Math worksheet for creating line plots with fractions, displaying five exercises with sets of fractional numbers to be plotted on number lines.

Let’s solve each line plot problem step by step. We’ll count how many times each number appears and place that many X’s above the correct spot on the number line.

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Problem 1:

Numbers given:
7½, 6½, 7, 6, 7, 7½, 5, 6
5½, 6½, 6, 7½, 5, 5½, 5½, 5

Let’s list them in order to make counting easier:

5, 5, 5, 5 → four 5s
5½, 5½, 5½ → three 5½s
6, 6, 6 → three 6s
6½, 6½ → two 6½s
7, 7 → two 7s
7½, 7½, 7½ → three 7½s

Now label the line plot from 5 to 8 (as shown). Place X’s above each value:

- Above 5: 4 X’s
- Above 5½: 3 X’s
- Above 6: 3 X’s
- Above 6½: 2 X’s
- Above 7: 2 X’s
- Above 7½: 3 X’s

(No numbers at 8, so no X’s there.)

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Problem 2:

Numbers:
8, 9½, 10, 8, 8½, 8, 8½, 10
9, 9, 9, 9½, 10, 9½, 8½, 10½

List in order:

8, 8, 8 → three 8s
8½, 8½, 8½ → three 8½s
9, 9, 9 → three 9s
9½, 9½, 9½ → three 9½s
10, 10, 10 → three 10s
10½ → one 10½

Line plot goes from 8 to 11.

Place X’s:

- 8: 3 X’s
- 8½: 3 X’s
- 9: 3 X’s
- 9½: 3 X’s
- 10: 3 X’s
- 10½: 1 X
- 11: 0 X’s

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Problem 3:

Numbers:
4⅛, 2⅞, 4⅞, 4⅞, 2, 3⅜, 3⅞
3⅞, 2⅞, 2¼, 4⅛, 4, 2⅞, 3⅞, 4⅞

Let’s convert all to eighths to compare easily:

2 = 16/8
2¼ = 18/8 = 2.25 → but we’ll keep as mixed numbers for plotting.

Actually, let’s just group by the exact values given:

Count each:

- 2 → once
- 2¼ → once
- 2⅞ → three times (appears 3x)
- 3⅜ → once
- 3⅞ → three times (appears 3x)
- 4 → once
- 4⅛ → twice
- 4⅞ → three times

Wait — let me recount carefully from the list:

Original list:

Row 1: 4⅛, 2⅞, 4⅞, 4⅞, 2, 3⅜, 3⅞
Row 2: 3⅞, 2⅞, 2¼, 4⅛, 4, 2⅞, 3⅞, 4⅞

So:

- 2 → 1 time
- 2¼ → 1 time
- 2⅞ → appears in row1 (once), row2 (twice) → total 3 times
- 3⅜ → 1 time
- 3⅞ → row1 (once), row2 (twice) → total 3 times
- 4 → 1 time
- 4⅛ → row1 (once), row2 (once) → 2 times
- 4⅞ → row1 (twice), row2 (once) → 3 times

Yes.

Line plot from 2 to 5.

Place X’s:

- 2: 1 X
- 2¼: 1 X
- 2⅞: 3 X’s
- 3⅜: 1 X
- 3⅞: 3 X’s
- 4: 1 X
- 4⅛: 2 X’s
- 4⅞: 3 X’s

(Note: 3⅜ is between 3 and 4, closer to 3.5; 4⅛ is just after 4; etc. But since the number line has marks only at whole numbers, you place the X above the closest mark? Wait — actually, looking at the number line in problem 3, it shows ticks at 2, 3, 4, 5 — but fractions like 2¼, 2⅞, etc., should be placed proportionally between the whole numbers. However, in typical elementary line plots with fractions, they often expect you to place the X directly above the fractional value even if not labeled — meaning you imagine the space between 2 and 3 divided into 8 parts for eighths.

But since the instruction says “create and label the line plot”, and the number line already has whole numbers marked, we assume students are to place X’s at the correct fractional positions between the wholes.

However, for simplicity in this format, I’ll describe where to put the X’s relative to the whole numbers.

But actually — looking back at the worksheet, the number lines have only whole numbers labeled, but the fractions are meant to be plotted between them. So for example, 2¼ goes a quarter of the way from 2 to 3; 2⅞ goes almost to 3, etc.

But since we’re describing the answer textually, we can say:

For Problem 3:

Between 2 and 3:
- At 2: 1 X
- At 2¼: 1 X
- At 2⅞: 3 X’s

Between 3 and 4:
- At 3⅜: 1 X
- At 3⅞: 3 X’s

At 4: 1 X
Between 4 and 5:
- At 4⅛: 2 X’s
- At 4⅞: 3 X’s

But wait — 4 is a whole number, so it gets its own tick. 4⅛ is just past 4, 4⅞ is close to 5.

In standard practice, you’d draw the number line with finer ticks or estimate position. Since this is text-based, I’ll note the counts per unique value.

Actually, perhaps the worksheet expects us to treat each fraction as a distinct point and stack X’s above their exact location — which may not align with whole number ticks. But since the number line only labels whole numbers, we must place the X’s visually between them.

To avoid confusion, I’ll provide the frequency of each value, and the student can plot accordingly.

