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is the same as . What number goes in the box?
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1st Grade Math
Practice Test 1 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Question 1 of 25
11−6=? is the same as 6+?=11. What number goes in the box?
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11−6=? is the same as 6+?=11. What number goes in the box?
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 10 - 3, we can think '3 plus what equals 10?' or write it as 3 + ? = 10, and the missing addend 7 is the difference. The problem states that 11 - 6 = ? is the same as 6 + ? = 11 and asks for the number that goes in the box. Choice A is correct because when we add 5 to 6, we get 11, so 6 + 5 = 11, which means 11 - 6 = 5. Choice C is a common error where students might make an off-by-one mistake, such as counting from 6 to 11 as 4 steps instead of 5, because counting on accurately requires practice and students may include the starting number. To help students: Use part-part-whole diagrams showing the relationship; practice on number lines with counting-on (start at 6, count forward to 11); teach fact families explicitly (6+5=11, 5+6=11, 11-6=5, 11-5=6); use 'think addition' language consistently ('to subtract 11-6, think what plus 6 equals 11'); 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.
Chen drew a circle. How many corners does it have?
Explanation: This question tests 1st grade understanding of defining attributes of circles, specifically the absence of corners (CCSS.1.G.A.1). Defining attributes for a circle include being a closed curve with no straight sides or corners, distinguishing it from polygons. Non-defining attributes like size or color do not alter its circular nature. The scenario involves Chen drawing a circle and asking about its corners, focusing on this key difference from angular shapes. Choice A is correct because a circle has zero corners, as it lacks the angled vertices found in shapes like triangles or squares. Choice D is a common error if students confuse circles with triangles, perhaps due to early misconceptions where 1st graders apply corner-counting to all shapes indiscriminately. To help students, trace circles with fingers to feel the smooth curve, compare to shapes with corners, and use activities like 'Corner Hunt' where they count corners on various shapes to reinforce that circles have none.
Which symbol makes this true: 45 23?
(correct answer)
Explanation: This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 45 > 23 because 4 tens is greater than 2 tens (we don't even need to look at the ones in this case). The stimulus shows two numbers, 45 and 23, that need to be compared with the correct symbol. Choice C is correct because the > symbol accurately shows 45 is greater than 23 since 4 tens > 2 tens. Choice B is a common error where students reverse the comparison symbols, thinking < means greater than, which happens because symbol direction is easily confused like an alligator mouth opening to the bigger number. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
Use a near double to solve 7+8: 7+7+1.
Explanation: This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Creating equivalent sums using doubles helps with near-doubles. For 7 + 8, we recognize these are close to the double 7 + 7, so we think: 7 + 8 = 7 + 7 + 1 = 14 + 1 = 15. The problem asks to use a near double to solve 7 + 8: 7 + 7 + 1. Choice C is correct because using doubles: 7 + 7 + 1 = 14 + 1 = 15. Choice B is a common error where for near-doubles, students forget to add the +1 and get 14; this happens because students may try to compute without using the strategy. To help students: For doubles, ensure all doubles facts are memorized (6+6, 7+7, 8+8, 9+9); for near-doubles, practice thinking 'double plus/minus 1'; provide daily practice with mixed strategies; help students select appropriate strategy for each problem type.
Complete: 8+6=8+2+ . What number goes in the blank?
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 complete 8 + 6 = 8 + 2 + _ by finding the blank. Choice C is correct because following making-10: after 8 + 2 = 10, the remainder of 6 is 4, so 10 + 4 = 14. Choice D is a common error where students don't decompose correctly and put the whole second number like 6, forgetting to split it; this happens because decomposing numbers flexibly is challenging. 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.
Lisa has 32 books. She gets 10 more books for her birthday, then gives 20 books to the library. How many books does she have left?
