Grade 4

Customary weight units

How heavy is a pound, and how can you tell whether a tent of 3 pounds or a tent of 44 ounces is the heavier one?

You need

The customary systemGrade 4

Where you are 3 in Mass and weight

Measurement12

Mass and weight3

Mass is not the same as weight

Customary weight units

Metric mass units

Why this exists

Varun is packing for a two-night hiking trip. He will carry everything on his back for hours, so what matters is not how much room each thing takes but how heavy it is. A big, puffy sleeping bag can be light. A small bottle of water can be heavy. His eyes cannot tell him which is which; a scale can.

To write down how heavy something is, he needs a unit of weight. In the United States the units of weight are the ounce, the pound and the ton. They belong to the family met in The customary system. This lesson looks closely at those three units: how heavy each one feels, how to read a scale, how to pick a sensible unit, and how to compare and add weights that are written in different units.

This lesson takes two days. Day 1 (Examples 1 to 3) is the three units, a picture for each, and reading a scale. Day 2 (Examples 4 to 7) is comparing, ordering and adding weights.

Definition

Day 1: the three units of weight

The weight of an object is how heavy it is: how hard it pulls down on your hand or on a scale. Weight is not size. Two things can take up the same room and have very different weights.

The customary units of weight, from lightest to heaviest:

unit	short form	equals
ounce	\text{oz}	the smallest unit here
pound	\text{lb}	16 ounces
ton	(none)	2{,}000 pounds

These two facts are exact:

1 \text{ lb} = 16 \text{ oz} \qquad 1 \text{ ton} = 2{,}000 \text{ lb}

The short form \text{lb} comes from libra, an old Roman unit of weight.

A fluid ounce is not a unit of weight. It measures capacity, how much a container holds, and it belongs with the cup and the gallon in Customary capacity units.

Intuition

Day 1: a picture for each unit

A unit is easier to use when you can feel how heavy it is. Keep an everyday object in mind for each one, a benchmark. Benchmarks are always “about”: slices and loaves differ, but a benchmark tells you whether a weight makes sense.

unit	about as heavy as
ounce	a slice of bread, which is about 1 ounce
pound	a loaf of bread, which is about 1 pound; a pint of water is also about 1 pound
ton	a small car, which weighs between 1 and 2 tons

Two more pictures help on a hiking trip and at a market. A full gallon jug of water weighs about 8 pounds. A medium apple weighs about 6 ounces, a bit less than half a pound.

Choosing a unit. Pick the unit closest to the size of the thing, so the number is easy to picture. Things lighter than a loaf of bread are weighed in ounces. Things you can lift are weighed in pounds. Cars, trucks and loads of hay are weighed in tons.

Weight is how heavy, not how big. A sleeping bag that fills half a backpack weighs about as much as two loaves of bread. A gallon jug of water is smaller and weighs about four times as much. What decides weight is how much stuff is packed inside and what that stuff is, so size alone can fool you.

Reading a scale. A scale has numbered marks, often one for each pound, and smaller marks between them. Before reading it, work out what one small space is worth: the numbered step is shared out equally among the spaces. Finding the value of one space is the subject of Measuring tools and reading their scales. With a weight scale the step between pound marks is 16 ounces, so the spaces divide 16.

Figure 1Each pound is cut into 8 equal spaces, so each space is 16 \div 8 = 2 ounces. The pointer reads 2 pounds 6 ounces.

Results

Day 2: comparing and adding weights

Bigger unit, smaller number. A pound is 16 times as heavy as an ounce, so the same bag of apples takes 16 times as many ounces as pounds to describe. The heavier the unit, the smaller the number.

Compare in one unit. To compare two weights written in different units, first write both in the same unit, then compare the numbers. Usually the smaller unit is easiest, since every amount then becomes a whole number:

3 \text{ lb} = 3 \times 16 \text{ oz} = 48 \text{ oz}

Changing a weight from one unit to another, with a table of values, is the work of Customary conversions. Here it is used only as one step on the way to a comparison.

