Telling time and displaying data
Reading a clock to the nearest five minutes, building a line plot from measurements, and reading picture and bar graphs
About four lessons of 35 to 45 minutes
Every mark on a clock counts for five minutes
You already read a clock to the hour and half hour. Now every one of the 12 marks the minute hand can point to counts for 5 minutes, not 1: the mark at the '3' means 15 minutes have passed, the mark at the '9' means 45 minutes have passed.
You will also turn measurements into a line plot, stacking a mark above each length value, and read picture graphs and bar graphs to answer real questions about a set of data.
- Hour hand between 4 and 5, minute hand at the '3' markthe '3' mark means 15 minutes, so the time is 4:15
- 6 pencils measured: 5, 6, 6, 7, 6, 8cma line plot shows how many pencils were each length
- An ice cream survey: vanilla, chocolate, strawberrya bar graph shows how many chose each flavour
- A pictograph where each picture stands for 2 books3 pictures means 3 x 2 = 6 books
What students will be able to do
Students will tell and write time to the nearest five minutes using AM and PM, measure several objects and show the lengths on a line plot, and read and answer questions about picture graphs and bar graphs.
- I can read a clock to the nearest five minutes.
- I can build a line plot from a set of measured lengths and answer questions about it.
- I can read a picture graph or bar graph and answer questions about the categories.
Standards this unit teaches
- 2.MD.C.7Common Core (US)Tell time to five minutes
Tell and write time from analog and digital clocks to the nearest five minutes, using AM and PM.
- 2.MD.D.9Common Core (US)Line plots of measurements
Measure several objects and show the lengths on a line plot marked in whole number units.
- 2.MD.D.10Common Core (US)Picture and bar graphs
Draw picture graphs and bar graphs to show data and answer simple questions about the categories.
- AC9M2M03Australian Curriculum v9 (ACARA)Read time to the quarter hour (Year 2)
Read the time on an analog clock to the hour, half-hour and quarter-hour.
- AC9M2ST01Australian Curriculum v9 (ACARA)Record categorical data (Year 2)
Collect and record data for categories in many ways, including tally marks, lists, drawings, symbols and digital tools.
- AC9M2ST02Australian Curriculum v9 (ACARA)Display and discuss data (Year 2)
Show category data in one-to-one displays, then compare the totals and talk about what the data shows.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Five-minute mark
- one of the 12 marks on a clock face that the minute hand can point to, each worth 5 minutes
- Line plot
- a display where each measured value gets a mark stacked above its position on a number line
- Picture graph (pictograph)
- a graph using repeated pictures to show data, where each picture stands for a set amount
- Bar graph
- a graph using bars of different heights or lengths to show and compare amounts in each category
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. Telling time to the nearest five minutes
AbstractThe minute hand can point to any of the 12 marks around the clock face, and each mark stands for 5 minutes, not 1. The mark at the top (the '12') is 0 minutes, the next mark clockwise (the '1') is 5 minutes, the mark at the '3' is 15 minutes, and the mark at the '9' is 45 minutes.
To read the time, find the hour from the hour hand's position (using the earlier hour if the minute hand has not yet reached 12 again), then count the minute hand's mark by fives: 5, 10, 15, 20, and so on around the face.
The hour hand is between 7 and 8, and the minute hand points at the mark labelled '9'. What time is it?
- The hour hand between 7 and 8 means the hour is still 7, since the new hour has not fully arrived.
- The minute hand at the '9' mark: count by fives around the clock from 12, 5, 10, 15, ..., reaching the ninth mark at 45 minutes.
- Combine the hour and the minutes.
Answer: 7:45.
- The minute hand points at the mark labelled '6'. How many minutes does that mark stand for?
- Why is each mark on the clock worth 5 minutes instead of 1?
2. Building a line plot from measurements
PictorialMeasure several objects to the nearest whole unit, then show the results on a line plot: a number line with a mark, such as an X, stacked above each value for every object measured at that length. Six pencils measured in centimetres give the lengths 5, 6, 6, 7, 6, and 8. On the line plot, the value 6 gets three stacked marks, since three pencils were exactly 6cm, and each other value gets one mark.
A line plot makes the shape of a whole data set visible at a glance: which value came up most often (the tallest stack), and how spread out the measurements were (from the shortest stack to the longest).
Six pencils are measured: 5cm, 6cm, 6cm, 7cm, 6cm, and 8cm. How many pencils were exactly 6cm, and what is the range (longest minus shortest)?
- Count how many pencils measured 6cm: three of the six pencils (6, 6, 6).
- Find the shortest and longest measurements: 5cm and 8cm.
- Find the range: 8 - 5 = 3.
Answer: 3 pencils were exactly 6cm long, and the range is 3cm.
- In the pencil data above, what is the most common length, the mode?
- Check that 1 + 3 + 1 + 1 (the stacked marks at 5, 6, 7 and 8cm) adds up to the total of 6 pencils measured.
3. Reading picture graphs and bar graphs
PictorialA picture graph shows data using repeated pictures, where a key tells you what each picture is worth, such as each picture standing for 2 books. A bar graph shows the same kind of data with bars instead, where a taller or longer bar means a bigger amount. Both let you compare categories at a glance and answer questions about totals and differences.
For a picture graph, always check the key first. If each picture stands for 2, then 3 pictures do not mean 3, they mean 3 x 2 = 6.
In the ice cream survey above, how many more students chose chocolate than strawberry?