Explanation: This is a multi-step word problem that requires you to track changes to Lisa's collection of books. When you see problems with multiple operations, work through them step by step in the order they happen. Start with Lisa's original amount: 32 books. First, she gets 10 more books for her birthday, so you add: 32+10=42 books. Next, she gives 20 books to the library, so you subtract: 42−20=22 books. Lisa ends up with 22 books after all the changes. Looking at the wrong answers: Choice B (12 books) happens if you subtract both the birthday books and library books from the original amount: 32−10−20=2, or if you make an error in your final subtraction. Choice C (42 books) is the amount Lisa had after getting birthday books but before giving any to the library—this happens when you forget the final step. Choice D (62 books) occurs if you add all the numbers together instead of following the story: 32+10+20=62. The correct answer is A. For multi-step word problems, always follow the story in order and keep track of your running total after each operation. Circle or underline key words like "gets" (addition) and "gives away" (subtraction) to help you identify which operation to use at each step.
Sofia adds ones: 39+8. What is the sum after regrouping?
Explanation: This question tests 1st grade addition within 100, specifically adding a two-digit and one-digit number requiring regrouping (CCSS.1.NBT.C.4). When adding within 100, use place value strategies: add tens to tens and ones to ones. For 39 + 8, add ones (9+8=17), composing 1 ten and 7 ones, so tens increase (3 tens + 1 = 4 tens), resulting in 47. The stimulus is Sofia adding ones in 39 + 8 and finding the sum after regrouping. Choice A is correct because 9 ones + 8 ones = 17 ones, composing 1 ten and 7 ones, so 3 tens + 1 ten = 4 tens with 7 ones = 47. Choice D (49) is a common error where students don't regroup properly and keep 9 ones or add extra, often because they treat digits separately without composing. To help students: Demonstrate regrouping with base-10 blocks; use place value charts for organization; teach 'regroup when ones are 10+'; practice examples with composing; connect to real contexts like adding scores.
Ana solved an addition problem by counting forward: "4,5,6,7". Then she solved a subtraction problem by counting backward: "7,6,5,4". What do you notice about the relationship between these two counting sequences?
Explanation: When you see counting sequences in math problems, think about how addition and subtraction relate to each other. Ana's counting shows a fundamental mathematical relationship. Let's examine what Ana did. She counted forward "4, 5, 6, 7" to solve an addition problem, likely 4+3=7. Then she counted backward "7, 6, 5, 4" for subtraction, probably 7−3=4. Notice that these operations completely reverse each other - addition took her from 4 to 7, and subtraction brought her right back from 7 to 4. This demonstrates that addition and subtraction are inverse operations, meaning they undo each other. Answer C correctly identifies this relationship. Answer A is wrong because addition and subtraction don't give the same answer - Ana got 7 from addition and 4 from subtraction. Answer B misses the point entirely; just because the sequences use the same numbers doesn't make addition and subtraction identical operations - the direction and result are completely different. Answer D focuses only on the counting technique rather than the mathematical relationship between the operations. The key insight is recognizing inverse relationships: when you add a number and then subtract the same number (or vice versa), you return to your starting point. Remember this pattern: whenever you see forward and backward counting sequences, look for inverse operations. This concept appears throughout math - addition/subtraction, multiplication/division - so understanding how operations can "undo" each other will help you solve many problems.
Look at the sorting chart. The teacher put shapes in groups based on whether they are 2D (flat) or 3D (take up space). Which shape is placed in the wrong group?
Explanation: Circle and square are correctly in the 2D group (flat shapes), and cube is correctly in the 3D group (takes up space). All shapes are sorted correctly.
Which equation is false?
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 6 + 3 = 9, it's true, but in 6 + 3 = 8, left is 9 and right is 8, so false. The problem presents several equations to evaluate and asks which is false. Choice C is correct because 6 + 3 = 8 is false since 6+3=9 and 9 ≠ 8. Choice A is a common error where students make subtraction errors in 14-4. This happens because evaluating both sides requires accurate computation. 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 mixed operations; provide mixed true/false equations for evaluation; discuss why false equations are false (different values).
Emma collects 34 shells at the beach. Then she finds 10 more shells in a tide pool. How many shells does Emma have altogether?
