Line graphs, tables and timetables
Comparison, sum and difference problems from line graphs, then completing and interpreting tables
About four lessons of 45 to 60 minutes
A graph turns a table into a visible story
A table can list the temperature at noon each day, but a line graph makes the rise, fall and overall change visible at a glance. The plotted points still carry the exact values, so the graph can answer calculation questions as well as trend questions.
Timetables organise two variables, such as service and time, into rows and columns. Reading the correct row and column intersection is the key before any elapsed-time calculation begins.
- Plant height recorded weeklycompare two points, add values or find the change
- Temperature through the daythe line shows both exact readings and the overall trend
- A train timetabletrace one service down its column before calculating a journey time
What students will be able to do
Pupils will read exact values and scales from line graphs, solve comparison, sum and difference questions, complete missing table entries, and interpret timetables including simple duration and service-choice problems.
- I can read a line-graph scale before reading a point.
- I can compare two values and find their difference.
- I can add values from two plotted points when the question asks for a sum.
- I can use row and column headings to locate a table entry.
- I can trace one timetable service and calculate a journey duration.
Standards this unit teaches
- uk-ks2-y5-ma-stats-01UK National Curriculum (England)Solve problems using line graphs
Solve comparison, sum and difference problems using information presented in a line graph.
- uk-ks2-y5-ma-stats-02UK National Curriculum (England)Complete and interpret tables
Complete, read and interpret information in tables, including timetables.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Axis
- a numbered or labelled line used to locate values on a graph
- Scale
- the value represented by each equal step on an axis
- Trend
- the overall pattern of increase, decrease or stability
- Difference
- how much greater or smaller one value is than another
- Table
- information organised into labelled rows and columns
- Timetable
- a table that organises events or journeys by time
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Read the scale and exact plotted values
PictorialRead the title, axis labels, unit and scale before looking at a point. If labelled marks rise 0, 10, 20 with one unlabelled gridline between, each small step represents 5, not 10.
- What unit is shown on the vertical axis?
- What does one small grid step represent?
- Which horizontal label matches the plotted point?
2. Solve comparison, sum and difference problems
AbstractRead each required value from the graph and write it with its label before calculating. Comparison questions ask which is greater, difference questions require subtraction, and sum questions require addition.
A line graph shows 18 visitors on Monday and 31 on Friday. How many more visited on Friday, and how many visited on the two days altogether?
- Difference: 31 - 18 = 13.
- Sum: 31 + 18 = 49.
- Attach the unit visitors to both answers.
Answer: Friday had 13 more visitors; the two days totalled 49 visitors.
- Which operation does 'how many more' require?
- Why should the values be copied from the graph before calculating?
3. Read and complete tables
PictorialTrace from the row heading and column heading until they meet. When a value is missing, use the relationship shown by the rest of the row or the stated total, then check the completed row.
A table gives 12 fiction books and 9 non-fiction books, with a blank total. Complete it.
- The total combines both categories.
- Calculate 12 + 9 = 21.
Answer: The total is 21 books.
- Which two headings identify this cell?
- What calculation or pattern supports the missing value?
4. Trace services and calculate durations
AbstractIn a timetable, stay within one service column unless the question explicitly asks you to compare services. Read departure and arrival times from the same column, then count forward to calculate duration.
A bus leaves at 09:35 and arrives at 10:20. How long is the journey?
- 09:35 to 10:00 is 25 minutes.
- 10:00 to 10:20 is 20 minutes.
- 25 + 20 = 45 minutes.
Answer: The journey takes 45 minutes.
- Are the departure and arrival from the same service?
- Where could you bridge through the next whole hour?
Common misconceptions and how to address them
MisconceptionEvery gridline has the value of the labelled interval.
Why it happens: Pupils read the difference between labels but do not divide it by the number of equal small steps.
How to address it: Count the spaces between two labelled values and divide the total interval equally before reading any data point.
MisconceptionA steeper line always means a larger value.
Why it happens: Slope and height are confused.
How to address it: Read the endpoint value from the vertical axis. A steep fall can end at a low value even though the line segment is visually dramatic.
MisconceptionA timetable journey can combine departure from one service column and arrival from another.
Why it happens: The pupil scans for convenient times without preserving the service identity.
How to address it: Highlight or cover all columns except the chosen service before reading its departure and arrival.
Guided practice (with answers)
1. A graph shows 24 mm in April and 39 mm in May. What is the difference?
Answer: 15 mm.
2. The same graph shows 24 mm and 39 mm. What is their sum?
Answer: 63 mm.
3. A table row has 17, 26 and a total cell. Complete the total.
Answer: 43.
4. A train leaves at 14:48 and arrives at 15:25. How long is the journey?
Answer: 37 minutes: 12 minutes to 15:00, then 25 minutes.
Independent practice worksheets
Use the new Year 5 age-equivalent line graphs for exact graph reading, then combine elapsed-time and 24-hour practice for timetables.
Differentiation
- Annotate the value of every small vertical-axis step before reading points.
- Use a ruler to track from a plotted point to each axis.
- Highlight one timetable service column at a time.
- Bridge elapsed-time calculations through the next whole hour.
- Write one comparison, one sum and one difference question for the same graph.
- Infer a missing graph point from a stated difference and plot it.
- Compare two timetable services and justify the latest possible departure for a required arrival time.
Assessment: exit ticket
Sample scale reading, graph calculation and timetable interpretation.
1. A graph shows 27 cm in week 3 and 35 cm in week 5. How much did the value increase?
Answer: 8 cm.
2. The same values are 27 cm and 35 cm. What is their sum?
Answer: 62 cm.
3. A service departs at 11:42 and arrives at 12:18. Find the duration.
Answer: 36 minutes.
Teacher notes and timings
- Line graphs are appropriate when the horizontal variable has an ordered progression, commonly time. Do not join unrelated category values merely to create a line.
- Require pupils to state the unit in every graph answer.
- Teach table structure before timetable arithmetic. Many errors come from selecting the wrong cell rather than calculating the duration incorrectly.