Add like units. To add weights given in pounds and ounces, add the pounds to the pounds and the ounces to the ounces. If the ounces reach 16 or more, every 16 of them make one more pound.

Why it is true

Why the numbers alone cannot be compared. The number in a weight counts units. “44 ounces” counts 44 small steps of weight, and “3 pounds” counts 3 big ones. Saying 44 is more than 3 compares counts of different things, like saying 44 pennies is more money than 3 dollar bills. Once both weights count the same unit, the larger count is the heavier weight.

Why 3 pounds is 48 ounces. Each pound is 16 ounces, so 3 pounds is 3 groups of 16 ounces, which is 3 \times 16 = 48 ounces.

Why 16 ounces can be traded for a pound. That is what a pound is: 16 ounces together weigh exactly one pound. Trading them leaves the total weight the same, just as trading ten ones for a ten leaves a number the same.

Why bigger things are not always heavier. Weight comes from how much matter is in an object and how hard the Earth pulls on it. A sleeping bag is mostly trapped air with a little fabric and stuffing. A jug of water is packed full of water. So the smaller jug holds more matter and is heavier.

Worked examples

Examples 1 to 3 go with Day 1, and Examples 4 to 7 with Day 2.

Example 1

Units for the packing list

Varun lists things to weigh before his hike: a granola bar, his tent, a large bottle full of water, a small box of matches, and the farm truck that drove his group to the trailhead. Which unit suits each one: ounces, pounds or tons?

Solution

Compare each one with the benchmarks.

A granola bar is lighter than a loaf of bread, about as heavy as one or two slices, so ounces suit it.
A hiking tent weighs as much as a few loaves of bread, so pounds suit it.
A large bottle of water is something you lift, heavier than a loaf of bread, so pounds suit it. A bottle holding about a quart of water weighs about 2 pounds.
A small box of matches is far lighter than a slice of bread, less than an ounce, so ounces suit it.
A truck is heavier than a small car, so tons suit it.

In each case the unit was chosen by asking which benchmark the object is closest to.

Example 2

Bigger is not heavier

Cem’s sleeping bag fills half his backpack and weighs about 2 pounds. His gallon jug of water fits in a side pocket and weighs about 8 pounds. Which one pulls harder on his shoulders, and by about how much?

Solution

Weight is how heavy, so compare the weights, not the sizes. Both are in pounds, so the numbers can be compared directly: 8 is greater than 2. The water is heavier, even though it is smaller. The difference is

8 - 2 = 6 \text{ pounds}

so the jug weighs about 6 pounds more, about the weight of six loaves of bread. Looking at the pack would have suggested the opposite answer, which is why weight is measured with a scale and not judged by size.

Example 3

Reading the farm market scale

At the farm market, Vasyl puts a bag of tomatoes on the scale in Figure 1. The scale is marked in pounds from 0 to 4, with 8 equal spaces between pound marks. The pointer is 3 small spaces past the 2. How much do the tomatoes weigh? Is it more or less than \displaystyle 2\frac{1}{2} pounds?

Solution

First find what one space is worth. From one pound mark to the next is 1 pound, which is 16 ounces, shared equally among 8 spaces:

16 \div 8 = 2 \text{ ounces per space}

The pointer has passed the 2 pound mark and 3 more spaces, which is 3 \times 2 = 6 ounces. So the tomatoes weigh 2 pounds 6 ounces.

Half a pound is 16 \div 2 = 8 ounces, which is 4 spaces, the middle tick between 2 and 3. The pointer is only 3 spaces past the 2, short of the middle tick, so the tomatoes weigh less than \displaystyle 2\frac{1}{2} pounds, by 2 ounces.

Example 4

Which tent is heavier

Cem’s tent weighs 3 pounds. Varun’s tent weighs 44 ounces. Which is heavier, and by how much?

