Graphing

Graphing

Middle School

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Learning Objectives

• Represent inequalities on a number line using the correct symbols.

• Describe the uses of bar graphs, line graphs, and circle graphs.

• Organize data using frequency tables, dot plots, and stem-and-leaf plots.

• Interpret distance-time and speed-time graphs to describe an object's motion.

Key Vocabulary

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Inequality

A comparison of two values, showing if one is less than, greater than, or not equal to another.

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Bar Graph

A chart that uses bars of different lengths to compare data across various distinct categories.

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Line Graph

A graph that displays data that changes continuously over periods of time by connecting data points.

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Pie Chart

A circular statistical graphic, divided into slices to illustrate numerical proportion or percentages of a whole.

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Frequency Table

A table that lists items and shows the number of times they occur in a dataset.

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Stem-and-Leaf Plot

A display where each data value is split into a 'leaf' (last digit) and a 'stem' (other digits).

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Graphing Inequalities

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Multiple Choice

How would you correctly represent the inequality 'x < 10' on a number line?

• A closed circle on 10 with shading to the left.

• An open circle on 10 with shading to the right.

• An open circle on 10 with shading to the left.

• A closed circle on 10 with shading to the right.

Types of Graphs

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Bar Graphs

• ​Used to compare data across different groups or categories.

• ​​Each bar shows the amount for a specific category.

• ​Example: comparing students' favorite types of ice cream.

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Line Graphs

• ​These are used to show how data changes over time.

• ​​Data points are connected with a line to show trends.

• ​Example: tracking temperature changes throughout a single day.

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Circle Graphs

• ​These are also called pie charts and show parts of a whole.

• ​​Each slice represents a percentage of the total data.

• ​All of the different parts will add up to 100%.

Multiple Choice

Which type of graph would be best to show the percentage of students in a class who own a dog, a cat, a fish, or no pet?

• A Bar Graph

• A Line Graph

• A Dot Plot

• A Circle Graph

Different Ways to Organize and Show Data

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Frequency Tables

• ​Frequency tables list items and show how often they occur.

• ​​They use tally marks or numbers to show the count.

• ​The number of times an item appears is its frequency.

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Dot Plots

• ​A dot plot uses a simple number line to show data.

• ​​Dots are placed above numbers to show an item's frequency.

• ​It provides a quick visual way to compare different counts.

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Stem-and-Leaf Plots

• ​This plot organizes data by splitting each value into two parts.

• ​​The 'stem' is the first digit and the 'leaf' is the last.

• ​It quickly shows how the data is distributed among values.

Multiple Choice

Which data organization method involves splitting each data value into two parts, typically the last digit and the remaining digits?

• Dot Plot

• Bar Graph

• Stem-and-Leaf Plot

• Frequency Table

Interpreting Distance-Time Graphs

• A horizontal line shows the object is not moving.

• An upward sloping line shows movement at a constant speed.

• A downward sloping line means the object is returning to its start.

Multiple Choice

On a distance-time graph, what does a straight, horizontal line indicate?

• The object is accelerating.

• The object is returning to the start.

• The object is moving at a constant speed.

• The object is at rest.

Interpreting Speed-Time Graphs

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Positive Slope

• ​This indicates that the object is experiencing constant acceleration.

• ​​The line on the graph goes up from left to right.

• ​The object's speed is steadily increasing over the recorded time.

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Zero Slope

• ​This means the object is moving at a constant speed.

• ​​The line on the graph is a flat, horizontal line.

• ​The object's speed is not changing as time passes on.

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Negative Slope

• ​This indicates the object is experiencing constant deceleration.

• ​​The line on the graph goes down from left to right.

• ​The object's speed is steadily decreasing over the recorded time.

Multiple Choice

What does a line with a positive slope on a speed-time graph represent?

• The object is at rest

• Constant deceleration

• Constant acceleration

• Constant speed

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Common Misconceptions

Misconception	Correction
An open circle on a number line means the number is a possible answer.	An open circle means the number is not included in the solution.
A horizontal line on a graph always means that movement has stopped.	On a speed-time graph, it means constant speed, not stopped.
Bar graphs and line graphs can be used for any type of data.	Bar graphs compare categories. Line graphs show changes over time.

Multiple Choice

If a bar graph shows the number of cars of different colors in a parking lot, and a circle graph shows the same data, what is the key difference in what they emphasize?

• The bar graph shows percentages, while the circle graph shows exact counts.

• The bar graph compares the exact number of cars for each color, while the circle graph shows each color's percentage of the total cars.

• The bar graph shows change over time, while the circle graph shows categories.

• There is no difference in what they emphasize.

Multiple Choice

A student starts walking away from their house, stops to talk to a friend, and then walks back home. How would this journey be represented on a distance-time graph?

• A line sloping down, then a horizontal line, then a line sloping up.

• A line sloping up, then a curved line, then a horizontal line.

• A line sloping up, then a horizontal line, then a line sloping down.

• A horizontal line, then a line sloping up, then a line sloping down.

Multiple Choice

An object's motion is shown on a speed-time graph. The line begins at 0, slopes upwards to a peak, then becomes a horizontal line. What does this sequence represent?

• Moving at a constant speed, then stopping.

• Decelerating, then stopping.

• Accelerating, then decelerating to a stop.

• Accelerating, then moving at a constant speed.

Multiple Choice

Analyze the inequality $$x \ge -4$$ . Which statement accurately describes its graph on a number line and provides a correct example of a solution and non-solution?

• A closed circle on -4 and shading to the left. A solution is -4, a non-solution is 0.

• A closed circle on -4 and shading to the right. A solution is 0, a non-solution is -5.

• An open circle on -4 and shading to the right. A solution is -3, a non-solution is -4.

• An open circle on -4 and shading to the left. A solution is -5, a non-solution is -3.

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Summary

• Inequalities are graphed on a number line using open or closed circles.

• Different graphs show data in different ways, like bar, line, or circle graphs.

• We can organize data using frequency tables, dot plots, and stem-and-leaf plots.

• Motion graphs tell us if an object is at rest, moving at a constant speed, or accelerating.

Poll

On a scale of 1-4, how confident are you about interpreting different types of graphs?

• 1

• 2

• 3

• 4