Making and Reading Graphs: a week of ready-to-teach maths
Five days of lessons for Year 3 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus graph and table cards, picture symbols, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the graph and table cards and the picture symbols once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. A column graph shows each count as the height of a column; the columns stand on one baseline against an even scale, so a taller column always means more. A picture graph shows each count as a row of symbols; when the counts are big, a key says how many each symbol stands for (one circle = 2 children). Reading a graph means turning heights and rows back into facts about the people counted.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Table to columns | Draw a column graph from a frequency table, on a common baseline with an even scale, by hand and on screen | Table to columns |
| 2 | Read the column graph | Read the tallest and shortest columns and their values against the scale, and say what they mean | Read the column graph |
| 3 | Picture graphs | Draw a picture graph with one symbol for each item, and compare it with a column graph of the same data | The picture graph |
| 4 | One symbol, many | Read and draw picture graphs where one symbol stands for 2 or 5, using the key | One symbol, many |
| 5 | Compare and choose | Answer how many more and how many altogether, and choose a display that suits a purpose | Compare on the graph; Which graph fits? |
How the week builds
Days 1 and 2 make and read column graphs. Day 3 shows the same kind of data as a picture graph and compares the two displays, and Day 4 adds a key so one symbol can stand for many. Day 5 uses graphs to compare, total and choose a display. It leans on Collecting and Recording Data (AC9M3ST01) and Multiply and Divide (AC9M3N04).
Materials for the week (one trip)
- From the classroom: scissors, glue sticks, rulers, coloured pencils, this pack printed.
- A computer or tablet with a spreadsheet, for one demonstration on Day 1 (not essential).
- Squared paper, for any child who wants to draw a second graph.
- Cut out once, use all week: the graph and table cards and the picture symbols.
Words for the word wall
graph, column graph, picture graph, column, baseline, scale, label, title, symbol, key, tallest, shortest, most, least, how many more, altogether, compare, display
Dear families
This week in maths, Year 3 is making column graphs and picture graphs from data, reading them, and saying what they tell us.
Try this at home
- Look for graphs in the newspaper, on the news or on food packets, and talk about what they show.
- Count the fruit in the fruit bowl by kind and draw a picture graph together.
- Ask: which column is tallest? What does that tell us?
- Make up a key: if one drawing stands for 2 apples, how many drawings show 8 apples?
Our graphs this week
Fill one row a day: a graph you saw or made, and one thing it told you.
| Day | The graph | What it told us |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik Making and Reading Graphs teaching pack · seegongsik.com/au/y3/statistics/AC9M3ST02/pack
Table to columns
A column graph turns a frequency table into heights. Each category gets one column, and its height is the count, read against an even scale up the side. All the columns stand on one baseline and are the same width, so a taller column always means more. A title and labels say what was counted.
We are learning to
- draw a column graph from a frequency table,
- use one baseline, an even scale, labels and a title,
- make the same graph on screen with a spreadsheet.
Success criteria
- I can draw a column graph from a table.
- I can check each column against the scale.
You need
Rulers and coloured pencils. The worksheet. A computer or tablet with a spreadsheet, if you have one.
Lesson flow (about 50 minutes)
| 10 min | Human graph Children line up by their favourite fruit, all starting from one line on the floor; the lines make a graph. Ask: “Which line is longest? Why must everyone start from the same line?” |
| 25 min | Draw the columns Grow the columns on the board (see the box). Children draw the fruit graph on the worksheet grid, colour it and give it a title. Ask: “Your banana column reaches 5 on the scale. How can you check it?” |
| 15 min | On screen Type the fruit table into a spreadsheet and insert a column chart. Hold a hand-drawn graph beside the screen. Ask: “What did the computer do that we did by hand? What is the same?” |
Two half-sessions instead? Split after the human graph and the board; start Session B with the worksheet.
Watch for these ideas
- Columns of different widths, or not on the baseline. Same width, same baseline.
