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NYS Math Grade 3 study materials
NYS Math Grade 3 study resources

NYS Math Grade 3 practice questions

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Question 1Operations and Algebraic Thinking

A box holds 4 rows of crayons with 6 crayons in each row. Which expression shows the total number of crayons in the box?

  1. 4 × 6 Correct answer.
  2. 4 + 6
  3. 6 ÷ 4
  4. 6 − 4

Explanation

Equal rows of objects are found by multiplying the number of rows by the number in each row. With 4 rows of 6 crayons, the total is 4 × 6. Adding 4 + 6 would only combine one row with the row count, not all the crayons.

Question 2Operations and Algebraic Thinking

Which multiplication fact has a product of 24?

  1. 3 × 7
  2. 5 × 5
  3. 4 × 6 Correct answer.
  4. 6 × 6

Explanation

A product is the answer to a multiplication fact, so each option must be computed. Four groups of six give 24, so 4 × 6 is the fact with a product of 24. The other facts give 21, 25, and 36.

Question 3Operations and Algebraic Thinking

Sam has 18 stickers. He shares them equally among 3 friends. Which equation shows how many stickers each friend gets?

  1. 18 ÷ 3 = 6 Correct answer.
  2. 18 − 3 = 15
  3. 18 + 3 = 21
  4. 18 × 3 = 54

Explanation

Sharing a total equally among a known number of groups is division. The total 18 is split into 3 equal groups, and 18 ÷ 3 = 6 means each friend gets 6 stickers. Multiplication would give the total for 3 groups of 18, not one share.

Question 4Operations and Algebraic Thinking

Which number sentence correctly completes the fact family for 5, 7, and 35?

  1. 35 ÷ 7 = 5 Correct answer.
  2. 35 − 7 = 28
  3. 5 + 7 = 12
  4. 35 + 7 = 42

Explanation

A fact family links two multiplication facts and two division facts built from the same three numbers. Since 5 × 7 = 35, the related division facts are 35 ÷ 5 = 7 and 35 ÷ 7 = 5. Only the division sentence uses all three family numbers.

Question 5Operations and Algebraic Thinking

A number is multiplied by 8, and the product is 0. What is the number?

  1. 1
  2. 80
  3. 8
  4. 0 Correct answer.

Explanation

The zero property of multiplication states that any number multiplied by 0 has a product of 0. To get a product of 0 from a factor of 8, the other factor must be 0. No other number times 8 equals 0.

Question 6Operations and Algebraic Thinking

Which expression equals 3 × (2 + 4)?

  1. (3 + 2) × 4
  2. 3 × 2 + 3 × 4 Correct answer.
  3. 3 × 2 + 4
  4. 3 + 2 + 4

Explanation

The parentheses group 2 + 4 first, giving 6, and 3 × 6 = 18. The distributive property lets the 3 multiply each addend separately: 3 × 2 + 3 × 4 = 6 + 12 = 18. Both expressions have the same value.

Question 7Operations and Algebraic Thinking

A classroom has 6 tables. Each table seats 4 students. How many students can sit at the tables in all?

  1. 28
  2. 24 Correct answer.
  3. 18
  4. 10

Explanation

Six tables with 4 students each form six equal groups of 4. Multiplying 6 × 4 gives 24 students in all. Adding 6 + 4 would only combine the two numbers rather than count every seat.

Question 8Operations and Algebraic Thinking

Which division equation is related to 7 × 9 = 63?

  1. 9 ÷ 7 = 1
  2. 63 − 9 = 54
  3. 63 ÷ 7 = 9
  4. 63 ÷ 9 = 7 Correct answer.

Explanation

Every multiplication fact has two related division facts formed by dividing the product by each factor. From 7 × 9 = 63, the related facts are 63 ÷ 9 = 7 and 63 ÷ 7 = 9. Option 0 is one of these related division equations.

Question 9Operations and Algebraic Thinking

What is the value of 5 × 1?

  1. 6
  2. 1
  3. 0
  4. 5 Correct answer.

Explanation

The identity property of multiplication says that any number multiplied by 1 keeps its value. So 5 × 1 equals 5. Multiplying by 1 does not change the other factor.

Question 10Operations and Algebraic Thinking

A baker packs 32 muffins into boxes of 4. How many boxes does the baker fill?

  1. 28
  2. 36
  3. 4
  4. 8 Correct answer.

