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Without counting by ones, what is ?
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1st Grade Math
Practice Test 11 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Question 1 of 25
Without counting by ones, what is 56+10?
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Without counting by ones, what is 56+10?
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 asks to find 56 + 10 without counting by ones, emphasizing mental strategy. Choice A is correct because adding 10 to 56 means adding 1 ten: 5 tens + 1 ten = 6 tens, ones stay 6, giving 66. Choice D is a common error where students do nothing or forget to change the tens digit, leaving it as 56; this happens because counting by ones is a fallback that can lead to errors when not using the efficient mental strategy. 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.
Jamal adds 4+7+3. Which change helps make 10 using both properties?
Explanation: This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The associative property of addition means that when adding three numbers, we can group them in different ways and get the same answer: (a + b) + c = a + (b + c), and combined with commutative, we can rearrange for easier grouping. This is especially useful for making 10: in 4 + 7 + 3, we can group 7 + 3 first to make 10, then add 4 to get 14, using both properties to choose the best way. The problem involves adding 4 + 7 + 3 and asks which change helps make 10 using both properties. Choice A is correct because 4 + (7 + 3) groups 7 and 3 to make 10 first, using associative property and implying commutative for rearrangement, then adds 4 for 14. Choice B is a common error where students choose a harder grouping rather than an easier one, which happens because the making-10 strategy must be explicitly taught and the connection between properties and strategy isn't automatic. To help students: Explicitly teach making-10 pairs and how to use them with associative and commutative properties; practice identifying pairs that make 10 in three-number problems; use physical objects to demonstrate groupings and order changes; provide many examples with different ways to group and order; use visual models like ten-frames; emphasize 'we can make 10 first' for associative and 'order doesn't matter' for commutative; connect properties to efficient mental math strategies.
In a game, Chen scored 6 points in round 1, 4 points in round 2, and 2 points in round 3. How many points did Chen score 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 find pairs making 10 (like 6+4), then add the third; flexible grouping helps. The story presents three quantities: 6 points in round 1, 4 in round 2, and 2 in round 3. Choice B is correct because adding all three gives 6 + 4 + 2 = 12; we can add 6+4=10, then 10+2=12. Choice A is a common error from adding only two, like 6+4=10, omitting the last; this occurs from focus loss. To help students: Use scoreboards; teach making-10; model (6+4)+2; game contexts; practice explaining.
Ben is counting his toy cars. He has 4 red cars on his shelf. In his toy box, he has 3 blue cars and some green cars. If Ben has 12 cars altogether, how many green cars are in his toy box?
Explanation: When you see a problem about finding missing parts of a whole, you're working with addition and subtraction together. Let's organize what Ben has and figure out what's missing. Ben has three groups of cars: 4 red cars on his shelf, 3 blue cars in his toy box, and some unknown number of green cars also in his toy box. All together, he has 12 cars total. First, let's add up the cars we know about: 4 red cars +3 blue cars =7 cars. Now we can find the green cars by asking: "What number plus 7 equals 12?" We can write this as 7+?=12, or solve it by subtraction: 12−7=5. So Ben has 5 green cars. Let's check why the other answers are wrong. Choice A (9 green cars) would give us 4+3+9=16 cars total, which is too many. Choice B (6 green cars) would give us 4+3+6=13 cars total, still too many. Choice C (7 green cars) would give us 4+3+7=14 cars total, also too many. Only choice D (5 green cars) gives us the correct total: 4+3+5=12 cars. Remember this strategy for "missing part" problems: add up what you know, then subtract from the total to find what's missing. Always check your answer by adding all the parts together to make sure they equal the total given in the problem.
Carlos has 6 toy cars. His sister gives him 4 more cars. Carlos counts on from 6 to find his total: "7,8,9,10". How many toy cars does Carlos have now, and did he count correctly?
Explanation: Carlos correctly used the counting-on strategy for addition. Starting with 6 cars and adding 4 more, he counted forward 4 numbers from 6: "7, 8, 9, 10". He counted 4 steps forward and landed on 10, which correctly shows 6 + 4 = 10. Choice B incorrectly adds the starting number again. Choice C stops counting too early. Choice D incorrectly suggests his counting method was wrong when it was correct.
Sara has 13 crayons in her box. She gives away 3 crayons to her friend. How should Sara describe the crayons she has left using tens and ones?