Solution

The units differ, so the numbers 3 and 44 cannot be compared as they stand. Write the pounds in ounces. Each pound is 16 ounces:

3 \text{ lb} = 3 \times 16 \text{ oz} = 48 \text{ oz}

Now both weights count ounces: 48 against 44. Since 48 > 44, Cem’s tent is heavier, by

48 - 44 = 4 \text{ ounces}

Figure 2Counted in ounces, 3 pounds is 48 cells and the other tent is 44. The shaded 4 cells are the difference.

The tent with the smaller number is the heavier one, because its number counts the heavier unit.

Example 5

Ordering bags of apples

Vasyl weighs four bags of apples at the market. They weigh 2 pounds 3 ounces, 37 ounces, \displaystyle 2\frac{1}{2} pounds and 34 ounces. Put them in order from lightest to heaviest.

Solution

Write every weight in ounces, the smallest unit used.

2 pounds 3 ounces is 2 \times 16 + 3 = 32 + 3 = 35 ounces.
37 ounces is already in ounces.
\displaystyle 2\frac{1}{2} pounds is 2 pounds and half a pound. Half of 16 ounces is 8 ounces, so it is 32 + 8 = 40 ounces.
34 ounces is already in ounces.

In ounces the bags weigh 35, 37, 40 and 34. From lightest to heaviest:

34 \text{ oz} < 2 \text{ lb } 3 \text{ oz} < 37 \text{ oz} < 2\tfrac{1}{2} \text{ lb}

Each answer is written back in the unit it was given in, since those are the labels on the bags.

Example 6

Adding up the pack

Varun’s packing list says: sleeping bag 2 pounds 4 ounces, stove and pot 1 pound 14 ounces, food 4 pounds 10 ounces. What do the three weigh together?

Solution

Add the pounds to the pounds and the ounces to the ounces, the way ones are added to ones and tens to tens:

\begin{aligned} \text{pounds: } & 2 + 1 + 4 = 7 \\ \text{ounces: } & 4 + 14 + 10 = 28 \end{aligned}

That gives 7 pounds 28 ounces, which is true but not finished: 28 ounces holds a whole pound. Since 28 = 16 + 12, trade 16 of the ounces for 1 pound, leaving 12 ounces:

7 \text{ lb } 28 \text{ oz} = 8 \text{ lb } 12 \text{ oz}

The three things weigh 8 pounds 12 ounces. Check in ounces: the items are 36, 30 and 74 ounces, which add to 140, and 8 \times 16 + 12 = 128 + 12 = 140.

Example 7

A ton of pumpkins

Vasyl’s family grows pumpkins that weigh about 20 pounds each. About how many pumpkins make one ton? Their truck brings 1{,}500 pounds of pumpkins to the market. Is that more or less than a ton, and about how many more pumpkins would make a full ton?

Solution

A ton is exactly 2{,}000 pounds. The question is how many groups of 20 pounds fit in 2{,}000 pounds. Since 20 \times 100 = 2{,}000,

2{,}000 \div 20 = 100

so about 100 pumpkins make a ton.

The load is 1{,}500 pounds, and 1{,}500 < 2{,}000, so it is less than a ton. It is short by

2{,}000 - 1{,}500 = 500 \text{ pounds}

and 500 \div 20 = 25, so about 25 more pumpkins would make a ton. The answers are “about” because each pumpkin is only about 20 pounds. The ton itself is exact.

Boundaries

Benchmarks are approximate; the unit facts are exact. A loaf of bread is about a pound, and loaves vary. A pound is exactly 16 ounces and a ton exactly 2{,}000 pounds.
An ounce is not a fluid ounce. Ounces weigh; fluid ounces measure how much a container holds. A label of 24 fluid ounces on a water bottle tells how much water fits, not how heavy it is.
Compare weights only with weights. A weight cannot be compared with a length or a capacity: asking whether 3 pounds is more than 3 feet has no answer.
This ton is the United States ton. The British long ton and the metric ton are heavier; see The customary system.
Weight depends on where you are. On the Moon the same tent would pull down much less, though it holds just as much matter. That difference between weight and mass is the subject of Mass is not the same as weight. Everyday weights in this lesson are weights on Earth.

