All questions
Question 1
Read the problem: Chairs are set in 7 rows with 5 chairs in each row. How many chairs altogether?
- 30 chairs
- 75 chairs
- 12 chairs
- 35 chairs (correct answer)
Explanation: This question tests solving word problems using multiplication and division within 100 (CCSS.3.OA.3), specifically applying these operations to situations with equal groups, arrays, or measurement quantities. To solve multiplication/division word problems: (1) Identify the structure—equal groups (groups × per group = total), array (rows × per row = total), or measurement (# of units × amount per unit = total). (2) Determine which is unknown—total (multiply), number in each group (divide total by # groups), or number of groups (divide total by per group). (3) Write equation with symbol for unknown (6×?=42 or 42÷6=?). (4) Solve and check if answer makes sense. For example: "6 bags with 7 pencils each, how many total?" → Structure: 6 groups of 7 → Multiply: 6×7=42 pencils. In this problem, chairs are set in 7 rows with 5 chairs in each row, representing an array. The unknown is the total, so we need to multiply. Choice C is correct because 7 rows × 5 chairs per row = 35 chairs total. This accurately solves the problem using the correct operation. Choice A is incorrect because it uses addition (7+5=12) instead of multiplication (7×5=35). This error occurs when students misidentify the operation. To help students solve multiplication/division word problems: Teach keywords as clues ("each", "per", "times as many" suggest multiplication; "divided", "shared equally", "per group" suggest division) but emphasize understanding structure over keywords. Draw pictures of equal groups/arrays. Practice writing equations before solving. Use manipulatives to model problems. Check reasonableness: Does 87 cookies per child make sense from 24 total? (No!) Relate multiplication and division: If 6×7=42, then 42÷6=7 and 42÷7=6. Watch for students who add when should multiply, or who don't connect the scenario to the correct operation.
Question 2
There are 36 flowers and 4 go in each vase. How many vases are needed?
- 9 vases (correct answer)
- 8 vases
- 40 vases
- 32 vases
Explanation: 36 flowers divided into groups of 4 per vase means 36 divided by 4, which equals 9 vases, so A is correct. Choice B (8) is one less than the correct quotient. Choice C (40) adds the numbers instead of dividing. Choice D (32) subtracts 4 from 36 instead of dividing.
Question 3
A farmer plants vegetables in rows. She plants 7 rows of carrots with 9 carrots in each row. She also plants 4 rows of tomatoes with 8 tomatoes in each row. How many more carrots than tomatoes did she plant?
- 95 more carrots than tomatoes were planted
- 25 more carrots than tomatoes were planted
- 31 more carrots than tomatoes were planted (correct answer)
- 27 more carrots than tomatoes were planted
Explanation: This is a multi-step word problem that requires you to find how many vegetables are planted in total, then compare the amounts. When you see "how many more," you're looking for the difference between two quantities.
First, let's find how many carrots were planted. The farmer planted 7 rows with 9 carrots each, so you multiply: 7×9=63 carrots.
Next, find how many tomatoes were planted. She planted 4 rows with 8 tomatoes each: 4×8=32 tomatoes.
Finally, subtract to find how many more carrots than tomatoes: 63−32=31 more carrots.
Answer C (31 more carrots) is correct.
Answer A (95) likely comes from adding all the vegetables together instead of finding the difference: 63+32=95. This misses the "how many more" part of the question.
Answer B (25) might result from calculation errors in the multiplication steps or subtracting incorrectly.
Answer D (27) could come from mixing up the numbers in the multiplication (perhaps calculating 6×9=54 for carrots instead of 7×9=63, then subtracting: 54−32=22, though this doesn't match exactly).
When you see "how many more" in word problems, always remember it means subtraction after you've calculated each quantity separately. Break the problem into steps: find the first amount, find the second amount, then subtract to compare them. Question 4
Sophie is filling bags with marbles for a party. She puts the same number of marbles in each bag. After filling 6 bags completely, she has 8 marbles left over. If she started with 74 marbles total, how many marbles did she put in each bag?
- 12 marbles were put in each bag
- 11 marbles were put in each bag (correct answer)
- 10 marbles were put in each bag
- 13 marbles were put in each bag
Explanation: When you see a problem about dividing items equally with leftovers, you're working with division and remainders. This type of problem asks you to figure out how many items go in each group when you can't divide evenly.
Let's work backwards from what we know. Sophie started with 74 marbles total, filled 6 bags with the same amount in each, and had 8 marbles left over. This means: (marbles per bag × 6 bags) + 8 leftover marbles = 74 total marbles.
First, subtract the leftover marbles: 74−8=66 marbles were used to fill the 6 bags completely. Now divide those 66 marbles by 6 bags: 66÷6=11 marbles per bag.
Let's check: 11×6+8=66+8=74 ✓
Looking at the wrong answers: Choice A gives us 12×6+8=80 marbles, which is too many. Choice C gives us 10×6+8=68 marbles, which is too few. Choice D gives us 13×6+8=86 marbles, which is way too many.
The answer is B) 11 marbles were put in each bag.
