Question 1 of 25
Is this equation true or false: ?
Opening subject page...
Loading your content
1st Grade Math
Practice Test 4 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
0%
0 / 25 answered
Question 1 of 25
Is this equation true or false: 8=5+3?
Question Navigator
Is this equation true or false: 8=5+3?
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 5 + 2 = 7, both sides equal 7, so it's true, but in 4 + 1 = 6, left is 5 and right is 6, so it's false. The problem presents the equation 8 = 5 + 3. Choice A is correct because 8 = 8 is true since both sides are 8 after computing 5 + 3. Choice C is a common error where students think the equal sign means 'the answer comes next' so they incorrectly judge equations like 8=5+3 as false because it's 'backwards.' This happens because students often learn equations only as 'operation = answer' format. To help students: Show equations in many structures (a+b=c, c=a+b, a=a); 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 equations like 8=5+3 are valid.
Complete the equation: 6+ ?=10.
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 6 + ? = 10), we find what number added to 6 equals 10 by subtracting: 10 - 6 = 4. Counting on from 6 to 10 (7,8,9,10) gives 4 steps. The equation is 6 + ? = 10. Choice C is correct because 6 + 4 = 10, so ? = 4. Choice B is a common error where students add the numbers, getting 6 + 10 = 16, instead of subtracting. To help students: Connect addend unknown to subtraction (CCSS.1.OA.4); use diagrams and objects; teach checking by substitution; practice fact families; vary unknown positions.
18−10=? Think: 10+?=18. 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 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 presents 18 - 10 = ? and suggests thinking 10 + ? = 18, asking for the missing number. Choice A (8) is correct because when we add 8 to 10, we get 18, so 10 + 8 = 18, which means 18 - 10 = 8. Choice C (7) is a common error where students make an off-by-one error, such as counting from 10 to 18 as seven steps instead of eight, which happens because they might include the starting number when counting. 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 (10+8=18, 8+10=18, 18-10=8, 18-8=10); use 'think addition' language consistently ('to subtract 18-10, think what plus 10 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.
Which symbol makes this true: 6767?
Explanation: This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.B.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. The stimulus requires selecting the correct symbol to compare 67 and 67. Choice C (=) is correct because both have 6 tens and 7 ones, so they are equal. Choice A (>) is a common error where students misuse symbols without checking equality, perhaps confusing it with inequality, which happens because symbol direction is easily confused. 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).
Ben wants to solve 7+4 using counting. He thinks: "I could count forward 4 numbers from 7, or I could count forward 7 numbers from 4". Which statement about Ben's thinking is correct?
Explanation: When you're adding two numbers, you can use counting to find the answer, and there's an important property of addition that makes this flexible. Let's see what happens with Ben's two methods for 7+4. If he counts forward 4 numbers from 7, he gets: 8, 9, 10, 11. If he counts forward 7 numbers from 4, he gets: 5, 6, 7, 8, 9, 10, 11. Both methods give him 11! This works because addition has something called the "commutative property" - you can switch the order of numbers you're adding and still get the same answer. So 7+4 equals 4+7. However, one method is smarter than the other. Counting 4 steps is much easier than counting 7 steps, so starting from 7 and counting forward 4 is more efficient. Answer choice A is wrong because addition doesn't require you to start with the first number - you can rearrange the numbers. Choice C is incorrect because you don't have to start with the smaller number, though it's often more efficient. Choice D is completely false because you absolutely can change the order of numbers in addition - that's exactly what the commutative property allows. The correct answer is B because both methods work and give 11, but counting from 7 (the larger number) requires fewer counting steps. Study tip: When adding by counting, always start with the larger number and count up by the smaller number - it saves time and reduces mistakes!
Kim counts by tens: 10,20,30. What number comes next and how many tens does it have?
Explanation: When you see a counting pattern like this, you're working with skip counting—counting by a certain number each time instead of by ones. Here, Kim is skip counting by tens, which means she adds 10 to each number to get the next one. Let's follow the pattern: Kim starts at 10, then adds 10 to get 20, then adds 10 again to get 30. To find what comes next, you add 10 to 30, which gives you 40. Now you need to figure out how many tens are in 40. Since 40=4×10, there are 4 tens in 40. Looking at the wrong answers: Choice A gives 31, but this breaks the pattern of counting by tens—31 would come from adding 1 to 30, not 10. While 31 does have 3 tens (plus 1 one), it's not the next number in Kim's sequence. Choice C also breaks the counting pattern by giving 33, which would come from adding 3 to 30. Choice D gets the next number right (40) but says it has 0 tens, which is incorrect—40 clearly contains 4 groups of ten. When you're skip counting, always add the same amount each time. For counting by tens, the ones place stays the same (here it's always 0) and the tens place increases by 1 each step. This makes it easy to spot both the next number and count the tens.