Explanation: When you see a problem asking you to describe a number using "tens and ones," you need to think about place value - how we break numbers into groups of ten and leftover ones. Let's solve this step by step. Sara starts with 13 crayons and gives away 3 crayons. First, we subtract: 13−3=10. So Sara has 10 crayons left. Now we need to express 10 using tens and ones. The number 10 means exactly 1 ten and 0 ones, because ten ones make one group of ten with nothing left over. Looking at the wrong answers: Choice A says "1 ten and 3 ones" but this would equal 13 total crayons, not 10. The reasoning is flawed because it focuses on what Sara gave away instead of what she has left. Choice B correctly calculates 13−3=10 but incorrectly describes 10 as "0 tens and 10 ones." While 10 ones does equal 10, we should group tens whenever possible in place value problems. Choice D ignores the subtraction entirely, describing Sara's original amount rather than what she has after giving some away. The correct answer is C: 1 ten and 0 ones, because 13−3=10, and 10 is best described as 1 ten with 0 ones remaining. Remember: always group into tens when possible, and make sure you're answering what the problem actually asks for - in this case, what Sara has left, not what she started with or gave away.
Jamal groups 10 counters. How many tens is that?
Explanation: This question tests 1st grade understanding that 10 ones can be bundled as one ten (CCSS.1.NBT.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 Jamal grouping 10 counters, which forms one bundled ten. Choice B is correct because grouping 10 counters equals 1 ten. Choice C is a common error where students think the number of ones directly equals the number of tens; this happens because understanding grouping requires concrete experiences. 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.
Jake writes the number 19 on his paper. His teacher asks him to show this number using place value. If Jake breaks apart 19 correctly, what will he write?
Explanation: When you see a question about place value, you need to understand what each digit's position means in a number. In any two-digit number, the left digit tells you how many tens you have, and the right digit tells you how many ones you have. Let's look at the number 19. The digit 1 is in the tens place, which means you have 1 ten (which equals 10). The digit 9 is in the ones place, which means you have 9 ones. So 19=10+9, showing 1 ten and 9 ones. This makes choice C correct: 19=10+9 showing 1 ten and 9 ones. Choice A gets the math right (9+10=19) but describes the place values backwards. It says 9 tens and 1 one, which would actually be 90+1=91, not 19. Choice B shows 1+9=10, not 19. This breaks apart just the digits without considering their place values. Also, describing this as "1 one and 9 ones" would only give you 10 total, missing the tens place entirely. Choice D uses subtraction (20−1=19), which is mathematically correct but doesn't show place value the way your teacher wants. Place value means breaking a number into tens and ones using addition, not subtraction. Remember: when breaking apart numbers by place value, always think "How many tens plus how many ones?" The tens digit tells you the tens, and the ones digit tells you the ones.
9−4=? is the same as 4+?=9. What is ??
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 do I add to get to the total?' For example, to solve 10 - 3, we can think '3 plus what equals 10?' or write it as 3 + ? = 10, and finding the missing addend (7) gives the subtraction answer. This strategy leverages the inverse relationship between addition and subtraction, making it easier for young learners to use known addition facts. The problem states that 9 - 4 = ? is the same as 4 + ? = 9 and asks for ?. Choice C (5) is correct because when we add 5 to 4, we get 9, so 4 + 5 = 9, which means 9 - 4 = 5. Choice B (13) is a common error where students add the two numbers instead of finding the difference, which happens because students may be more familiar with the 'taking away' model of subtraction. To help students: Use part-part-whole diagrams showing the relationship; practice on number lines with counting-on (start at smaller number, count forward to larger); teach fact families explicitly (4+5=9, 5+4=9, 9-4=5, 9-5=4); use 'think addition' language consistently ('to subtract 9-4, think what plus 4 equals 9'); 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.
Observe the figure. Maria used identical dominos to measure her rectangular placemat. Each domino is exactly the same size. Based on what you see, how long is the placemat?
Explanation: Counting the dominos placed end-to-end that span the placemat's length, there are exactly 4 dominos with no gaps or overlaps. This represents the length measurement of the placemat. Choice B overcounts by one domino. Choice C undercounts by one domino. Choice D overcounts by two dominos.
Amir cut a paper circle into two equal parts. Each part is a .
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 Amir cutting a paper circle into two equal parts. Choice C is correct because each of the two equal parts is a half. Choice A is a common error where students use quarter instead of half, 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.
Look at the line of children below. If you start counting from the left, which child is 5th in line?
Explanation: Counting from the left, the girl with pigtails is in the 5th position. Students must understand the starting point (left) and count ordinal positions accurately. The other choices represent children in different positions in the line.
Read the problem. On Monday, Amir read 2 books. On Tuesday, he read 8 books. On Wednesday, he read 4 books. How many books did Amir read 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: 2 books on Monday, 8 books on Tuesday, and 4 books on Wednesday. Choice A is correct because adding all three numbers gives 2 + 8 + 4 = 14; we can add 2+8=10 first, then 10+4=14. Choice B is a common error where students only add two of the three numbers, such as 8+4=12 and forgetting the 2, or make a calculation error like 2+8=10 and 10+2=12 by miscounting the 4; this happens because keeping track of three numbers is challenging and calculation facts may not be automatic. 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: (2+8)+4 or 2+(8+4); 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.
