Elementary School Math Quiz: Relate Counting To Addition And Subtraction
20 questions · exam conditions
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Relate Counting To Addition And SubtractionQuestion 1 of 20

Maria has 88 stickers. She wants to give away 33 stickers to her friends. Instead of subtracting, Maria decides to count backwards from 88 to find how many stickers she will have left. Which counting pattern should Maria use?

8,7,6,58, 7, 6, 5 and she will have 55 stickers left
8,7,68, 7, 6 and she will have 66 stickers left
8,9,10,118, 9, 10, 11 and she will have 1111 stickers left
8,58, 5 and she will have 55 stickers left immediately
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Elementary School Math Quiz

Elementary School Math Quiz: Relate Counting To Addition And Subtraction

Practice Relate Counting To Addition And Subtraction in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Relate Counting To Addition And Subtraction, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Maria has 88 stickers. She wants to give away 33 stickers to her friends. Instead of subtracting, Maria decides to count backwards from 88 to find how many stickers she will have left. Which counting pattern should Maria use?

  1. 8,7,6,58, 7, 6, 5 and she will have 55 stickers left (correct answer)
  2. 8,7,68, 7, 6 and she will have 66 stickers left
  3. 8,9,10,118, 9, 10, 11 and she will have 1111 stickers left
  4. 8,58, 5 and she will have 55 stickers left immediately
Explanation: To subtract 3 by counting backwards, Maria starts at 8 and counts back 3 numbers: 8→7 (back 1), 7→6 (back 2), 6→5 (back 3). She lands on 5, so she will have 5 stickers left. Choice B stops counting after only 2 steps back. Choice C counts forward instead of backward. Choice D jumps directly without showing the counting process.

Question 2

Sarah is teaching her little brother how to use counting for 6−36 - 3. She shows him two methods. Method 1: "Start at 66, count back 33: 5,4,35, 4, 3". Method 2: "Start at 33, count up to 66: 4,5,64, 5, 6, which is 33 steps". Why do both methods give the correct answer of 33?

  1. Both methods use the same numbers, so they must give the same answer always
  2. Both methods count the same distance between 33 and 66 on the number line (correct answer)
  3. Both methods start with 33, which is the answer to the subtraction problem
  4. Both methods count exactly 33 numbers, which matches the number being subtracted
Explanation: When you see subtraction problems solved with counting methods, think about what's really happening on the number line. Both of Sarah's methods are finding the distance between two numbers, just from different starting points. Method 1 starts at 66 and counts backward 33 steps to reach 33. Method 2 starts at 33 and counts forward until it reaches 66, which takes 33 steps. Both methods are measuring the same gap on the number line - the distance between 33 and 66. This distance is always 33, no matter which direction you count. It's like measuring the length of a stick - you get the same measurement whether you start from the left end or the right end. Choice A is incorrect because using the same numbers doesn't guarantee the same answer unless you're measuring the same thing. Choice C is wrong because Method 1 starts with 66, not 33 - the starting numbers are different. Choice D misses the point because while both methods do count 33 steps, that's the result of measuring the distance, not the reason why both methods work. The key insight is that subtraction finds the distance between numbers. Whether you count up from the smaller number or count back from the larger number, you're measuring the same distance on the number line. Remember: When solving subtraction with counting, both "counting back" and "counting up" work because they measure the same distance between two points.

Question 3

Carlos has 66 toy cars. His sister gives him 44 more cars. Carlos counts on from 66 to find his total: "7,8,9,107, 8, 9, 10". How many toy cars does Carlos have now, and did he count correctly?

  1. He has 1010 cars and counted correctly by counting on 44 numbers (correct answer)
  2. He has 1111 cars because he forgot to count the starting number 66
  3. He has 99 cars because he should have stopped counting at 99
  4. He has 1010 cars but he counted wrong by starting from 77
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.

Question 4

Jake is playing a board game. He is on space 44 and rolls a die that shows 55 dots. To find his new position, he counts forward: "5,6,7,8,95, 6, 7, 8, 9". What addition problem did Jake solve by counting forward this way?

  1. 4+5=94+5=9 (correct answer)
  2. 5+4=95+4=9
  3. 5+5=105+5=10
  4. 4+4=84+4=8
Explanation: Jake started on space 4 and counted forward 5 more spaces, landing on 9, so he solved 4+5=94+5=9. 5+4=95+4=9 swaps the order of the starting space and the amount he moved. 5+5=105+5=10 uses the wrong numbers and gives the wrong total. 4+4=84+4=8 repeats the starting space instead of using the number he counted forward. Only 4+5=94+5=9 matches the spaces Jake actually moved.

