1st Grade Math
Practice Test 6 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Kevin uses identical stamps to measure two different envelopes. The large envelope measures 8 stamps long. The small envelope measures 3 stamps long. If Kevin places the small envelope on top of the large envelope, starting from the same end, how much of the large envelope will not be covered by the small envelope?
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Kevin uses identical stamps to measure two different envelopes. The large envelope measures 8 stamps long. The small envelope measures 3 stamps long. If Kevin places the small envelope on top of the large envelope, starting from the same end, how much of the large envelope will not be covered by the small envelope?
Explanation: The uncovered portion of the large envelope equals the difference between the two lengths: 8 stamps - 3 stamps = 5 stamps worth of length will remain uncovered. Choice A incorrectly adds the lengths. Choice C gives the total length of the large envelope. Choice D gives the length of the small envelope.
Chen has 14 apples and eats 5; start at 14 and count back 5. What number is left?
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 14−5, start at 14 and count back 5: '13, 12, 11, 10, 9'—the last number you say (9) is the answer. The problem asks to subtract 14−5 by counting back from 14 in a story context. Choice B is correct because starting at 14 and counting back 5 gives '13, 12, 11, 10, 9,' so the answer is 9. Choice A is a common error where students count back only four steps, landing on 10; 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; use story problems to make it relatable.
Is this equation true or false: 12−3=10?
Explanation: This question tests 1st grade understanding of the equal sign and evaluating equations as true or false (CCSS.1.OA.7). The equal sign (=) means 'is the same as' or 'has the same value as.' To determine if an equation is true, compute the value of both the left side and the right side, then check if they're equal. For example, in 12 - 3 = 9, both sides equal 9, so it's true, but in 12 - 3 = 10, left is 9 and right is 10, so it's false. The problem presents the equation 12 - 3 = 10. Choice B is correct because it's false since 12-3=9 and 9 ≠ 10. Choice C is a common error where students make calculation errors like thinking 12-3=8. This happens because subtraction can be tricky and students may miscount. To help students: Show equations in many structures (a+b=c, c=a+b, a=a, a+b=c+d); use balance scales to represent equations (both sides must balance); emphasize 'equal sign means same value on both sides'; practice evaluating both sides separately before comparing; include subtraction examples; provide mixed true/false equations for evaluation; discuss why false equations are false (different values).
Find the unknown number: 12−□=7.
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 the subtrahend (like in 12 - ? = 7), we find what number subtracted from 12 gives 7, which can be done by subtracting: 12 - 7 = 5. We can also think of it as addition: what plus 7 equals 12, so 7 + 5 = 12. The equation is 12 - □ = 7. Choice B is correct because 12 - 5 = 7, so the unknown is 5. Choice A is a common error where students add instead, getting 12 + 7 = 19, not recognizing the need for inverse operations. To help students: Teach subtrahend unknown by connecting to addition; use fact families (12 - 5 = 7, 7 + 5 = 12); practice checking by substituting; use manipulatives; emphasize different unknown positions.
Tommy is solving 8−2 by counting backwards. He says: "I start at 8, then count 7,6 and my answer is 6". His friend Maya says: "I start at 8, count back 2 steps: 8 to 7 is one step, 7 to 6 is two steps, so the answer is 6". Who used the counting method correctly?
Explanation: When you're learning subtraction by counting backwards, there are different ways to think about the counting process, and it's important to understand that multiple approaches can work correctly. Let's examine what Tommy and Maya each did with 8−2. Tommy started at 8 and counted backwards by saying the numbers: "7, 6" and got 6. Maya also started at 8 but thought about it as taking steps: one step from 8 to 7, then another step from 7 to 6, landing on 6. Both students arrived at the correct answer of 6, and both used valid counting methods. Now let's look at why the other answers miss the mark. Answer A incorrectly suggests that only Maya's step-counting method is valid, but Tommy's number-naming approach is also a legitimate way to count backwards. Answer B makes the opposite mistake, claiming only Tommy's method works, when Maya's step-counting is equally correct. Answer D suggests both students made an error by not including 8 in their final count, but this misunderstands subtraction—when you subtract 2 from 8, you move away from 8, so 8 shouldn't be part of your final answer. The key insight is that counting backwards can be done by naming the numbers you land on (like Tommy) or by counting the steps you take (like Maya). Both approaches are mathematically sound ways to solve subtraction problems. When you practice counting backwards for subtraction, try both methods to see which one feels more natural for you.