Strategy tip: For division with remainder problems, always work backwards by subtracting the remainder first, then dividing. Double-check your answer by multiplying back and adding the remainder to make sure you get the original total. Question 5
Jake is making identical gift boxes. Each box needs 4 ribbons. He has already made 9 boxes and used 36 ribbons. Then he makes 3 more boxes. How many ribbons has Jake used in total?
- 12 ribbons used in total for all boxes
- 51 ribbons used in total for all boxes
- 39 ribbons used in total for all boxes
- 48 ribbons used in total for all boxes (correct answer)
Explanation: Jake has used 48 ribbons in total, since he used 36 ribbons for his first 9 boxes, then 3 more boxes need 3x4=12 more ribbons, and 36+12=48. Choice A (12) only counts the ribbons for the 3 new boxes, not the total. Choice B (51) doesn't match either 36+12 or any straightforward combination. Choice C (39) adds only 3 ribbons for the new boxes instead of 12.
Question 6
A school has 72 students going on a field trip. The principal plans to put 8 students in each group. Then 3 students get sick and cannot go, leaving 69 students. If she still puts 8 students in every full group, how many groups will she need to fit all 69 students, even if the last group has fewer than 8?
- 9 groups with some students left over (correct answer)
- 8 groups with some students left over
- 9 complete groups with no students left over
- 8 complete groups with no students left over
Explanation: After 3 students get sick, 69 students remain. Grouping them 8 at a time gives 8 full groups of 8, which is 64 students, with 5 students left over, so a 9th group is still needed to fit everyone. Choice A is correct. Choice B (8 groups with some left over) does not include a group for the last 5 students. Choice C and Choice D both claim there are no students left over, which is not possible since 69 is not evenly divisible by 8.
Question 7
Each song is 4 minutes long. Lila listens to 6 songs. What is the total time?
- 2 minutes
- 46 minutes
- 10 minutes
- 24 minutes (correct answer)
Explanation: Multiplying 6 songs by 4 minutes each gives 6 times 4, which is 24 minutes. Choice A, 2 minutes, comes from subtracting instead of multiplying. Choice B, 46 minutes, does not match multiplying 6 by 4. Choice C, 10 minutes, comes from adding 6 and 4 instead of multiplying them.
Question 8
Jamal has 4 times as many stickers as Carlos. Carlos has 7 stickers. How many stickers does Jamal have?
- 11 stickers
- 28 stickers (correct answer)
- 49 stickers
- 4 stickers
Explanation: 28 stickers is correct because 4 times 7 equals 28. 11 stickers is incorrect because it adds 4 and 7 instead of multiplying them. 49 stickers is incorrect because it does not match multiplying 4 by 7. 4 stickers is incorrect because it repeats a number from the problem instead of giving the product.
Question 9
There are 36 flowers, and Jordan puts 4 flowers in each vase. How many vases are needed?
- 40 vases
- 9 vases (correct answer)
- 8 vases
- 32 vases
Explanation: This question tests solving word problems using multiplication and division within 100 (CCSS.3.OA.3), specifically applying these operations to situations with equal groups, arrays, or measurement quantities. To solve multiplication/division word problems: (1) Identify the structure—equal groups (groups × per group = total), array (rows × per row = total), or measurement (# of units × amount per unit = total). (2) Determine which is unknown—total (multiply), number in each group (divide total by # groups), or number of groups (divide total by per group). (3) Write equation with symbol for unknown (6×?=42 or 42÷6=?). (4) Solve and check if answer makes sense. For example: "6 bags with 7 pencils each, how many total?" → Structure: 6 groups of 7 → Multiply: 6×7=42 pencils. In this problem, there are 36 flowers with 4 flowers in each vase, representing equal groups where the total is divided by the amount per group to find the number of groups, so we need to divide. Choice B is correct because 36 flowers ÷ 4 flowers per vase = 9 vases. This accurately solves the problem using the correct operation. Choice C is incorrect because it multiplies 4×10=40, perhaps miscounting or using the wrong operation. This error occurs when students misidentify the operation or make computational mistakes. To help students solve multiplication/division word problems: Teach keywords as clues ("each", "per", "times as many" suggest multiplication; "divided", "shared equally", "per group" suggest division) but emphasize understanding structure over keywords. Draw pictures of equal groups/arrays. Practice writing equations before solving. Use manipulatives to model problems. Check reasonableness: Does 87 cookies per child make sense from 24 total? (No!) Relate multiplication and division: If 6×7=42, then 42÷6=7 and 42÷7=6. Watch for students who add when should multiply, or who don't connect the scenario to the correct operation.
Question 10
42 cards are packed equally into 6 packs. How many cards are in each pack?
- 7 cards (correct answer)
- 36 cards
- 8 cards
- 6 cards
Explanation: Dividing 42 cards by 6 packs gives 42 divided by 6, which is 7 cards per pack, matching choice A. Choice B results from subtracting instead of dividing. Choice C comes from an incorrect division. Choice D is the number of packs, not the number of cards in each pack.
Question 11
A garden has 4 rows of 9 plants in each row. How many plants in all?
