Addition & Subtraction on a Number Line | Grade 2 Math

Grade 2 Math Hub › Unit 5: Measurement & Number Lines › Lesson 26

Grade 2 Math — Unit 5: Measurement & Number Lines

Addition & Subtraction on a Number Line

Learn to add and subtract on a number line with equal unit intervals. Show a number as a distance from zero, make jumps right or left, break jumps into tens and ones, and find missing numbers within 100.

Explore 25 step-by-step worked examples, 30 independent practice problems, a 15-question lesson test, and hidden answer keys. This lesson follows Lesson 25: Length Word Problems.

Grade 2 MathCCSS 2.MD.B.6Number Lines to 100Count On & Count BackFree Practice & Test

🎯 What You Will Learn

Read a number line

Notice equal spaces and describe a number as its distance from zero.

Add and subtract with jumps

Move right to add or left to subtract, and count spaces rather than tick marks.

Use tens and ones

Split a large jump into smaller jumps, sometimes stopping at a friendly multiple of ten.

Find missing distances

Count on to find a difference or a missing number and check the calculation.

Common Core alignment: The main focus is CCSS 2.MD.B.6: represent whole numbers as lengths from 0 on a number line with equal intervals, and represent whole-number sums and differences within 100 on number lines. The lesson also reinforces 2.NBT.B.5 (place-value addition and subtraction within 100) and uses selected word-problem situations related to 2.OA.A.1; they are supporting connections, not the lesson’s primary standard. The familiar-number jumps to 100 are within Grade 2 expectations, not a requirement to use a specific single strategy.

🧠 Key Vocabulary

Number line

A straight line with numbers at evenly spaced points. Values increase to the right and decrease to the left.

Unit interval

One space between neighboring whole-number marks, such as 6 and 7.

Starting point

The number where a jump begins; you do not count it as the first jump.

Landing point

The number at which a jump stops.

Jump

A move along the line. For the problems here, moving right shows adding; moving left shows subtracting.

Difference

The amount between two numbers. You can find it by subtracting or by counting forward from the smaller number.

Big idea: A whole number on this number line can be represented as a distance from zero, and each equal space represents one unit. Count spaces, not marks. The final landing number and the distance traveled are different ideas: when finding a difference by counting on, add the jump lengths.

📖 1. Read the Marks and Equal Intervals

From 0 to 5 there are five spaces between six whole-number points (0, 1, 2, 3, 4, 5). In the model, only selected points have printed number labels. Each neighboring pair of whole numbers is one unit apart. On a long line, small marks can show single units, while taller labeled marks emphasize tens. The space from 40 to 50 contains ten unit intervals.

Five one-unit intervals run from 0 to 5.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

➕ 2. Adding Means Moving Right

To model 7 + 4, start on 7 and move four unit spaces right. The landing point is 11, so 7 + 4 = 11. For bigger numbers, a jump of +10 covers exactly ten unit intervals, even when only the tens marks are labeled.

Seven plus four ends at eleven.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

➖ 3. Subtracting Means Moving Left

To model 16 − 6, start at 16 and move six unit spaces left. You land at 10. A backward jump of 20 means moving twenty unit lengths to the left, not moving two tick marks unless those marks are exactly ten apart.

Six one-unit spaces left of sixteen is ten.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

🔟 4. Split Jumps into Tens and Ones

For 38 + 25, split the extra 25 as 20 + 5: 38 → 58 → 63. A different helpful route uses +2 to reach 40, +20 to reach 60, and +3 to reach 63. Both routes show a total increase of 25. Choose a path that you can explain.

🌈 5. Cross a Friendly Ten

When you add 27 + 8, jumping +3 takes you to 30. Then the remaining +5 takes you to 35. For 62 − 9, a jump of −2 lands at 60 and −7 more lands at 53. Splitting a number into useful parts does not change how far you travel.

❓ 6. Find Unknown Starts or Jumps

For □ + 7 = 42, the end is known: jump backward by 7 to find the start, 35. For 54 − □ = 31, both endpoints are known: find the distance between them, 23. Check each unknown by putting it back into the original equation.

