1st Grade Math
Practice Test 9 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Look at the pattern below. Sara makes a butterfly by putting together 2 half-circles and 1 rectangle. If she wants to make 3 butterflies that are exactly the same, which shapes does she need in total?
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Look at the pattern below. Sara makes a butterfly by putting together 2 half-circles and 1 rectangle. If she wants to make 3 butterflies that are exactly the same, which shapes does she need in total?
Explanation: Each butterfly needs 2 half-circles and 1 rectangle. For 3 butterflies: 3 √ó 2 = 6 half-circles and 3 √ó 1 = 3 rectangles. Choice B only gives enough shapes for 1 butterfly. Choice C gives incorrect amounts with unnecessary extras. Choice D has the wrong ratio and incorrect totals.
Sofia wakes up at 7 o'clock. What time is it?
Explanation: This question tests 1st grade ability to tell and write time in hours and half-hours (CCSS.1.MD.3). When we say a time is 'o'clock,' the digital display shows :00 for the minutes. The question states Sofia wakes up at '7 o'clock,' which translates to 7:00 in digital format. Choice C (7:00) is correct because it accurately represents 7 o'clock. Choice A (7:30) would be 'half past 7,' not '7 o'clock.' Choices B (6:00) and D (8:00) represent different hours entirely. To help students: Reinforce that 'o'clock' means exactly on the hour with :00 minutes; practice reading both analog clocks (minute hand on 12) and digital displays; connect time-telling to familiar daily routines like waking up; use morning routine times for practice.
To subtract 10−2, start at 10 and count back 2: 9, 8. What is the answer?
Explanation: This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting back is a strategy for subtraction. Start at the first number (minuend) and count backward by the second number (subtrahend). For example, to solve 10 - 2, start at 10 and count back 2: '9, 8'—the last number you say (8) is the answer. The problem asks to subtract 10 - 2 by counting back from 10. Choice C is correct because starting at 10 and counting back 2 gives '9, 8,' so the answer is 8. Choice B is a common error where students miscount by one, such as stopping after the first count back; this happens because counting back is more challenging than counting forward for many students. To help students: Demonstrate counting back with number line showing backward movement; use fingers to track counts while saying numbers aloud; practice with physical objects (start with group, remove by counting back); emphasize the direction of counting; practice with small subtrahends (1-5) first; connect counting to written subtraction equations; compare to counting on for addition.
Sofia has 5 red crayons and 9 blue crayons. How many crayons does Sofia have altogether?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is a putting together problem with total unknown. We combine two amounts to find the total. The story tells us Sofia has 5 red crayons and 9 blue crayons. Choice B is correct because to find how many crayons Sofia has altogether, we add: 5 + 9 = 14. We can represent this as an equation with unknown: 5 + 9 = ?. Choice D is a common error where students might add incorrectly, like 5 + 9 = 15, or add an extra 1. To help students: Act out problems with physical objects; draw pictures representing the situation; teach problem type structures explicitly (adding to, taking from, putting together, taking apart, comparing); use consistent language for each type; practice writing equations with boxes for unknowns; emphasize keywords carefully ('altogether' means add); model thinking aloud ('I have 5 red and 9 blue, to find the total, so I add'); practice all unknown positions; connect to familiar experiences.
Solve: 11=?+2. What is ?
Explanation: This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is an addend (like in ? + b = c), we need to find what number added to b equals c; we can think of this as subtraction: c - b = ?. Or we can count on from b to c and count how many—that's the unknown. The equation is 11 = ? + 2, which is the same as ? + 2 = 11. Choice B is correct because when we add 9 + 2 = 11, so the unknown is 9. Choice A is a common error where students add the two given numbers instead of subtracting, getting 11 + 2 = 13; this happens because finding unknowns in different positions requires different strategies and the inverse relationship between operations must be understood. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for addend unknown, connect to subtraction and 'unknown addend' thinking (covered in CCSS.1.OA.4); use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 9+2=11, then 11-2=9); emphasize checking: substitute answer back into equation to verify it's true.