Jamal put two squares side by side. What shape did he make?
Explanation: This question tests 1st grade shape composition and decomposition (CCSS.1.G.2). Shape composition means putting smaller shapes together to make a new, larger shape. For example, two triangles can be arranged to make a square, or two squares can be put next to each other to make a rectangle. The reverse—decomposition—means dividing a shape into smaller parts. The scenario involves Jamal putting two squares side by side to form a new shape. Choice A is correct because two squares placed side by side create a longer shape with four equal sides in pairs, forming a rectangle. Choice C is a common error where students might think the shape remains a square, often because they don't recognize how arrangement changes the overall form or confuse area with shape. To help students: Provide physical pattern blocks or shape manipulatives for hands-on exploration; demonstrate multiple compositions with same shapes (2 triangles can make square OR rectangle depending on arrangement); practice both composition (building up) and decomposition (taking apart); use real-world examples like pizza slices or sandwiches cut in half; draw or trace shapes to show combinations.
Which shape has no corners?
Explanation: This question tests 1st grade understanding of defining attributes of shapes, particularly recognizing shapes by their corners, per CCSS.1.G.A.1. Defining attributes include the number of sides and corners, with circles uniquely having zero corners and one continuous curved side. Non-defining attributes like color or size do not affect this identification. The question asks which shape has no corners, comparing common shapes like triangles, squares, circles, and rectangles. Choice C is correct because a circle's defining attribute is its curved, continuous boundary with no corners. Choice B is a common error where students might pick square, possibly confusing it with having 'no' corners if they miscount or think of rounded squares, as young learners sometimes overlook corners in familiar shapes. To help students: Provide shape tracers and have children feel for corners with their fingers, compare circles to polygons by counting corners, and engage in activities like 'corner hunts' on various shapes to build awareness of this attribute.
Chen adds ones: What is 61+7?
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 one-digit, like 61 + 7, add the one-digit number to the ones place (1 + 7 = 8), keeping the tens the same (6 tens). The question asks Chen to add ones for 61 + 7. Choice A is correct because adding 1 one + 7 ones gives 8 ones, with 6 tens unchanged, making 68. Choice C is a common error where students write digits side-by-side instead of adding (617 instead of 68); this happens because they treat numbers as separate digits rather than place values. 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).
Jamal has 14 cookies. He eats 6 cookies. How many cookies does Jamal have left? 14−6=?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is a taking from problem with result unknown. We start with one amount and take away some to find what is left. The story tells us Jamal has 14 cookies and eats 6 cookies. Choice D is correct because to find how many cookies Jamal has left, we subtract: 14−6=8. We can represent this as 14−6=?. Choice B is a common error where students select a number from the story without solving, such as picking the amount eaten, 6. 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 started with 14, took away 6, now I need to find what's left, so I subtract'); practice all unknown positions; connect to familiar experiences.
Look at this equation: ?−3=9. Jake says the answer is 6 because 9−3=6. Is Jake correct?
Explanation: When you see an equation with a missing number (shown as ?), you need to figure out what number makes the equation true. The equation ?−3=9 is asking: "What number minus 3 equals 9?" To solve this, think about it as a puzzle. You need a number that, when you subtract 3 from it, gives you 9. You can work backwards: if something minus 3 equals 9, then that something must be 9 plus 3. So ?=9+3=12. Let's check: 12−3=9 ✓ Now let's see why each answer choice is right or wrong: A) Jake's answer of 6 is wrong because he mixed up the equation. He calculated 9−3=6, but that's not what the equation is asking for. B) The answer 3 is wrong. If you try 3−3=0, not 9. C) The answer 12 is correct, as we showed above: 12−3=9. D) The answer 27 is wrong. If you try 27−3=24, not 9. Jake made a common mistake by reading the equation backwards. He saw the numbers 9 and 3 and just subtracted them without paying attention to what the equation was actually asking. Study tip: When solving missing number equations, always substitute your answer back into the original equation to check if it makes the equation true. This helps you catch mistakes and builds confidence in your answer.
Which number is the same as 4 tens and 0 ones?
