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Worksheet Grade 11 Art & Music

Calder Basin Water Use: Designing an Isotype Chart

Grade 11 students convert a fictional district's daily water use into icon counts, fit the rows to a report column, and test a scaled-icon distortion.

Objectives

  1. Students will convert quantities into icon counts using a stated pictogram key.
  2. Students will fit a row of repeated icons inside a fixed column width.
  3. Students will explain why scaling an icon in two dimensions misstates a quantity.

Vocabulary

Key words: isotype, pictogram, key, pitch, precision

Teacher overview

An isotype chart counts rather than measures, because a repeated icon of fixed size lets a reader compare rows by counting whole units instead of judging length. That works only while every icon stays the same size, and a chart that varies the icon gives up the property it was chosen for. This worksheet uses the fictional Calder Basin Water District's daily use by customer class, and it ends with a common distortion, in which an icon is scaled in both height and width to show a larger quantity. Item 10 asks for the factor by which the area grows before item 11 asks for the explanation, since the doubled icon usually looks reasonable until its area is computed.

Calder Basin Water Use: Designing an Isotype Chart — Grade 11 Art & Music
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Calder Basin Water District wants a pictogram chart of its average daily water use. The four customer classes are given below.

Customer class Average use, gallons per day
Homes 4,250,000
Businesses 1,750,000
Schools 700,000
Parks 300,000

The chart key sets one icon equal to 500,000 gallons per day. Each icon is 9 mm wide and 12 mm tall. A gap of 3 mm follows every icon, so the step from the left edge of one icon to the left edge of the next is 12 mm. Part icons are drawn by cutting the icon vertically.

  1. What is the total average daily use for all four classes?
  2. How many icons does the Homes row need?
  3. How many icons does the Businesses row need?
  4. How many icons does the Schools row need?
  5. How many icons does the Parks row need?
  6. The chart rounds every row to the nearest half icon. What do the Schools and Parks rows become?
  7. Add the four rounded row counts. Compare that sum with the exact icon count for the total from item 1.
  8. The Homes row holds 8 full icons and then a half icon. Measure from the left edge of the first icon to the right edge of the half icon. How wide is the row?
  9. The report column is 105 mm wide. How much room is left after the Homes row?
  10. A designer proposes showing double an amount by drawing one icon at double the height and double the width. By what factor does that icon's area grow?
  11. Explain why the proposal in item 10 misstates the quantity for a reader.
  12. District meters are reported to the nearest 25,000 gallons per day. What is the smallest icon fraction that this reporting precision supports?
  13. The chart needs a one-line key so a reader can decode it. Write that line.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 7,000,000 gallons per day. Adding 4,250,000, 1,750,000, 700,000, and 300,000 gives 7,000,000.
  2. Answer: 8.5 icons. Dividing 4,250,000 by 500,000 gives 8.5.
  3. Answer: 3.5 icons. Dividing 1,750,000 by 500,000 gives 3.5.
  4. Answer: 1.4 icons. Dividing 700,000 by 500,000 gives 1.4.
  5. Answer: 0.6 icons. Dividing 300,000 by 500,000 gives 0.6.
  6. Answer: 1.5 and 0.5 icons. The Schools count of 1.4 rounds up to 1.5, and the Parks count of 0.6 rounds down to 0.5. The Homes and Businesses counts already sit on a half.
  7. Answer: 14 icons. The rounded rows are 8.5, 3.5, 1.5, and 0.5, which sum to 14. The exact total of 7,000,000 divided by 500,000 is also 14, so the rounding did not change the total here. That will not always happen, and a designer has to check it each time.
  8. Answer: 100.5 mm. Eight steps of 12 mm reach the left edge of the ninth icon at 96 mm, and the half icon adds half of 9 mm, or 4.5 mm.
  9. Answer: 4.5 mm. Subtracting the 100.5 mm row from the 105 mm column leaves 4.5 mm.
  10. Answer: 4 times. Doubling the width and the height multiplies the area by 2 times 2.
  11. Answer: The reader judges the icon by the ink on the page, which is its area. An icon drawn to show twice as much covers four times the area, so the row reads as four times the original rather than twice it. Repeating a fixed icon avoids the problem, because the count and the ink then rise together.
  12. Answer: 0.05 icons. Dividing 25,000 gallons per day by the 500,000 gallons per day key gives 0.05, so any icon fraction finer than that reports precision the meters never produced.
  13. Answer: One icon equals 500,000 gallons per day. The line has to name the icon, the quantity, and the time period, since a count with no period attached cannot be checked against the table.

Differentiation

Support

Provide the four division steps for items 2 through 5 already set up, so students carry out one operation rather than choose it. Give a printed strip marked every 12 mm for item 8 so the row can be counted rather than multiplied. Work item 6 with a small group and name the rule for rounding a value that sits below the midpoint.

Extension

Ask students to redesign the chart for a column half as wide, choosing a new icon key so that no row runs past the column. They should state the key, list all four new row counts, show that the widest row fits, and write two sentences on what the coarser key costs a reader who wants to compare the two smallest rows.

ELL supports

Pre-teach icon, key, row, and precision against a printed sample chart with each term labeled on the drawing, and keep that sample posted. Provide a bilingual card that pairs the words count, half, and area with small diagrams. Allow items 11 and 13 to be answered with a labeled sketch plus a short phrase, and offer the frame "The bigger icon is wrong because a reader sees ___."

Extensions

Have students test the chart on a reader who has not seen the data. Ask that reader to name the largest class and to estimate how many times larger it is than the smallest, then compare the estimate against the table. Discuss what the test says about whether the icon count is doing the work the designer intended, and what a single wrong estimate does and does not prove about the design.