↔️ 7. Count On to Find a Difference

To find 72 − 48, you may count forward from 48 to 72: jump +2 to 50, +20 to 70, then +2 to 72. Add the lengths 2 + 20 + 2 = 24. The difference is 24, not 72. This is another way to represent subtraction; it does not change the fact that the original operation is subtraction.

Count forward to find the distance from forty-eight to seventy-two.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Watch for: The tick marks must have equal unit spacing. If you count a starting mark as one jump, you will be off by one. A jump of 10 is 10 units, whether or not every unit is labeled. All number-line figures here are schematic diagrams, not physical rulers.

🌟 25 Worked Examples

Begin with equal intervals and small jumps. Then move to tens and ones, crossing tens, missing numbers, counting on, comparing strategies, and an error check. Read the question and diagram before opening the step-by-step solution.

1Count unit intervals

A number line starts at 0. Count to the mark at 8. How many one-unit intervals are there from 0 to 8?

From 0 to 8: count the spaces between marks, not the marks.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at 0, not at the first space after 0.

Step 2. Count the intervals: 0 to 1 is one, 1 to 2 is two, and continue to 8.

Step 3. There are eight equal one-unit lengths. That is why 8 is eight units from 0.

Answer: 8 unit intervals.

2Land after four steps

Start at 0 and move 4 unit intervals to the right. Which number do you reach?

Each of four unit intervals moves one number to the right.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. A move to the right increases the number.

Step 2. Count four intervals: 0 → 1 → 2 → 3 → 4.

Step 3. The last point is 4, not 3: the starting point is not counted as a jump.

Answer: 4.

3Add with a forward jump

Show 5 + 3 on a number line. Where do you land?

Start at 5, then move three equal units to the right.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Find 5 first. It is the starting number, not the first jump.

Step 2. Addition of 3 means travel three unit spaces to the right.

Step 3. You pass 6 and 7 and land on 8: 5 + 3 = 8.

Answer: 8.

4Subtract with a backward jump

Start at 12 and subtract 5. Which mark is the answer?

Starting at 12, move five unit intervals left.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at the mark 12.

Step 2. Count backward five intervals: 11, 10, 9, 8, 7.

Step 3. The landing point is 7, so 12 − 5 = 7.

Answer: 7.

5Compare two distances from zero

Point 10 is 10 units from zero, and point 17 is 17 units from zero. How many units farther from zero is point 17?

Compare the distance from zero to 10 with the distance from zero to 17.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. The distance from 0 to 10 is ten one-unit spaces.

Step 2. The distance from 0 to 17 is seventeen one-unit spaces.

Step 3. Compare the distances: 17 − 10 = 7. Point 17 is seven units farther from zero than point 10.

Answer: 7 units farther.

6Add a one-digit number

Use a number line to solve 14 + 5.

Five spaces to the right of 14.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Mark 14 as the starting point.

Step 2. Move right five unit intervals: 15, 16, 17, 18, 19.

Step 3. Check that 19 is five more than 14.

Answer: 19.

7Add one ten

Solve 21 + 10 with one jump. What changes and what stays the same?

A jump of ten moves one full group of ten to the right.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Locate 21 between 20 and 30.

Step 2. Jump ten unit lengths to the right; the ones digit stays 1.

Step 3. You land at 31: the tens digit increases by one.

Answer: 31; the ones digit stays 1.

8Subtract one ten

Solve 38 − 10 on the number line.

A ten-unit jump moves left without changing the ones digit.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Find 38, eight spaces after 30.

Step 2. Move one ten to the left while keeping the 8 ones.

Step 3. The landing number is 28.

Answer: 28.

9Jump two tens forward

Use jumps of tens to solve 25 + 20.

Two successive jumps of ten; find the ending number.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at 25.

Step 2. Jump ten to 35, then ten more to 45. Together the jumps total 20.

Step 3. Write 25 + 20 = 45.

Answer: 45.

10Jump three tens backward

Use three jumps of 10 to solve 64 − 30.

Three equal backward jumps of ten.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at 64.

Step 2. Jump left: 64 → 54 → 44 → 34.

Step 3. Three tens make 30, so the answer is 34.

Answer: 34.