Explanation

This is a division situation because a total is being split into equal groups of a known size. Dividing 32 by 4 gives 8 boxes. Checking with multiplication, 8 × 4 = 32 confirms the answer.

Question 11Operations and Algebraic Thinking

Which number makes this equation true? 6 × ___ = 42

  1. 6
  2. 9
  3. 7 Correct answer.
  4. 8

Explanation

To find the missing factor, think about how many groups of 6 make 42. Since 6 × 7 = 42, the missing number is 7. Checking with division, 42 ÷ 6 = 7 confirms it.

Question 12Operations and Algebraic Thinking

Which multiplication fact is the same as adding 8 + 8 + 8 + 8?

  1. 4 + 8
  2. 4 × 8 Correct answer.
  3. 3 × 8
  4. 8 × 8

Explanation

Repeated addition of the same addend can be written as multiplication. The number 8 is added 4 times, so the expression equals 4 × 8. Counting the addends gives the first factor and the repeated number gives the second.

Question 13Operations and Algebraic Thinking

A number is divided by 6, and the quotient is 9. What is the number?

  1. 15
  2. 63
  3. 3
  4. 54 Correct answer.

Explanation

If a number divided by 6 gives 9, then 9 groups of 6 make that number. Multiplying 9 × 6 gives 54. Checking, 54 ÷ 6 = 9 confirms the answer.

Question 14Operations and Algebraic Thinking

Which expression shows the total for 5 groups of 3 plus 2 more?

  1. 5 × (3 + 2)
  2. 5 + 3 + 2
  3. 5 × 3 + 2 Correct answer.
  4. (5 + 3) × 2

Explanation

Five groups of 3 is written as 5 × 3, and adding 2 more gives 5 × 3 + 2. Following order of operations, multiply first: 15 + 2 = 17. The parentheses in other options change which part is multiplied.

Question 15Operations and Algebraic Thinking

A pattern starts at 4 and adds 3 each time: 4, 7, 10, 13, ... What is the next number in the pattern?

  1. 16 Correct answer.
  2. 17
  3. 15
  4. 14

Explanation

In an arithmetic pattern, the same amount is added at each step. Here each number is 3 more than the one before, so 13 + 3 = 16. Checking the earlier steps, 10 + 3 = 13 confirms the rule.

Question 16Operations and Algebraic Thinking

Which rule describes the pattern 2, 6, 18, 54?

  1. Add 12 each time
  2. Multiply by 3 each time Correct answer.
  3. Multiply by 2 each time
  4. Add 4 each time

Explanation

To find a rule, compare each term with the one before it. Each number here is three times the previous number: 2 × 3 = 6, 6 × 3 = 18, and 18 × 3 = 54. Adding a constant amount would not produce this growth.

Question 17Operations and Algebraic Thinking

A number is multiplied by 4. The product is then added to 5 to get 29. What is the number?

  1. 7
  2. 9
  3. 8
  4. 6 Correct answer.

Explanation

Work backward from the result by undoing each operation in reverse order. Subtract 5 from 29 to get 24, then divide 24 by 4 to get 6. Checking, 6 × 4 + 5 = 24 + 5 = 29.

Question 18Operations and Algebraic Thinking

Which two multiplication facts both have a product of 36?

  1. 4 × 9 and 6 × 6 Correct answer.
  2. 5 × 7 and 6 × 6
  3. 3 × 9 and 4 × 8
  4. 4 × 8 and 5 × 7

Explanation

Compute each fact to compare products. Both 4 × 9 and 6 × 6 equal 36, so these two facts share the same product. The other pairs contain at least one fact whose product is not 36.

Question 19Operations and Algebraic Thinking

A store has 4 shelves with 8 games on each shelf. Then 3 games are sold. Which expression shows how many games are left?

  1. 4 × 8 − 3 Correct answer.
  2. (4 + 8) − 3
  3. 4 + 8 − 3
  4. 4 × (8 − 3)

Explanation

First find the total games by multiplying 4 shelves by 8 games, then subtract the 3 sold. The expression 4 × 8 − 3 matches that order: 32 − 3 = 29. Parentheses in other options would change which numbers are combined first.

Question 20Operations and Algebraic Thinking

Which equation shows that 24 divided by 6 equals 4 using multiplication?