Yuki has some shells. She finds 5 more shells. Now she has 14 shells. How many shells did Yuki have at the start?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is an adding to problem with start unknown. We add an amount to an unknown start to reach a total, and find the start. The story tells us Yuki has some shells, finds 5 more, now has 14. Choice A is correct because to find how many shells Yuki had at the start, we subtract: 14 - 5 = 9. We can represent this as an equation with unknown: ? + 5 = 14. Choice D is a common error where students might add instead: 14 + 5 = 19, using the wrong operation for the unknown position. To help students: Act out problems with physical objects; draw pictures representing the situation; teach problem type structures explicitly (adding to, taking from, putting together, taking apart, comparing); use consistent language for each type; practice writing equations with boxes for unknowns; emphasize keywords carefully ('some' and 'more' with total given means start unknown); model thinking aloud ('Ended with 14 after adding 5, to find start, I subtract'); practice all unknown positions; connect to familiar experiences.
Kate wants to put exactly 10 crayons in her pencil box. She puts in 8 crayons, but then realizes 3 of them are broken, so she takes those out. How many good crayons does she need to add?
Explanation: When you see word problems with multiple steps like this one, you need to carefully track what happens at each stage to find out how many items you actually have before figuring out what you still need. Let's follow Kate's crayon situation step by step. She starts by putting 8 crayons in her box. Then she discovers that 3 of those crayons are broken and removes them. This means she now has 8−3=5 good crayons in her box. Since Kate wants exactly 10 crayons total, you need to find the difference: 10−5=5. She needs to add 5 more good crayons. Looking at the wrong answers: Answer B (2 crayons) might come from only thinking about the 3 broken crayons that were removed and miscalculating the final step. Answer C (3 crayons) likely comes from focusing only on replacing the 3 broken crayons without considering that Kate still needs more to reach her goal of 10 total. Answer D (7 crayons) appears to come from subtracting the 3 broken crayons directly from 10, ignoring the fact that Kate already has 5 good crayons in the box. Answer A is correct because it accounts for both steps: the removal of broken crayons and the calculation of what's still needed to reach the target. For multi-step word problems, always work through each action in order and keep track of your running total. Write down what you have after each step before calculating what you still need.
To add 7+5, start at 7 and count on 5: 8, 9, 10, 11, 12. What is the sum?
Explanation: This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 7 + 5, start at 7 and count forward 5 numbers: '8, 9, 10, 11, 12'—the last number you say (12) is the answer. The problem asks to add 7 + 5 by counting on from 7 and find the sum. Choice B is correct because starting at 7 and counting on 5 gives '8, 9, 10, 11, 12,' so the sum is 12. Choice A is a common error where students stop counting too early, perhaps by miscounting the steps; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
Lily has 90 stickers arranged in groups of ten. She gives away 30 stickers to her friends. How many groups of ten does she have left?
Explanation: Lily starts with 90 stickers = 9 groups of ten. She gives away 30 stickers = 3 groups of ten. So she has 9 - 3 = 6 groups of ten left. Choice B shows only the groups given away. Choice C shows the original groups. Choice D gives the remaining number of stickers, not groups.
Maya cut a sandwich into two equal parts. How many halves make a whole?
Explanation: This question tests 1st grade understanding of partitioning circles and rectangles into halves and fourths (CCSS.1.G.3). When a circle or rectangle is divided into 2 equal parts, each part is called a half, and 2 halves make the whole. When divided into 4 equal parts, each part is called a fourth (or quarter), and 4 fourths make the whole. The stimulus describes Maya cutting a sandwich into two equal parts. Choice B is correct because two halves make a whole sandwich. Choice C is a common error where students think of fourths instead, which happens because fraction language is new and challenging. To help students: Use real objects like pizzas, cookies, or brownies to demonstrate partitioning; emphasize equal means same size; compare halves and fourths side-by-side to show fourths are smaller; practice vocabulary explicitly (halves, fourths, quarters, half of, fourth of); use hands-on cutting and folding activities with paper circles and rectangles; reinforce that 2 halves=whole and 4 fourths=whole.
Jamal has 47 marbles and gets 10 more; how many now?