Explanation: When you see a word problem asking "how many altogether," it's telling you to add numbers together. This is an addition problem where Emma starts with some shells and finds more. Let's work through this step by step. Emma begins with 34 shells from the beach. Then she finds 10 more shells in the tide pool. To find how many shells she has altogether, you need to add: 34+10=44 shells. Looking at the answer choices, A) 44 shells is correct because it's the sum of 34+10. B) 24 shells is wrong because this would be the result if you subtracted instead of added (34−10=24). When you see "altogether" or "in total," you should add, not subtract. C) 35 shells is incorrect because this only adds 1 to the original amount (34+1=35). This might happen if you misread the problem and thought Emma found only 1 more shell instead of 10. D) 43 shells is wrong because this adds 9 instead of 10 (34+9=43). This could result from a simple counting error. Remember: When a word problem asks for a total, altogether, or in all, look for addition keywords and add the numbers together. Always double-check your addition by counting carefully or adding the numbers in reverse order.
Keisha has 7 marbles. Carlos has 3 marbles. Yuki has 6 marbles. How many marbles do they have altogether?
Explanation: This question tests 1st grade ability to add three whole numbers with sum ≤20 (CCSS.1.OA.2). When adding three numbers, students can use helpful strategies to make it easier. One strategy is to find pairs that make 10 (like 7+3), add first, then the third; doubles or easy adds work too, with flexible ordering. The story presents three quantities: 7 marbles from Keisha, 3 from Carlos, and 6 from Yuki. Choice C is correct because adding all three gives 7 + 3 + 6 = 16; we can add 7+3=10 first, then 10+6=16. Choice D is a common error from misadding after pairing, like 10+4=14 instead of 6; this stems from non-automatic facts or distraction. To help students: Use marble bags for groups; teach making-10 explicitly; model with parentheses (7+3)+6; connect to sharing games; have students practice and explain.
Maria has 12 pennies and wants to trade them for other coins. She needs to know which coins equal 12 cents. What should Maria do FIRST?
Explanation: When you need to find which coins equal a certain amount, the best approach is to use hands-on exploration with real coins. This helps you see and feel the different combinations that work. Option C is correct because getting real nickels and dimes lets Maria physically test different trades. She can group her 12 pennies and then try replacing 5 pennies with 1 nickel, or 10 pennies with 1 dime. By handling the actual coins, she'll discover that 12 cents can be made with 2 nickels and 2 pennies, or 1 dime and 2 pennies, or other combinations. This concrete experience makes the math concept stick. Option A won't help Maria learn about coin equivalents - she already knows she has 12 pennies. Option B misses a great learning opportunity. While teachers can provide answers, Maria will learn much more by exploring the problem herself first. Option D focuses on memorizing coin names rather than understanding their values and relationships, which doesn't solve her trading problem. The key difference is that option C involves active problem-solving with manipulatives (the coins themselves), while the other choices either avoid the problem or approach it in ways that don't build understanding. Study tip: When working with money problems, always try to use real coins or coin models first. Seeing and touching the coins helps you understand their relationships much better than just thinking about numbers on paper.
Look at the number line. Point A shows a number that has the same number of tens as which other number?
Explanation: Point A is at 80, which has 8 tens. The number 82 also has 8 tens (8 tens and 2 ones). Choice A has 2 tens, Choice C has 9 tens, and Choice D has 3 tens.
Look at the bar graph. Children voted for their favorite playground equipment. Swings got 6 votes, slides got 9 votes, and monkey bars got 4 votes. If the same number of children who voted for monkey bars also vote for swings, how many total votes will there be?
Explanation: Original votes: Swings = 6, Slides = 9, Monkey bars = 4. Total original = 6 + 9 + 4 = 19. Additional votes for swings = 4 (same as monkey bars). New total = 19 + 4 = 23. Choice A gives only the original total. Choice C incorrectly calculates 6 + 9 = 15. Choice D adds the monkey bar votes to the original total instead of adding them to swings (19 + 4 = 23, but miscalculated as 21).
Maya bundles 10 sticks with a rubber band. What is it called?
