At a glance. One lesson of about 60 minutes. Students draw and read bar charts against a scale, then draw grouped measurements as a histogram with touching bars.
Calculator: no calculator. Nothing here needs one. Bar heights come from friendly scales, such as 0.5 cm per student or 4 students per centimetre.
What students will learn
Know
- The height of a bar is its frequency.
- A bar chart has equal-width bars with gaps; a histogram of classes has touching bars.
- A chart needs a title, labelled axes and an even scale starting at 0.
Understand
- The scale is chosen by the maker, and it changes how big a difference looks.
- A gap between bars says there are no values there, which is false for measurements.
- A histogram is for grouped measurements; in this unit the classes have equal width, so heights can be compared.
Do
- Choose a scale and work out bar heights from frequencies.
- Read a frequency from a bar and a scale.
- Say whether bars should touch or not.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: reading bars and choosing a scale (questions 1 to 7).
- Criterion B. Investigating patterns: the scale figure. Ask students to predict the top of the axis for each gridline step before sliding, and to write the rule: the first multiple of the step that is at least the largest frequency.
- Criterion C. Communicating: explaining in a full sentence why measurements are drawn with touching bars (the check and question 9).
- Criterion D. Applying mathematics in real-life contexts: favourite sports, journeys to school and run times (the hook and worked examples).
The one thing to do with the figure
Ask for a prediction before the first slide. “Next to the Football bar, how tall will Other look?” Take guesses as fractions of the height, then draw.
Keep the same bar selected while changing the gridline step and ask what stays the same (the frequency) and what changes (how tall it looks against the top). In the second figure switch to gaps and ask what a reader would think.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook and the first figure on bars and scales. |
| 10 min | Key idea; the second figure on classes and touching bars. |
| 10 min | Worked example on travel to school; students finish the faded run-times example in pairs. |
| 5 min | Question 1, the check. If many choose A, go back to the second figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 20; 45%; 3. |
|---|---|
| Worked example | 6 cm, 9 cm, 3.5 cm and 1.5 cm. |
| Faded example | Top of the scale 8; 9 runners took 20 minutes or more. |
| 1. Touching or separate bars | B. A treats classes as separate categories; C varies the width; D is not a bar chart. |
| 2. Read between gridlines | 15. (10 + 20) ÷ 2. |
| 3. Compare two bars | 8. 14 − 6. |
| 4. Features of a good chart | B. A, C and D each leave out something a reader needs. |
| 5. Use the scale | 14. 3.5 × 4. |
| 6. Missing bar in a histogram | 8. 40 − 32. |
| 7. Choose the top of the scale | 40. The first multiple of 5 that is at least 37. |
| 8. Reading a histogram | B. A reads a class as a single value; C reads the frequency as an age; D confuses height with position. |
| 9. Choose touching or separate bars | C. A and D are categories; B is a count. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A, C or D in question 1 | Treated classes as separate categories, varied widths, or named another chart. | Ask whether any value can fall between 5 and 10 kg. |
| 10 or 20 in question 2 | Read the nearest gridline instead of the bar. | Ask where the top of the bar is, in relation to both lines. |
| 20 or 14 in question 3 | Added the two bars, or gave one bar. | Underline 'how much taller' and ask for a subtraction. |
| 5 in question 3 | Compared with the wrong bar. | Ask students to circle the two bars named. |
| A, C or D in question 4 | Valued appearance over information. | Ask what a stranger needs to know to read the chart. |
| 3.5, 7.5 or 0.875 in question 5 | Gave the height, added, or divided. | Ask if there are more students or more centimetres, and which operation that means. |
| 32 or 40 in question 6 | Gave the sum so far, or the total. | Draw the four bars with the last one blank and the total on the right. |
| 37 or 35 or 45 in question 7 | Used the frequency, the gridline below, or one too many. | List the gridlines in fives and circle the first one at or above 37. |
| A, C or D in question 8 | Read a class as an age, or a frequency as an age. | Ask what the vertical axis counts. |
| A, B or D in question 9 | Confused categories or counts with measurements. | Ask: could a value fall between two neighbouring bars? |
Questions worth asking
- Why must a bar chart's scale start at 0? So that a bar twice as tall means twice the frequency. Listen for “the height matches the number”.
- How does changing the gridline step change what a reader sees? Smaller steps make differences look bigger. Listen for “same numbers, different look”.
- Why do bars for categories have gaps, but bars for measurements touch? A gap would say there are no values between two classes, which is false for measurements. Listen for “the classes run on from each other”.
- When might a histogram have a bar of height 0? When no values fall in the class: a gap in the data is real, but the bars still touch.
Differentiation
A way in for anyone stuck
- Give squared paper with the vertical axis already drawn and the step written in.
- Start with scales of 5 and 10 only, where heights come in whole numbers of squares.
- Provide a template with category labels and a ruler for the heights.
Stretch
- Question 7, then: a bar chart has largest frequency 63 and gridlines every 10. What is the top? (70.)
- Redraw lesson 3's plant data with classes starting at 5 instead of 4 and say what changes about the shape.
- Boys and girls give their favourite sport. Draw two bars side by side for each sport (a dual bar chart). Which sport has the biggest difference between boys and girls, and how do you read it?
Students learning in English as an additional language
A “bar” here is a rectangle. “Scale” means the numbers along the side, and “gridlines” are the lines that cross the chart. Say “height” with a hand held up.
| Word | Plain meaning | Example |
|---|---|---|
| bar chart | bars of equal width whose heights show frequencies, for categories or counts | favourite sport |
| histogram | touching bars for grouped measurements on a number line | heights in classes 2 cm wide |
| scale | the numbers and steps along an axis | 0, 5, 10, 15 |
| axis | a line with a scale and a label | the vertical axis shows frequency |
| gridline | a line across a chart that helps read a value | a line at 10 |
| title | the words that say what the chart shows | Favourite sport of 40 students |
Sentence starters for explaining aloud or in writing:
- The bar for … reaches …, so its frequency is …
- The bars touch because …
- The scale goes up to … because the largest frequency is …
Two things not to say
“Make the bars look nice.” Neatness is not the aim; reading the right value is.
“The tallest bar is the best.” Tall means most frequent, not best.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- ReadA bar ends exactly on the 30 gridline. Gridlines are 0, 10, 20, 30 and 40. What is the frequency?
30. - Scale1 cm stands for 5 students. A bar is 6 cm tall. How many students?
30. 6 × 5.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA market stall sells apples 24 kg, pears 18 kg, plums 12 kg and figs 6 kg in a day. A bar chart axis is 12 cm tall for 24 kg. How tall is the pears bar?
9 cm. 12 cm per 24 kg is 0.5 cm per kg, and 18 × 0.5 = 9. - Earlier work (Unit 2, lesson 3)A bar is 40% of the height of the tallest, which is 15 cm. How tall is it?
6 cm. 40% of 15.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningA histogram of 60 values has classes 0 to under 10, 10 to under 20, 20 to under 30 and 30 to under 40. The first two bars are 15 and 21 and the last is 9. How tall is the third?
15. 60 − 15 − 21 − 9. - Spot the faultA histogram has bars of widths 5, 5 and 10 with heights 4, 6 and 6. Why does this chart mislead the eye?
The 10-wide bar covers twice the area for the same frequency, so the eye reads it as more. Unequal widths need a different vertical scale, met in later years.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Use squared paper: 1 square per student for the bars, and a ruler for the histogram.