Explanation: This question tests 1st grade ability to mentally find 10 more or 10 less than a two-digit number (CCSS.1.NBT.C.5). To add or subtract 10 mentally, use place value understanding: since 10 equals 1 ten and 0 ones, adding 10 means adding 1 ten (so the tens digit increases by 1), while the ones digit stays the same. For example, 34+10=44 because 3 tens + 1 ten = 4 tens, and the 4 ones remain unchanged; similarly, subtracting 10 means removing 1 ten (tens digit decreases by 1), while ones stay the same: 67−10=57 because 6 tens - 1 ten = 5 tens, and the 7 ones remain unchanged. The question presents a word problem where Jamal starts with 47 marbles and adds 10 more. Choice B is correct because adding 10 to 47 means adding 1 ten: 4 tens + 1 ten = 5 tens, ones stay 7, giving 57. Choice A is a common error where students add 1 instead of 10, resulting in 48; this happens because understanding 10 as 1 ten is abstract and students sometimes change the ones digit instead of tens. To help students: Use base-10 blocks to show physically adding 1 ten-rod while ones stay constant; practice on hundred charts (add 10 = down one row); emphasize pattern 'tens change by 1, ones stay same'; provide many examples showing ones digit constant; connect to skip counting by 10s; use number lines with jumps of 10; practice mental math daily with quick '10 more' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
A square must have sides that are what?
Explanation: This question tests 1st grade understanding of defining attributes of squares, as outlined in CCSS.1.G.A.1. Defining attributes for a square include four sides of equal length and four right angles. Non-defining attributes like color or curvature are not part of its definition. The question asks what sides a square must have, focusing on equality of length. Choice A is correct because all sides being the same length is a key defining attribute of a square. Choice B is a common error where students might think sides are curved, confusing squares with circles, as young children sometimes mix up straight versus curved lines in shapes. To help students: Measure sides of square cutouts with rulers to confirm equality, compare to rectangles with unequal sides, and build squares using equal-length sticks while stressing 'All four sides must be the same length to make a square.'
Maria has 8 stickers. She wants to give away 3 stickers to her friends. Instead of subtracting, Maria decides to count backwards from 8 to find how many stickers she will have left. Which counting pattern should Maria use?
Explanation: To subtract 3 by counting backwards, Maria starts at 8 and counts back 3 numbers: 8→7 (back 1), 7→6 (back 2), 6→5 (back 3). She lands on 5, so she will have 5 stickers left. Choice B stops counting after only 2 steps back. Choice C counts forward instead of backward. Choice D jumps directly without showing the counting process.
Ana draws 6 stars in one group and 8 stars in another group. She writes the number 14 below her picture. What math story matches Ana's drawing and number?
Explanation: When you see a picture with two groups of objects and a total number, you're looking at an addition story. Ana drew 6 stars in one group and 8 stars in another group, then wrote 14 below. This means she's showing that 6+8=14. The correct answer is B because Ana found 6 stars and then found 8 more stars. This matches exactly what her drawing shows - two separate groups that she's combining together. When you "find" something and then "find more," you're adding the amounts together to get a total. Let's see why the other choices don't work. Choice A says Ana had 14 stars and gave away 8 stars. This would be subtraction (14−8=6), not addition. Choice C says Ana had 6 stars and lost 8 stars. This is also subtraction, and you can't lose more than you have! Choice D talks about putting stars away from a group of 14, which would again be subtraction, not the addition story that Ana's picture shows. Remember this pattern: When you see two separate groups of objects with a total written below, look for the math story that talks about combining, finding more, or adding together. Stories about giving away, losing, or taking away are subtraction stories, even if the numbers in the problem are the same.
Sarah has 58 marbles. She wants to have 10 fewer marbles. How many marbles should she give away?
Explanation: When you see a problem asking "how many fewer," you're being asked to find the difference between two amounts through subtraction. Sarah starts with 58 marbles and wants to have 10 fewer marbles than she currently has. To find how many fewer, you subtract: 58−10=48. So Sarah wants to end up with 48 marbles. Since she starts with 58 and wants to have 48, she needs to give away 58−48=10 marbles. Let's check why the other answers don't work. Choice A suggests giving away 9 marbles, but 58−9=49, which means she'd still have 49 marbles instead of the 48 she wants. Choice B says to give away 48 marbles, but that would leave her with 58−48=10 marbles, which is far too few. Choice C suggests 11 marbles, but 58−11=47, giving her one marble less than her goal of 48. Choice D is correct because giving away exactly 10 marbles results in 58−10=48 marbles, which is exactly 10 fewer than her starting amount. Remember this strategy: when a problem asks "how many fewer," first figure out what the final amount should be, then subtract that from the starting amount to find how many to remove.
