4th Grade · 4.MD.A.2

Money word problems in 4th grade

Money word problems ask your child to work out a total, a price or the change from a purchase. In 4th grade they are part of a bigger group called measurement word problems, which also cover distance, time, liquid volume and weight. Your child adds, subtracts, multiplies and divides, changes larger units into smaller ones and draws number lines to show the amounts.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

What it means, in plain words

A measurement word problem is a short story with amounts that have units, such as dollars, miles, minutes, liters or kilograms. Money word problems are the ones most children meet outside school. Prices use a decimal point: 3 dollars and 25 cents is written 3.25 with a dollar sign in front. The two digits after the point are the cents, and 100 cents make 1 dollar.

Many problems get easier when every amount is in the smaller unit. Your child can change 2 dollars to 200 cents, 3 hours to 180 minutes or 4 kilometers to 4,000 meters, and then work with whole numbers. A larger unit is made of many smaller ones, so the number gets bigger.

Distance word problems and time problems often come with a number line. The line has a real scale, such as one mark for every 10 minutes or every 250 meters. Your child draws jumps on the line to show what is added or taken away, then reads the answer from the scale. Some problems also include simple fractions, such as half a liter or a quarter of an hour.

Your child should be able to:

Solve money word problems that ask for a total or for change
Change dollars to cents, hours to minutes or kilometers to meters partway through a problem
Show a distance or a length of time as jumps on a number line with a scale
Work with simple fractions and decimals inside a story, such as half a liter or 75 cents written as 0.75 dollars

Example

A notebook costs 6 dollars and 45 cents. You pay with a 10-dollar bill. How much change do you get?

Change both amounts to cents: 10 dollars is 1,000 cents, and 6 dollars and 45 cents is 645 cents.
$1{,}000 - 645 = 355$
Check by counting up from 6.45: 5 cents makes 6.50, and 3 dollars and 50 cents more makes 10.00.
355 cents is 3 dollars and 55 cents, so the change is 3 dollars and 55 cents.

Example

A bike trail is 3 kilometers long. A family stops to rest after 1,250 meters. How many meters are left to ride?

Change kilometers to meters: 3 kilometers is 3,000 meters.
$3{,}000 - 1{,}250 = 1{,}750$
On a number line marked every 250 meters, the jump from 1,250 to 3,000 covers 7 marks, and $7 \times 250 = 1{,}750$ .
There are 1,750 meters left to ride.