Question 5

To add 7+57+5, start at 7 and count on 5: 8, 9, 10, 11, 12. What is the sum?​

  1. 13
  2. 12 (correct answer)
  3. 11
  4. 7
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 7 + 5, start at 7 and count forward 5 numbers: '8, 9, 10, 11, 12'—the last number you say (12) is the answer. The problem asks to add 7 + 5 by counting on from 7. Choice B is correct because starting at 7 and counting on 5 gives '8, 9, 10, 11, 12,' so the answer is 12. Choice A is a common error where students count one extra, perhaps starting from 7 as the first count; this happens because distinguishing between the starting point and 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.

Question 6

Refer to the number line. What number is missing to complete the equation shown by the hops: □−3=4\square - 3 = 4?

  1. 1
  2. 6
  3. 7 (correct answer)
  4. 8
Explanation: When you see an equation with a missing number like □−3=4\square - 3 = 4, think of it as a puzzle: "What number, when I take away 3, leaves me with 4?" A helpful trick is to use the opposite operation. Since subtraction and addition are opposites, you can find the missing number by adding: 4+3=74 + 3 = 7. On a number line, this matches what the hops show — you start at 7, hop back 3 spaces, and land on 4. That makes C) 7 the correct answer. Now let's look at why the other choices don't work. Choice A) 1 comes from subtracting instead of adding (4−34 - 3), which is the wrong operation for finding the starting number. Choice B) 6 is close, but if you start at 6 and hop back 3, you land on 3, not 4 — this is a common "off by one" mistake. Choice D) 8 overshoots; starting at 8 and hopping back 3 lands you on 5, not 4. A great strategy to remember: whenever you see a subtraction equation with the first number missing (like □−3=4\square - 3 = 4), add the two numbers you can see to find the answer. You can always check your work by plugging your answer back in: 7−3=47 - 3 = 4 ✓. Using the number line to count hops is a helpful way to picture what subtraction really means — moving backward.

Question 7

Ben wants to solve 7+47 + 4 using counting. He thinks: "I could count forward 44 numbers from 77, or I could count forward 77 numbers from 44". Which statement about Ben's thinking is correct?

  1. Only counting from 77 will work because that's the first number in the problem
  2. Both methods will work and give the same answer, but counting from 77 is more efficient (correct answer)
  3. Only counting from 44 will work because you must start with the smaller number
  4. Neither method will work because you cannot change the order of numbers in addition
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+47 + 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+47 + 4 equals 4+74 + 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!

Question 8

Refer to the number line. A bug started at some number, then hopped forward 4 to land on 10. Where did the bug start?

  1. 5
  2. 6 (correct answer)
  3. 7
  4. 14
Explanation: When a bug "hops forward," it moves to a bigger number on the number line. So if the bug ended at 10 after hopping forward 4, it must have started at a number that is 4 less than 10. To find the starting point, you work backwards by subtracting: 10−4=610 - 4 = 6 You can also check this by hopping forward: start at 6, then count up 4 spaces — 7, 8, 9, 10. That lands you exactly on 10, so B) 6 is correct. Now look at the wrong answers. A) 5 is what you'd get if you accidentally hopped forward 5 instead of 4, or miscounted the spaces. C) 7 is a common trap — if you start at 7 and hop forward 4, you land on 11, not 10 (this happens when students count the starting number as the first hop instead of the next space). D) 14 is the result of adding 4 to 10 instead of subtracting. This is the classic mistake of moving the wrong direction — since the bug hopped forward to reach 10, you need to go backward to find where it began. Study tip: When a word problem tells you the ending spot and asks for the starting spot, do the opposite operation. "Hopped forward" (added) means you subtract to work backwards. Drawing arrows on a number line can help you see the direction clearly.

Question 9

Look at the cubes in the picture. Which addition sentence shows counting on 2 to find the total?