Where this goes next

Customary conversions turns any number of pounds into ounces, or ounces back into pounds and ounces, using the facts here. Multi-step problems with unit conversions uses weights as one step in longer problems. The metric system measures the same heaviness with grams and kilograms in Metric mass units, where every step is a power of ten. Comparing two objects on a balance, without any numbers at all, is Balancing to compare mass.

Exercises

Day 1: the units, benchmarks and scales

Which of these are units of weight: ounce, foot, ton, quart, pound, fluid ounce?
Put these in order from lightest to heaviest: a pound, a ton, an ounce.
Choose ounces, pounds or tons for each: (a) a carrot; (b) a sack of potatoes at the market; (c) a farm tractor; (d) a packed hiking backpack; (e) one strawberry; (f) a truckload of hay.
Choose the sensible weight: (a) a watermelon: 15 ounces, 15 pounds or 15 tons; (b) a packet of trail mix: 6 ounces, 6 pounds or 6 tons; (c) a farm tractor: 4 ounces, 4 pounds or 4 tons; (d) a sleeping bag: 2 ounces, 2 pounds or 2 tons.
Each label has the wrong unit. Fix it by changing only the unit: (a) a tomato weighs 6 pounds; (b) a tent weighs 5 tons; (c) a wagon piled with hay weighs 2 pounds.
Varun’s trail mix comes in packs of 4 ounces each. How many packs weigh 1 pound?
A scale has each pound cut into 4 equal spaces. How many ounces is one space? The pointer is 3 spaces past the 1 pound mark. What is the weight?
A scale has each pound cut into 16 equal spaces. The pointer is 9 spaces past the 2 pound mark. What is the weight?
A potato scale has marks labeled 0, 10, 20 and 30 pounds, with 5 equal spaces between labels. How many pounds is one space? The pointer is 3 spaces past 20. What is the weight?
A basketball and a bowling ball are about the same size. Are they about the same weight? What does this say about judging weight by looking?
Cem’s water bottle is labeled 24 fluid ounces. He says the label tells him the bottle weighs 24 ounces. What does the label really tell him?

Day 2: comparing, ordering and adding

Which is heavier, 4 pounds or 60 ounces? By how much?
Which is heavier, 1 pound 10 ounces or 30 ounces? By how much?
Which is heavier, 1 ton or 1{,}900 pounds? By how much?
Put in order from lightest to heaviest: 3 pounds, 45 ounces, 2 pounds 14 ounces, \displaystyle 3\frac{1}{2} pounds.
A jar of honey at the market weighs 12 ounces. Do 3 jars weigh more or less than 2 pounds? By how much?
Cem packs a lantern of 1 pound 2 ounces, a first-aid kit of 9 ounces and a rope of 13 ounces. What is their total weight in pounds and ounces?
Varun’s tent weighs 4 pounds, his sleeping bag 2 pounds 12 ounces and his food 3 pounds 6 ounces. What do they weigh together, in pounds and ounces?
Hay at the farm is sold in bales of about 50 pounds. About how many bales make a ton?
A farm truck can carry 2 tons. Vasyl has loaded 3{,}200 pounds of potatoes. How many more pounds can it carry?
Varun’s pack weighs 11 pounds 8 ounces. He adds a gallon jug of water (about 8 pounds) and a bag of trail mix weighing 12 ounces. About how much does the pack weigh now?
Without working out any numbers, which is heavier: 7 pounds or 7 ounces? 7 tons or 7 pounds? Explain.

Reasoning

Vasyl says 40 ounces is heavier than 3 pounds because 40 is bigger than 3. Is he right? Explain.
A truck’s weight is a small number in tons and a large number in pounds. Explain why, without choosing a truck.
Which is heavier, a ton of feathers or a ton of rocks? Which takes up more room? Explain.