Explanation: This question tests 1st grade understanding that 10 ones can be bundled as one ten (CCSS.1.NBT.B.2.a). In our number system, 10 individual ones can be grouped or bundled together to make one ten. This doesn't change the amount—10 ones and 1 ten are the same quantity—but bundling helps us count and organize larger numbers more efficiently. The scenario describes Maya bundling 10 sticks with a rubber band, representing the grouping of 10 ones into one ten. Choice A is correct because the bundled group of 10 ones is called 'one ten.' Choice B is a common error where students believe bundling creates ten tens, confusing the unit; this happens because the terminology 'one ten' is confusing when it represents 10 ones. To help students: Provide extensive hands-on practice with base-10 blocks, physically bundling 10 unit cubes to match a ten-rod; use real objects like craft sticks with rubber bands to bundle 10 into 'one ten'; emphasize 'same amount, different name' when showing 10 ones = 1 ten; use ten-frames consistently; practice language explicitly ('ten ones' vs 'one ten'); demonstrate trading: exchange 10 ones for 1 ten; connect to counting by tens; avoid moving too quickly to symbolic notation.
Maya wants to find 7+8. She has her fingers, paper, and counting cubes. Maya thinks "7+8 is the same as 8+7." Which tool should Maya use with this thinking?
Explanation: When you're adding two numbers, you can use the fact that addition is commutative — meaning you can add in any order and get the same answer. So 7+8 really does equal 8+7. The key question is which tool works best with this smart thinking. Since Maya knows she can switch the order, she should pick the approach that makes counting easier. Starting with the larger number (8) and counting up by the smaller number (7) requires less work than starting with 7 and counting up by 8. With fingers, Maya can hold up 8 fingers, then count up 7 more in her head or use her remaining fingers. This makes the addition much simpler. Let's look at why the other choices don't work as well: Choice B suggests paper to write both number sentences, but writing them down doesn't actually help Maya solve the problem faster. Choice C recommends counting cubes to make separate groups, but this approach doesn't take advantage of her smart thinking about switching the numbers. Choice D suggests using fingers to count 7 first, but this ignores the whole point of starting with the larger number to make counting easier. Study tip: When adding two different numbers, always start with the larger number and count up by the smaller one. This strategy works especially well with fingers since you have limited fingers to work with — starting with 8 leaves you with just 2 more fingers needed, while starting with 7 would require 8 more!
Ben has 7 toy cars. His sister has some toy cars too. Together they have 13 toy cars. Which two equations both show how many cars Ben's sister has?
Explanation: Ben has 7 cars, sister has ? cars, total is 13. This gives us 7 + ? = 13. We can also write this as 13 - 7 = ? (total minus Ben's cars equals sister's cars). Both equations find the same unknown. Choice B mixes addition and subtraction incorrectly. Choice C has the wrong relationships. Choice D uses incorrect operations.
Amir says 10 means 1 ten. What is 10 more than 23?
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, 23 + 10 = 33 because 2 tens + 1 ten = 3 tens, and the 3 ones remain unchanged. The scenario involves Amir recognizing that 10 means 1 ten and finding 10 more than 23. Choice C is correct because adding 10 to 23 means adding 1 ten: 2 tens + 1 ten = 3 tens, ones stay 3, giving 33. Choice A is a common error where students add 1 instead of 10, resulting in 24; this happens because students sometimes focus on the digit '1' in 10 rather than its place value meaning as 1 ten. 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.
Sofia has 4 tens and 38 ones. She makes as many new tens as possible from her ones. After regrouping, how many tens and ones does she have?
Explanation: When you see a problem about regrouping, you're working with place value - understanding that 10 ones can be traded for 1 ten. Let's start with what Sofia has: 4 tens and 38 ones. To make as many new tens as possible from her ones, you need to group every 10 ones into 1 ten. Looking at 38 ones, ask yourself: "How many groups of 10 can I make?" You can make 3 groups of 10 (since 3×10=30), with 8 ones left over (since 38−30=8). Now add up all the tens: Sofia's original 4 tens plus the 3 new tens she made equals 7 tens. She has 8 ones remaining. So the answer is 7 tens and 8 ones. Looking at the wrong answers: Choice B (6 tens and 18 ones) shows you only made 2 new tens instead of 3, leaving too many ones ungrouped. Choice C (4 tens and 38 ones) means you didn't regroup at all - you kept everything the same. Choice D (8 tens and 3 ones) shows you made 4 new tens, but 38 ones can only make 3 complete tens, not 4. Remember: Always divide the ones by 10 to see how many new tens you can make, then add those new tens to the original tens. The remainder becomes your final number of ones.