11Cross a ten while adding

Find 27 + 6 by first jumping to 30.

Break six into three and three to land on a ten first.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Split 6 into 3 + 3.

Step 2. From 27, jump +3 to 30; then jump +3 again.

Step 3. The landing point is 33, and 3 + 3 = 6.

Answer: 33.

12Cross a ten while subtracting

Find 52 − 7 by jumping to 50 first.

Subtract two to reach 50, then five more.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Break 7 into 2 + 5.

Step 2. Jump left from 52 to 50 by subtracting 2.

Step 3. Jump left another 5 to 45. Because 2 + 5 = 7, 52 − 7 = 45.

Answer: 45.

13Add tens and ones

Solve 36 + 24 by jumping 20 and then 4.

First add two tens, then four ones.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Break 24 into 20 + 4.

Step 2. Start at 36 and add 20 to get 56.

Step 3. Move four more units to 60. Check that the total jump is 24.

Answer: 60.

14Subtract tens and ones

Solve 75 − 23 with a jump of 20 and a jump of 3.

Subtract two tens and then three ones.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Write 23 as 20 + 3.

Step 2. Start at 75 and jump left 20 to 55.

Step 3. Subtract 3 more to land on 52, so 75 − 23 = 52.

Answer: 52.

15Make a friendly ten

Use 47 + 18. First reach 50, then complete the 18-unit jump.

A jump of 18 is regrouped as 3, 10, and 5.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Break 18 into 3 + 10 + 5.

Step 2. Jump 47 → 50 (+3), then 50 → 60 (+10).

Step 3. Jump +5 to 65. The jumps total 18, so 47 + 18 = 65.

Answer: 65.

16Use a friendly ten to subtract

Solve 83 − 26 using jumps through 80 and 60.

Break twenty-six into three, twenty, and three.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Break 26 into 3 + 20 + 3.

Step 2. Jump left: 83 → 80 → 60.

Step 3. Jump 3 more to 57. The full decrease was 26.

Answer: 57.

17Find a missing starting number

A number plus 9 equals 52: □ + 9 = 52. What was the start?

The end, 52, and the +9 jump are known; the starting number is missing.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. We know the landing point and the amount added, not the start.

Step 2. Work backward from 52 by 9 to undo the forward jump.

Step 3. 52 − 9 = 43; check 43 + 9 = 52.

Answer: 43.

18Find the size of a backward jump

A backward jump starts at 68 and lands at 42. What amount was subtracted: 68 − □ = 42?

The start and end are known, but the backward jump length is not.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. A jump to the left is subtraction, so the missing number is the distance between 68 and 42.

Step 2. Find the distance: 68 − 42 = 26.

Step 3. Check: 68 − 26 = 42.

Answer: 26.

19Find the missing amount added

A forward jump starts at 31 and stops at 57: 31 + □ = 57. Find the unknown.

Both endpoints are given; find the length of the forward jump.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. The missing amount is the increase from 31 to 57.

Step 2. Count on: 31 → 40 takes 9; 40 → 57 takes 17.

Step 3. Add 9 + 17 = 26; so 31 + 26 = 57.

Answer: 26.

20Find an unknown subtraction amount

Ninety minus an unknown number is 57: 90 − □ = 57. Use a number line to find □.

Count on from the result back to the starting number.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. We can find the missing subtraction amount by counting forward from 57 to 90.

Step 2. Jump +3 to 60 and +30 to 90.

Step 3. The jumps total 33; therefore 90 − 33 = 57.

Answer: 33.

21Find a distance by counting on

How many units separate the points 38 and 62 on a number line?

Find the full distance by combining all three forward jumps.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Count forward from 38 to a friendly ten: +2 reaches 40.

Step 2. Go from 40 to 60 (+20), and from 60 to 62 (+2).

Step 3. The distance is 2 + 20 + 2 = 24 units.

Answer: 24 units.

22Subtract by counting forward

Use counting on to find 73 − 48. Explain why your answer is not 73.

Count up from 48 to 73; the sum of the jumps gives the difference.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at 48 and count up to 73, keeping track of each jump.