Answers

Ounce, ton and pound. A foot is a length, a quart is a capacity, and a fluid ounce is a capacity too, despite its name.
An ounce, then a pound, then a ton, since a pound is 16 ounces and a ton is 2{,}000 pounds.
(a) Ounces, since a carrot is lighter than a loaf of bread. (b) Pounds. (c) Tons, since a tractor is heavier than a small car. (d) Pounds. (e) Ounces. (f) Tons.
(a) 15 pounds. (b) 6 ounces. (c) 4 tons. (d) 2 pounds. A 15-ounce watermelon would be lighter than a loaf of bread, and a 2-ton sleeping bag would weigh as much as one or two small cars.
(a) 6 ounces: 6 pounds is six loaves of bread, far too heavy for one tomato. (b) 5 pounds: 5 tons is heavier than two small cars. (c) 2 tons: 2 pounds is two loaves of bread.
4 packs, since 4 \times 4 = 16 ounces, which is 1 pound.
4 ounces per space, since 16 \div 4 = 4. The weight is 1 pound 12 ounces, since 3 \times 4 = 12.
2 pounds 9 ounces. With 16 spaces in a pound, each space is 16 \div 16 = 1 ounce, and 9 spaces are 9 ounces.
2 pounds per space, since 10 \div 5 = 2. The weight is 20 + 3 \times 2 = 26 pounds.
No. A bowling ball is much heavier, often several times as heavy as a basketball. The basketball is mostly air inside a thin skin; the bowling ball is solid. Size does not tell weight, so weight is found with a scale, not by eye.
It tells how much water the bottle holds, a capacity. Fluid ounces measure room in a container; ounces measure weight. The weight of the bottle would have to be found on a scale.
4 pounds, by 4 ounces. 4 \times 16 = 64 ounces, and 64 - 60 = 4.
30 ounces, by 4 ounces. 1 pound 10 ounces is 16 + 10 = 26 ounces, and 30 - 26 = 4.
1 ton, by 100 pounds. 1 ton is 2{,}000 pounds, and 2{,}000 - 1{,}900 = 100.
45 ounces, then 2 pounds 14 ounces, then 3 pounds, then \displaystyle 3\frac{1}{2} pounds. In ounces they are 45, 32 + 14 = 46, 48 and 48 + 8 = 56.
More, by 4 ounces. 3 \times 12 = 36 ounces, 2 pounds is 32 ounces, and 36 - 32 = 4.
2 pounds 8 ounces. Pounds: 1. Ounces: 2 + 9 + 13 = 24 = 16 + 8, which is 1 pound 8 ounces, so the total is 1 + 1 = 2 pounds and 8 ounces.
10 pounds 2 ounces. Pounds: 4 + 2 + 3 = 9. Ounces: 12 + 6 = 18 = 16 + 2, so one more pound and 2 ounces left: 10 pounds 2 ounces.
About 40 bales, since 2{,}000 \div 50 = 40 (check: 40 \times 50 = 2{,}000).
800 pounds. 2 tons is 2 \times 2{,}000 = 4{,}000 pounds, and 4{,}000 - 3{,}200 = 800.
About 20 pounds 4 ounces. Pounds: 11 + 8 = 19. Ounces: 8 + 12 = 20 = 16 + 4, so one more pound and 4 ounces: 20 pounds 4 ounces. It is “about” because the water is about 8 pounds.
7 pounds is heavier than 7 ounces, and 7 tons is heavier than 7 pounds. The counts are the same, so the heavier unit gives the heavier weight: a pound is heavier than an ounce, and a ton is heavier than a pound.
No. 3 pounds is 3 \times 16 = 48 ounces, and 48 > 40, so 3 pounds is heavier, by 8 ounces. The numbers 40 and 3 count different units and cannot be compared until both are in ounces.
A ton is 2{,}000 pounds, so each ton counted stands for 2{,}000 pounds counted. The same truck needs 2{,}000 times as many pounds as tons to describe it, so its number in pounds is much larger. The heavier the unit, the fewer of it are needed.
They weigh the same: each is exactly 2{,}000 pounds. The feathers take up far more room, because feathers hold much less matter in each bit of space than rock does. Weight measures how heavy, not how big.