Distractors that aren't silly: how good wrong answers are built, and how to write your own

1 What a wrong answer is for

The wrong options in a multiple choice question are called distractors. Most of us write them last and fast, and it shows: the answer is 56 and the other boxes say 3 and 100. A student who doesn't know 7 × 8 still gets it right, because only one option is close. The question checked nothing.

A good distractor does two jobs. It is believable to a student who has the misunderstanding, so they pick it honestly. And it is specific, so when they pick it, you know which misunderstanding they have. A class where half the room chose the same wrong box has told you exactly what tomorrow's lesson is.

Two habits make most of the difference:

• One near miss: an answer that comes from a small slip, such as counting one too many or reading the next row of the table.
• One real misconception: an answer that comes from a wrong idea, such as adding when the question says times, or turning the digits around.

That pairing is how the wrong boxes in Peabody's practice games are built, and the quiz maker uses the same boxes when you make a quiz from its math facts, sight words or word meanings.

2 How the math boxes are built

For a math fact, the practice brain picks one box from a list of near misses and one from a list of misconceptions, then checks both against a few rules before it uses them.

• Times tables: the near misses are the neighboring rows, so for 7 × 8 a box might be 48 (6 × 8) or 63 (7 × 9). The misconceptions are adding instead (7 + 8) and the digits turned around (65 for 56).
• Adding: one more or one less, then multiplying instead of adding, taking away instead, or the digits turned around.
• Taking away: one more or one less, then adding instead, the number already in the question, the digits turned around, or the well-known slip of taking the smaller digit from the bigger one: for 13 − 5, writing 12, because 5 − 3 is 2.
• Dividing: one more or one less, then the number you divided by, or taking away instead.
• Missing numbers such as 3 + ? = 7: one more or one less, the total itself, the number already shown, and 10, from reading the equals sign as "work it out" and adding 3 and 7.

Then the filters. A box can never be the answer or a repeat. It can't be below zero. It has to be close enough to tempt: within six of the answer, or within about a quarter of it for bigger answers. So for 7 × 8, adding gives 15, which is too far from 56 to fool anyone and is left out. For 3 × 4, adding gives 7, which is close to 12 and is a real mistake young students make, so it can appear.

Every wrong number must also match a named mistake. A number no rule can explain is never offered. When no misconception fits, the second box is another near miss on the other side of the answer, so the two wrong boxes are never both higher or both lower.

3 How the word boxes are built

Words have their own kinds of slips, and the brain builds those boxes from a bank of real words a child might confuse, read by hand, before any rule.

• Sight words the teacher reads aloud: one box starts with the same letter and has the same length, such as way for was. The other is the word turned around or a rhyme, such as saw for was or she for the.
• First sounds: one letter that sounds like the right one and one that looks like it. Never two letters that could both be right, so c and k never appear together for cat.
• Spelling: a misspelling a child might really write, such as shipp for ship or cak for cake, plus a real word that is easy to confuse, such as chip. Never a jumble no child would write.
• Word meanings: each word in the vocabulary bank has its own two wrong meanings, written for that word, so a quiz on a word never offers a meaning from a different topic that gives itself away.

Notice the pattern. Every wrong box is something a student could believe. None is there to make the right answer obvious.

4 When nobody wrote the wrong answers: passages and your own lists

A reading passage's questions and a list you paste into the quiz maker come with right answers only. The maker still prints three boxes for them, and it finds the two wrong ones in a set order.

1. Its own wrong answers, if the question has them. A Peabody Set pasted as data keeps its own two wrong boxes.
2. Other answers of the same kind from the same quiz: a passage's literal question borrows from its other literal answers, an inference question from other inferences.
3. Any other answer in the same source.
4. Number slips, when the answer is a number: the digits turned around, one or two more or less, or ten more or less.

If it still can't find two different wrong answers, it prints that question with a line to write on instead, and a note above the quiz says how many questions did so.

This tells you how to paste a list that gets good boxes. Keep the answers alike: all numbers, all dates, all definitions, all place names. Then every wrong box comes from a neighbor that looks like it could be right. Mix a date with a definition and a name, and the right answer stands out.

5 Writing your own: six rules

When you write a question by hand, for a test, an exit ticket or a review game, the same thinking works.

1. Start from the mistake. Ask, "What do students who don't get this actually say?" Write that answer down first. Last year's wrong answers are the best source you have.
2. One near miss, one misconception. A slip and a wrong idea tell you different things. Two slips only tell you the student was careless.
3. Same kind, same length. If the right answer is a number, every option is a number. If it is a short phrase, every option is a short phrase. The longest, most careful option is too often the right one.
4. No joke options. "A purple elephant" wastes a box and tells a student which two to choose between.
5. No "all of the above" or "none of the above". They test whether a student spotted the trick, not the content.
6. Move the right answer around. Put it in a different box from question to question. The quiz maker does this for you, and its version B moves every answer again.

Read the finished question as a student who has the misunderstanding you are aiming at. If they would pick your distractor confidently, it works. If they would laugh at it, rewrite it.

6 Examples across subjects

Here are a few questions with distractors built on the near miss and misconception idea. Each line gives the right answer first.

• Science, grade 3: What does a plant need from the air to make food? Carbon dioxide. Near miss: oxygen (the other gas they learned). Misconception: soil (many students think plants eat soil).
• Reading, grade 4: Why did the character hide the letter? The reason the story gives. Near miss: something that happened in the story, but later. Misconception: the reason a reader might have, not the character.
• Fractions, grade 4: Which is bigger, 1/3 or 1/4? 1/3. Near miss: they are the same. Misconception: 1/4, because 4 is bigger than 3.
• Measuring, grade 2: A pencil starts at the 1 on the ruler and ends at the 6. How long is it? 5 inches. Near miss: 4 inches. Misconception: 6 inches (reading the end without checking the start).
• Place value, grade 2: In 352, what is the value of the 5? 50. Near miss: 500 (the right digit, the wrong place). Misconception: 5 (the digit, not its value).

In each one, a student who chose a wrong box has told you something you can teach to. The fractions question is the clearest: a class full of "1/4" is a lesson on what the bottom number means, not on fractions in general.

7 Reading the wrong picks

Good distractors pay off only if you look at which ones students chose. That takes a minute, not an evening.

• Ask for hands per box when you go over a quiz: "Who chose the left box? The middle?" The counts go on a sticky note.
• Tally three questions, not ten. Pick the ones that matter most and count which wrong box was most popular.
• Name the mistake out loud to the class without naming any student: "A lot of us chose 7 for 3 × 4. That's adding. What does times mean?"
• Turn the popular wrong answer into tomorrow's warm-up. Ask the same idea a new way and see if the box empties.

Over a few weeks you build your own list of the mistakes your students make, and your distractors get better every time. To see every question and every source the quiz maker can draw on, open what the quiz bank holds.