Lesson 2 of 8 · Grades 3 to 5
Length in customary units
Customary length uses inches, feet, yards and miles. These units do not step in tens, so each one has its own fact to remember. This lesson shows you those facts and how to read an inch ruler.
Inches on a ruler
The customary system of length starts with the inch (in). An inch is about the width of an adult thumb at the joint. Twelve inches make one foot (ft), and rulers in this system usually show a foot split into twelve inches, with half inches and quarter inches marked in between. The eraser in the picture below runs from the 3 inch mark to the 9 inch mark, so it is 6 inches long.
Feet, yards and miles
Customary units do not step in tens, so each step has its own fact. Twelve inches make a foot. Three feet make a yard (yd), so a yard is 36 inches. A mile (mi) is much longer: 5,280 feet, which is the same as 1,760 yards. To make the size real, a loaf of bread is about a foot long, a guitar is about a yard long, and a mile is about the length of twenty football fields laid end to end.
Choosing a sensible unit
Match the unit to the size of the thing you are measuring. Inches suit small objects: a paperclip is about 1 in long, and a phone is about 6 in tall. Feet suit people and rooms: a tall adult is about 6 ft, and a table is about 3 ft high. Yards suit fields and fabric, and miles suit distances between places. A walk to a friend might be 1 mi, and a drive to the next town might be 20 mi.
Because the facts are not based on ten, estimates help you catch a wrong answer. One yard is a little less than a metre, so a room that is 4 m long is about 4 and a half yards. A mile is longer than a kilometre, so a 5 mi trip is a little over 8 km.
Feet and inches together
Customary lengths are often written in two units, especially heights. A child might be 4 ft 8 in tall, and a doorway might be 6 ft 8 in high. To change 5 ft 4 in into inches, work with the foot part first: 5 ft is 5 × 12 = 60 in. Then add the extra inches: 60 + 4 = 64 in. Going the other way, share the inches into groups of twelve. The length 46 in is 3 ft 10 in, because 46 = 36 + 10 and 36 in is 3 ft.
Watch out for this
A decimal point does not belong between feet and inches. A height of 5 ft 4 in can be written 64 in, or 5 ft 4 in, but it must not be written 5.4 ft. The 4 in is part of the next foot, and a foot holds 12 inches, not 10. If you see 5.4 ft, the 0.4 ft is about 4.8 in, which is nearly 5 in, so 5.4 ft is close to 5 ft 5 in.
Worked example
A fence rail is 2 yd 2 ft long. Write the length in feet, then in inches.
Step 1: change the yards to feet. 1 yd = 3 ft, so 2 yd = 6 ft.
Step 2: add the extra feet. 6 ft + 2 ft = 8 ft.
Step 3: change the feet to inches. 1 ft = 12 in, so 8 ft = 8 × 12 = 96 in.
Step 4: check the size. The rail is a little longer than a tall person, and 8 ft is about 2 and a half metres, which fits.
Answer: 8 ft, which is 96 in.
Remember
- Twelve inches make one foot.
- Three feet make one yard, and a yard is 36 inches.
- One mile is 5,280 feet, or 1,760 yards.
- Write heights as feet and inches, not as one decimal number.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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How many inches are in one foot?
Show answer
12 inches. A one foot ruler is divided into twelve equal inches.
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How many feet are in two yards?
Show answer
6 feet. Each yard has 3 feet, so 2 × 3 = 6 ft.
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A doorway is 7 feet tall. How many inches is that?
Show answer
84 inches. 7 × 12 = 84 in.
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Which is longer, 1 yard or 30 inches?
Show answer
1 yard. It is 36 in, which is longer than 30 in.
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A trail is 2 miles long. How many yards is that?
Show answer
3,520 yards. Each mile is 1,760 yd, and 2 × 1,760 = 3,520 yd.
Puzzle · Ruler marks
Puzzle time
A ribbon starts at the 3 inch mark on a 12 inch ruler and ends at the 9 inch mark. How long is the ribbon?
Show a hint
Subtract the start mark from the end mark: 9 - 3.
Show the answer
Answer: 6 in. The ribbon starts at 3 in and ends at 9 in. 9 - 3 = 6, so the ribbon is 6 inches long.