Jake has 6 baseball cards. His friend gives him 4 more cards. Later, Jake trades 3 cards for a special card. Which equation represents how many cards Jake had after his friend gave him more but before he made any trades?
Explanation: When you see a word problem with multiple steps, you need to read carefully to understand what the question is asking for. This problem has three things happening to Jake's cards, but the question asks specifically about one moment in time. Let's follow Jake's story step by step. Jake starts with 6 baseball cards. Then his friend gives him 4 more cards. At this point, Jake has 6+4=10 cards. Later, he trades 3 cards for a special card. The question asks how many cards Jake had "after his friend gave him more but before he made any trades" - which means we only care about the first two steps, not the trading part. Choice B, 6+4=10, correctly shows Jake's cards after receiving the gift but before trading. This matches exactly what the question asks for. Choice A, 6+4−3=7, includes all three steps in Jake's story, but the question specifically asks us to stop before the trading happened. Choice C, 10−3=7, only shows the trading part and assumes you already know Jake had 10 cards, but it doesn't show how he got to 10 cards in the first place. Choice D, 6−3+4=7, mixes up the order of events - it shows Jake losing cards before gaining them, which isn't what happened. Always identify exactly what moment in time the question is asking about, especially when the word problem has multiple steps happening in sequence.
Add tens to tens: 34+20=
Explanation: This question tests 1st grade addition within 100, specifically adding two-digit and one-digit numbers or two-digit and multiples of 10 (CCSS.1.NBT.4). When adding within 100, use place value strategies: add tens to tens and ones to ones. For two-digit plus multiple of 10 (like 34 + 20), add the tens (3 tens + 2 tens = 5 tens), keeping the ones the same (4 ones), giving 54. The stimulus is an equation prompting to add tens to tens: 34 + 20. Choice A is correct because adding 3 tens + 2 tens gives 5 tens, and the 4 ones stay the same, making 54. Choice C is a common error where students don't understand place value and add 20 to the ones instead of to the tens (like 34 + 2 = 36, then misplaced 0 giving 44). This happens because regrouping/composing is complex. To help students: Use base-10 blocks extensively to show tens combining with tens, ones with ones; demonstrate regrouping with physical exchange (10 unit cubes for 1 ten-rod); use place value charts to organize thinking; practice language 'add tens to tens, ones to ones'; teach 'when ones add to 10 or more, compose a new ten'; connect visual models to written equations; provide many examples with and without composing; use number lines for counting on; relate to real contexts (stickers, toys, pages).
Complete the equation: □−2=8
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 the minuend in subtraction (like in ? - b = c), we work backwards by adding the subtrahend to the result: c + b = ?. We can check by subtracting: ? - b should equal c. The equation is □ - 2 = 8. Choice A is correct because adding 8 + 2 = 10, and we can verify: 10 - 2 = 8. Choice D is a common error where students multiply or use a different operation, like 8 x 2 - something leading to 12, which happens because working backwards is less intuitive. To help students: Teach each unknown position explicitly (result, addend, start); show how to check answer by substituting back into equation; for minuend unknown, explicitly teach 'work backwards' by adding subtrahend to result; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 10 - 2 = 8, then 8 + 2 = 10); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
13−8=? is the same as 8+?=13. What is the missing number?
