many km are in 4.19 cm?
A
41.9
B
0.0419
C
0.419
D
0.0000419
5. What is 48 inches in yards?
A
B
4
C
12
D
144
6. How many pints are equal to 32 fluid ounces?
A
B
2
C
4
D
8 7. Which of the following estimation is not appropriate?
A
temperature of the surface of the Sun in Celsius
B
circumference of the Earth
C
cabinet measurement
D
number of minutes it takes to finish homework
8. Which real world plots do translate into actual distances (to be found using the distance formula)?
A
celestial points
B
longitude and latitude coordinates
C
astronomical plots of sun and Earth
D
local rain on weather map
9. When might capacity units be used?
A
measuring the length of a parking space
B
measuring how much soda a soda bottle contains
C
measuring the mass one occupies
D
measuring the weight of the family dog
Multiple-Choice Answer Key:
1. C
2. A
3. D
4. D
5. A
6. B
7. C
8. D
9. B
Short-Answer Items:
10. Find the length of the missing leg in the triangle shown below. Show the process, using the Pythagorean Theorem and the Distance Formula.
11. Convert 2.13 m to mm, cm, and km.
12. Provide three examples where estimation is preferred when converting.
Short-Answer Key and Scoring Rubrics:
10. Find the length of the missing side in the triangle shown below. Show the process, using the Pythagorean Theorem and the Distance Formula.
Points
Description
2
The student correctly finds the length of the missing leg (6) AND:
- Shows the correct process for finding the length via the Pythagorean Theorem.
- Shows the correct process for finding the length via the Distance Formula.
1
The student correctly writes one or two of the three answers.
0
The student does not provide an answer or incorrectly answers all three parts.
11. Convert 2.13 m to mm, cm, and km.
Points
Description
2
The student correctly writes:
- 2.13 m = 2130 mm
- 2.13 m = 213 cm
- 2.13 m = .00213 km
1
The student correctly writes one or two of the three answers.
0
The student does not provide an answer or incorrectly answers all three parts.
12. Provide three examples where estimation is preferred when converting.
Acceptable answers vary. Representative answer: When the result of the computation is close to a whole number, rounding and estimating are appropriate. For example, when converting 8 meters to inches, 39.37 inches per meter × 8 meters = 314.96 inches. When rounded, 8 meters » 315 inches.
Points
Description
2
The student provides three acceptable examples.
1
The student provides one or two acceptable examples.
0
The student does not provide an example.
Performance Assessment:
Which distance or conversion topic is of most interest to you? Present the topic in the form of an electronic document for placement in your e-portfolio. The file must include:
- statement of the topic you are describing.
- three illustrations/diagrams with explanations.
- explanation relating your topic to a real-world example.
Performance Assessment Scoring Rubric:
Points
Description
4
The assessment includes:
- statement of the topic you are describing.
- three illustrations/diagrams with explanations.
- explanation relating topic to a real-world example, all of which are mathematically correct.
3
The assessment includes four of the five components, all of which are mathematically correct.
2
The assessment includes three of the five components, all of which are mathematically correct.
1
The assessment includes one or two of the five components, both of which are mathematically correct.
0
The student does not present any parts of the assessment or provides incorrect information for all five parts.
DRAFT 10/10/2011
