Jake has 28 crayons. His sister has 17. A student writes '28 + 17' as the number sentence. What type of subtraction situation is this problem, and why is addition wrong?
AThis is a 'take away' problem — something is being removed, so addition overcounts
BThis is a 'comparison' problem — we want the difference between the two quantities, not their combined total
CThis is an 'equal sharing' problem — we need to divide, not add or subtract
DAddition is actually correct here — both quantities are present at the same time
No one is taking anything away — both Jake and his sister still have their crayons. The question asks how many MORE Jake has, which means finding the gap between the two quantities. That gap is the difference, found by subtraction (28 − 17 = 11). Addition would give the total number of crayons they have together, which is not what was asked.
Question 2 Multiple Choice
What is the best first step when solving a subtraction word problem you haven't seen before?
AWrite the subtraction number sentence immediately so you don't forget the numbers
BSubtract the smaller number from the larger number as a default
CDraw a picture or act out the situation to understand what is happening before choosing an operation
DCheck whether the answer will be greater or less than 100
Rushing to numbers before understanding the situation is the main cause of errors in word problems. Drawing the scenario or acting it out with objects forces you to identify the whole, the known part, and the unknown — making the correct operation obvious. Students who jump to numbers first often choose the wrong operation or subtract in the wrong direction because they are guessing rather than reasoning.
Question 3 True / False
A comparison subtraction problem — such as 'Jake has 28, his sister has 17, how many more does Jake have?' — requires subtraction even though no one is taking anything away.
TTrue
FFalse
Answer: True
Subtraction models three different situations: take away (removing an amount), comparison (finding the gap between two quantities), and missing part (finding the unknown piece of a whole). Comparison subtraction is often confusing because nothing disappears — both quantities remain. But finding 'how many more' always means finding the difference, which is subtraction.
Question 4 True / False
If a word problem contains two numbers and asks a question, you should add those numbers together to find the answer.
TTrue
FFalse
Answer: False
The operation depends on the situation described in the problem, not on the presence of two numbers. 'Maria had 34 stickers and gave away 15' requires subtraction. 'Jake has 28 and his sister has 17, how many more?' requires subtraction. 'There are 18 basketball players and 22 readers, how many total?' requires addition. You must understand the story first — then choose the operation.
Question 5 Short Answer
Describe the three types of subtraction situations. Give a brief example of each.
Think about your answer, then reveal below.
Model answer: The three types are: (1) Take away — you start with a quantity and remove part of it. Example: 'I had 20 grapes and ate 8. How many are left?' (2) Comparison — two quantities exist side by side and you find the difference between them. Example: 'Sam has 15 cards, Lily has 9. How many more does Sam have?' (3) Missing part — you know the whole and one part, and must find the other. Example: 'There are 30 students in the class. 13 are outside. How many are inside?'
Naming the situation type before solving helps students avoid guessing at the operation. All three situations use subtraction, but they tell very different stories. Recognizing the structure — particularly for comparison and missing-part problems, which don't obviously 'feel' like subtraction — is the skill that prevents students from defaulting to addition whenever no one is explicitly taking something away.