Step 2. Move +2 to 50, +20 to 70, and +3 to 73.

Step 3. The total distance is 2 + 20 + 3 = 25. The number 73 is the landing point, not the difference.

Answer: 25.

23Compare two correct strategies

Kim uses +10 then +7 to find 46 + 17. Eli uses +20 then −3. Do both methods give the same sum?

Kim’s method uses a ten-unit jump and a seven-unit jump.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Kim jumps from 46 to 56 and then to 63: 10 + 7 = 17.

Step 2. Eli can jump +20 to 66 and then −3 to 63; the net change is +17.

Step 3. Both land at 63. Different, correct jump strategies can show the same sum.

Answer: Yes. Both give 63.

24Spot an incorrect number-line jump

Jamal says 72 − 19 = 52. He jumped left 10 to 62 and then left 10 more to 52, but labeled the second jump “−9.” What was the mistake?

The first ten-unit jump is correct; decide how long the remaining jump must be.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Jamal’s second jump was 10 units long, not the 9 units he wrote.

Step 2. After 72 − 10 = 62, subtract 9 more: 62 − 9 = 53.

Step 3. Check that 10 + 9 = 19. His answer 52 subtracts 20 instead of 19.

Answer: The second jump was one unit too far; 72 − 19 = 53.

25Follow two moves

A game piece starts at 28, moves forward 35 spaces, then moves backward 17 spaces. Where does it finish?

The first move is forward and the second is backward.

↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

Show solutionHide solution

Step 1. Start at 28. Add 35 by jumping right: 28 + 35 = 63.

Step 2. Move backward 17 from 63, first to 60 and then 46.

Step 3. The final point is 46. Check: 63 − 17 = 46.

Answer: 46.

✍️ Independent Practice — 30 Problems

Directions: Solve all 30 problems before opening the answer key. Use number-line jumps, equal unit spaces, or a matching equation. Draw your own jumps if there is no printed diagram. For missing numbers, check by reversing the operation. For a difference found by counting on, give the combined distance, not the ending point.

1. A point is 9 unit intervals to the right of 0. What number is it?

   Count the nine unit intervals from zero.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

2. Start at 4 and jump 6 units right. What is the landing number?

   Find the ending number after a six-unit forward jump.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

3. Start at 18 and jump 7 units left. Where do you stop?

   Use a seven-unit backward jump from eighteen.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

4. Show 35 + 10 as one jump of ten. Give the sum.
5. Solve 67 − 20 with two backward jumps of ten.
6. From 42, jump right 9. Find the sum.

   The jump begins at forty-two.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

7. From 61, jump left 8. Where do you land?
8. Use tens to solve 24 + 30.

   Three tens added on the number line.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

9. Find 88 − 40 using four jumps of ten.
10. Make a ten first to solve 49 + 6. Show the split of 6.
11. Compute 72 − 5 by jumping through 70.

    Start at seventy-two and split minus five into two and three.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

12. Break 26 into tens and ones to solve 17 + 26 on a number line.
13. Solve 84 − 27 using jumps through a friendly ten.

    The jumps total twenty-seven, but the endpoint is unlabeled.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

14. Find the missing start: □ + 8 = 36.
15. Find the missing backward-jump length: 59 − □ = 34.
16. Find □ in 22 + □ = 49. Explain the forward-jump distance.

    Find the unknown forward-jump distance between the known endpoints.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

17. Find □ in 90 − □ = 68.
18. How far apart are the points at 45 and 70?
19. The points 36 and 63 are marked. Find their distance by counting on.
20. Find 38 + 25 using +2 to 40, +20 to 60, and a final jump. How long is that final jump, and what is the sum?
21. Solve 75 − 38 by jumping back 5, then 30, then 3.

    The three backward jumps total thirty-eight.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

22. How many one-unit intervals are between 0 and 100? Explain why the answer is not 101.
23. The major marks on this number line are labeled every 10. One major label is missing. What number belongs in the blank?