Where children usually get stuck

To add 2 dollars 50 cents and 1 dollar 75 cents, your child writes 3 dollars 125 cents.
The cents were added like whole numbers, and nothing reminded the child that 100 cents make a dollar. It is the same trade as 10 ones for a ten, only at 100.
What helps. Use real coins and bills. Ask how many cents make a dollar, then trade 100 of the 125 cents for a dollar bill. The total is 4 dollars and 25 cents.
To find how long a trip from 9:40 to 11:15 takes, your child subtracts $1{,}115 - 940$ and gets 175 minutes.
Clock times look like whole numbers, but an hour has 60 minutes, not 100. Subtracting the digits treats the clock as if it counted in tens.
What helps. Draw a number line and count up in jumps: 9:40 to 10:00 is 20 minutes, 10:00 to 11:00 is 1 hour and 11:00 to 11:15 is 15 minutes. The trip takes 1 hour 35 minutes.
Your child reads "how much more does the bike cost than the helmet" and adds the two prices.
The child has learned key words as a shortcut, and "more" sounds like adding. This question asks for the difference between two prices.
What helps. Ask your child to tell the story back without the numbers, then draw two bars side by side for the two prices. The question is about the gap between the bars.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Liam saved $11.25 from his allowance last week. This week, he saved $5.50 more. How much has Liam saved in all?
$
Show the answer and how to solve it
Answer. 16.75
Liam has saved $16.75 in all.
1. 1Liam saved $11.25 last week and $5.50 this week. Add the two amounts to find the total he saved.
2. 2Line up the decimal points and add column by column.
3. 3Add the cents: $25 + 50 = 75$ cents. Write $75$ in the cents column.
4. 4Add the dollars: $11 + 5 = 16$ dollars. The total is $16.75.
Common mistake. A common mistake is not lining up the decimal points before adding. If digits are shifted, dollars and cents get added in the wrong place-value columns, giving an incorrect answer. Always place the decimal points directly above each other.
The idea underneath. Money problems use place-value addition with two decimal places. When the cents add to more than 100, the extra dollar carries to the dollars column, just like ones carry to tens in whole-number addition.
2On level
Liam is filling a fish tank with water. He starts with 50 mL of water and pours in 50 mL more. His work to find the total amount of water is shown on the number line below.
Which statement best describes this number-line work?
A
Liam's jump length does not match the scale.
B
Liam's placement is correct.
C
Liam jumped in the wrong direction.
D
Liam did not start at the beginning measurement.
Show the answer and how to solve it
Liam's jump length does not match the scale. Each tick is 25 mL, so adding 50 mL means jumping 2 ticks, but Liam jumped 4 ticks — landing at 150 mL instead of the correct 100 mL.
1. 1First, find what Liam is trying to compute. He starts with 50 mL of water and adds 50 mL more, so the total amount of water should be 100 mL.
2. 2Read the scale on the number line. The labeled tick marks are 0, 25, 50, 75, 100, 125, 150, 175, 200 — so each tick is 25 mL apart. To add 50 mL, Liam needs to jump 2 ticks, because $2 \times 25 = 50$ .
3. 3Now examine Liam's jump. His arrow goes from 50 to 150, which is 4 ticks. That means his jump covers $4 \times 25 = 100$ mL, not the 50 mL he needed. His starting point is correct (50 mL) and his direction is correct (right, for addition), but his jump length is twice as far as the scale requires. So 'Liam's jump length does not match the scale' best describes the work.
Common mistake. A common mistake is to check only the direction or starting point and miss the jump length error. To check a scaled number-line jump, count the number of ticks the jump covers and multiply by the tick value — that should equal the change you wanted to make.
The idea underneath. On a scaled number line, each tick mark represents a fixed amount. To check addition or subtraction, count the ticks the jump covers and multiply by the tick value — that product should equal the change you wanted to make.
3On level
Sam has 6 meters of ribbon. He divides it equally into 3 pieces, then adds 40 centimeters of extra ribbon to each piece. How many centimeters long is each piece now?
A
42 centimeters
B
240 centimeters
C
640 centimeters
D
2040 centimeters
Show the answer and how to solve it
Each piece is 240 centimeters long. After converting 6 meters to 600 centimeters, dividing 600 by 3 gives 200 centimeters per piece, and adding 40 centimeters makes 240 centimeters.
1. 1First, change meters to centimeters. There are 100 centimeters in 1 meter, so multiply 6 by 100.
2. 2Now divide the 600 centimeters of ribbon equally into 3 pieces.
3. 3Each piece also gets 40 centimeters of extra ribbon added. Add 40 to the ribbon in one piece.
4. 4Each piece is now 240 centimeters long.
Common mistake. A common mistake is forgetting to convert meters to centimeters before doing the other steps. A student who skips the conversion gets $6 \div 3 + 40 = 42$ instead of $600 \div 3 + 40 = 240$ . Always convert units first.
The idea underneath. When a problem mixes units, convert FIRST so every quantity is in the same unit, then perform the operations. Check what unit the answer must be in, and make sure all numbers in your work match that unit.
4Stretch
Liam's garden path is 12.4 meters long. He adds another section that is 7.8 meters long. How many meters long is the path now?
meters
Show the answer and how to solve it
Answer. 20.2
The garden path is now $20.2$ meters long: $12.4 + 7.8 = 20.2$ .
1. 1Adding a new section joins the two lengths together. To find the total length of the path, add the two measurements.
2. 2Add 12.4 and 7.8. Align the decimal points, add the tenths column first (getting 12 tenths, which regroups to 1 one and 2 tenths), then add the ones and tens:
3. 3The path is now 20.2 meters long.
Common mistake. A common mistake is subtracting instead of adding. Adding a new section makes the path longer, so add: $12.4 + 7.8 = 20.2$ meters. Another mistake is misaligning the decimal points before adding, which leads to a wrong answer like $12.4 + 0.78 = 13.18$ .
The idea underneath. When two measurements use the same unit, you add or subtract the numbers directly without changing the unit. The action in the problem (joining, using, or comparing) tells you which operation to use.