Mathematics
Grade 11
15 min
Compare and convert customary units of length
Compare and convert customary units of length
What you'll learn
- Identify the correct customary unit of length (inches, feet, yards) to measure common objects with 80% accuracy.
- Solve conversion problems between inches and feet using visual aids and manipulatives with 75% accuracy.
- Explain the relationship between feet and yards in their own words, demonstrating understanding with at least two examples.
- Apply knowledge of customary units to solve real-world measurement problems involving length, such as comparing the length of two objects, with 70% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Recall and apply the primary conversion factors for customary units of length (inches, feet, yards, miles).
Use dimensional analysis to perform single and multi-step unit conversions.
Convert all length measurements in a trigonometric word problem to a consistent unit before solving.
Solve right-triangle problems involving angles of elevation and depression where initial measurements are given in mixed customary units.
Analyze how inconsistent units would invalidate a trigonometric ratio and lead to an incorrect solution.
Calculate arc lengths and sector areas, ensuring the radius and resulting length are in compatible or specified units.
How can you find the angle of the sun's rays if a 1,454-foot-tall skyscraper casts a shadow that is 0.25 miles lo...
2
Key Concepts & Vocabulary
TermDefinitionExample
Customary Units of LengthThe system of measurement for length predominantly used in the United States. The primary units, from smallest to largest, are inches (in), feet (ft), yards (yd), and miles (mi).A standard football field is 100 yards long.
Conversion FactorA ratio equal to one, used to convert a measurement from one unit to another. It is formed from the equivalence statement between two units, such as '1 foot = 12 inches'.The conversion factor to convert feet to inches is (12 in / 1 ft).
Dimensional AnalysisA problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is used to convert units by multiplying with a series of conversion factors, ensuring the original units cancel out...
3
Core Formulas
Fundamental Conversion Equivalencies
1 \text{ foot} = 12 \text{ inches} \\ 1 \text{ yard} = 3 \text{ feet} \\ 1 \text{ mile} = 1760 \text{ yards} \\ 1 \text{ mile} = 5280 \text{ feet}
These core equivalencies are the basis for all conversion factors. Memorizing them is essential for efficient problem-solving.
Dimensional Analysis Formula
\text{Given Quantity} \times \frac{\text{Desired Unit}}{\text{Equivalent Given Unit}} = \text{Result in Desired Unit}
This is the structure for applying a conversion factor. The 'Given Unit' in the denominator cancels the unit of the 'Given Quantity', leaving the 'Desired Unit'.
Right Triangle Trigonometric Ratios (SOH CAH TOA)
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \quad \cos(\theta) = \...
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Challenging
From a point on the ground 1/8 of a mile from the base of a building, the angle of elevation to the bottom of a flagpole on the roof is 20°. The angle of elevation to the top of the flagpole is 22°. What is the height of the flagpole itself, to the nearest inch?
A.27 inches
B.320 inches
C.240 inches
D.27 feet
Challenging
A ramp is exactly 10 yards long and rises to a platform. The angle of elevation of the ramp is 15°. What is the height of the platform in inches, to the nearest tenth of an inch?
A.310.6 inches
B.34.9 inches
C.93.2 inches
D.103.5 inches
Challenging
A student measures the height of a tree as 50 feet and the horizontal distance to the tree as 20 yards. They incorrectly calculate the angle of elevation using tan(θ) = 50/20. Another student correctly converts units before calculating. What is the approximate difference between the incorrect angle and the correct angle?
A.5.2°
B.28.4°
C.39.8°
D.68.2°
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Frequently asked questions
What grade level is "Compare and convert customary units of length"?
Compare and convert customary units of length is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Compare and convert customary units of length?
You'll be able to: Identify the correct customary unit of length (inches, feet, yards) to measure common objects with 80% accuracy; Solve conversion problems between inches and feet using visual aids and manipulatives with 75% accuracy; Explain….
Is "Compare and convert customary units of length" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Compare and convert customary units of length?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.