    Each tall mark is ten unit intervals after the previous tall mark.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

24. Does 50 + 12 equal 50 + 10 + 2? Show where both methods land.
25. A student adds 17 to 29 using jumps of +10 and +8. Is that correct? Fix the jumps and find the sum.
26. A board-game token starts at 26, moves 18 spaces right, and then 7 spaces left. Where is it now?
27. A marker begins at 83, moves left 36 spaces, and then moves right 9. Where is it?
28. To get from 41 to 68, Dana uses jumps +9, +10, +8. Ben uses +9, +10, +7. Whose total matches the distance? Explain.
29. Use counting on to find 70 − 46: 46 → 50 and 50 → 70. What do the jump lengths add to?
30. An open number line shows 34 + □ = 82. Count on: 34 → 40 → 80 → 82. What is □? Explain the three jumps.

🏆 Lesson Test — 15 Questions

Directions: Work on your own without opening any answer key. Show a useful jump or short explanation when asked. All answers remain at or between 0 and 100.

1. A number line has the whole-number marks 0 through 13, including both endpoints. How many one-unit intervals are between 0 and 13? Explain why the answer is not 14.
2. Show 18 + 4 on a number line. Name the final point.

   Four forward unit steps from eighteen.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

3. Show 25 − 9 with a backward jump. Find the result.

   Nine backward unit steps from twenty-five.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

4. What is 48 + 20? Explain how two tens appear on the line.
5. Compute 91 − 30 by using tens jumps.
6. Split 17 into 10 and 7 to solve 36 + 17. Show your landing point.

   One ten-unit jump and one seven-unit jump.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

7. Find 74 − 28 by subtracting 20, then 8.

   Subtract twenty, then eight.

   ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

8. Find the missing start: □ + 7 = 43.
9. Find the missing amount: 85 − □ = 54.
10. Find □ in 29 + □ = 61. What distance is the forward jump?
11. Count on from 52 to 79 to find 79 − 52. Write the jump sizes.
12. A student solves 73 − 26 by jumping back 20 and then 6, arriving at 47. Is this correct? Explain.
13. For 56 + 18, Ari uses +4, +10, +4. Bea uses +4, +10, +3. Which set of jumps represents 18, and what is the sum?
14. A token starts at 44, moves 29 places forward, then 18 backward. Where does it stop?

    The token moves right and then left.

    ↔ If the number line extends beyond its card, scroll sideways; with a keyboard, focus the model and press the arrow keys.

15. A student claims 92 − 47 = 55. Their count-on path is 47 → 50 (+3), 50 → 90 (+40), 90 → 92 (+2). Are the jumps correct? What is the actual difference?

🔐 Complete Answer Key

Keep both sections closed until you finish the corresponding problems. Open one set at a time to check your thinking.

Show practice answer keyHide practice answer key

Practice Answers

1. 9. Nine unit intervals from zero lead to the point 9.

2. 10. 4 + 6 = 10; count six spaces, not six tick labels.

3. 11. 18 − 7 = 11; the landing point is 11.

4. 45. One ten-unit move to the right takes 35 to 45.

5. 47. 67 → 57 → 47. Two jumps of ten subtract 20.

6. 51. 42 + 8 = 50, then +1 = 51; all nine units are counted.

7. 53. 61 − 1 = 60; subtract seven more to reach 53.

8. 54. 24 + 30 = 54. Three tens increase the tens digit by three.

9. 48. Move left through 78, 68, 58, and 48. The total backward distance is 40.

10. 55. Jump +1 to 50 and +5 to 55. The jumps make 6.

11. 67. 72 − 2 = 70 and 70 − 3 = 67; 2 + 3 = 5.

12. 43. 17 + 20 = 37; 37 + 6 = 43.

13. 57. 84 − 4 = 80; 80 − 20 = 60; 60 − 3 = 57. The jumps subtract 27.

14. 28. Work backward: 36 − 8 = 28. Check 28 + 8 = 36.

15. 25. 59 − 34 = 25; the difference is the distance moved left.

16. 27. 49 − 22 = 27; check 22 + 27 = 49.

17. 22. 90 − 68 = 22; check 90 − 22 = 68.

18. 25 units. 70 − 45 = 25. The distance is 25 unit intervals.

19. 27 units. 36 → 40 is 4, 40 → 60 is 20, and 60 → 63 is 3. Total 27.