Explanation: When you see a question about tens and ones, you're working with place value - understanding what each digit position means in a number. Let's break down "4 tens and 0 ones" step by step. The word "tens" tells you how many groups of 10 you have, and "ones" tells you how many single units you have. So 4 tens means 4×10=40, and 0 ones means 0×1=0. Adding these together: 40+0=40. This matches answer choice B. Looking at why the other answers don't work: Answer choice A gives you 4, which would be "0 tens and 4 ones" - the opposite of what the question asks for. Answer choice C gives you 44, which represents "4 tens and 4 ones" - this has the right number of tens but adds 4 ones instead of 0 ones. Answer choice D gives you 400, which is actually "4 hundreds, 0 tens, and 0 ones" - this number is much too large because it puts the 4 in the hundreds place instead of the tens place. Remember this helpful trick: when you see "X tens and Y ones," multiply the tens by 10 and add the ones. So 4 tens becomes 40, plus 0 ones stays 40. This place value concept will appear often in math, so practice identifying which digit goes in which position.
Look at this pattern: 4+3=7, 5+3=8, 6+3=9. Following the same pattern, what number completes this equation? ?+3=11
Explanation: In each equation, the first number plus 3 equals the sum. To find ?, we need ? + 3 = 11, so ? = 11 - 3 = 8. Following the pattern: 8 + 3 = 11. Choice A (7) gives 7 + 3 = 10. Choice C (9) gives 9 + 3 = 12. Choice D (14) gives 14 + 3 = 17.
Emma has 8 stickers. She wants to share them equally with her friend Jake. What tool would be BEST to help Emma figure out how many stickers each person gets?
Explanation: When you need to share objects equally between people, you're working on division and fair sharing. The best way to understand this concept is by using hands-on materials that you can actually move around and group. Choice A is correct because real stickers let Emma physically divide them into equal groups. She can take her 8 stickers and give one to herself, one to Jake, then another to herself, another to Jake, and so on until all stickers are shared. By moving the actual objects, she can see that each person gets 4 stickers. This hands-on approach makes the math concrete and easy to understand. Choice B is wrong because while writing numbers is useful, a first grader learning to share equally needs to see and touch the objects being divided. Just writing "8 ÷ 2" doesn't help Emma visualize what equal sharing actually means. Choice C is incorrect because a ruler measures length, not quantity. You can't use a ruler to figure out how many stickers each person should get when sharing equally. Choice D is wrong because calculators are for computing with numbers you already know how to set up. Emma needs to understand what equal sharing means first, and adding numbers won't help her divide the stickers fairly. Remember: When you see problems about sharing equally or dividing objects, think about using real items you can move around. Physical materials help you see the math happening, making division much clearer than just working with numbers alone.
Refer to the picture below. If you use the marker to measure both the notebook and the scissors, what would you find out?
Explanation: This tests the ability to use a third object as a measuring tool to compare two other objects. Looking at the relative sizes, the notebook is approximately twice the length of the marker, while the scissors are approximately the same length as the marker. Choice A correctly estimates these measurements. Choices B and D provide incorrect measurements. Choice C suggests both objects are the same length, which contradicts the visual evidence.
Look at the shapes in the diagram. Ben wants to put all shapes with straight sides in one box and all shapes with curved sides in another box. Which shape will Ben have trouble sorting?
Explanation: A shape with both straight and curved sides (like a semicircle with a flat bottom) cannot fit in either box because it has both types of sides. Shapes with only straight sides go in one box, shapes with only curved sides go in the other box.
Use the chart to answer the question. Tom wants to make the number 15. Which combination of blocks should he choose?
Explanation: The number 15 is composed of 1 ten and 5 ones, so Tom needs 1 ten-block and 5 one-blocks. Choice B reverses the place values. Choice C uses only ones instead of recognizing the ten. Choice D uses too many blocks (would make 25).
Yuki has 4 tens and 7 ones; Carlos has 4 tens and 9 ones. Which is greater: 47 or 49?
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, 49 > 47 because both have 4 tens, but 9 ones > 7 ones. The stimulus describes Yuki with 4 tens and 7 ones (47) and Carlos with 4 tens and 9 ones (49), asking which is greater. Choice B is correct because 49 is greater than 47 since tens are equal but 9 ones > 7 ones. Choice A is a common error where students might think fewer ones mean greater, but that's not the case, 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).
Solve the problem. Marcus has 12 toy cars. Yuki has 9 toy cars. How many more cars does Marcus have 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 has 12 toy cars and Yuki has 9. Choice D is correct because to find how many more cars Marcus has, we subtract: 12 - 9 = 3. We can represent this as 12 - 9 = ?. Choice A is a common error where students add to find the total instead of the difference, getting 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, how many more? I line them up and subtract'); practice all unknown positions; connect to familiar experiences.