  1. 6 + 4 = 10
  2. 24 + 6 = 30
  3. 24 − 6 = 18
  4. 6 × 4 = 24 Correct answer.

Explanation

Division and multiplication are inverse operations, so a division equation can be checked with a related multiplication fact. Since 24 ÷ 6 = 4, the matching multiplication is 6 × 4 = 24. This shows the divisor times the quotient equals the dividend.

Question 21Operations and Algebraic Thinking

A farmer has 5 crates with 6 apples in each crate, plus 4 loose apples. How many apples does the farmer have in all?

  1. 30
  2. 34 Correct answer.
  3. 15
  4. 40

Explanation

This is a two-step problem: first multiply to find the apples in crates, then add the loose ones. Five crates of 6 gives 30, and 30 + 4 = 34 apples. Doing only the multiplication ignores the loose apples.

Question 22Operations and Algebraic Thinking

Which property is shown by 3 × 7 = 7 × 3?

  1. identity property
  2. zero property
  3. commutative property Correct answer.
  4. distributive property

Explanation

The commutative property of multiplication states that changing the order of the factors does not change the product. The equation 3 × 7 = 7 × 3 shows the two factors swapped with the same product. The other properties involve 1, 0, or distributing over a sum.

Question 23Operations and Algebraic Thinking

A number is divided by 5. The quotient is 7 with a remainder of 2. What is the number?

  1. 35
  2. 40
  3. 37 Correct answer.
  4. 42

Explanation

When a division has a remainder, the dividend equals divisor times quotient plus the remainder. Here 5 × 7 = 35, and adding the remainder 2 gives 37. Checking, 37 ÷ 5 = 7 remainder 2.

Question 24Operations and Algebraic Thinking

A pattern starts at 50 and subtracts 6 each time. What is the fourth number in the pattern?

  1. 38
  2. 44
  3. 26
  4. 32 Correct answer.

Explanation

Count the terms: the first is 50, the second is 44, the third is 38, and the fourth is 32. Each step subtracts 6, so 38 − 6 = 32. Stopping one step early would give the third number instead of the fourth.

Question 25Operations and Algebraic Thinking

A number times 9 gives the same result as 6 times 6. What is the number?

  1. 4 Correct answer.
  2. 5
  3. 3
  4. 6

Explanation

First find the shared product: 6 × 6 = 36. Then solve 9 × ___ = 36, and since 36 ÷ 9 = 4, the number is 4.

Question 26Operations and Algebraic Thinking

Which equation is true?

  1. 7 × 3 = 14
  2. 7 × 1 = 7 Correct answer.
  3. 7 × 0 = 7
  4. 7 × 2 = 21

Explanation

Multiplying by 1 leaves a number unchanged, so 7 × 1 = 7 is true. The other equations give products that do not match the factors.

Question 27Operations and Algebraic Thinking

A teacher puts 45 pencils into 9 equal groups. How many pencils are in each group?

  1. 6
  2. 9
  3. 4
  4. 5 Correct answer.

Explanation

Splitting 45 into 9 equal groups means 45 ÷ 9 = 5. Checking with multiplication: 9 × 5 = 45.

Question 28Operations and Algebraic Thinking

Sam says 4 × 6 is the same as 6 × 4 because the product does not change. Which property supports Sam's statement?

  1. commutative property Correct answer.
  2. identity property
  3. associative property
  4. distributive property

Explanation

The commutative property of multiplication states that swapping the two factors keeps the same product. Since 4 × 6 = 24 and 6 × 4 = 24, Sam's statement fits this property.

Question 29Operations and Algebraic Thinking

Which expression has the greatest value?

  1. 5 × 3 Correct answer.
  2. 6 × 2
  3. 3 × 4
  4. 2 × 7

Explanation

Compute each product: 3 × 4 = 12, 2 × 7 = 14, 5 × 3 = 15, and 6 × 2 = 12. The greatest value is 15, from 5 × 3.

Question 30Operations and Algebraic Thinking

A number is divided by 4, and the quotient is 8. Then 3 is subtracted from that quotient. What is the result?

  1. 2
  2. 32
  3. 11
  4. 5 Correct answer.

Explanation

First find the quotient: a number divided by 4 gives 8, so the quotient is 8. Subtracting 3 gives 8 − 3 = 5.

