Chapter 3 · Statistics
Lesson 3.1 · Bar chart (II)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 71–73).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Draw a bar chart from a data table, including title, axes, and a sensible scale. (Question 1)
- 02Read values from a bar chart and name the greatest / least category. (Question 2, 4)
- 03Interpret what one grid square represents on the vertical scale. (Question 3)
- 04Calculate totals and differences from bar heights (including combining two related categories). (Question 4)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. (Question 1–4) |
| 3.OA.A.3 | Use multiplication and division within 100 to solve word problems (here: scale × number of grids). (Question 3) |
| 3.NBT.A.2 | Fluently add and subtract within 1000 (totals and differences from chart values). (Question 4) |
Eureka Math Correspondence
This lesson aligns mainly with Eureka Math Grade 3 Module 6 (Collecting and Displaying Data).
| Shanghai Maths 3.1 | Focus | Eureka Math (corresponding) |
|---|---|---|
| Question 1 | Draw bars from a table; choose scale | G3 M6 Topic B (scaled bar graphs) |
| Question 2 | Read river lengths; find longest | G3 M6 Topic B (interpret scaled graphs) |
| Question 3 | Value of one grid; height × scale | G3 M6 Topic B (scale factor) |
| Question 4 | Most/least; total; difference of combined categories | G3 M6 Topic C (solve problems using graphs) |
Core Concepts
How to build, scale, and read a bar chart — the teaching focus of pages 71–73.
Parts of a Bar Chart
Use this checklist every time students draw or read a chart.
| Part | What to include | Example from Q1 |
|---|---|---|
| Title | What the chart is about | “Results of shuttlecock kicking” |
| Vertical axis | Quantity + unit + scale numbers | “No. of kicks” with marks 0, 10, 20… |
| Horizontal axis | Categories (names / groups) | XD, XP, XQ, XY, XH |
| Bars | Equal width; height = value | XQ tallest for kicks (49) |
How to Draw (Question 1)
From a table → bar chart:
- Write a clear title.
- Label both axes (include units).
- Choose a scale so the tallest bar fits the grid.
- Draw bars of equal width; height matches each value.
- Label each category under its bar.
Q1 data (kicks): Dingding 40, Pang 24, Qiao 49, Ya 46, Hong 35.
Q1 data (skips): 95, 50, 118, 150, 76 — needs a larger scale (e.g. 25 per grid).
Q1 data (skips): 95, 50, 118, 150, 76 — needs a larger scale (e.g. 25 per grid).
Choosing a Scale (Question 1 & 3)
Rule: Look at the largest value. Pick a friendly step (1, 2, 5, 10, 20, 25, 50, 100…) so the tallest bar fits.
| Data set | Largest value | Sensible scale |
|---|---|---|
| Shuttlecock kicks | $49$ | $1$ grid $= 10$ kicks |
| Rope skips | $150$ | $1$ grid $= 25$ skips |
| River lengths (Q2) | about $6300$ km | $1000$ km marks on the axis |
| Tonnes bar (Q3) | $40$ | $1$ grid $= 5$ tonnes |
Question 3 trap: If the axis marks $0, 10, 20, \ldots$ but there are two grid squares between marks, then $1$ grid $= 5$ tonnes, not $10$. Count grids carefully: $8$ grids $\times 5 = 40$.
Reading a Bar Chart (Question 2)
River chart — lengths of Heilongjiang, Yellow, Yangtze, Zhujiang:
- Find the tallest bar → longest river (Yangtze).
- Read the height against the scale → about $6300$ kilometres.
When a bar sits between grid lines, estimate (e.g. a little above $6000$).
Compare & Calculate (Question 4 — Enhancement)
Class 3(1) PE activities (everyone does one activity only):
| Activity | Pupils |
|---|---|
| Long rope skipping | $10$ |
| Shuttlecock kicking | $12$ |
| Short rope skipping | $6$ |
| Badminton | $2$ |
- Most / least: Shuttlecock kicking (12); Badminton (2).
- Total: $10 + 12 + 6 + 2 = 30$ pupils.
- Difference trap: “Rope skipping” means long + short $= 10 + 6 = 16$. Difference from shuttlecock: $16 - 12 = 4$ (not $10 - 12$).
Combine categories when the question says “rope skipping” and the chart splits long / short.
Key Terms & Definitions (Reference)
| Term | Definition |
|---|---|
| Bar chart / bar graph | A chart that uses bars to show amounts for different categories. |
| Category | A group named on the horizontal axis (e.g. a child’s name or an activity). |
| Scale | What each unit (or grid) on the vertical axis stands for. |
| Axis | A reference line: vertical (quantity) or horizontal (categories). |
| Title | A short name that tells what the chart shows. |
| How many more / less | The difference between two bar heights (subtract). |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Draw bar charts
- Shuttlecock kicks — title e.g. “Results of shuttlecock kicking”; axis “No. of kicks”; scale e.g. 1 grid = 10. Bars: Dingding 40, Pang 24, Qiao 49, Ya 46, Hong 35.
- Rope skipping — title e.g. “Results of rope skipping”; axis “No. of skips”; scale e.g. 1 grid = 20 or 25. Bars: 95, 50, 118, 150, 76.
2. Rivers
Yangtze is the longest; about $6300$ kilometres.
3. Scale
$1$ grid $= 5$ tonnes; the bar represents $40$ tonnes.
4. PE activities
- Most: shuttlecock kicking; least: badminton.
- Total $10+12+6+2=30$ pupils.
- Rope skipping (long + short) $10+6=16$; difference $16-12=4$.