Lisa has 15 buttons. She puts some in a box and keeps 7 buttons out. To find how many buttons are in the box, Lisa says "I'll count backwards from 15 until I get to 7." Will this strategy work?
Explanation: When you see a word problem asking "how many are left" or "how many are in the box," you're dealing with subtraction. Lisa started with 15 buttons and kept 7 out, so we need to find 15−7. Lisa's counting backwards strategy won't help her here. If she counts backwards from 15 to 7, she'll say "15, 14, 13, 12, 11, 10, 9, 8, 7" - but this doesn't tell her how many buttons are in the box. The better approach is to count forward from 7 until she reaches 15, keeping track of each number: "8, 9, 10, 11, 12, 13, 14, 15." That's 8 jumps forward, so 8 buttons are in the box. Let's check the wrong answers: Choice A is incorrect because counting backwards doesn't always work for subtraction - it depends on what you're trying to find. Choice C misses the point - even if Lisa counts backwards carefully, she still won't get the answer she needs. Choice D suggests using addition to check, but that's not necessary to solve the original problem. Choice B is correct because counting forward from the smaller number (7) to the larger number (15) will give Lisa the difference she's looking for. Remember: When you need to find the difference between two numbers in a word problem, count forward from the smaller number to the larger number, or simply subtract the smaller from the larger.
A square must have 4 sides that are what?
Explanation: This question tests 1st grade understanding of square attributes, specifically that all sides must be equal length (CCSS.1.G.1). A square is a special rectangle where all four sides are the same length and all corners are right angles. The question asks what the 4 sides of a square must be. Choice B (All the same length) is correct because equal side length is a defining attribute of squares. Choice A (Curved) is incorrect because squares have straight sides, Choice C (2 long and 2 short) describes a rectangle but not a square, and Choice D (Different colors) refers to a non-defining attribute. Students often confuse squares and rectangles because both have 4 sides and 4 corners. To help students: Use rulers to measure square sides and verify they're equal; compare squares and rectangles side-by-side; practice the definition 'A square has 4 sides that are all the same length.'
Jake had some toy cars. He bought 6 more toy cars. Now he has 15 toy cars in total. Which number sentence shows how many toy cars Jake had at the start?
Explanation: When you see a word problem where someone gets more of something and ends up with a total, you need to work backwards to find what they started with. Think of it like undoing what happened in the story. Jake started with some cars (we don't know how many), bought 6 more, and ended up with 15 total. To find how many he started with, you need to subtract the 6 cars he bought from his final total of 15. This gives you 15−6=9, so Jake started with 9 toy cars. Let's check why the other answers don't work. Answer B shows 15+6=21, which would mean Jake ended up with 21 cars instead of 15 - this adds the 6 cars he bought to his final total instead of finding his starting amount. Answer C shows 6+9=15, which is actually a correct math fact, but it doesn't answer the question of how many cars Jake had at the start. Answer D shows 9−6=3, which takes away the cars Jake bought from his starting amount, giving a meaningless result of 3. You can double-check answer A by thinking forward: if Jake started with 9 cars and bought 6 more, he'd have 9+6=15 cars total, which matches the story. Study tip: When someone gains something and you know their final total, subtract what they gained to find what they started with. Always check your answer by working forward through the story.
Chen has 15 blocks. 15 is 1 ten and ones.
Explanation: This question tests 1st grade understanding that teen numbers (11-19) are composed of 1 ten and ones (CCSS.1.NBT.B.2.b). All teen numbers—11, 12, 13, 14, 15, 16, 17, 18, and 19—have the same structure: exactly 1 ten plus some ones (between 1 and 9 ones). For example, 15 is made of 1 ten and 5 ones, which we can also write as 10 + 5 = 15. This structure helps students understand place value and connects the teen number names to their composition. The scenario asks to fill in 15 is 1 ten and ones for Chen's 15 blocks. Choice C is correct because all teen numbers contain 1 ten, and this one has 5 ones making it 15. Choice D is a common error where students think the teen number itself represents the number of ones (15 has 15 ones), which happens because understanding that 'fifteen' means 5 beyond 10 requires explicit instruction. To help students: Use base-10 blocks extensively—always show 1 ten-rod plus unit cubes for teens; connect number names to structure ('fif-teen' = 5 + 10); practice building each teen number with 1 ten and ones repeatedly; emphasize ALL teen numbers have 1 ten, only the ones vary; use ten-frames with one full frame (the ten) and partial second frame (the ones); write equations (10 + 5 = 15); practice decomposing teens into 10 + ones; compare teens to show same ten structure.
Which is true about rectangles?