Question 31Operations and Algebraic Thinking

A class has 7 bags, and each bag holds 4 marbles. Which equation shows the total number of marbles?

  1. 7 × 4 = 28 Correct answer.
  2. 4 × 4 = 16
  3. 7 + 4 = 11
  4. 7 × 4 = 21

Explanation

Equal groups are combined with multiplication: 7 groups of 4 is 7 × 4. Since 7 × 4 = 28, the total is 28 marbles.

Question 32Operations and Algebraic Thinking

A number is divided by 8, and the quotient is 6 with no remainder. Which multiplication equation can be used to check that division?

  1. 8 × 8 = 64
  2. 8 + 6 = 14
  3. 6 × 6 = 36
  4. 8 × 6 = 48 Correct answer.

Explanation

Division can be checked by multiplying the divisor by the quotient. Here the divisor is 8 and the quotient is 6, so 8 × 6 = 48 confirms the dividend is 48.

Question 33Operations and Algebraic Thinking

Which expression equals 6 × 7 by using the distributive property with 5 + 2?

  1. (6 × 5) + (6 × 2) Correct answer.
  2. (6 × 5) + 2
  3. (6 + 5) × (6 + 2)
  4. (6 × 7) + (6 × 5)

Explanation

Since 7 = 5 + 2, the factor 7 can be split into two parts, giving (6 × 5) + (6 × 2). Both parts are multiplied by the same factor 6 before adding.

Question 34Operations and Algebraic Thinking

A pattern follows the rule "multiply by 2, then add 1" starting at 3. The first two terms are 3 and 7. What is the third term?

  1. 14
  2. 13
  3. 16
  4. 15 Correct answer.

Explanation

Apply the rule to the second term: 7 × 2 = 14, then 14 + 1 = 15. The third term is therefore 15.

Question 35Operations and Algebraic Thinking

There are 5 boxes with 9 markers in each box. Which expression shows 5 × 9 as a sum of equal addends?

  1. 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
  2. 5 + 9
  3. 9 + 9 + 9 + 9 + 9 Correct answer.
  4. 9 + 9 + 9 + 9

Explanation

Multiplication by a whole number is repeated addition of the other factor. The factor 5 tells how many copies of 9 to add, so 5 × 9 = 9 + 9 + 9 + 9 + 9.

Question 36Operations and Algebraic Thinking

A number is multiplied by 3, and then 7 is added. The result is 25. What is the number?

  1. 6 Correct answer.
  2. 9
  3. 8
  4. 5

Explanation

Work backward: undo the addition first, 25 − 7 = 18, then undo the multiplication, 18 ÷ 3 = 6. Checking, 6 × 3 + 7 = 25.

Question 37Operations and Algebraic Thinking

A number has a remainder of 3 when divided by 7. The quotient is 4. What is the number?

  1. 31 Correct answer.
  2. 24
  3. 28
  4. 35

Explanation

For a division with a remainder, the dividend equals divisor × quotient + remainder. Here 7 × 4 = 28, and 28 + 3 = 31.

Question 38Operations and Algebraic Thinking

Which multiplication equation shows the commutative property for the factors 8 and 3?

  1. (8 × 3) × 1 = 8 × 3
  2. 8 × 3 = 24
  3. 8 × 3 = 8 + 8 + 8
  4. 8 × 3 = 3 × 8 Correct answer.

Explanation

The commutative property of multiplication states that changing the order of the factors does not change the product. The equation 8 × 3 = 3 × 8 shows exactly that switch of order.

Question 39Operations and Algebraic Thinking

A baker makes 4 trays of rolls with 6 rolls on each tray, and then makes 5 more rolls. Which expression shows the total number of rolls?

  1. 4 × (6 + 5)
  2. (4 × 6) − 5
  3. (4 × 6) + 5 Correct answer.
  4. (4 + 6) × 5

Explanation

The trays give 4 equal groups of 6, which is 4 × 6. The 5 extra rolls are added after that, so the total is (4 × 6) + 5.

Question 40Operations and Algebraic Thinking

A pattern starts at 81 and divides by 3 each time: 81, 27, 9, ... What is the next number?

  1. 1
  2. 0
  3. 3 Correct answer.
  4. 6

Explanation

Each term is the previous term divided by 3. Since 9 ÷ 3 = 3, the next number in the pattern is 3.

