Skip to content
LessonPrint

Finding the Hidden Question

A 50-minute Grade 4 lesson on multi-step problems that teaches students to find the unstated middle question, and to judge whether a remainder should be rounded up, down, or reported.

Finding the Hidden Question is a free 50-minute Grade 4 maths lesson plan for Common Core standard 4.OA.A.3 — solve story problems that take several steps. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 4
Length:
50 minutes
Standard:
4.OA.A.3

Grade 4 · Operations & Algebraic Thinking

4.OA.A.3

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations.

Objective

Students will be able to solve multi-step word problems using the four operations, and justify what to do with a remainder in context.

Students are successful when they can

  • Identifies the intermediate quantity a problem does not name.
  • Writes an equation for each step, with a letter for the unknown.
  • Decides whether a remainder means round up, drop it, or report it, and says why in terms of the story.

What you need

  • Problem cards, four per pair
  • Whiteboards
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — what is the question underneath?

6 min
  1. Read: 'A box holds 8 pencils. Mr Ito buys 6 boxes and gives 12 pencils away. How many are left?'
  2. Do not solve it. Ask only: what do we need to know first that the problem never asks for?
  3. Establish the phrase 'hidden question' for the total number of pencils. It gets used all lesson.

Teach — one step at a time, on paper

15 min
  1. Solve the warm-up problem in full, writing each step as its own equation: 8 × 6 = p, then p − 12 = a.
  2. Point out that the first answer is not the answer. Circle it and label it 'hidden'.
  3. Introduce a second problem with a remainder: '53 students, each van holds 8. How many vans?'
  4. Do the division: 53 ÷ 8 = 6 remainder 5. Then stop and ask what 6 vans would mean for the last five students.
  5. Establish three remainder decisions, tied to the story rather than to a rule: round up when the leftovers still need one, drop it when the leftovers cannot be used, and report it when the question asks how many are left over.
  6. Give one example of each in a sentence, and leave them on the board.
“The division gave you 6 remainder 5. It did not tell you the answer — the story tells you what to do with the 5.”

Guided practice — label before you solve

15 min
  1. Pairs get four problem cards, at least one with a remainder that must be rounded up and one where it must be dropped.
  2. Required before any arithmetic: write the hidden question in words.
  3. Then write one equation per step, using a letter for each unknown.
  4. Circulate and read the hidden questions rather than the answers. A wrong hidden question guarantees a wrong answer and is far more diagnostic.

Independent practice

10 min
  1. Students work a multi-step page alone, still writing the hidden question first.
  2. Include at least one problem with a remainder to interpret.

Close

4 min
  1. Put up one problem with the answer 6 remainder 2 and ask for three different real questions where the answer would be 6, 7, and 2.
  2. That the same arithmetic supports three answers is the lesson worth leaving on.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Uses the two numbers that appear in the problem and ignores the third step.

Why: Word problems have usually been single-step, so grabbing the visible numbers and choosing an operation has been a winning strategy up to now. It is a learned heuristic, not laziness.

Fix: Make the hidden question a required, marked step. When it is written down before any calculation, the missing step cannot be skipped silently.

Writes 6 r 5 as the final answer to the van problem.

Why: Division has been taught as a procedure that terminates in a quotient and a remainder, and the answer to the procedure is being handed in as the answer to the question.

Fix: Ask the child to describe the scene. Six vans pull away and five children are standing there. Nobody who pictures it leaves the answer at six.

Rounds every remainder up, having learned the van problem.

Why: The correct decision from one problem has been stored as a rule for all problems, which is exactly how the previous heuristic formed.

Fix: Follow the van problem immediately with a problem where rounding up is wrong — how many complete boxes can be packed. The two side by side prevent the rule from forming.

If they are not there yet

  • Give the hidden question already written for the first two problems, so the practice is on executing the steps.
  • Restrict to two-step problems with friendly numbers until the structure is reliable.
  • Provide a bar model template. Seeing the intermediate quantity as a length makes it much harder to skip.

If they finish early

  • Give a three-step problem with a distractor number that is not needed.
  • Ask them to write a problem for a partner whose remainder must be dropped, then check whether the partner agrees it must be.
  • Ask for an estimate before solving, and afterwards ask whether the estimate should have caught the error.

Exit ticket

A teacher has 100 stickers. She gives 7 stickers to each of 12 students. How many are left? Write the hidden question first.

What to look for: Hidden question: how many stickers were given out. Then 7 × 12 = 84 and 100 − 84 = 16. An answer of 88 (100 − 12) or 93 (100 − 7) shows the grab-the-numbers heuristic is still running and the hidden-question step needs to stay mandatory for another week.

Printable practice for 4.OA.A.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Finding the Hidden Question

How long does the Finding the Hidden Question lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 15 min, independent practice 10 min, close 4 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Finding the Hidden Question teach?

CCSS.MATH.CONTENT.4.OA.A.3 — 4.OA.A.3, Operations & Algebraic Thinking for Grade 4: “Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations.” In plain terms, solve story problems that take several steps.

What do I need to teach this lesson?

Problem cards, four per pair, whiteboards and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: uses the two numbers that appear in the problem and ignores the third step; writes 6 r 5 as the final answer to the van problem and rounds every remainder up, having learned the van problem. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “A teacher has 100 stickers. She gives 7 stickers to each of 12 students. How many are left? Write the hidden question first.” Hidden question: how many stickers were given out. Then 7 × 12 = 84 and 100 − 84 = 16. An answer of 88 (100 − 12) or 93 (100 − 7) shows the grab-the-numbers heuristic is still running and the hidden-question step needs to stay mandatory for another week. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Finding the Hidden Question?

Yes — 2 printable 4.OA.A.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Finding the Hidden Question free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 4 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-04. Aligned to 4.OA.A.3 of the Common Core State Standards for mathematics.