Explanation: This question tests 1st grade understanding of subtraction as an unknown-addend problem (CCSS.1.OA.4). Subtraction can be solved by thinking about addition, where instead of taking away, we ask what number added to the subtrahend equals the minuend. For example, to solve 13 - 8, we can think '8 plus what equals 13?' or write it as 8 + ? = 13, and finding the missing addend (5) gives the subtraction answer. This strategy highlights the inverse relationship between addition and subtraction, making it easier for young learners to compute differences by counting on. The problem presents the subtraction 13 - 8 as equivalent to the unknown addend equation 8 + ? = 13. Choice A is correct because when we add 5 to 8, we get 13, so 8 + 5 = 13, which means 13 - 8 = 5. Choice B is a common error where students add the two numbers instead of finding the difference, resulting in 21, which happens because the connection between addition and subtraction can be abstract for beginners. To help students: Use part-part-whole diagrams showing the relationship; practice on number lines with counting-on (start at 8, count forward to 13); teach fact families explicitly (8+5=13, 5+8=13, 13-8=5, 13-5=8); use 'think addition' language consistently ('to subtract 13-8, think what plus 8 equals 13'); provide many examples connecting subtraction to unknown addend; emphasize that this strategy is especially useful when numbers are close together; use context problems where 'how many more needed' feels natural; practice writing both forms of the problem.
Jake needs to solve 13−8. He has counting bears, a number line, and paper. Jake says "13 is close to 10, so I should use that." Which tool would work BEST with Jake's thinking?
Explanation: When you're solving subtraction problems, there are different strategies you can use, and the best tool depends on your approach. Jake noticed that 13 is close to 10, which suggests he wants to use a "friendly number" strategy - breaking down the problem using numbers that are easier to work with. Option C works perfectly with Jake's thinking because it uses paper to write out exactly what he's planning: 10−8=2, then add the remaining 3 back. Since 13=10+3, Jake can subtract 8 from the friendly number 10 first (getting 2), then add back the extra 3 he set aside (getting 2+3=5). Paper is the ideal tool for showing these written steps clearly. Option A uses counting bears for direct subtraction, but this doesn't connect to Jake's insight about using 10 as a helper number. Option B suggests jumping from 8 to 13 on a number line, which would help find the difference but again ignores Jake's strategy of using 10. Option D mentions starting at 10 on a number line, which sounds related to Jake's thinking, but "adjust" is too vague - it doesn't clearly show the two-step process Jake needs. When you see a problem where someone mentions using a "friendly number" or says a number is "close to" another number, look for the answer choice that breaks the problem into clear, written steps using that friendly number.
Yuki has 13 shells. Carlos has 9 shells. How many more shells does Yuki have than Carlos? 13−9=?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is a comparing problem with difference unknown. We compare two amounts to find how many more or fewer. The story tells us Yuki has 13 shells and Carlos has 9 shells. Choice B is correct because to find how many more shells Yuki has than Carlos, we subtract: 13−9=4. We can represent this as 13−9=?. Choice A is a common error where students find the total instead of the difference, adding: 13+9=22. This happens because in compare problems, students may not recognize 'how many more' as subtraction. 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 ('Yuki has 13, Carlos 9, to find how many more, I subtract'); practice all unknown positions; connect to familiar experiences.
Tim has 1 quarter and 1 nickel. Emma has 6 coins that are all the same type. If Tim and Emma have the same amount of money, what coins does Emma have?
Explanation: Tim has 1 quarter + 1 nickel = 25 + 5 = 30 pennies worth. If Emma has 6 of the same coin worth 30 pennies total, each coin is worth 30 ÷ 6 = 5 pennies. A nickel is worth 5 pennies. 6 pennies = 6 pennies (too little), 6 dimes = 60 pennies (too much), 6 quarters = 150 pennies (too much).
Carlos uses blocks to solve 8+?=11. He puts out 8 blocks, then adds more blocks until he has 11 blocks total. How can Carlos show what he found using words and numbers?