  1. 6+2=86 + 2 = 8 (correct answer)
  2. 2+6=82 + 6 = 8
  3. 6+3=96 + 3 = 9
  4. 8+2=108 + 2 = 10
Explanation: "Counting on" is a strategy where you start with the bigger number and then count up by the smaller number to find a total. It's faster than counting every single cube from 1, so first graders learn to start with the larger group already in mind. In this problem, you have a group of 6 cubes and a group of 2 cubes. To "count on 2," you start at 6 and say: "6... 7, 8." You added 2 more to 6, which gives you 6+2=86 + 2 = 8. That matches choice A perfectly — the bigger number comes first, and you count on the smaller number (2). Choice B, 2+6=82 + 6 = 8, has the correct total, but it starts with the smaller number. That would mean counting on 6 from 2, which is not "counting on 2." Choice C, 6+3=96 + 3 = 9, adds the wrong amount — you're supposed to count on 2, not 3. Choice D, 8+2=108 + 2 = 10, uses 8 as the starting number, but 8 is the answer, not one of the groups you started with. A helpful tip: when a question says "count on  ," that number tells you how many jumps to take, and the other number is where you start. Always put the bigger number first when counting on — it saves time and matches the strategy your teacher is testing.

Question 10

To add 9+29+2, count on from 99. What number do you end at?

  1. 10
  2. 12
  3. 11 (correct answer)
  4. 9
Explanation: Counting on 2 more from 9 gives 10, then 11, so you end at 11. 10 stops one count too early. 12 counts on one too many. 9 repeats the starting number without counting on at all. Only 11 correctly shows where you end after counting on 2 from 9.

Question 11

To add 7+27+2, count on from 77. What number do you end at?

  1. 7
  2. 8
  3. 10
  4. 9 (correct answer)
Explanation: Counting on 2 more from 7 gives 8, then 9, so you end at 9. 7 repeats the starting number without counting on at all. 8 stops one count too early. 10 counts on one too many. Only 9 correctly shows where you end after counting on 2 from 7.

Question 12

The number line shows a starting point and some hops. Which equation does the picture show?

  1. 6+3=96 + 3 = 9 (correct answer)
  2. 6+2=86 + 2 = 8
  3. 9−3=69 - 3 = 6
  4. 6−3=36 - 3 = 3
Explanation: When you see a number line problem with hops, think of it like a frog jumping. The starting point tells you the first number, and each hop moving to the right means you're adding. Hops moving to the left mean you're subtracting. To find the equation, count where you start, count the hops, and see where you land. In this picture, the frog starts at 6 and takes 3 hops to the right, landing on 9. That matches the equation 6+3=96 + 3 = 9, which is choice A. Choice B, 6+2=86 + 2 = 8, would only be right if there were 2 hops instead of 3 — always count the hops carefully. Choice C, 9−3=69 - 3 = 6, gets the numbers involved correct but reverses the action; this would show a frog starting at 9 and hopping left 3 times to land on 6, not starting at 6 and moving right. Choice D, 6−3=36 - 3 = 3, would show hops going left from 6, ending at 3 — but the picture shows the frog moving forward (right), not backward. A helpful tip: right hops = plus, left hops = minus. Always check three things on a number line question: where you start, which direction the arrows point, and where you end up. The starting number goes first in the equation, and the landing number goes after the equals sign.

Question 13

The number line shows a jump. Which best describes the jump?

  1. Count on 2 from 8.
  2. Count back 2 from 8. (correct answer)
  3. Count on 2 from 6.
  4. Count back 8 from 2.
Explanation: When you see a jump on a number line, look carefully at two things: where the arrow starts and which direction it moves. If the arrow moves to the right, you are counting on (adding). If it moves to the left, you are counting back (subtracting). The length of the jump tells you how many you add or subtract. In this problem, the jump starts at 8 and moves 2 spaces to the left, landing on 6. Because the movement goes left, you are counting back, and because the jump covers 2 spaces, you count back 2. That matches choice B: count back 2 from 8, giving 8−2=68 - 2 = 6. Choice A is wrong because "count on" means moving right (adding). Counting on 2 from 8 would land on 10, not 6. Choice C is wrong because it starts at the ending point (6) instead of the starting point (8), and it also uses "count on" instead of "count back." This is a common trap — always check which number the arrow leaves from, not where it lands. Choice D mixes up the numbers entirely: it treats 2 as the starting point and 8 as the jump size, which would take you far below zero. A helpful tip: before choosing an answer, put your finger on the arrow's tail (the start) and trace it to the tip (the end). Left = count back, right = count on. The number you start on always comes after "from."

Question 14

The number line shows Anna's hops. Which addition sentence matches Anna's hops?

