A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which third-grade students have to solve a word problem using subtraction.
This question tells us that two students were collecting rocks for a science project. One of the students was able to collect 489 rocks, and we’re supposed to figure out how many rocks the other student collected, given that she collected 100 fewer rocks than the first student.
The words “fewer than” are special math words that give us a hint about what we need to do in order to get the right answer. Fewer than means the same as less than or a smaller number. We know that the second student has fewer rocks than the first, so that tells us that we need to subtract.
How many rocks does the first student have? 489.
How many fewer rocks does the second student have? 100 (shown in purple).
What does the word “fewer” tell us to do? Subtract (shown in red).
The first step to getting the right answer is to look for the special words that tell you what to do—fewer than means you probably need to subtract—in order to solve the question. The other very important part is to do the math very carefully. Don’t write 10 or 110 down instead of the correct number (100) when doing the subtraction.
How to solve word problems in general
A word problem is like a little story about a math question. The first step in solving the question is to read the story very carefully. You need to look for the special word or words that give you hints about what to do in order to get the right answer. Here are some examples:
- Adding words: more than, bigger than, taller than, greater than
- Subtracting words: fewer than, smaller than, shorter than, less than
The second step to take in solving the question is to look for the numbers in the story and then to do the correct math operation: adding or subtracting.
The last step is to check your work.
If you would like additional problems to help you master this skill, go to our online card catalog at VoxLearn.org, select one of the math collections, and enter the search terms “word problems grade 2”.
Try a few on your own
Remember to follow the three steps when solving these word problems.
1. You collect 376 leaves for an art project. Your friend collects 100 fewer leaves than you do. How many leaves does your friend collect?
2. Your dad has saved 300 pennies in a jar, and your mom says she has 255 more pennies than your dad has. How many pennies does your mom have?
3. If you have read 50 more pages of a book than your brother, how many pages have you read if your brother has read 131 pages?
4. A pine tree on your lawn is 112 inches tall. A maple tree is 40 inches taller than the pine tree. How tall is the maple tree?
5. A box of math books weighs 250 pounds (those are some heavy textbooks). Luckily, a box of science books weighs 90 pounds less than the math books. How much does the box of science books weigh?
The Answers
(1) Collecting leaves for an art project
Step 1: Look for the key words. Here, I see the words “fewer than” in the problem, so I’m guessing I’m going to have to subtract somewhere in the process.
Step 2: Look for the numbers that I want to use. The problem says I collected 376 leaves and my friend collected 100 fewer leaves. The numbers involved are 376 and 100.
Step 3: Check it. If the problem says my friend collected fewer leaves than I did, then his number should be lower than mine. Since 276 is less than 376, it seems to be correct.
(2) “Pennies for Parents”
Step 1: Key words: “more than” means I will probably have to add.
Step 2: Numbers: 300 for dad, 255 more for mom.
Therefore mom has 555 pennies, which means that she is richer than dad.
Step 3: Checking it out: Mom was supposed to have more pennies than dad, and that’s how the problem worked out, since 555 is greater than 300.
(3) Reading books
Step 1: Key words: “more” means to add.
Step 2: Numbers: 131 for my brother, 50 more for me.
Step 3: Check it. The problem says I read 50 more pages than my brother. Me – 181 pages, Brother – 131, which is less than the 181 pages that I read, so it makes sense.
(4) Pine and Maple
Step 1: “taller than” means to add.
Step 2: 112 inches for the pine tree, 40 taller for the maple tree.
Step 3: Check it. The problem says that the maple tree is taller than the pine tree.
(5) Heavy books
Step 1: “less than” means to subtract.
Step 2: Numbers. Math books – 250. Science books – 90 less.
Step 3: Check it. 160 is less than 250, so it makes sense.
Illinois Alignment
Illinois Grade Level 3
Illinois Learning Standard 6.B.1 (early elementary) Solve one- and two-step problems with whole numbers using addition, subtraction, multiplication and division.
Illinois Assessment Framework 6.3.08 (3rd grade) Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than).