Explanation: When you see an addition problem with a missing number like 8+?=11, you're looking for what needs to be added to the first number to reach the total. Carlos is using a smart strategy called "adding on" - he starts with 8 blocks and keeps adding until he reaches 11. Let's think through Carlos's process step by step. He starts with 8 blocks and needs to get to 11 blocks total. To find how many more he needs, you can count up from 8: "8... 9, 10, 11." That's 3 more blocks. So 8+3=11, which makes choice B correct. Looking at the wrong answers: Choice A says Carlos added 4 blocks, but 8+4=12, not 11 - that would give him too many blocks. Choice C talks about taking away blocks, but Carlos is adding blocks to solve an addition problem, not subtracting. Choice D says he added 2 blocks, but 8+2=10, which falls short of the target of 11. Notice that choices A and D both show addition (which matches what Carlos is doing) but use the wrong numbers, while choice C uses the right numbers but the wrong operation. When solving missing addend problems like this, always check that your addition sentence equals the target number. Count up from the starting number or use blocks yourself to verify your answer makes sense.
Chen adds 9+5 by counting on: start at 9 and say 10, 11, 12, 13, 14. 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 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 9 + 5 by counting on from 9. Choice B is correct because starting at 9 and counting on 5 gives '10, 11, 12, 13, 14,' so the answer is 14. Choice A is a common error where students count one too few, perhaps by stopping at the fourth count instead of fifth; 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.
Is this equation true or false: 15=12+4?
Explanation: This question tests 1st grade understanding of the equal sign and evaluating equations as true or false (CCSS.1.OA.7). The equal sign (=) means 'is the same as' or 'has the same value as.' To determine if an equation is true, compute the value of both the left side and the right side, then check if they're equal. For example, in 15=12+3, left is 15 and right is 15, so true, but in 15=12+4, left is 15 and right is 16, so false. The problem presents the equation 15=12+4. Choice B is correct because it's false since 12+4=16 and 15=16. Choice C is a common error where students make addition errors like thinking 12+4=15. This happens because students may miscount when adding larger numbers. To help students: Show equations in many structures (a+b=c, c=a+b, a=a, a+b=c+d); use balance scales to represent equations (both sides must balance); emphasize 'equal sign means same value on both sides'; practice evaluating both sides separately before comparing; explicitly teach that number=operation is valid if values match; provide mixed true/false equations for evaluation; discuss why false equations are false (different values).
Sara collects 10 shells at the beach. She finds 6 shells in the morning. In the afternoon, she finds 2 more shells, but 1 breaks. How many shells did she find in the evening?
Explanation: When you see a word problem with multiple steps like this one, you need to carefully track what happens to Sara's shells throughout the day and work backwards to find the missing piece. Let's organize what we know: Sara ends up with 10 shells total, finds 6 in the morning, finds 2 in the afternoon but 1 breaks (so she keeps 1 from the afternoon), and finds some unknown number in the evening. You can set up the problem like this: Morning shells + Afternoon shells kept + Evening shells = Total shells. So: 6+1+Evening shells=10. This means Evening shells = 10−6−1=3. Looking at the wrong answers: Answer B (1 shell) might come from only counting the shells Sara kept from the afternoon, ignoring that we need to find the evening amount. Answer C (4 shells) could result from forgetting to subtract the broken shell - if you mistakenly used 2 afternoon shells instead of 1, you'd get 10−6−2=2, but then miscalculated. Answer D (2 shells) comes from the same error about the broken shell: 10−6−2=2. The correct answer is A (3 shells). Study tip: In multi-step word problems, always organize the information first and pay close attention to things that are lost, broken, or taken away. These details change your calculations and are easy to miss when you're working quickly.
Anna needs exactly 35 pennies to buy a toy. She has 1 quarter and 1 nickel. What is the least number of additional pennies she must add?
Explanation: Anna has 1 quarter + 1 nickel = 25 + 5 = 30 pennies total. She needs 35 pennies, so she needs 35 - 30 = 5 more pennies. Wait, that would make B correct. Let me recalculate: She needs 35 - 25 = 10 more pennies if she only had the quarter, but she also has a nickel worth 5, so 35 - 30 = 5 more pennies needed.
A teacher shows students that 119 can be written as 1 hundred, 1 ten, and 9 ones. A student says they can also write it as 0 hundreds, 11 tens, and 19 ones. Is the student correct?
