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Practice Number Puzzles questions for the Cognitive Abilities Test — Grade 3 (Level 9). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
16 questions available · medium difficulty · CogAT Grade 3 · Free, no registration required
The child is given an equation with a missing value, or a pair of equations sharing a symbol, and works out what the unknown must be. It is the most school-like of the CogAT subtests and the closest thing on the test to early algebra, though it is pitched well below the arithmetic a child of the age meets in class.
A single equation with a shape or question mark standing in for a number - something plus four equals nine - and four or five numeric choices. The operations are addition and subtraction on small whole numbers.
At level 9 — grade 3
Level 9 keeps to a single equation with addition or subtraction on small whole numbers. The difficulty at this grade is more often the unfamiliar format than the arithmetic, so exposure to the notation does more for a third grader than extra calculation practice.
Finding a missing addend requires subtraction, and children who see a plus sign and add are following the symbol rather than the structure. The offered choices include the result of doing exactly that.
Putting the chosen number into the original equation and checking it balances takes a few seconds and catches nearly every error on these items. It is the cheapest check on the whole test and the most often skipped.
A triangle or a question mark standing for a number is unfamiliar to some children at this age, and the unfamiliarity alone can stall an item they could otherwise do. A few minutes of exposure removes it entirely.
Write missing-number equations on paper and let your child fill them in, using a shape rather than a letter for the unknown. The aim is for the format to feel ordinary, since a good deal of the difficulty at this age is unfamiliarity rather than arithmetic. Insist on the check afterwards - read the equation back with the number in place and confirm both sides match.
It is the reasoning that algebra formalises - a symbol standing for an unknown - but with arithmetic well below the level a child of this age meets in class. No algebraic technique is needed or expected.
Because a shape is more approachable for children who have not met letters as variables. It means the same thing, and getting used to the convention is worth a few minutes of exposure.
Substituting the answer back into the equation and checking it balances. It takes seconds and catches nearly every error children make on these items.
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Correct answer: B
The two sides of an equals sign must be worth the same, so the missing number is whatever 7 needs to reach 15. Taking 7 away from 15 leaves 8, so B is correct. Choice D comes from adding the two numbers instead of subtracting. Choice B is one too many, and choice A repeats the 7 that is already shown.
Correct answer: C
Work out the side that has no missing number first: 9 + 2 = 11. Now the left side must also come to 11, so the missing number plus 4 must be 11, which means it is 7. That makes C correct. Choice B is the value of the right-hand side rather than the missing number, which is the most common slip here. Choice D comes from subtracting 4 from 9 and ignoring the 2, and choice A from adding everything together.
Correct answer: D
The missing number is the one that leaves 12 after 5 is taken away, so add the 5 back: 12 + 5 = 17. That makes D correct. Choice C comes from subtracting 5 from 12 instead of adding it, which is the most common slip. Choice B comes from multiplying, and choice A does not satisfy the equation at all.
Correct answer: A
The missing number is how many sixes make 30, which is 30 ÷ 6 = 5. That makes A correct. Choice C comes from subtracting 6 from 30 rather than dividing, and choice D from adding 6. Choice A repeats the number already shown, which never satisfies the equation here.
Correct answer: B
Start with the side that has no missing number: 4 + 8 = 12. The left side must also come to 12, so the missing number plus 7 is 12, which makes it 5. That makes B correct. Choice D is the total of the right-hand side rather than the missing number, which is the usual mistake. Choice B comes from adding 7 to 12, and choice A from adding 4 and 7.
Correct answer: C
Work out the right-hand side first: 6 + 6 = 12. Now the left side must also equal 12, so you need the number of threes that make 12, which is 12 ÷ 3 = 4. That makes C correct. Choice B is the value of the right-hand side rather than the missing number. Choice D comes from multiplying 3 by 12, and choice A from halving 12 instead of dividing by 3.
Correct answer: D
The missing number is the one that leaves 15 once 8 is taken away, so add the 8 back: 15 + 8 = 23. That makes D correct. Choice A comes from subtracting 8 from 15 instead of adding, which is the most common slip. Choice B comes from multiplying the two numbers, and choice C is one short of the right total.
Correct answer: A
The missing number is how many nines make 45, which is 45 ÷ 9 = 5. That makes A correct. Choice C comes from subtracting 9 from 45 rather than dividing, and choice A from adding 9. Choice D repeats the number already shown, and 9 × 9 is 81 rather than 45.
Correct answer: B
Work out the right-hand side first: 8 + 8 = 16. The left side must also equal 16, so you need the number of fours that make 16, which is 16 ÷ 4 = 4. That makes B correct. Choice A is the value of the right-hand side rather than the missing number. Choice B comes from halving 16 instead of dividing by 4, and choice D does not satisfy the equation.
Correct answer: C
Work out the right-hand side first: 6 + 5 = 11. Now the left side must also come to 11, so you need the number that leaves 11 when taken from 20, which is 20 − 11 = 9. That makes C correct. Choice B is the value of the right-hand side rather than the missing number. Choice A comes from adding 11 to 20 instead of subtracting, and choice D from subtracting 6 only.