Mathematics
Grade 10
15 min
Create pictographs (Tutorial Only)
Create pictographs (Tutorial Only)
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1
Introduction & Learning Objectives
Learning Objectives
Design and create pictographs where the area of a two-dimensional figure represents data frequency.
Develop a key for a pictograph that uses fractional or scaled versions of a base two-dimensional figure to represent data values.
Analyze how geometric transformations, specifically scaling, of symbols in a pictograph can lead to data misinterpretation.
Justify the selection of specific polygons or circles as symbols to thematically and accurately represent a given dataset.
Construct a pictograph to compare geometric properties of different sets of figures.
Critically evaluate the geometric integrity of a given pictograph, identifying potential sources of visual bias.
Ever seen a chart in the news that just *feels* wrong or exaggerated? 📊 Let's explor...
2
Key Concepts & Vocabulary
TermDefinitionExample
PictographA type of chart that uses two-dimensional pictures or symbols (icons) to represent data. The symbols are chosen to be thematically relevant to the data's subject matter.Using circle icons to show the number of pizzas sold each day, where each circle represents 10 pizzas.
Key (or Legend)An essential component of a pictograph that explains the quantitative value represented by a single symbol.In a chart about car sales, the key might state: 'One car symbol = 500 cars sold'.
Area Proportionality PrincipleA rule stating that when the size of a symbol is used to represent data, the ratio of the areas of two symbols must be equal to the ratio of the data values they represent.If City A has twice the population of City B, a circle representing City...
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Core Formulas
Frequency Representation Rule
N = n \times v
This is the fundamental rule for basic pictographs. Use it when the *count* of identical symbols represents the data. Here, 'N' is the total data value for a category, 'n' is the number of symbols shown, and 'v' is the value per symbol defined in the key.
Area Proportionality Formula
\frac{A_1}{A_2} = \frac{d_1}{d_2}
Use this rule when the *area* of a symbol represents its value. The area of a symbol for one data point (A₁) divided by the area of a symbol for another (A₂) must equal the ratio of their corresponding data values (d₁ and d₂).
Area Scaling Factor Rule
A_{new} = k^2 \times A_{original}
This rule connects the linear scale factor (k) to the resulting area. If you scale the side lengt...
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Challenging
A pictograph represents the number of electric cars sold. A sale of 500 cars is represented by a circle with an area of 10π cm². To maintain area proportionality, what should be the radius of a circle representing a sale of 1250 cars?
A.5 cm
B.12.5 cm
C.√25 cm
D.√50 cm
Challenging
A pictograph compares data for two groups. Group A's data is shown using squares, and Group B's data is shown using equilateral triangles. The key is '1 symbol = 1000 units' for both. If the side length of the square is equal to the side length of the triangle, why might this pictograph be geometrically misleading?
A.It is not misleading, as the key is consistent for both groups.
B.The base areas of the two different symbols are not equal, so a symbol for Group A does not visually represent the same quantity as a symbol for Group B.
C.Triangles are visually more appealing than squares, creating an emotional bias towards Group B.
D.The number of vertices is different (4 vs 3), which confuses the viewer.
Challenging
You need to create a pictograph for the annual budgets of three departments: { $72,000, $108,000, $84,000 }. You must use a regular hexagon as the symbol. Which key is the most effective choice and why?
A.1 hexagon = $1,000, because it is a round number.
B.1 hexagon = $72,000, because it is the smallest data value.
C.1 hexagon = $6,000, because it is a common divisor but requires many symbols.
D.1 hexagon = $12,000, because it is the GCD and balances clarity with a manageable number of symbols.
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