Mathematics
Grade 10
15 min
Conversion tables - customary units
Conversion tables - customary units
What you'll learn
- Identify the correct conversion factor between different customary units of length (inches, feet, yards, miles) with 80% accuracy on a worksheet.
- Solve word problems involving conversions between customary units of weight (ounces, pounds, tons) by applying the appropriate conversion factor and showing all work, achieving at least 70% accuracy.
- Explain the relationship between customary units of volume (fluid ounces, cups, pints, quarts, gallons) using a conversion table as a reference, demonstrating understanding in a written explanation of at least 3 sentences.
- Apply learned conversion skills to convert measurements from one customary unit to another within a real-world scenario (e.g., a recipe, a building project), and justify the reasonableness of their answer.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the standard customary units of length (inch, foot, yard, mile).
Construct and use conversion factors from a conversion table to change between customary units.
Convert all side lengths of a right triangle to a single, consistent customary unit before performing calculations.
Apply the Pythagorean theorem to right triangles with side lengths given in different customary units.
Calculate trigonometric ratios for right triangles after converting side lengths to a common unit.
Solve multi-step word problems involving right triangles and customary unit conversions.
Ever tried to build a ramp and realized your measurements are in feet but the wood is sold by the inch? 📏 Let's see how to make those units work together!
This tutorial connects you...
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Key Concepts & Vocabulary
TermDefinitionExample
Customary Units of LengthThe system of measurement for length primarily used in the United States. The most common units are inches (in), feet (ft), yards (yd), and miles (mi).A standard ruler is 1 foot long, which is also 12 inches long.
Conversion TableA chart that shows the equivalent values for different units of measurement within the same system.A table showing that 1 yard = 3 feet, and 1 foot = 12 inches.
Conversion FactorA ratio (or fraction) derived from a unit equality, used to convert a measurement from one unit to another. The value of the ratio is always equal to 1.To convert feet to inches, you can use the conversion factor (12 inches / 1 foot).
Dimensional AnalysisA problem-solving method that uses the fact that any number or expression can be multipli...
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Core Formulas
Fundamental Length Conversions
1 \text{ foot} = 12 \text{ inches} \\ 1 \text{ yard} = 3 \text{ feet} \\ 1 \text{ mile} = 5280 \text{ feet}
These are the foundational equalities for the customary system of length. Memorize these to create conversion factors for any length conversion problem.
Conversion Factor Setup
\text{Original Quantity} \times \frac{\text{New Unit}}{\text{Original Unit}} = \text{New Quantity}
To convert, multiply your original measurement by a fraction. The denominator of the fraction must have the unit you are trying to cancel, and the numerator must have the unit you want to end up with.
Pythagorean Theorem
a^2 + b^2 = c^2
In a right triangle with legs 'a' and 'b' and hypotenuse 'c', this formula relates the side len...
4 more steps in this tutorial
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Challenging
A rectangular box has a length of 4 feet, a width of 1 yard, and a height of 24 inches. What is the length of the space diagonal (the longest interior diagonal) in feet?
A.√29 feet
B.√24 feet
C.√21 feet
D.7 feet
Challenging
From the top of a lighthouse 44 yards high, the angle of depression to a boat at sea is 45°. How far is the boat from the base of the lighthouse, in miles? (Note: tan(45°) = 1)
A.0.025 miles
B.0.05 miles
C.0.1 miles
D.0.25 miles
Challenging
A hiker walks 880 yards due south, then turns and walks 0.75 miles due east, forming a right-angled path. If the hiker can walk at a constant speed of 3 miles per hour, how many minutes will it take them to walk this entire path?
A.20 minutes
B.22.5 minutes
C.25 minutes
D.30 minutes
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Frequently asked questions
What grade level is "Conversion tables - customary units"?
Conversion tables - customary units is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Conversion tables - customary units?
You'll be able to: Identify the correct conversion factor between different customary units of length (inches, feet, yards, miles) with 80% accuracy on a worksheet; Solve word problems involving conversions between customary units of weight….
Is "Conversion tables - customary units" 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 Conversion tables - customary units?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.