Mathematics
Grade 10
15 min
Choose the best type of graph
Choose the best type of graph
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1
Introduction & Learning Objectives
Learning Objectives
Identify the purpose of different graph types, including bar graphs, pie charts, line graphs, and scatter plots.
Differentiate between categorical and numerical data derived from the properties of two-dimensional figures.
Analyze a dataset related to geometric properties (e.g., area, perimeter, number of sides, angle measures).
Select the most appropriate graph type to represent a given geometric dataset and goal.
Justify their choice of graph using mathematical reasoning.
Critique the effectiveness of a given graph in representing relationships between properties of 2D figures.
You've just measured the areas of 50 different circular objects. How can you visually show the relationship between a circle's radius and its area? 📈
This tutorial wil...
2
Key Concepts & Vocabulary
TermDefinitionExample
Categorical DataData that can be sorted into distinct groups or categories. It describes qualities or characteristics.Types of triangles (equilateral, isosceles, scalene) or types of quadrilaterals (square, rhombus, kite).
Numerical DataData that consists of numbers and represents a measurement or count. It can be discrete (countable values) or continuous (any value within a range).Discrete: The number of vertices in a polygon (4, 5, 6). Continuous: The area of a circle (e.g., 12.57 cm²).
Bar GraphA graph that uses rectangular bars to compare the amounts or frequencies of different categories of data.A graph comparing the number of right angles in a square, a right trapezoid, and a pentagon.
Pie ChartA circular graph divided into slices to illustrate numerical propor...
3
Core Formulas
Graph Selection for Data Type
Categorical Data → Bar Graph (to compare) or Pie Chart (for parts of a whole). Numerical Data → Line Graph or Scatter Plot (to show relationships/trends).
This is the fundamental decision-making rule. First, identify your data type. If you are comparing distinct categories like 'types of shapes', use a bar graph. If you are showing how these categories make up a whole, use a pie chart. If you are exploring the relationship between two sets of numbers, like radius and area, use a scatter plot or line graph.
Relationship vs. Trend
Use a Scatter Plot to investigate a potential correlation. Use a Line Graph to display a known functional relationship or trend.
When you collect data points (e.g., measuring the base and area of various rectan...
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Challenging
A student is testing the theorem that for a quadrilateral inscribed in a circle, opposite angles are supplementary (sum to 180°). They measure the opposite angles (∠A and ∠C) for 20 such quadrilaterals, expecting small measurement errors. To best visualize their results and compare them to the theorem, what should they do?
A.Create a scatter plot of ∠C vs. ∠A and look for points clustering around the line y = 180 - x.
B.Create a bar graph comparing the sums (∠A + ∠C) for each of the 20 quadrilaterals.
C.Create a pie chart showing the proportion of angles that were acute vs. obtuse.
D.Create a line graph connecting the 20 angle sums in the order they were measured.
Challenging
You are presented with two scenarios. Scenario 1: Graphing the areas of five different lakes, which are all triangular. Scenario 2: Graphing the percentage of a single triangular park that is covered by a playground, a garden, and a pond. A student incorrectly chooses a pie chart for Scenario 1 and a bar graph for Scenario 2. What are the two fundamental errors in their choices?
A.Error 1: Pie charts can't use area. Error 2: Bar graphs are only for non-geometric data.
B.Error 1: The data is categorical. Error 2: The data is numerical.
C.Error 1: The areas are not parts of a whole. Error 2: The percentages are parts of a whole.
D.Error 1: There are too many lakes for a pie chart. Error 2: There are too few sections for a bar graph.
Challenging
A student calculates the ratio of a regular n-gon's area to the area of its circumscribed circle for n = 3, 4, 5, ..., 30. They want to create a graph that most effectively demonstrates that this ratio approaches a limit (gets closer and closer to 1) as 'n' becomes large. Which graph is the best choice?
A.bar graph comparing the ratio for each value of n.
B.line graph plotting the ratio (y-axis) against the number of sides 'n' (x-axis).
C.scatter plot of the same data.
D.pie chart showing the final ratio when n=30.
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