Maya has 3 coins in her pocket. She knows that together they are worth the same as 7 pennies. Which coins could Maya have?
Explanation: A nickel is worth 5 pennies, so 1 nickel + 2 pennies = 5 + 2 = 7 pennies total. Choice B gives 25 + 2 = 27 pennies. Choice C gives 10 + 2 = 12 pennies. Choice D has 4 coins, not 3.
Mia has 7 stickers and gets 6 more; make ten to find how many.
Explanation: This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). The making-10 strategy helps add numbers that cross 10. To use it, decompose the second number into the amount needed to make 10, plus the remainder. For example, for 8+6, we think: 8 needs 2 more to make 10, so break 6 into 2+4. Then: 8+6=8+(2+4)=(8+2)+4=10+4=14. The problem asks to solve 7+6 using making ten in a word problem context. Choice C is correct because following making-10: 7+6=7+3+3=10+3=13. Choice A is a common error where students make a calculation error, such as forgetting to add the remainder; this happens because keeping track of parts while combining them is cognitively demanding. To help students: For making-10, explicitly teach pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5) and practice decomposing; use ten-frames to visualize making 10; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
Maria wants to show her friend that 5+3=8. She draws circles to represent the numbers. Which combination of representations would BEST help her friend understand this addition problem?
Explanation: Choice A uses multiple representations effectively: visual (circles in groups), symbolic (equation), and verbal/kinesthetic (counting). This combination helps connect the concrete representation to the abstract equation. Choice B only shows the result without the addition process. Choice C focuses only on symbols without connecting to meaning. Choice D shows subtraction rather than addition.
Keisha has 15 points in a game. She scores 4 more points. How many points does Keisha have now? 15+4=?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is an adding to problem with result unknown. We start with one amount and add more to find the total. The story tells us Keisha has 15 points and scores 4 more. Choice B is correct because to find how many points Keisha has now, we add: 15 + 4 = 19. We can represent this as 15 + 4 = ?. Choice A is a common error where students use the wrong operation, subtracting instead of adding: 15 - 4 = 11. This happens because choosing the operation from word problem context is challenging. To help students: Act out problems with physical objects; draw pictures representing the situation; teach problem type structures explicitly (adding to, taking from, putting together, taking apart, comparing); use consistent language for each type; practice writing equations with boxes for unknowns; emphasize keywords carefully ('more' can mean add or compare); model thinking aloud ('I started with 15, added 4, need the total, so I add'); practice all unknown positions; connect to familiar experiences.
At a zoo, there were 10 monkeys playing. 4 monkeys went to eat lunch. Then 2 monkeys came back from lunch to play again. Which equation represents how many monkeys were playing after 4 went to lunch but before 2 came back?
Explanation: When you see a word problem with multiple steps, you need to carefully read what the question is asking for. This problem has three things happening: monkeys start playing, some leave for lunch, and some come back. But the question asks specifically about the situation "after 4 went to lunch but before 2 came back." Let's work through this step by step. We start with 10 monkeys playing. Then 4 monkeys go to eat lunch, so we subtract: 10−4=6. At this exact moment - after the 4 left but before any came back - there were 6 monkeys playing. This matches answer choice D. Now let's see why the other answers are wrong. Choice A shows 10+2−4=8, which adds the returning monkeys first, but that doesn't match the order of events. Choice B shows 10−4+2=8, which includes the 2 monkeys coming back, but the question asks for the count before they returned. Choice C shows 6+2=8, which also includes the monkeys coming back from lunch. The key strategy here is to read word problems very carefully and identify exactly what moment in time the question is asking about. Even though the problem tells you about monkeys coming back, the question stops at an earlier point in the story. Always underline or highlight the specific question being asked so you don't accidentally solve for the wrong step.
