Question 1 of 25
Emma shows the number by drawing group of ten dots and single dots. Her brother wants to write this same idea using numbers and symbols. Which choice matches Emma's drawing?
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1st Grade Math
Practice Test 10 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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Question 1 of 25
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?
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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.
Look at 80 shown with 8 ten-rods and 0 ones. How many ones are in 80?
Explanation: This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 80 is 8 tens and 0 ones, which we can see by showing 8 ten-rods with no unit cubes; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus shows 80 represented with 8 ten-rods and no unit cubes. Choice C is correct because 80 is composed of 8 tens and 0 ones, shown by 8 ten-rods. Choice A is a common error where students reverse tens and ones (think 8 ones instead of 0); this happens because the 0 in ones place is sometimes overlooked and students confuse decade structure with teen structure. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (80 vs 88: both have 8 tens, but 88 also has 8 ones); write equations showing 8 tens + 0 ones = 80; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Maya counted birds in her yard for 4 days. She wants to make a picture graph where each bird symbol equals 3 real birds. If she saw 6 birds on Monday, 9 birds on Tuesday, 12 birds on Wednesday, and 3 birds on Thursday, how many bird symbols should she draw for Wednesday?
Explanation: Wednesday had 12 birds. Since each symbol represents 3 birds, she needs 12 ÷ 3 = 4 symbols. Choice A uses Tuesday's symbol count (9 ÷ 3 = 3). Choice C uses Tuesday's bird count. Choice D uses Wednesday's actual bird count instead of symbols.
Sofia has 38 cards and gives away 10; how many left?
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 Sofia starts with 38 cards and subtracts 10. Choice A is correct because subtracting 10 from 38 means removing 1 ten: 3 tens - 1 ten = 2 tens, ones stay 8, giving 28. Choice B is a common error where students subtract 1 instead of 10, resulting in 37; this happens because understanding 10 as 1 ten is abstract and students sometimes change the ones digit. To help students: Use base-10 blocks to show physically removing 1 ten-rod while ones stay constant; practice on hundred charts (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 less' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
Sofia has 9 crayons. Some are red. Now she has 15 crayons. How many crayons did Sofia get?
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 change unknown. We start with one amount, end with another, and find what was added. The story tells us Sofia has 9 crayons and now has 15 crayons (noting 'some are red' is extra information). Choice B is correct because to find how many crayons Sofia got, we subtract what she started with from what she has now or add up: 15 - 9 = 6 or 9 + ? = 15. We can represent this as an equation with unknown: 9 + ? = 15. Choice A is a common error where students add the numbers instead of solving for the unknown (9 + 15 = 24); this happens because in change unknown problems, students don't recognize they need to work backwards. 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 9, ended with 15, need to find what was added, so I subtract or count up'); practice all unknown positions; connect to familiar experiences.
If 8+3=11, what is 3+8 (order doesn’t change the sum)?
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 8 + 3 = 11, we also know that 3 + 8 = 11 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 the equation 8 + 3 = 11 and asks for 3 + 8. Choice C is correct because the commutative property tells us 3 + 8 gives the same sum as 8 + 3, which is 11. Choice A is a common error where students think reversing the order changes the sum, perhaps by subtracting instead of adding when order is reversed; 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); explicitly teach making-10 pairs and how to use them with associative property; practice with equations side by side (8+3=11, 3+8=11); use visual models like ten-frames; emphasize 'order doesn't matter' for commutative, 'we can make 10 first' for associative; connect properties to efficient mental math strategies; practice identifying pairs that make 10 in three-number problems.
18−11=? is like 11+?=18. What number is missing?
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. Instead of 'taking away,' we can ask 'what do I add to get to the total?' For example, to solve 10 - 8, we can think '8 plus what equals 10?' or write it as 8 + ? = 10. Finding the missing addend (2) gives us the answer to the subtraction problem. This strategy is often easier than counting back, especially when the numbers are close together. The problem presents 18-11 = ? and equates it to the unknown addend equation 11 + ? = 18, asking for the missing number. Choice A is correct because when we add 7 to 11, we get 18, so 11 + 7 = 18, which means 18 - 11 = 7. Choice B is a common error where students add the two numbers instead of finding the difference, getting 29, because the connection between addition and subtraction is abstract. 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 (11+7=18, 7+11=18, 18-11=7, 18-7=11); use 'think addition' language consistently ('to subtract 18-11, think what plus 11 equals 18'); 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.
Sofia has 6 stickers and gets 4 more. Start at 6 and count on 4. How many now?