Solve 6+7 using doubles plus 1. What is the sum?
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 6 + 7, we recognize these are close to the double 6 + 6. We think: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13. The problem asks to solve 6 + 7 using doubles plus 1. Choice C is correct because using doubles: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13. Choice A is a common error where for near-doubles, students forget to add the +1; 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.
Read the problem. Keisha has 4 toys in a box, 4 toys on a shelf, and 7 toys on the floor. How many toys 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 doubles (like 4+4), add those first, then the third number; another is to make 10 with other pairs and use commutative and associative properties. The story presents three quantities: 4 toys in a box, 4 toys on a shelf, and 7 toys on the floor. Choice C is correct because adding all three numbers gives 4 + 4 + 7 = 15; for example, add the doubles 4+4=8 first, then 8+7=15. Choice A is a common error where students only add two numbers, like 4+4=8 and forget the 7; this happens because keeping track of three numbers is challenging and applying strategies requires practice. To help students: Use physical objects in three groups that students can count and combine; teach doubles facts explicitly (4+4=8); practice making-10 strategy; model different groupings using parentheses like (4+4)+7; use visual representations showing three groups; emphasize that order doesn't matter; have students explain their strategy; connect to real contexts with three groups.
Maria reads this problem: 'There are 11 children on the playground. 6 children are on the swings. The rest are on the slide. How many children are on the slide?' Maria isn't sure what 'the rest' means. How should she figure this out?
Explanation: When you see a word problem with unfamiliar phrases like "the rest," don't panic! These problems are testing whether you understand what the words mean and can use that understanding to solve math problems. Let's think about what "the rest" means in this problem. You know there are 11 children total on the playground, and 6 are on the swings. "The rest" refers to all the remaining children - the ones who are NOT on the swings. Since the problem says the rest are on the slide, you need to figure out how many children that is. You can subtract: 11−6=5 children are on the slide. Choice D is correct because it shows the right approach: understanding that "the rest" means the children who are not on swings. Choice A is wrong because skipping problems won't help you learn, and "the rest" isn't actually confusing once you think about it. Choice B is incorrect because you should never change the numbers in a problem - that would give you a completely different problem to solve. Choice C is wrong because assuming "the rest" means 0 doesn't make sense and would give you the wrong answer. Remember this strategy: when you see phrases like "the rest," "the remaining," or "what's left," they're telling you to think about the difference between the total amount and the amount already mentioned. Take time to understand what these key phrases mean before you start calculating.
Maya stacked two cubes. What new shape did she build?
Explanation: This question tests 1st grade shape composition and decomposition (CCSS.1.G.2). Shape composition means putting smaller shapes together to make a new, larger shape. For example, two triangles can be arranged to make a square, or two squares can be put next to each other to make a rectangle. The reverse—decomposition—means dividing a shape into smaller parts. The scenario involves Maya stacking two cubes to build a new 3D shape. Choice C is correct because stacking two cubes creates a taller rectangular prism, like a box shape. Choice B is a common error where students confuse 3D stacking with 2D flat shapes, often because spatial reasoning between dimensions is developing. To help students: Provide physical pattern blocks or shape manipulatives for hands-on exploration; demonstrate multiple compositions with same shapes (2 triangles can make square OR rectangle depending on arrangement); practice both composition (building up) and decomposition (taking apart); use real-world examples like pizza slices or sandwiches cut in half; draw or trace shapes to show combinations.
Use the chart to answer the question. Which two numbers from the chart have a total of 7 tens when you add their tens together?
Explanation: Looking at the tens in each number: 20 has 2 tens, 50 has 5 tens, and 2 + 5 = 7 tens total. Choice A: 3 + 4 = 7 tens but 40 is not in the chart. Choice C: 6 + 1 = 7 tens but 60 is not in the chart. Choice D: 4 + 2 = 6 tens, not 7.
Maya is at 45 on a number line. What is 10 less?
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 involves Maya at 45 on a number line, asking for 10 less. Choice B is correct because subtracting 10 from 45 means removing 1 ten: 4 tens - 1 ten = 3 tens, ones stay 5, giving 35. Choice A is a common error where students subtract 1 instead of 10, changing the ones digit to 4; this happens because understanding 10 as 1 ten is abstract and students sometimes focus on the digit '10' rather than its place value meaning. 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.