Explanation: The student's decomposition gives 11 × 10 + 19 = 110 + 19 = 129, not 119. Choice B incorrectly calculates 110. Choice C incorrectly states the calculation equals 119. Choice D gives a false rule about place value decomposition.
What number makes this equation true: 8+ ?=13?
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 a + ? = c), we need to find what number added to a equals c, which we can do by subtracting: c - a = ?. We can also count on from a to c and count how many steps—that gives the unknown. The equation is 8 + ? = 13. Choice A is correct because when we add 8 + 5 = 13, so the unknown is 5, or subtracting 13 - 8 = 5. Choice B is a common error where students add the two given numbers, like 8 + 13 = 21, which happens because they don't recognize they need to use the inverse operation. 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 8 + 5 = 13, then 13 - 8 = 5); emphasize checking: substitute answer back into equation to verify it's true; provide many examples with unknowns in all positions.
Look at the pattern shown in the diagram. Sarah wants to explain to her little brother what comes next in the pattern. Which explanation uses the BEST combination of mathematical representations?
Explanation: Choice C uses multiple representations most effectively: visual (drawing the next shape), spatial (pointing to repeating groups), and verbal (explaining the pattern rule). This helps the child see, hear, and understand the pattern structure. Choice A only uses counting without showing the pattern structure. Choice B relies only on verbal communication. Choice D uses symbolic representation but may be too abstract for the context.
Lily uses her fingers to show 3+4. She holds up 3 fingers on one hand and 4 fingers on the other hand. Which other way shows the same math idea as Lily's fingers?
Explanation: When you see a question about showing math with fingers, you're working with addition and understanding that the same math problem can be represented in different ways. Let's think about what Lily is doing. She holds up 3 fingers on one hand and 4 fingers on the other hand to show 3+4. If you count all her fingers together, you get 7 total fingers. This means 3+4=7. Choice A is correct because it shows the same math idea as Lily's fingers. Counting to 7 and writing 3+4=7 gives the exact same result as counting all of Lily's raised fingers. Choice B is wrong because it changes the problem completely. Instead of adding 3+4, it shows subtraction (4−3=1), which is a different operation that gives a different answer. Choice C has the right addition problem (3+4) but the wrong answer. It says 3+4=8, but when you count Lily's fingers or add 3+4, you get 7, not 8. Choice D also has the correct addition setup but gives 12 as the answer. This is way too big - if you multiply 3×4 you get 12, but that's not what Lily is showing with her fingers. Remember: When solving addition problems, the key is making sure your answer matches what you're actually counting or adding. Whether you use fingers, objects, or just numbers, 3+4 always equals 7.
Look at the pictograph. Students voted for their favorite sport. Soccer has 4 soccer balls, basketball has 3 soccer balls, and tennis has 2 soccer balls. Each soccer ball symbol represents 2 votes. After 4 more students vote for tennis, which sport will have the second-most votes?
Explanation: Original votes: Soccer = 4 √ó 2 = 8, Basketball = 3 √ó 2 = 6, Tennis = 2 √ó 2 = 4. After 4 more tennis votes: Soccer = 8, Basketball = 6, Tennis = 4 + 4 = 8. Soccer and tennis tie for first place with 8 votes each, so basketball with 6 votes has the second-most votes.
Sofia cut a brownie rectangle into two equal parts. What are they called?
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 Sofia cutting a brownie rectangle into two equal parts. Choice A is correct because the two equal parts are called halves. Choice B is a common error where students confuse halves with fourths, 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.
Chen has 67 stickers. He gives away 10. 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.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 stimulus describes Chen with 67 stickers giving away 10, asking how many now. Choice B is correct because subtracting 10 from 67 means removing 1 ten: 6 tens - 1 ten = 5 tens, ones stay 7, giving 57. Choice A is a common error where students subtract 11 instead of 10, changing both digits; this happens because counting by ones is a fallback that can lead to errors or the connection between 10 and tens place isn't automatic yet. To help students: Use base-10 blocks to show physically adding/removing 1 ten-rod while ones stay constant; practice on hundred charts (add 10 = down one row, subtract 10 = up 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/less' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
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.