Use the diagram to answer the question. Jake measured two ribbons using the same size buttons. The red ribbon measured 4 buttons long. The blue ribbon measured 6 buttons long. If Jake puts both ribbons end to end to make one long ribbon, how many buttons long will the combined ribbon be?
Explanation: When combining the ribbons end to end, add their lengths: 4 buttons + 6 buttons = 10 buttons long. Choice A adds an extra button, possibly from double-counting where ribbons connect. Choice C subtracts one button incorrectly. Choice D represents a common error of adding extra length.
Marcus saw 12 birds. Yuki saw 9 birds. How many more birds did Marcus see than Yuki?
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 Marcus saw 12 birds and Yuki saw 9 birds. Choice C is correct because to find how many more birds Marcus saw, we subtract: 12 - 9 = 3. We can represent this as an equation with unknown: 12 - 9 = ?. Choice A is a common error where students find the total instead of the difference (12 + 9 = 21); this happens because compare problems require understanding '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 ('Marcus has 12, Yuki 9, need how many more for Marcus, so I subtract'); practice all unknown positions; connect to familiar experiences.
Read the problem. There are 7 apples on the table, 3 apples on the counter, and 2 apples in a bowl. How many apples are there in all?
Explanation: This question tests 1st grade ability to add three whole numbers with sum ≤20 (CCSS.1.OA.2). When adding three numbers, students can use helpful strategies to make it easier. One strategy is to look for two numbers that make 10 (like 6+4 or 7+3), add those first, then add the third number; another strategy is to look for doubles (like 4+4) or numbers that are easy to add together, combine those first, then add the remaining number; students can add in any order because of the commutative and associative properties. The story presents three quantities: 7 apples on the table, 3 apples on the counter, and 2 apples in a bowl. Choice A is correct because adding all three numbers gives 7 + 3 + 2 = 12; we can add 7+3=10 first, then 10+2=12. Choice B is a common error where students forget to add the third number after making 10, such as adding 7+3=10 and stopping, or misidentify which numbers make 10; this happens because students may focus on two numbers and lose track of the third, and applying strategies requires practice. To help students: Use physical objects in three groups that students can count and combine; teach making-10 strategy explicitly with pairs that sum to 10; practice doubles facts (3+3, 4+4, 5+5); model different groupings using parentheses: (7+3)+2 or 7+(3+2); use visual representations showing three groups; emphasize that order doesn't matter; have students explain their strategy; practice with various number combinations; connect to real contexts with three groups.
Using the bar graph shown, what is the total number of students who chose outdoor sports (soccer and baseball)?
Explanation: From the graph: soccer = 7 students, baseball = 6 students. These are the outdoor sports. Total: 7 + 6 = 13 students. Choice A (8) might come from reading the wrong bars. Choice B (11) might result from miscounting one sport. Choice D (19) adds all sports instead of just the outdoor ones.
Is this equation true or false: 4+1=3+2?
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 4 + 1 = 3 + 2, left is 5 and right is 5, so it's true, but in 4 + 1 = 5 + 2, it's 5 = 7, false. The problem presents the equation 4 + 1 = 3 + 2. Choice B is correct because 4 + 1 = 3 + 2 is true since both sides equal 5. Choice C is a common error where students think both sides must have the same numbers, not realizing different expressions can have the same value. This happens because students need to see many varied equation structures. To help students: Show equations in many structures (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; show how 4 + 1 = 3 + 2 is true (both 5); provide mixed true/false equations for evaluation; discuss why false equations are false (different values); avoid only using 'operation = answer' format; use language like 'same as' and 'equal to.'