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 6+4, start at 6 and count forward 4 numbers: '7, 8, 9, 10'—the last number you say (10) is the answer. The problem asks to add by counting on from 6 after Sofia gets 4 more stickers. Choice B is correct because starting at 6 and counting on 4 gives '7, 8, 9, 10,' so the total is 10. Choice A is a common error where students start counting from the wrong number or miscount by one, perhaps by including the starting number as a count; this happens because distinguishing between the starting point and the counts requires practice. 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.
Lisa is working on a problem where she needs to find how many groups of 5 she can make with 17 objects. She has counting bears, paper, and a calculator available. She wants to see both the groups and any leftover objects clearly. Which tool combination addresses both needs?
Explanation: Counting bears allow Lisa to physically create groups of 5 and see the 2 leftover objects, while paper provides a way to record the findings (3 groups with 2 remaining). Choice A doesn't show the grouping visually. Choice C starts with abstract representation. Choice D doesn't address seeing the groups and remainders clearly.
Look at the picture graph. If we combine the two activities with the fewest votes, how many children would that represent?
Explanation: The graph shows reading = 9, drawing = 3, singing = 5, dancing = 7. The two activities with fewest votes are drawing (3) and singing (5). Combined: 3 + 5 = 8 children. Choice A (6) might come from miscounting one category. Choice C (10) might result from adding wrong activities. Choice D (12) might come from adding three activities instead of two.
Emma has 7 stickers. She gets 5 more stickers. How many stickers does Emma have now? 7+5=?
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 Emma has 7 stickers and gets 5 more. Choice B is correct because to find how many stickers Emma has now, we add: 7 + 5 = 12. We can represent this as 7 + 5 = ?. Choice C is a common error where students select a number from the story without solving, such as picking the starting amount of 7. 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 7, got 5 more, now I need to find the total, so I add'); practice all unknown positions; connect to familiar experiences.
A rectangle always has 4 sides and 4 what?
Explanation: This question tests 1st grade understanding of rectangle attributes (CCSS.1.G.1). Rectangles are defined by having 4 straight sides and 4 corners (vertices), with opposite sides being equal in length. The question asks what rectangles always have 4 of besides sides. Choice B (Corners) is correct because having 4 corners is a defining attribute of rectangles. Choice A (Colors) is incorrect because color is non-defining, Choice C (Curves) is wrong because rectangles have straight sides not curves, and Choice D (Points in the middle) is not an attribute of rectangles. Students benefit from counting both sides and corners to fully identify rectangles. To help students: Practice counting sides and corners on various rectangles; use the chant '4 sides, 4 corners, that's a rectangle!'; compare to triangles (3 and 3) and circles (0 and 0) to reinforce the pattern.
Subtract the tens: 90−70=
Explanation: This question tests 1st grade subtraction of multiples of 10 in the range 10-90 (CCSS.1.NBT.6). When subtracting multiples of 10, use place value strategy: subtract tens from tens. Since both numbers end in 0 (have 0 ones), we only work with the tens place. The scenario directly asks to subtract the tens for 90-70. Choice B is correct because 9 tens - 7 tens = 2 tens = 20. Choice A is a common error where students add instead of subtract, getting 90 + 70 = 160, which happens because subtraction is more challenging than addition. To help students: Use base-10 blocks to physically remove ten-rods, counting what remains; practice on number lines with backward jumps of 10; emphasize 'subtract tens from tens' strategy; connect to skip counting backward by 10s; provide many examples showing pattern; use place value charts to organize tens; connect to addition as inverse (90 - 70 = 20, check: 20 + 70 = 90); practice mental math with quick subtraction of tens; relate to real contexts like packages, dimes, groups of 10.
Jamal has 82 points. He loses 10 points. How many points does he have 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, subtracting 10 means removing 1 ten (tens digit decreases by 1), while the ones digit stays the same. For example, 82 - 10 = 72 because 8 tens - 1 ten = 7 tens, and the 2 ones remain unchanged. The scenario involves Jamal starting with 82 points and losing 10, requiring mental subtraction of 10 from 82. Choice A is correct because subtracting 10 from 82 means removing 1 ten: 8 tens - 1 ten = 7 tens, ones stay 2, giving 72. Choice B is a common error where students subtract 1 instead of 10, resulting in 81; 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 removing 1 ten-rod while ones stay constant; practice on hundred charts (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 less' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
Tom counts 1 ten and 7 ones. Then he counts 2 more ones. What number does he have now?