- An uneven scale, such as 1, 2, 5, 10. Each step up the scale is the same.
- Leaving off the labels and the title. A graph must say what was counted.
Answers
- Columns: apple to 7, banana to 5, orange to 3, grapes to 6, all the same width, on the baseline.
- Tallest: apple, so it is the class’s favourite fruit. A title such as “Our favourite fruit”.
Table to columns
“What is your favourite fruit?” Draw a column for each fruit. Use a ruler.
| Fruit | Frequency |
|---|---|
| apple | 7 |
| banana | 5 |
| orange | 3 |
| grapes | 6 |
Title: ______________________________________
What does it show?
Which column is the tallest? ______________ What does that tell you?
Read the column graph
Reading a column graph is asking it questions. The tallest column is the most common answer and the shortest the least; the value of a column is read by running a finger straight across from its top to the scale. Then the graph is turned back into words about the people counted: most children chose the swings.
We are learning to
- find the tallest and shortest columns,
- read the value of a column against the scale,
- say what a graph tells us about the people counted.
Success criteria
- I can read the value of any column.
- I can say what a graph tells us, in a sentence.
You need
Rulers (to read across to the scale). The graph and table cards (cut-out sheet 1). The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Graph talk Show a children’s Day 1 fruit graph. Children say three things the graph tells them. Ask: “Is the tallest column always the most popular? How do you know?” |
| 25 min | Read it Read the graph on the board (see the box). Children answer the questions about the playground graph on the worksheet, laying a ruler across from each column to the scale. Ask: “How does a ruler help you read the monkey bars column?” |
| 15 min | Match it Pairs match each graph card with its table card. The graphs use the same three numbers, so every column must be read. Ask: “Two graphs both have a column at 6. How did you tell them apart?” |
Two half-sessions instead? Split after the worksheet questions; start Session B with the card match.
Watch for these ideas
- Reading the value from the wrong column. Run a ruler straight across from the top of the column.
- Thinking the widest or brightest column is the biggest. Only the height counts.
- Reading the graph but saying nothing about the context. Say what it means for the children.
Answers
- 1 the swings, 2 the sandpit, 3 5, 4 7, 5 5, 6 23.
- What it tells: most children like the swings; the sandpit is the least popular.
- Card pairs: the graph and the table with the same red, blue and green numbers.
Read the column graph
Our favourite playground equipment. Read each column across to the scale.
- Which has the tallest column? ______________
- Which has the shortest column? ______________
- How many children chose the slide? ______________
- How many chose the monkey bars? ______________
- How many more chose the swings than the sandpit? ______________
- How many children were asked altogether? ______________
What does the graph tell the school?
Picture graphs
A picture graph shows each count as a row of symbols, one symbol for each item: six circles in the dog row means six dogs. The rows start at one line and the symbols are the same size and evenly spaced, so the longest row is the biggest count. The same data can be a column graph too: one display uses the length of a row, the other the height of a column.
We are learning to
- draw a picture graph with one symbol for each item,
- line up and space the symbols, so the rows compare fairly,
- compare a picture graph and a column graph of the same data.
Success criteria
- I can draw a picture graph.
- I can say how it is like and unlike a column graph.
You need
The picture symbols (cut-out sheet 2) and glue sticks, or coloured pencils. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Symbols in rows Show the symbols on the board (see the box), then put the Day 1 column graph beside it. Ask: “If one row had its circles spread further apart, would it look bigger? Would it be bigger?” |
| 25 min | Draw the pets Children draw, or glue symbols for, the pet picture graph on the worksheet, one circle in each space, then compare it with the column graph of the same pets. Ask: “Which display tells you fastest which pet is the most common?” |
| 15 min | Graph our group Groups ask one quick question (favourite colour, say) and show the answers as a picture graph with the symbols. Ask: “Why must every symbol be the same size?” |
Two half-sessions instead? Split after the pet graph; start Session B with the comparison.