- 13 plants
- 95 plants
- 49 plants
- 36 plants (correct answer)
Explanation: 4 rows of 9 plants each means 4 times 9, which equals 36 plants in all, so D is correct. Choice A (13) adds the numbers instead of multiplying. Choice B (95) does not match multiplying 4 by 9. Choice C (49) reverses the digits of the correct product.
Question 12
Maya has 4 bags with 9 marbles in each bag. How many marbles total?
- 9 marbles
- 36 marbles (correct answer)
- 45 marbles
- 13 marbles
Explanation: Four bags of 9 marbles each means 4 times 9, which equals 36. Choice A only counts the marbles in one bag. Choice C comes from multiplying by 5 bags instead of 4. Choice D comes from adding 4 and 9 instead of multiplying them.
Question 13
Carlos has 7 stickers. Jamal has 4 times as many stickers as Carlos. How many stickers does Jamal have?
- 4 stickers
- 11 stickers
- 28 stickers (correct answer)
- 21 stickers
Explanation: Jamal has 4 times as many stickers as Carlos, so 4 times 7 gives 28 stickers. Choice A (4 stickers) repeats the multiplier instead of finding Jamal's total. Choice B (11 stickers) comes from adding 7 and 4 instead of multiplying. Choice D (21 stickers) comes from multiplying 7 by 3 instead of 4.
Question 14
Chairs are set up in 7 rows with 5 chairs in each row. How many chairs are there altogether?
- 12 chairs
- 35 chairs (correct answer)
- 40 chairs
- 30 chairs
Explanation: Multiplying 7 rows by 5 chairs per row gives 7 times 5, which is 35 chairs. Choice A, 12 chairs, comes from adding 7 and 5 instead of multiplying. Choice C, 40 chairs, is close to the answer but is not the product of 7 and 5. Choice D, 30 chairs, is also not the correct product.
Question 15
Look at the measurement problem shown in the table. A ribbon is cut into equal pieces. What is the length of each piece?
- Each piece of ribbon is 8 inches long (correct answer)
- Each piece of ribbon is 6 inches long
- Each piece of ribbon is 7 inches long
- Each piece of ribbon is 9 inches long
Explanation: The ribbon was 56 inches long and cut into 7 equal pieces. 56 ÷ 7 = 8 inches per piece. Choice B (6) comes from incorrect division. Choice C (7) confuses the number of pieces with the length per piece. Choice D (9) results from a calculation error.
Question 16
A bakery sells cupcakes in boxes. Each box holds exactly 6 cupcakes. On Monday, they sold 8 boxes. On Tuesday, they sold enough cupcakes to fill 5 more boxes, but 2 cupcakes were damaged and couldn't be sold. How many cupcakes did the bakery actually sell over both days?
- 78 cupcakes
- 76 cupcakes (correct answer)
- 80 cupcakes
- 74 cupcakes
Explanation: Monday's 8 boxes give 48 cupcakes, and Tuesday's 5 boxes give 30 more, for 78 total, minus the 2 damaged cupcakes leaves 76 cupcakes sold. Choice A (78 cupcakes) forgets to subtract the 2 damaged cupcakes. Choice C (80 cupcakes) comes from an error in the box multiplication. Choice D (74 cupcakes) subtracts too many cupcakes for the damaged ones.
Question 17
A garden has 4 rows with 9 plants in each row. How many plants are there altogether?
- 45 plants
- 13 plants
- 36 plants (correct answer)
- 40 plants
Explanation: There are 4 rows with 9 plants in each row, so the total is 4 times 9, which is 36 plants. Choice A (45 plants) comes from multiplying with the wrong number of rows. Choice B (13 plants) comes from adding 4 and 9 instead of multiplying. Choice D (40 plants) is close to the product but not the correct result.
Question 18
Mrs. Chen has 84 stickers. She gives each student 9 stickers, and 3 stickers are left over. How many students are in her class?
- 7 students
- 12 students
- 9 students (correct answer)
- 10 students
Explanation: Subtracting the 3 leftover stickers from 84 gives 81 stickers evenly distributed, and dividing 81 by 9 stickers per student gives 9 students. Choice A and Choice D come from division errors. Choice B comes from a similar miscalculation using the wrong total.
Question 19
There are 9 teams with 6 players on each team. How many players are there in all?
- 45 players
- 15 players
- 63 players
- 54 players (correct answer)
Explanation: There are 9 teams with 6 players each, so the total is 9 times 6, which is 54 players. Choice A (45 players) comes from multiplying with the wrong numbers. Choice B (15 players) comes from adding 9 and 6 instead of multiplying. Choice C (63 players) is close to the product but not the correct result.
Question 20
Maya has 6 packs of cards with 7 cards in each pack. How many cards are there in all?
- 36 cards
- 13 cards
- 49 cards
- 42 cards (correct answer)
Explanation: Maya has 6 packs with 7 cards in each, so the total is 6 times 7, which is 42 cards. Choice A (36 cards) comes from multiplying with the wrong numbers. Choice B (13 cards) comes from adding 6 and 7 instead of multiplying. Choice C (49 cards) comes from multiplying 7 by 7 instead of 6 by 7.