A category is a named group, such as vegetables, eggs, meat, or aquatic products. In a single-series bar chart, each category gets one bar. Later in this lesson, paired bars will show two groups within each category.
category → one bar → one measured height
The picture does not replace the table
The table keeps the exact values. The chart makes “more,” “less,” and “about the same” easy to notice.
table = exact values · chart = visible comparison
Use a bar chart when you want to compare amounts across separate categories. In Lesson 2.6, line graphs will be used to emphasize change across an ordered sequence such as time.
2
Mission 2
Meet every part of a complete bar chart
Not completed
Sample chart: three book categories, measured in books.
Title tells what the whole chart is about.
Category axis names the groups being compared.
Number axis shows the measured values and unit.
Scale is the equal numerical step between tick marks.
Bars have equal width and use the same baseline and scale.
Legend is needed when two or more bar styles represent different groups.
3
Mission 3
Choose one fair, useful scale
Not completed
The largest value in our market data is 14 stalls. A useful number axis can run from 0 to 16 in steps of 2:
0, 2, 4, 6, 8, 10, 12, 14, 16
Try a scale interval. A good scale includes the largest value, uses equal steps, and is easy to read.
Steps of 2 keep the axis compact. Odd values such as 5 and 7 end halfway between adjacent labeled ticks.
Fair-chart habit: for elementary bar charts, begin the numerical axis at 0 so the visible heights are proportional to the values.
4
Mission 4
Build the market-stall bar chart
Not completed
A market manager placed each stall in exactly one of these five categories and counted the stalls:
Category
Vegetables
Soy products
Eggs
Meat
Aquatic products
Stalls
14
7
8
12
5
Set every bar height
Your bars update immediately. The number axis remains fixed from 0 to 16.
Construction routine: label → scale → locate the value → draw a level top → check against the table.
5
Mission 5
Read, compare, and calculate from the chart
Not completed
A chart answers visual comparison questions quickly; calculations confirm the exact amount.
6
Mission 6
Become a bar-chart quality inspector
Not completed
A chart can contain the right numbers and still communicate them poorly. Diagnose each problem.
Chart A: unequal bar widths
Chart B: ticks 0, 2, 5, 7 placed equally
0 2 5 7
Chart C: numbers but no unit
The number axis says 0, 5, 10, 15—but the reader cannot tell whether these are people, books, dollars, or points.
Chart D: axis begins at 10 for values 12 and 14
The visible 14-bar looks twice as tall as the 12-bar even though 14 is not twice 12.
7
Mission 7
Use paired bars to compare two groups
Not completed
Two classes took the same five tests, each marked out of 100 points. The table gives each class’s mean score on each test. A grouped bar chart places the two class bars side by side at each test.
Test
1
2
3
4
5
Class A
70.0
75.0
84.6
85.3
87.5
Class B
62.4
69.5
80.1
85.0
93.6
Class AClass B
The legend tells which bar belongs to which class. Paired bars answer “who scored higher on this test?”
70.0Class A mean score
62.4Class B mean score
7.6difference
8
Mission 8
Highest score is not the same as greatest improvement
Not completed
Class A improvement
87.5 - 70.0 =
Class B improvement
93.6 - 62.4 =
To compare improvement, calculate final value − starting value for each group. Do not simply compare the final bars.
9
Mission 9
Bar-chart laboratory
Not completed
Part A — Build a school-group chart
The six after-school groups have 50 memberships in total. A student who joins two groups counts once in each group. Set the bar heights from the table.
Group
Calligraphy
Model aircraft
Mathematics
Computer
Music
Chinese painting
Students
10
11
9
8
5
7
Use a 0–12 scale. The six bars should total 50 memberships; the number of different students is not given.
Part B — Read a sports-event grouped bar chart
The values count event entries. One student could enter more than one event, so the grand total is not automatically the number of different students.
Event
800 m
Jump rope
High jump
Throwing
60 m
Boys
8
7
5
6
4
Girls
6
9
4
3
6
BoysGirls
Compare paired bars within an event; add the pair to find total entries for that event.
original challenge · Put your skills together
Build a grouped sports-event chart
Build both series from these counts. For this task, use blue for boys and purple for girls, matching the chart in Mission 9. In event order (800 m, jump rope, high jump, throwing, 60 m), the boys’ counts are 8, 7, 5, 6, 4 and the girls’ counts are 6, 9, 4, 3, 6. The numbers count event entries, so the graph does not prove how many different children competed.
Enter the ten bar heights
Series
800 m
Jump rope
High jump
Throwing
60 m
Blue
Purple
Choose the blue seriesChoose the purple series
The preview keeps a fixed 0–10 scale; the scale question asks you to identify that scale. Blank values leave a bar empty. Check each pair against the table, then check the labels and legend.
See a worked explanation
Boys: 8, 7, 5, 6, 4. Girls: 6, 9, 4, 3, 6. Put each pair above the matching event. Use a zero baseline, equal tick steps and a top value at least 9. The legend must identify both series. Pair totals are 14, 16, 9, 9, 10: 58 entries altogether.
11
Mission 11
Exit ticket
Not completed
Complete all five questions without using the lesson checks above.
↻
Keep building
Review the scale and comparison questions, then try again.
▥ ★ ▥
CERTIFICATE OF MASTERY
Bar-Chart Architect
This certifies that
can choose a fair scale, construct accurate bars, read comparisons, and interpret grouped bar charts.
Lesson 2.5 · Grade 5 Math Lab
Teaching notes
This lesson is self-contained for students.
The independent grouped-chart challenge uses this lesson Exercise 11 ().