Watch for these ideas
- Spacing the symbols unevenly. A spread-out row looks longer but holds no more.
- Starting rows at different places. Every row starts at the line.
- Using symbols of different sizes. Each symbol is the same size and stands for one.
Answers
- Picture graph: dog 6 circles, cat 4 circles, fish 3 circles, rabbit 2 circles, each row from the line.
- Compare: both show dog as the most common pet; the picture graph can be counted one by one, and the column graph is read against the scale. Any sensible reason is right.
Picture graphs
Draw the picture graph
Our pets: dog 6, cat 4, fish 3, rabbit 2. Draw one circle in a space for each pet. Start each row at the line.
The same pets as a column graph
Compare the two
Which graph shows the most common pet more quickly? Why?
Write one thing that is the same about the two graphs.
One symbol, many
When counts are big, one symbol can stand for several, and a key says how many: one circle = 2 children. Four circles then mean 4 × 2 = 8 children, so reading a picture graph starts with the key. Drawing one works the other way: 10 books with a key of 2 is 10 ÷ 2 = 5 circles.
We are learning to
- read the key of a picture graph first,
- find a count from the symbols and the key,
- draw a picture graph with a key of 2 or 5.
Success criteria
- I can read a picture graph with a key.
- I can draw a picture graph with a key.
You need
The picture symbols and key strips (cut-out sheet 2). The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Count by the key Hold up three symbols with the key “one circle = 2 children”, then the same three with “one circle = 5 children”. Children skip count each time. Ask: “The symbols stayed the same. Why did the number change?” |
| 25 min | Read and draw Work out the car row on the board (see the box). Children read the fruit graph, then draw the book graph with a key of 2 on the worksheet. Ask: “Yellow group read 4 books. How many circles is that with a key of 2?” |
| 15 min | Key of 5 Children answer the key-of-5 questions; pairs build a small picture graph with the “one circle = 5 children” key strip. Ask: “Why might a graph of the whole school use a key of 5 or 10?” |
Two half-sessions instead? Split after reading the fruit graph; start Session B with drawing.
Watch for these ideas
- Counting the symbols and forgetting the key. Read the key first, then multiply.
- Drawing one symbol for each item when the key is 2. Halve the count to find the symbols.
- Mixing up the keys of two graphs. Check each graph’s own key before reading it.
Answers
- Fruit: 1 12, 2 8, 3 6, 4 36.
- Books, key of 2: Red group 5 circles, Blue group 3 circles, Green group 4 circles, Yellow group 2 circles.
- Key of 5: 20 children is 4 circles, 15 children is 3 circles, 35 children is 7 circles.
One symbol, many
Read the key first
Our favourite fruit.
- How many children chose apple? ______
- How many chose banana? ______
- How many more chose apple than orange? ______
- How many children were asked altogether? ______
Draw with a key
Books read this week: Red group 10, Blue group 6, Green group 8, Yellow group 4. Use the key: one circle = 2 books.
A key of 5
One circle = 5 children. How many circles show 20 children? ______ 15 children? ______ 35 children? ______
Compare and choose
A graph answers comparison questions. How many more is the difference between two columns: 9 wraps and 8 pies is 1 more. How many altogether is the total of every column. Choosing a display is a judgement: a picture graph is friendly for young readers, a column graph compares at a glance, and a table gives the exact numbers.
We are learning to
- answer how many more and how many altogether from a graph,
- say what a graph means for the people counted,
- choose a display that suits a purpose, and say why.
Success criteria
- I can answer how many more from a graph.
- I can choose a display and give a reason.