Final counts for Problem 3:

Value : Count
2 : 1
2¼ : 1
2⅞ : 3
3⅜ : 1
3⅞ : 3
4 : 1
4⅛ : 2
4⅞ : 3

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Problem 4:

Numbers:
5¼, 5¾, 4¾, 4¼, 5, 5¼, 4, 6
4¼, 5, 6¼, 5¾, 6, 6, 6¼, 5

List:

4 : 1
4¼ : 2 (from first row and second row)
4¾ : 1
5 : 3 (first row: one 5; second row: two 5s? Let's check)

First row: 5¼, 5¾, 4¾, 4¼, 5, 5¼, 4, 6 → that’s one 5
Second row: 4¼, 5, 6¼, 5¾, 6, 6, 6¼, 5 → that’s two 5s → total 3 fives

5¼ : first row has two (positions 1 and 6), second row none → 2
5¾ : first row one, second row one → 2
6 : first row one, second row two → 3
6¼ : second row two → 2

Also 4¼: first row one, second row one → 2
4¾: first row one → 1
4: first row one → 1

So:

4 : 1
4¼ : 2
4¾ : 1
5 : 3
5¼ : 2
5¾ : 2
6 : 3
6¼ : 2

Number line from 4 to 7.

Plot accordingly.

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Problem 5:

Numbers:
7⅞, 5⅞, 6⅛, 7⅜, 5⅞, 5⅞, 5⅞, 6⅞
6⅞, 6⅞, 7⅞, 5⅞, 7¼, 5⅞, 5⅞, 6⅞

Let’s count:

First, list all:

From row 1:
7⅞, 5⅞, 6⅛, 7⅜, 5⅞, 5⅞, 5⅞, 6⅞ → that’s:
5⅞: four times
6⅛: once
7⅜: once
7⅞: once
6⅞: once

Row 2:
6⅞, 6⅞, 7⅞, 5⅞, 7¼, 5⅞, 5⅞, 6⅞ →
5⅞: three more → total 5⅞: 4 + 3 = 7
6⅞: three more → total 6⅞: 1 + 3 = 4
7⅞: one more → total 7⅞: 1 + 1 = 2
7¼: once
6⅛: still one (only in row1)

Wait, let’s tabulate:

Make a table:

Value | Count
5⅞ | row1: positions 2,5,6,7 → 4; row2: positions 4,6,7 → 3 → total 7
6⅛ | row1 pos3 → 1
6⅞ | row1 pos8 → 1; row2 pos1,2,8 → 3 → total 4
7¼ | row2 pos5 → 1
7⅜ | row1 pos4 → 1
7⅞ | row1 pos1 → 1; row2 pos3 → 1 → total 2

So:

5⅞: 7
6⅛: 1
6⅞: 4
7¼: 1
7⅜: 1
7⅞: 2

Number line from 5 to 8.

Plot these between 5 and 8.

Specifically:

Between 5 and 6:
- 5⅞ (close to 6): 7 X’s

Between 6 and 7:
- 6⅛ (just after 6): 1 X
- 6⅞ (close to 7): 4 X’s

Between 7 and 8:
- 7¼ (quarter after 7): 1 X
- 7⅜ (three-eighths after 7): 1 X
- 7⅞ (close to 8): 2 X’s

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Now, since the question asks to "solve" and the final answer should be provided, but these are graphical tasks, I think the expected "answer" is the completed line plots. However, since we can't draw here, I'll summarize the frequency for each problem as the solution.

But looking back at the user request: "Solve the problem accurately." and "Final Answer: [Provide only the final correct answer]"

Since these are multiple problems, and each requires a line plot, perhaps the best approach is to state that the line plots should be created with the following frequencies.

Alternatively, maybe the worksheet expects the student to fill in the X’s, so our "answer" is the description of how many X’s go where.

Given the constraints, I’ll provide for each problem the list of values with their counts, which allows constructing the line plot.

But to match the format, perhaps for each problem, we can say:

After careful counting, here are the frequencies for each value in each problem.

However, the instruction says "Final Answer" should come after all reasoning, and be only the final correct answer.

Since there are 5 separate problems, I need to provide answers for all.

Perhaps the safest is to box the frequency distributions.

But let me see if there's a better way.

Another thought: in some contexts, "solve" might mean to complete the plots, but since we can't draw, maybe the answer is implied by the counts.

I think for clarity, I'll write the final answer as a summary for each problem.

Final Answer:

For Problem 1:
5: 4, 5½: 3, 6: 3, 6½: 2, 7: 2, 7½: 3

For Problem 2:
8: 3, 8½: 3, 9: 3, 9½: 3, 10: 3, 10½: 1

For Problem 3:
2: 1, 2¼: 1, 2⅞: 3, 3⅜: 1, 3⅞: 3, 4: 1, 4⅛: 2, 4⅞: 3

For Problem 4:
4: 1, 4¼: 2, 4¾: 1, 5: 3, 5¼: 2, 5¾: 2, 6: 3, 6¼: 2

For Problem 5:
5⅞: 7, 6⅛: 1, 6⅞: 4, 7¼: 1, 7⅜: 1, 7⅞: 2

This allows the student to create the line plots by placing the specified number of X's above each value on the number line.