20. Final jump +3; sum 63. The jumps total 2 + 20 + 3 = 25, and 60 + 3 = 63.

21. 37. 75 → 70 → 40 → 37, so 75 − 38 = 37.

22. 100 intervals. There are 101 integer tick marks from 0 through 100, but just 100 spaces between neighboring marks.

23. 30. The major labels rise by 10 each time: 0, 10, 20, 30, 40, 50.

24. Yes; both land at 62. 50 + 12 = 62. Splitting 12 into 10 + 2 gives 50 → 60 → 62.

25. No; correct sum 46. 10 + 8 is 18, not 17. Use +10 and +7: 29 → 39 → 46.

26. 37. 26 + 18 = 44; 44 − 7 = 37.

27. 56. 83 − 36 = 47; 47 + 9 = 56.

28. Dana; 27 units. 68 − 41 = 27. Dana’s 9 + 10 + 8 is 27; Ben’s is only 26.

29. 24. The forward jumps are 4 and 20. Their sum is the difference 70 − 46 = 24.

30. 48. The jumps are 6, 40, and 2; 6 + 40 + 2 = 48, so 34 + 48 = 82.

Show test answer keyHide test answer key

Test Answers

1. 13. There are 14 whole-number marks from 0 through 13, but only 13 spaces between neighboring marks.

2. 22. 18 + 2 = 20, then +2 = 22.

3. 16. 25 − 5 = 20; 20 − 4 = 16, a total of nine spaces.

4. 68. 48 → 58 → 68 are two forward ten-unit jumps.

5. 61. 91 → 81 → 71 → 61; three backward tens subtract 30.

6. 53. 36 + 10 = 46; 46 + 7 = 53.

7. 46. 74 − 20 = 54; 54 − 8 = 46.

8. 36. 43 − 7 = 36, and 36 + 7 = 43.

9. 31. 85 − 54 = 31; check 85 − 31 = 54.

10. 32. 61 − 29 = 32 unit intervals, so 29 + 32 = 61.

11. 27; jumps +8 and +19, or +8, +10, +9. 52 → 60 is +8, 60 → 70 is +10, and 70 → 79 is +9. Total 27.

12. Yes; 47. 73 − 20 = 53 and 53 − 6 = 47. The jumps total 26.

13. Ari; 74. 4 + 10 + 4 = 18; 56 → 60 → 70 → 74. Bea’s jumps total only 17.

14. 55. 44 + 29 = 73; 73 − 18 = 55.

15. The jumps are correct, but the difference is 45. 3 + 40 + 2 = 45, not 55. So 92 − 47 = 45.

💡 Common Mistakes to Watch For

Counting tick marks instead of spaces

From 0 to 6 there are six unit spaces, not seven. Start at zero, and count each move.

Mixing directions

Adding a positive number moves right; subtracting a positive number moves left. Counting forward to find a difference is a separate subtraction strategy.

Forgetting part of a split jump

If you split +18 as +3 and +10, you still need +5. Add the parts to check the full jump length.

Confusing the ending point with the difference

Counting on from 48 to 73 ends at 73, but the distance traveled is 25.

🏡 Family Practice Idea

Floor number line: Make a short 0–20 number line with equally spaced paper marks or cards. Ask the child to stand at 7, step forward 5 spaces, then backward 3. Count the steps aloud. Next, draw a 0–100 number line on paper and practice jumps of 10, then 1. Ask, “Did you count the spaces or the numbers you saw?”

🔗 Related Lessons

Grade 2 Lesson 25 — Length Word ProblemsConnect addition and subtraction to lengths and missing parts.Grade 2 Lesson 13 — Mental StrategiesReview adding and subtracting with tens, ones, and friendly numbers.

🖨️ Printable Companion

Print from the browser: Use Ctrl+P (Windows) or Command+P (Mac) to print lesson pages, the Independent Practice section, or the Lesson Test. The diagrams are schematic and their tick spacing matters. Check the print preview before printing. No separate downloadable worksheet is offered here.

← Lesson 25: Length Word ProblemsGrade 2 Math HubNext: Lesson 27 — Measurement Data & Line Plots →