- Chocolate: 8 students. Strawberry: 4 students.
- Find the difference: 8 - 4.
- 8 - 4 = 4.
Answer: 4 more students chose chocolate than strawberry.
- In a pictograph where each picture stands for 2 books, and Tuesday shows 3 pictures, how many books were read on Tuesday?
- In the ice cream survey, which flavour was the most popular?
Common misconceptions and how to address them
MisconceptionThe child reads the minute hand's position as its ones value, such as thinking the mark labelled '3' means 3 minutes rather than 15 minutes.
Why it happens: Grade 1 clock reading was to the hour and half hour, where the key marks (12 and 6) were memorised individually rather than counted by fives, so the by-fives counting habit for every mark is new.
How to address it: Count around the clock face by fives out loud, touching each mark in turn: 5, 10, 15, 20..., so the mark-to-minutes link is built through counting, not memorising each mark separately.
MisconceptionOn a line plot, the child miscounts how many marks are stacked above a value, or reads a stack of marks as belonging to a neighbouring value instead of the one directly below it.
Why it happens: When several marks are stacked closely together, it is easy to lose count or misjudge which number line position a stack sits above, especially with a compact hand-drawn plot.
How to address it: Count each stack out loud while pointing to it, then check the count against the exact position on the number line directly beneath the stack, not a neighbouring one.
MisconceptionReading a picture graph, the child counts the number of pictures shown and reports that count directly as the answer, ignoring the key's value per picture.
Why it happens: Counting pictures is the most visually obvious action, and the key is a small separate detail that is easy to overlook under time pressure.
How to address it: Read the key out loud before answering any question: 'each picture is worth ___.' Multiply the picture count by the key's value every single time, as a fixed first step.
MisconceptionIn a bar or picture graph, the child answers a 'how many more' question by reporting one category's total alone, rather than subtracting the two categories being compared.
Why it happens: Reading a single bar or a single set of pictures is a smaller, more familiar step than comparing two categories with subtraction.
How to address it: For 'how many more' questions, write both category totals side by side first, then subtract the smaller from the larger, rather than reading one category alone.
Guided practice (with answers)
1. The minute hand points at the mark labelled '9'. How many minutes does that mark stand for?
Answer: 45 minutes.
2. The hour hand is between 4 and 5, and the minute hand points at the mark labelled '3'. What time is it?
Answer: 4:15.
3. 5 books are measured to the nearest cm: 10, 12, 12, 10, 14. How many books measured exactly 10cm?
Answer: 2 books.
4. In the same book data, what is the range (longest minus shortest)?
Answer: 4cm, because 14 - 10 = 4.
5. In a pictograph where each picture stands for 2 stickers, Wednesday shows 4 pictures. How many stickers were earned on Wednesday?
Answer: 8 stickers, because 4 x 2 = 8.
6. A bar graph shows 7 students chose red and 5 chose blue. How many more chose red than blue?
Answer: 2, because 7 - 5 = 2.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Telling time practises five-minute clock reading directly, and the bar graph, pictograph and tally chart worksheets cover this unit's data-display skills.
Differentiation
- Count around the clock face by fives with a finger before reading any specific time.
- Start line plots with all-different measured values (no stacking) before introducing repeated values that stack.
- Use a pictograph with a key of 1 first, before introducing a key of 2 or more.
- Keep bar and picture graphs to two categories before extending to three or more.
- Read a digital clock time and convert it to what the matching analog clock would look like, or the reverse.
- Build a line plot from a real set of measurements taken in the classroom.
- Create a pictograph or bar graph from a small class survey, choosing a sensible key value.
- Answer a two-step data question, such as the combined total of two categories compared to a third.
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling five-minute time, a line plot, and a picture or bar graph.
1. The hour hand is between 8 and 9, and the minute hand points at the mark labelled '6'. What time is it?
Answer: 8:30.
2. 5 crayons are measured: 8, 9, 9, 8, 10cm. How many crayons measured exactly 9cm?
Answer: 2 crayons.
3. A pictograph key shows each picture is worth 2. A row shows 5 pictures. How many does that row represent?
Answer: 10, because 5 x 2 = 10.
Teacher notes and timings
- Rough timing across four lessons: Lesson 1 five-minute time (section 1), Lesson 2 line plots (section 2), Lessons 3 to 4 picture and bar graphs (section 3) plus the exit ticket.
- These three standards cluster naturally under the Measurement and Data domain's later, display-focused half: reading a finer-grained clock, and turning a set of measurements or a survey into a display that can actually be questioned and interpreted.
- The clock face and the true stacked-mark line plot have no dedicated diagram in ChalkBee's figure engine yet, so both are taught through worked description and the printable worksheets rather than an on-page diagram; the bar/picture graph section reuses the existing part-whole bar model figure.
- Language to keep saying: count the marks by fives, check the key before answering, and subtract to compare two categories. These phrases pre-empt the misconceptions above.
- Curriculum note: US Grade 2 splits five-minute time (2.MD.C.7), line plots (2.MD.D.9) and picture/bar graphs (2.MD.D.10) into three standards. ACARA Year 2 covers clock reading to the quarter hour under Measurement (AC9M2M03) and splits data recording (AC9M2ST01) from data display and discussion (AC9M2ST02) under Statistics, a close conceptual match across three AU descriptors.
- Present mode and print both work: use the Print button for a student worksheet, or project the page and build a real line plot or bar graph together from a quick class survey.