Amir shares the same pizza. Which is bigger: one half or one quarter?
Explanation: This question tests 1st grade understanding of comparing fractional parts from the same whole (CCSS.1.G.3). When comparing parts of the same whole, fewer parts means each part is bigger—so one half is larger than one fourth. The more you divide something, the smaller each piece becomes. Amir's pizza comparison involves halves (2 equal parts) versus quarters (4 equal parts). Choice C is correct because one half of a pizza is bigger than one quarter of the same pizza. Choice A (one quarter) reverses the relationship, while B (same size) is a common misconception that all 'parts' are equal regardless of how many divisions. To help students: Use same-sized paper circles, fold one in half and another in fourths, then compare the sizes directly; use real food examples where students can see and feel the difference; emphasize 'same whole' when comparing.
Emma shows the number 18 by drawing 1 group of ten dots and 8 single dots. Her brother wants to write this same idea using numbers and symbols. Which choice matches Emma's drawing?
Explanation: When you see a problem about showing numbers with groups of ten and single units, you're working with place value - understanding that numbers can be broken down into tens and ones. Emma drew 1 group of ten dots plus 8 single dots to show 18. To write this with numbers and symbols, you need to translate what she drew directly into math. She has 1 group of ten (which equals 10) plus 8 single dots, so the equation should be 10+8=18. This matches choice B perfectly. Let's check why the other answers don't work. Choice A shows 1+8=9, but this treats the group of ten as just "1" instead of recognizing it represents 10. This is a common mistake - forgetting that 1 group of ten means 10, not 1. Choice C shows 18−8=10, which is subtraction rather than addition, and doesn't represent how Emma built up the number 18 from its parts. Choice D shows 8+10=19, which has the right idea about adding 10 and 8, but gets the wrong total - 19 instead of 18. Remember this key strategy: when you see "groups of ten" in a problem, always think "10" in your equation, not "1." One group of ten equals 10, two groups of ten equals 20, and so on. This place value understanding will help you translate between pictures and number equations correctly.
Carlos solves 13−8 by covering up 8 dots on a ten-frame that shows 13 dots total. He then counts the uncovered dots to get his answer. What addition fact is Carlos finding?
Explanation: Carlos is finding the unknown addend in 8+?=13 by using a visual method. When he covers 8 dots out of 13, he sees 5 remaining dots, discovering that 8+5=13. Choice B adds the total to one part incorrectly. Choice C uses the wrong numbers entirely. Choice D doubles 8, which is unrelated to the problem.
Look at the rectangle below. Tom wants to share this rectangle equally among 4 friends (including himself). After he divides it correctly, what should Tom say about the size of each person's piece compared to if he had shared it equally among just 2 friends?
Explanation: When you divide the same rectangle among more people, each person gets a smaller piece. Sharing among 4 friends means dividing into 4 equal parts (quarters). Sharing among 2 friends means dividing into 2 equal parts (halves). Since quarters are smaller than halves, each piece is smaller when shared among 4 friends. This demonstrates that decomposing into more equal shares creates smaller shares. Choice A is wrong because having more people means smaller pieces for each person. Choice C is wrong because even though the rectangle stays the same size, each piece becomes smaller. Choice D is wrong because more pieces means each individual piece is smaller.
Look: 6+4=10 and 4+6=10. Which property is shown?
Explanation: This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The commutative property of addition means that order doesn't matter when adding two numbers: a + b = b + a. For example, if we know that 6 + 4 = 10, we also know that 4 + 6 = 10 without having to calculate again. This is useful because we can choose to add in the easier order, like starting with the larger number. The problem shows 6 + 4 = 10 and 4 + 6 = 10 and asks which property is shown. Choice A is correct because the commutative property tells us order doesn’t matter when adding, demonstrating that switching the numbers gives the same sum. Choice C is a common error where students think the sum changes when you switch numbers, perhaps confusing addition with subtraction. This happens because properties are abstract concepts and students need extensive experience with many examples. To help students: Provide many concrete examples showing both orders give same answer; use physical objects to demonstrate commutative property (count group A then B, or B then A—same total); practice with equations side by side (6+4=10, 4+6=10); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.