Free 7th Grade Math Worksheets covering key math concepts including inequalities, geometry, square roots, and data analysis, provided by Mashup Math.

Let’s solve each problem on the worksheets step by step. We’ll go one worksheet at a time, starting with the easiest and building up.

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Worksheet 1: Graphing Inequalities

We’re given inequalities to graph on number lines. Let’s do a few examples:

1.) x < 2
→ Draw an open circle at 2 (since it’s “less than”, not “less than or equal to”) and shade everything to the left.

3.) x + 1 ≤ 9
→ Subtract 1 from both sides: x ≤ 8
→ Closed circle at 8, shade left.

5.) -2x > 10
→ Divide both sides by -2 → remember to flip the inequality sign!
→ x < -5
→ Open circle at -5, shade left.

7.) 3x + 6 ≤ 12
→ Subtract 6: 3x ≤ 6
→ Divide by 3: x ≤ 2
→ Closed circle at 2, shade left.

9.) -6 < x
→ Same as x > -6
→ Open circle at -6, shade right.

11.) x/2 < -3
→ Multiply both sides by 2: x < -6
→ Open circle at -6, shade left.

You’d draw these on number lines accordingly.

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Worksheet 2: Area of Right Triangles

Formula for area of triangle: A = (base × height) / 2

In right triangles, the two legs are base and height.

1.) Legs: 6 m and 8 m
A = (6 × 8) / 2 = 48 / 2 = 24 m²

2.) Legs: 3 cm and 4 cm
A = (3 × 4) / 2 = 12 / 2 = 6 cm²

3.) Legs: 5 yd and 12 yd
A = (5 × 12) / 2 = 60 / 2 = 30 yd²

(Note: The hypotenuse is given but we don’t need it for area — only the two perpendicular sides.)

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Worksheet 3: Estimating Square Roots

We estimate square roots by finding perfect squares around them.

Example: √7 is between √4=2 and √9=3 → so between 2 and 3.

Now let’s do the problems:

1.) √5 → between √4=2 and √9=3 → between 2 and 3

2.) √19 → between √16=4 and √25=5 → between 4 and 5

3.) √10 → between √9=3 and √16=4 → between 3 and 4

4.) √51 → between √49=7 and √64=8 → between 7 and 8

5.) √29 → between √25=5 and √36=6 → between 5 and 6

6.) √88 → between √81=9 and √100=10 → between 9 and 10

7.) √63 → between √49=7 and √64=8 → between 7 and 8

8.) √45 → between √36=6 and √49=7 → between 6 and 7

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Worksheet 4: Analyzing Box-and-Whisker Plots

First plot: Robinson’s Points Scored Per Game

Box plot shows:
- Minimum: 8
- Q1 (first quartile): 13
- Median: 19
- Q3 (third quartile): 25
- Maximum: 36

A.) Highest total points scored? → 36

B.) Lowest total points scored? → 8

C.) Median number of points? → 19

D.) Percent of games he scored 19 or more?
→ Median splits data in half → 50% scored 19 or more → 50%

E.) Percent of games he scored 13 or fewer?
→ Q1 is 13 → that means 25% of data is below Q1 → 25%

F.) How many points next game? Opinion-based, but you could say:
“He usually scores between 13 and 25, maybe around 19. But sometimes he scores high like 36, so maybe 20–25?”

Second plot: Science Test Scores (as Percents)

Values:
- Min: 53
- Q1: 77
- Median: 84
- Q3: 96
- Max: 100

A.) Highest grade? → 100

B.) Lowest grade? → 53

C.) Median test score? → 84

D.) Percent greater than 96%?
→ Q3 is 96 → top 25% are above Q3 → 25%

E.) Percent less than 96%?
→ Everything except top 25% → 75%

F.) Did students perform well overall?
→ Median is 84, which is a B. Half scored 84 or higher. Only 25% got below 77. So yes, most did pretty well. Some struggled (min 53), but overall good performance.

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Final Answer:

Graphing Inequalities: Graphs drawn based on solved inequalities (e.g., x < 2 → open circle at 2, shade left).

Area of Right Triangles:
1.) 24 m²
2.) 6 cm²
3.) 30 yd²

Estimating Square Roots:
1.) between 2 and 3
2.) between 4 and 5
3.) between 3 and 4
4.) between 7 and 8
5.) between 5 and 6
6.) between 9 and 10
7.) between 7 and 8
8.) between 6 and 7

Analyzing Box-and-Whisker Plots – Robinson:
A.) 36
B.) 8
C.) 19
D.) 50%
E.) 25%
F.) Around 20–25 points (reasonable estimate)

Science Test Scores:
A.) 100
B.) 53
C.) 84
D.) 25%
E.) 75%
F.) Yes, most students performed well — median was 84, and only 25% scored below 77.