Explanation: When you see a problem about counting tens and ones, you're working with place value - understanding that numbers are made up of different positions that represent different amounts. Let's work through this step by step. Tom starts with 1 ten and 7 ones. One ten equals 10, so 1 ten plus 7 ones gives us 10+7=17. Then Tom counts 2 more ones, so we add those: 17+2=19. Looking at the wrong answers: Choice A (17) is what Tom had before adding the 2 more ones - this forgets the final step. Choice C (29) likely comes from mistakenly thinking 1 ten plus 7 ones plus 2 ones equals 1+7+2=10, then incorrectly placing that as 29 instead of recognizing it should be 19. Choice D (27) might result from adding 10+7+2+8 or some other calculation error. The correct answer is B (19) because 1 ten (10) plus 7 ones plus 2 more ones equals 10+7+2=19. Remember: when working with tens and ones, always convert the tens to their full value first (1 ten = 10), then add all your ones together. Take problems like this one step at a time, and double-check that you've included all the numbers mentioned in the problem.
Chen has 12 crayons and gives away 4. Start at 12 and count back 4. How many 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 12−4, start at 12 and count back 4: '11, 10, 9, 8'—the last number you say (8) is the answer. The problem asks to subtract 12−4 by counting back from 12 after Chen gives away 4 crayons. Choice A is correct because starting at 12 and counting back 4 gives '11, 10, 9, 8,' so 8 are left. Choice B is a common error where students count back one too few, perhaps by stopping too early or including the starting number; 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 last number said is the answer; compare to counting on for addition; practice with small subtrahends (1-5) first; connect counting to written subtraction equations.
Use counting on to solve 8+3. Start at 8 and count on.
Explanation: This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). Counting on is a strategy for addition where you start with the first number and count forward by the second number. For example, for 8 + 3, start at 8 and count: 9, 10, 11. The problem asks to use counting on to solve 8 + 3, starting at 8 and counting on. Choice B is correct because 8 + 3: starting at 8, count on three: 9, 10, 11. Choice C is a common error where students make a calculation error like counting one extra to 12; this happens because keeping track of parts while combining them is cognitively demanding. To help students: Practice counting on with small numbers first; use number lines or fingers to visualize; provide daily practice with mixed strategies; emphasize that facts within 10 should be automatic (fluent).
Examine the dot arrangement below. This pattern shows dots organized in groups. How many dots are there altogether?
Explanation: The arrangement contains 15 dots total, organized in three groups of 5 dots each. Students should be able to subitize each group of 5 and then combine them (5 + 5 + 5 = 15). This tests both subitizing skills and simple addition within a structured arrangement. Other choices represent common counting errors.
Carlos has 1 group of 10 shells and 8 shells. 1 ten and 8 ones makes .
Explanation: This question tests 1st grade understanding that teen numbers (11-19) are composed of 1 ten and ones (CCSS.1.NBT.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, 18 is made of 1 ten and 8 ones, which we can also write as 10 + 8 = 18. This structure helps students understand place value and connects the teen number names to their composition. The scenario describes Carlos with 1 group of 10 shells and 8 shells, representing 1 ten and 8 ones making a teen number. Choice A is correct because 1 ten plus 8 ones equals 18. Choice C is a common error where students reverse the digits (81 instead of 18). To help students: Use base-10 blocks extensively—always show 1 ten-rod plus unit cubes for teens; connect number names to structure ('eigh-teen' = 8 + 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 + 8 = 18); practice decomposing teens into 10 + ones; compare teens to show same ten structure.
A circle always has no what?
Explanation: This question tests 1st grade understanding of circle attributes (CCSS.1.G.1). Circles are unique among basic shapes because they have no straight sides and no corners—they are completely curved. The question asks what a circle always has none of. Choice A (Corners) is correct because circles are defined by their curved edge with no corners or vertices. Choices B (Color), C (Size), and D (Place on the page) are non-defining attributes that circles can have in various forms. Students sometimes struggle with this because they're used to counting sides and corners on other shapes. To help students: Have them trace circles with their finger to feel the continuous curve; compare circles to shapes with corners by feeling the 'pointy' parts; use the phrase 'round and round with no corners found' to reinforce the concept.
Sam has 3 blocks. One block is shaped like a ball and can roll. One block has 6 flat faces that are all squares. One block has 2 flat circular faces and 1 curved face. Which statement about Sam's blocks is true?
Explanation: All three blocks (sphere/ball, cube, cylinder) are 3D shapes because they take up space and are not flat. 2D shapes are flat and include circles, triangles, rectangles, and squares.
Marcus has 18 stamps. 10 stamps are animals. How many stamps are not animals? 10+?=18
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 addend unknown, or taking apart with part unknown. We know the total and one part, and find the other part. The story tells us Marcus has 18 stamps, of which 10 are animals. Choice C is correct because to find how many stamps are not animals, we subtract: 18−10=8, or add up: 10+8=18. We can represent this as 10+?=18. Choice B is a common error where students select a number from the story without solving, such as picking 10. This happens because calculation facts may not be automatic yet. 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 have 18 total, 10 are animals, need the non-animals, so I subtract'); practice all unknown positions; connect to familiar experiences.