Explanation: This question evaluates 1st grade understanding of defining attributes of rectangles (CCSS.1.G.A.1). Rectangles must have four straight sides, four right-angle corners, and be closed, with opposite sides equal. Non-defining attributes like size (e.g., not 'must be tiny') do not impact classification. The question lists statements, requiring selection of the true one about rectangles. Choice B is correct because 'they have 4 corners' accurately describes a defining attribute of rectangles. Choice C is a distractor, claiming 'they must be tiny,' which confuses non-defining size with essentials; young students might pick this if they've only seen small examples, overlooking that size varies. To help students: Build rectangles of various sizes using blocks, count corners each time, and contrast with other shapes, reinforcing 'Rectangles always have four sides and four corners, but they can be big or small.'
Look at the ten frame diagram. Michael wants to show his math partner why this represents the number 9. Which explanation would BEST communicate the mathematical concept using the ten frame representation?
Explanation: Choice C best uses the ten frame as a mathematical tool by emphasizing the relationship between part and whole (9 out of 10), which is the key mathematical concept that ten frames are designed to teach. This explanation connects counting, spatial relationships, and place value understanding. Choice A focuses only on counting without using the ten frame structure. Choice B is too simple and doesn't explain the ten frame concept. Choice D uses counting and symbolic representation but misses the part-whole relationship.
Look at the shape sorting mat below. Which shape does NOT belong in the section where it is placed?
Explanation: Shape B is a rectangle in the 'shapes with 3 sides' section, but rectangles have 4 sides. Shape A (triangle) correctly belongs in the 3-sides section, and Shape C (square) correctly belongs in the 4-sides section.
To add 13+4, start at 13 and count on 4: 14, 15, 16, 17. What is the answer?
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 13 + 4, start at 13 and count forward 4 numbers: '14, 15, 16, 17'—the last number you say (17) is the answer. The problem asks to add 13 + 4 by counting on from 13. Choice B is correct because starting at 13 and counting on 4 gives '14, 15, 16, 17,' so the answer is 17. 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.
Read the problem. Yuki has 3 crayons in her desk, 7 crayons in her backpack, and 2 crayons on the table. How many crayons does Yuki have 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 3+7), add those first, then the third number; another is to add easy pairs and use commutative and associative properties. The story presents three quantities: 3 crayons in her desk, 7 crayons in her backpack, and 2 crayons on the table. Choice A is correct because adding all three numbers gives 3 + 7 + 2 = 12; for example, add 3+7=10 first, then 10+2=12. Choice B is a common error where students only add two numbers, like 3+7=10 and forget the 2; this happens because calculation facts may not be automatic and students may lose track of one number. 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 with various number combinations; model different groupings using parentheses like (3+7)+2; use visual representations showing three groups; emphasize that order doesn't matter; have students explain their strategy; connect to real contexts with three groups.
To add 2+6+4, which two should you add first to make 10?
Explanation: This question tests 1st grade understanding of properties of operations as addition strategies (CCSS.1.OA.3). The associative property of addition means that when adding three numbers, we can group them in different ways and get the same answer: (a + b) + c = a + (b + c). This is especially useful for making 10: in 2 + 6 + 4, we can group 6 + 4 first to make 10, then add 2 to get 12. Choosing the right grouping makes computation much easier. The problem asks which two to add first to make 10 in 2 + 6 + 4. Choice C is correct because grouping 6 and 4 first gives 10, and 10 + 2 = 12, making the calculation easier. Choice B is a common error where students don't recognize that grouping two numbers that make 10 is easier, perhaps choosing two smaller numbers instead. This happens because the making 10 strategy must be explicitly taught. To help students: Provide many concrete examples showing both groupings give same answer; use physical objects to demonstrate; explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side; use visual models like ten-frames; emphasize 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.
There are 5 apples in a basket, 5 apples on the table, and 4 apples on the counter. 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 identify doubles (like 5+5), add them first, then the third; grouping helps, and addition is commutative and associative. The story presents three quantities: 5 apples in a basket, 5 on the table, and 4 on the counter. Choice A is correct because adding all three gives 5+5+4=14; we can add the doubles 5+5=10, then 10+4=14. Choice B is a common error where students only add two numbers, like 5+5=10, forgetting the third; this is due to challenges in tracking multiple addends. To help students: Use fruit manipulatives in groups; teach doubles explicitly; demonstrate groupings like (5+5)+4; use pictures of locations; practice with similar problems and discuss errors.
Is this statement true: 67=67?
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, 67 = 67 because both have 6 tens and 7 ones. The stimulus shows a comparison statement: 67 = 67, asking if it's true. Choice A is correct because the statement is true since both numbers are identical in tens and ones places. Choice B is a common error where students might miscount or confuse equality with inequality, which happens because place value understanding is still developing. 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).