Mathematics Year 6: From data to conclusion, report and infographic
Mathematics, Year 6 (Portugal): Read the distribution, draw a conclusion backed by numbers, decide, ask more, and tell it all in a report and in a rigorous infographic.
A story told with numbers
A study does not end at the table. First you read the distribution: where the data gather, the smallest and greatest values, whether any lies far from the rest. Then you write a conclusion backed by numbers, a decision that follows from it and a new question it opens. In the report you tell this story to whoever will read it, in words that suit that audience. The digital infographic tells it in a picture that is understood at a glance.
Why the audience changes the report
The same data say different things depending on the question and on who reads them. The school board cares how many pupils are affected; classmates care what can be done now. A conclusion without numbers is just opinion; a decision without a conclusion is a guess. And the new question lets others carry the study on. Since many people only look at the picture, the infographic must be rigorous, effective and not misleading.
The backpacks of a class
Twenty backpacks were weighed (kg): [2, 4[ has 3; [4, 6[ has 9; [6, 8[ has 5; [8, 10[ has 3. Reading: the modal class is [4, 6[, with 9 (45%). Conclusion with numbers: 8 backpacks weigh 6 kg or more (5 + 3 = 8), that is 8 out of 20 = 40%. Decision: propose to the school board a place to leave materials. New question: does the weight change from day to day? Report: one sentence for the board, with the 40%, the table and the source (the class weighing).
The chart that fattens the difference
Two values: 45 and 60. The ratio is 60 ÷ 45 ≈ 1.33: the second is one third bigger. But if the infographic's axis starts at 40 instead of 0, the bars measure 60 − 40 = 20 and 45 − 40 = 5, and the second looks 4 times the first. Every number is right and the picture still misleads. In a bar chart, bar height must be proportional to the values: so the axis starts at zero, and decorative images must not change the proportions.
What to check before publishing
Before sharing a digital infographic, run through a short checklist: it has a clear title; it says where the data come from; the bars start at zero and the classes are labelled; the legend explains each colour; images bring the topic to life but do not change proportions; and it carries one or two ideas, not twenty. You see infographics in newspapers, websites and posters, and the same list helps you doubt other people's.
Test what you learned
A study found that 5 out of 20 backpacks weigh 8 kg or more. Which of these sentences is a new question raised by that conclusion?
- a) 25% of the backpacks weigh 8 kg or more.
- b) The school must buy lockers now.
- c) What is in the heaviest backpacks, and is it the same on other days of the week?
- d) 5 is less than half of 20.
Correct answer: c) What is in the heaviest backpacks, and is it the same on other days of the week? — Yes: it asks something the data cannot answer yet, and it points to a next study.
A class of 25 recorded daily homework time: [0, 20[ min has 6; [20, 40[ has 11; [40, 60[ has 5; [60, 80[ has 3. A support club opens if at least 30% of the pupils work 40 minutes or more. Does it open?
- a) Yes: 8 out of 25 is 32%, and 32% is at least 30%
- b) No: the modal class is [20, 40[, which is below 40 minutes
- c) No: only 5 out of 25 is 20%, below 30%
- d) No: 32% is less than half of the pupils
Correct answer: a) Yes: 8 out of 25 is 32%, and 32% is at least 30% — Right: the classes from 40 minutes up have 5 + 3 = 8 pupils, and 8 ÷ 25 = 32%.
In an infographic, the bar for 60 looks 4 times as tall as the bar for 45, but 60 ÷ 45 is only about 1.33. What is the most likely explanation?
- a) The bars have different colours
- b) The axis starts at 40, not at 0, so the heights are 20 and 5
- c) Because 60 is greater than 45
- d) Because infographics may not use images
Correct answer: b) The axis starts at 40, not at 0, so the heights are 20 and 5 — Yes: 60 − 40 = 20 and 45 − 40 = 5, and 20 ÷ 5 = 4. The numbers are right, but the picture misleads.
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