  1. 2+5=72 + 5 = 7 (correct answer)
  2. 2+4=62 + 4 = 6
  3. 2+7=92 + 7 = 9
  4. 7−2=57 - 2 = 5
Explanation: When you see a number line problem with "hops," think of it like counting jumps forward. The starting point tells you the first number, and the number of hops tells you what you're adding. To find the total, look at where Anna lands after all her hops. In this problem, Anna starts at 2 and makes 5 hops forward, landing on 7. That matches the addition sentence 2+5=72 + 5 = 7, which is choice A. The starting point (2) plus the hops (5) equals the ending point (7). Choice B, 2+4=62 + 4 = 6, is wrong because Anna made 5 hops, not 4 — it's easy to miscount hops if you count the starting number as a hop instead of just counting the jumps between numbers. Choice C, 2+7=92 + 7 = 9, confuses the ending point with the number of hops; 7 is where Anna lands, not how far she jumped. Choice D, 7−2=57 - 2 = 5, is a subtraction sentence, but the question asks for an addition sentence that matches the forward hops. A helpful tip: on number line questions, always count the arrows or jumps, not the numbers you land on. The first number is your starting spot, the jumps are what you add, and the final spot is your answer. Say it out loud: "Start at  , hop   times, land on  ."

Question 15

Refer to the number line. What subtraction sentence matches the hops shown?

  1. 9−4=59 - 4 = 5 (correct answer)
  2. 9−5=49 - 5 = 4
  3. 5−4=15 - 4 = 1
  4. 9−3=69 - 3 = 6
Explanation: When you see a number line with hops for subtraction, think of it as a story: you start at the bigger number, then hop backward (to the left) by the amount you're subtracting. Where you land is your answer. Since the hops start at 9 and move left by 4 spaces, landing on 5, this matches 9−4=59 - 4 = 5, making A correct. The starting point tells you the first number, the number of hops tells you what you're subtracting, and the landing spot is the difference. Choice B, 9−5=49 - 5 = 4, swaps the hops and the landing spot. If you took 5 hops back from 9, you'd land on 4 — but the picture shows 4 hops landing on 5, not the other way around. Choice C, 5−4=15 - 4 = 1, uses the wrong starting number. You always begin at the largest number on the hop path, which is 9, not 5. Choice D, 9−3=69 - 3 = 6, miscounts the hops. If there were only 3 hops from 9, you would land on 6, but there are 4 hops shown. A helpful tip: when reading a subtraction number line, put your finger on the starting number, then count each hop out loud as you move left. The number where your finger stops is the answer. Always double-check by counting the arcs (hops) carefully — miscounting by one is the most common mistake!

Question 16

Ana solved an addition problem by counting forward: "4,5,6,74, 5, 6, 7". Then she solved a subtraction problem by counting backward: "7,6,5,47, 6, 5, 4". What do you notice about the relationship between these two counting sequences?

  1. The sequences show that you always get the same answer in addition and subtraction
  2. The sequences are the same numbers, so addition and subtraction are the same operation
  3. The sequences are opposites and show that addition and subtraction undo each other (correct answer)
  4. The sequences prove that counting forward and backward always use the same numbers
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=74 + 3 = 7. Then she counted backward "7, 6, 5, 4" for subtraction, probably 7−3=47 - 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.

Question 17

Lisa wants to solve 5+35 + 3 by counting forward. She starts counting: "6,7,86, 7, 8". Her teacher asks her to explain why she didn't start counting from 55. What should Lisa's explanation be?

  1. When counting on to add, you sometimes need to skip numbers
  2. When counting on to add, you count the numbers you already have first
  3. When counting on to add, you always start with the larger number in the problem
  4. When counting on to add, you start from the next number after your starting amount (correct answer)
Explanation: When you're learning to add by counting on, you need to understand exactly where to start your counting. This strategy helps you add numbers without having to count everything from the beginning. Let's look at Lisa's problem: 5+35 + 3. She already has 5 items, so she needs to add 3 more by counting forward. The key insight is that she starts counting from 6, not 5, because she's counting the new items being added to what she already has. Think of it this way: Lisa has 5 toys in her hand. To add 3 more, she picks up the first new toy and says "6" (because this is the 6th toy total), then "7" for the second new toy, and "8" for the third new toy. She counts 3 numbers forward from where she started, landing on 8 as her answer. Choice A is wrong because you're not skipping the first number to avoid double-counting - you're simply counting the additional items. Choice B incorrectly suggests counting what you already have, but the whole point of counting on is to avoid recounting those items. Choice C is wrong because the strategy works regardless of which number is larger; you typically start with the first number in the problem. Choice D correctly explains that you start from the next number after your starting amount because you're counting the new items being added. Remember: When counting on, you're adding to what you already have, so start counting from the very next number.

