Quantitative battery
CogAT Number Puzzles, explained for parents
Number Puzzles ask your child to work out a missing amount. In K–2 the puzzles are made of pictures; from 3rd grade they become short equations with a missing number, like ? + 5 = 14.
Key takeaways
- In K–2 (Levels 5/6 to 8) Number Puzzles are picture puzzles about making amounts come out equal, with directions read aloud and no reading needed.
- From 3rd grade (Level 9) they are written equations with a missing number, such as ? − 4 = 7 or 3 × ? = 12, with 10 minutes for the subtest.
- The core idea is balance: “=” means “the same amount as,” so your child finds what must match, undoes the step, then puts the answer back in to check.
- Common traps are copying a number from the problem, doing the operation they see (14 + 5), and counting the starting number when counting on.
- Number Puzzles is not on the Screening Form; two plates of snacks, a hiding cup and block trains make “the same amount” easy to see at home.
On this page
What a Number Puzzles question looks like
Every Number Puzzles question has something missing, and your child works out what it must be. It is part of the CogAT® Quantitative battery, together with Number Analogies and Number Series. Number Puzzles is not on the CogAT Screening Form.
Kindergarten to 2nd grade: picture puzzles
At Levels 5/6, 7 and 8, the puzzles use pictures, the teacher reads the directions aloud, and no reading is needed. The teacher sets the pace. The practice sample below uses two trains that must carry the same number of apples. One car in the bottom train is empty: what should go in it?
Read aloud: “Both trains should carry the same number of apples. Which car finishes the bottom train?”
Show the answer
Answer: A. The top train carries 3 + 5 = 8 apples. The bottom train has 4, so it needs 4 more: 4 + 4 = 8.
An original practice question from Thinkling, in the same format as the test. Not a real test item.
The top train carries 3 apples and 5 apples, so 8 in all. The bottom train already has 4 apples, and it needs 8 too. Four more apples fill the gap, because 4 + 4 = 8. Your child doesn’t need to write anything; counting on from 4 up to 8 is enough.
3rd grade and up: missing-number equations
From Level 9 (usually 3rd grade), the puzzles become written equations with a missing number. Children work on their own, and the subtest is timed at 10 minutes.
Which number should replace the question mark?
- 9Choice A
- 11Choice B
- 14Choice C
Show the answer
Answer: A. Work backward: 14 − 5 = 9, and 9 + 5 = 14.
An original practice question from Thinkling, in the same format as the test. Not a real test item.
Something plus 5 makes 14. Working backwards, 14 − 5 = 9, and a quick check confirms it: 9 + 5 = 14. Notice that 14 is among the choices. It is already in the problem, which makes it look tempting, but it cannot be right: 14 + 5 is 19, not 14. And 11 + 5 is 16, so 11 does not work either.
What it trains
Number Puzzles is about balance: both sides of a problem must come out the same. In the picture version that might look like two trains with equal loads; from 3rd grade it looks like an equal sign.
Children who understand that “=” means “the same amount as”, rather than “write the answer here”, find these puzzles far less confusing. The subtest also builds the habit of working backwards, undoing a step to find what was there before, which is an early step toward algebra.
How many questions there are
Number Puzzles has fewer questions than most other subtests. Here are the counts for each level of CogAT Form 7 and Form 8:
| Level | 5/6 | 7 | 8 | 9 | 10–11 |
|---|---|---|---|---|---|
| Usual grade | K | 1st | 2nd | 3rd | 4th–5th |
| Questions | 10 | 12 | 14 | 16 | 16 |
| Timing | Read aloud, teacher-paced | 10 minutes | |||
Puzzle ideas to know
- Make it equal: one side has a total; find what the other side needs, as in the train sample.
- Missing number in an addition: ? + 5 = 14. Subtract to find it: 14 − 5 = 9.
- Missing number in a subtraction: ? − 4 = 7. Add to undo it: 7 + 4 = 11.
- Missing number in a multiplication: 3 × ? = 12. Ask “3 times what makes 12?” The answer is 4.
- Bigger numbers, same idea: 25 + ? = 40 works just like the small ones: 40 − 25 = 15.
A simple routine for solving them
- Find what has to match. In the trains, it is the total in each train; in an equation, it is the number on the other side of “=”.
- Undo the step. If something was added, subtract it; if something was taken away, add it back.
- Put your answer back in. Does 9 + 5 really make 14? Do both trains really hold 8?
- Then pick the choice. Working it out first keeps tempting wrong answers from steering you.
For K–2, let your child use real objects. Building two “trains” out of toy cars and counters makes “the same amount” something they can see and touch.
Common mistakes and how to fix them
Copying a number from the puzzle
A number that already appears in the problem feels familiar. In the train sample, 3 and 5 are right there in the picture; in the equation sample, 14 is. Teach your child that a number copied straight from the problem deserves a second look, and the “put it back in” check will catch it.
Doing the operation they see
Seeing “+” makes children add: 14 + 5 = 19. Ask “What number goes in the box so the sentence is true?” rather than “What’s the answer?”
Counting on from the wrong place
When counting on from 4 to 8, children sometimes count the 4 as well (“4, 5, 6, 7, 8”) and say 5 more. Practice saying the starting number in your head, then lifting one finger for each new number: 5, 6, 7, 8. Four fingers, four more.
Practice ideas for home
- Two plates: put 6 grapes on one plate and 2 on another. “How many more does this plate need to match?”
- Hiding cup: show 7 buttons, hide some under a cup, and show what’s left. “How many are hiding?”
- Block trains: line up two rows of blocks and make them equal in as many different ways as you can.
- Older children: write mystery equations on sticky notes (? − 6 = 9) and let your child write some for you.
In Thinkling, K–2 Number Puzzles are read aloud and use the two-train format, and from grade 3 missing-number equations take over. If your child gets one wrong, the explanation uses pictures, voice and counting badges, and a fresh puzzle of the same kind comes back later for review. For more number play, see our logic games for kids and the 2nd grade guide.
Frequently asked questions
What are CogAT number puzzles like in kindergarten?
At Levels 5/6 to 8, Number Puzzles use pictures instead of written equations, and the teacher reads the directions aloud. Your child works out a missing amount from the pictures, which comes down to counting, comparing and understanding “the same as”. Practicing with real objects, like two plates of snacks that should match, builds this skill naturally.
Is Number Puzzles on the CogAT Screening Form?
No. The Screening Form uses three subtests: Verbal Analogies, Number Analogies and Figure Matrices. Number Puzzles is part of the full Quantitative battery, with Number Analogies and Number Series. Ask your school or district which form your child will take, since schools use the test in different ways.
My 3rd grader can add and subtract. Why are missing-number equations hard?
Many children learn the equal sign as “the answer goes here”, so ? + 5 = 14 feels upside down. The fix is to read it as a sentence: “What number plus 5 is the same as 14?” Then undo the step by subtracting. Practicing a few at home, and always checking the answer by putting it back in, makes them feel normal quickly.
Should my child count on fingers or objects?
Yes, especially in K–2. Fingers and objects make amounts visible and reduce slips, and most children rely on them less as number facts become automatic. For older children practicing at home, a quick written check does the same job. What matters most is getting the reasoning right; speed builds with practice.
How are Number Puzzles different from Number Analogies?
Number Analogies asks your child to find a rule in a pair, such as “add 2”, and apply it to a new number. Number Puzzles asks your child to find one missing amount so that both sides come out equal. Analogies are about spotting a change; puzzles are about balance and working backwards. Both use the same counting and number skills.