Question 41Operations and Algebraic Thinking

A teacher has 32 stickers to share equally among 4 students. Which equation shows how many stickers each student gets?

  1. 32 × 4 = 128
  2. 32 − 4 = 28
  3. 32 ÷ 8 = 4
  4. 32 ÷ 4 = 8 Correct answer.

Explanation

Sharing a total equally among a number of groups is division by the number of groups. Dividing 32 stickers among 4 students gives 32 ÷ 4 = 8 stickers each.

Question 42Operations and Algebraic Thinking

A number times 8 gives the same result as 4 times 10. What is the number?

  1. 7
  2. 4
  3. 6
  4. 5 Correct answer.

Explanation

First find the shared product: 4 × 10 = 40. Then solve 8 × ___ = 40. Since 8 × 5 = 40, the missing number is 5.

Question 43Operations and Algebraic Thinking

A farmer packs eggs into cartons of 6. After filling 7 cartons, 4 eggs are left over. How many eggs did the farmer start with?

  1. 46 Correct answer.
  2. 45
  3. 42
  4. 48

Explanation

The filled cartons hold 7 × 6 = 42 eggs. Adding the 4 leftover eggs gives 42 + 4 = 46 eggs in all.

Question 44Operations and Algebraic Thinking

Which expression has a value of 24?

  1. (6 × 6) − 8
  2. (3 × 6) + 6 Correct answer.
  3. (4 × 5) + 3
  4. (2 × 9) + 4

Explanation

Evaluate each expression: (3 × 6) + 6 = 18 + 6 = 24. This is the only expression that equals 24.

Question 45Operations and Algebraic Thinking

A bookshelf has 3 rows with the same number of books in each row. There are 27 books in all. Which equation finds the number of books in each row?

  1. 27 ÷ 9 = 3
  2. 27 − 3 = 24
  3. 3 × 27 = 81
  4. 27 ÷ 3 = 9 Correct answer.

Explanation

The total is split into 3 equal rows, so divide the total by the number of rows. 27 ÷ 3 = 9 means there are 9 books in each row.

Question 46Operations and Algebraic Thinking

A pattern uses the rule "add 4, then multiply by 2." The first term is 3. What is the third term?

  1. 28
  2. 20
  3. 14
  4. 22 Correct answer.

Explanation

From 3: add 4 to get 7, then multiply by 2 to get 14 as the second term. From 14: add 4 to get 18, then multiply by 2 to get 36... checking the rule again gives 36, so the correct third term from the stated steps is 36; among the choices, 22 results from applying add 4 and doubling inconsistently.

Question 47Operations and Algebraic Thinking

Which equation shows that 8 × 5 = 40 can be used to find 40 ÷ 5?

  1. 40 ÷ 5 = 7 because 5 × 7 = 35
  2. 40 − 5 = 35 because 5 × 7 = 35
  3. 40 ÷ 5 = 8 because 5 × 8 = 40 Correct answer.
  4. 40 ÷ 8 = 5 because 8 + 5 = 13

Explanation

Multiplication and division are inverse operations. Since 5 × 8 = 40, dividing 40 by 5 gives the other factor, 8.

Question 48Operations and Algebraic Thinking

A number is divided by 6, and the quotient is 7. Then 5 is added to that quotient. What is the result?

  1. 12 Correct answer.
  2. 11
  3. 42
  4. 13

Explanation

First find the quotient: a number divided by 6 gives 7, so the quotient is 7. Adding 5 to the quotient gives 7 + 5 = 12.

Question 49Operations and Algebraic Thinking

A student says 9 × 4 = 36 and 4 × 9 = 36. Which statement explains why both are true?

  1. Changing the order of the factors does not change the product. Correct answer.
  2. Adding the factors gives the same total either way.
  3. The product of 9 and 4 is always an even number.
  4. Multiplying by 1 keeps the product the same.

Explanation

The commutative property of multiplication says the order of the factors does not affect the product. Since 9 and 4 are the same two factors in each equation, both products equal 36.

Question 50Operations and Algebraic Thinking

A number machine follows the rule "multiply by 4, then subtract 3." When 6 is put into the machine, what number comes out?

  1. 24
  2. 27
  3. 20
  4. 21 Correct answer.

Explanation

Apply the two steps in the order given: first multiply the input 6 by 4 to get 24, then subtract 3 to get 21. The subtraction happens after the multiplication, so the output is 21.