A pie chart is a circular statistical graphic that is divided into slices to illustrate numerical proportion. The arc length of each slice is proportional to the quantity it represents. It is a useful way to represent data with categories and show the proportion of each category in relation to the whole.

**Sector:**Each slice of the pie chart is called a sector, representing a category or data point.**Angle:**The angle of each sector is proportional to the quantity it represents, with the total angle in a pie chart always equal to 360 degrees.**Percentage:**Pie charts often display the percentage or proportion of each category relative to the whole.**Labels:**Categories or data points are typically labeled within or outside the pie chart for clarity.

To create a pie chart, follow these steps:

**Collect Data:**Gather the numerical data that you want to represent in the pie chart.**Calculate Total:**Find the total of all the data values to determine the whole that the pie chart will represent.**Calculate Percentages:**Calculate the percentage of each data value relative to the total.**Determine Angles:**Convert the percentages to angles (in degrees) by multiplying by 360.**Draw the Chart:**Use a protractor or graphing software to draw the sectors and label the categories.

When interpreting a pie chart, consider the following:

**Comparisons:**Compare the sizes of the sectors to understand the relative proportions of the categories.**Trends:**Identify any obvious trends or patterns in the data represented by the pie chart.**Limitations:**Be aware of the limitations of pie charts, such as difficulty in comparing multiple pie charts or accurately judging angles.

Here are some examples of pie charts:

Try solving the following practice problems to test your understanding of pie charts:

- Given the following data, create a pie chart to represent the distribution of sales for a company:
- Category A: 25%
- Category B: 35%
- Category C: 20%
- Category D: 20%

- Interpret the pie chart below and identify the category that represents the largest proportion of the data:

Good luck with your pie chart studies!

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.