Question 18

Tommy is solving 8−28 - 2 by counting backwards. He says: "I start at 88, then count 7,67, 6 and my answer is 66". His friend Maya says: "I start at 88, count back 22 steps: 88 to 77 is one step, 77 to 66 is two steps, so the answer is 66". Who used the counting method correctly?

  1. Only Maya is correct because you must count the steps, not just the numbers
  2. Only Tommy is correct because you must say all the numbers when counting
  3. Both Tommy and Maya got the same correct answer using valid counting methods (correct answer)
  4. Neither is correct because they both forgot to include 88 in their final count
Explanation: When you're learning subtraction by counting backwards, there are different ways to think about the counting process, and it's important to understand that multiple approaches can work correctly. Let's examine what Tommy and Maya each did with 8−28 - 2. Tommy started at 8 and counted backwards by saying the numbers: "7, 6" and got 6. Maya also started at 8 but thought about it as taking steps: one step from 8 to 7, then another step from 7 to 6, landing on 6. Both students arrived at the correct answer of 6, and both used valid counting methods. Now let's look at why the other answers miss the mark. Answer A incorrectly suggests that only Maya's step-counting method is valid, but Tommy's number-naming approach is also a legitimate way to count backwards. Answer B makes the opposite mistake, claiming only Tommy's method works, when Maya's step-counting is equally correct. Answer D suggests both students made an error by not including 8 in their final count, but this misunderstands subtraction—when you subtract 2 from 8, you move away from 8, so 8 shouldn't be part of your final answer. The key insight is that counting backwards can be done by naming the numbers you land on (like Tommy) or by counting the steps you take (like Maya). Both approaches are mathematically sound ways to solve subtraction problems. When you practice counting backwards for subtraction, try both methods to see which one feels more natural for you.

Question 19

The number line shows a frog starting at 4. The frog hops forward 3 times, landing on a new spot each hop. Where does the frog land?

  1. 6
  2. 7 (correct answer)
  3. 8
  4. 3
Explanation: When you see a hopping problem on a number line, think of it as addition: each hop forward means adding 1 to where you are. So "hops forward 3 times" is the same as adding 3 to the starting number. Start at 4, then count the hops: hop 1 lands on 5, hop 2 lands on 6, hop 3 lands on 7. You can also just add: 4+3=74 + 3 = 7. That matches choice B. Choice A (6) is a common trap — it happens when you count the starting spot as the first hop instead of only counting the jumps. Remember, the frog begins on 4, and the first hop takes it off of 4. Choice C (8) is what you'd get if you took one extra hop, adding 4 instead of 3. Choice D (3) mixes up "forward" with "backward" — moving backward 1 from 4 would give 3, but the frog is hopping the other direction. A helpful tip: when a problem says "hops forward" or "moves up," picture the number line and count only the jumps, not the starting number. Touch each new number as you say it out loud: "5… 6… 7." This little habit prevents the off-by-one mistake that shows up again and again in number-line questions.

Question 20

The number line shows two students' hops. Which statement is TRUE based on the picture?

  1. Neither student moved forward.
  2. Ben landed on a bigger number than Lin.
  3. Lin landed on a bigger number than Ben.
  4. Both students landed on the same number. (correct answer)
Explanation: When you see a number line question with "hops," think of each hop as one jump forward. To find where a student lands, start at their beginning number and count the hops to the right. Whoever ends on the higher number "landed on a bigger number." If both end at the same spot, they tied. Since both Ben and Lin's hops end at the very same tick mark on the number line, they landed on the same number. That makes D correct — a tie is a real, valid outcome even when the students take different-sized or different-numbered hops to get there. Choice A is wrong because the arrows clearly show forward movement (hops going to the right); both students did move. Choice B is wrong because Ben did not go past Lin — his final landing spot matches hers, not exceeds it. Choice C makes the opposite mistake: Lin didn't land farther right than Ben either. Students often pick B or C because they assume one student must be ahead, but the picture shows equal endings. A helpful tip: on number line problems, always look at the final landing spot, not the number or size of the hops. Two students can take different paths — like one big hop versus two small hops — and still finish at the same number. Put your finger on where each arrow ends, then compare those two spots directly.