You need
The worksheet. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | How many more? Compare on the board (see the box). Ask: “To find how many more, do we add or take away? Why?” |
| 25 min | Compare and choose Choose displays on the board. Children answer the lunch questions and choose a display for each purpose on the worksheet, with a reason. Ask: “Could a column graph work for the Prep class too? What would help them read it?” |
| 15 min | Class quiz Run the self-check quiz as a team game: teams hold up one, two or three fingers for their choice. Ask: “Which picture from this week would prove that answer?” |
Two half-sessions instead? Split after the lunch questions; start Session B with choosing and the quiz.
Watch for these ideas
- Adding to find how many more. How many more is the difference: take the smaller from the bigger.
- Leaving a column out of the total. Add every column once.
- Thinking only one display can be right. Each one suits some purposes better than others.
Answers
- Lunch: 1 1, 2 5, 3 24. The canteen should make the most wraps.
- Displays (accept any sensible choice with a reason): 1 a picture graph: the symbols are easy for young children to read; 2 a frequency table, or a column graph with numbers: it shows the exact counts; 3 a column graph: the heights compare at a glance.
Compare and choose
Lunch orders today.
- How many more chose a wrap than a pie? ______
- How many more chose a pie than a salad? ______
- How many children ordered lunch altogether? ______
- Which lunch should the canteen make the most of? Why? ______________________________
Choose a display
Choose a picture graph, a column graph or a frequency table. Say why.
| The purpose | My display, and why |
|---|---|
| to show the Prep class which lunch is the favourite | |
| to find exactly how many children chose each lunch | |
| to compare the four lunches at a glance in the newsletter |
Graph and table cards
Cut out the twelve cards: six column graphs of the weather over a few weeks and six tables. On Day 2, pairs match each graph with its table. Every card uses 2, 4 and 6, so each column must be read against the scale.
| sunny | 4 |
| rainy | 2 |
| windy | 6 |
| sunny | 2 |
| rainy | 4 |
| windy | 6 |
| sunny | 4 |
| rainy | 6 |
| windy | 2 |
| sunny | 2 |
| rainy | 6 |
| windy | 4 |
| sunny | 6 |
| rainy | 2 |
| windy | 4 |
| sunny | 6 |
| rainy | 4 |
| windy | 2 |
Teacher note, the pairs: sunny 4, rainy 6, windy 2; sunny 6, rainy 2, windy 4; sunny 2, rainy 6, windy 4; sunny 4, rainy 2, windy 6; sunny 6, rainy 4, windy 2; sunny 2, rainy 4, windy 6.
Picture symbols and keys
Cut out the symbols along the dashed lines, and the three key strips. On Days 3 and 4, children glue the symbols in rows to build picture graphs, with a key strip beside each graph.
What we know: Making and Reading Graphs
Work on your own. Our favourite season:
- Which season has the tallest column? ______________
- How many children chose spring? ______
- How many more chose summer than winter? ______
- How many children were asked altogether? ______
- In this picture graph of our pets, how many children have a cat? ______
- With the key one circle = 5 children, how many circles show 15 children? ______
- Why must all the columns of a column graph start from the same baseline? ______________________________
- Write one way a picture graph and a column graph of the same data are alike. ______________________________
Answers and marking guide
Answers
- Summer.
- 6.
- 6.
- 22.
- 6 (3 circles, each 2 children).
- 3.
- So the heights can be compared fairly; a taller column then always means more.
- Either: both show the same counts, and the longest row and the tallest column are the same category.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Reading graphs (Q1, Q2, Q5) | finds the tallest column, but not values | reads values against a scale and through a key | explains why a graph needs an even scale and a key |
| Interpreting (Q3, Q4) | reads values but does not compare them | answers how many more and how many altogether | says what the data means for the people counted |
| Creating and comparing (Q6, Q7, Q8) | draws rows or columns that do not line up | draws graphs on one baseline, with a key when needed | compares two displays and chooses one for a purpose |
Eight questions, three ideas. A child at standard reads a value off a scale or through a key, and turns a comparison into a sentence about the people counted.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Draws columns | Reads a graph | Picture graphs | Keys | Compares |
|---|---|---|---|---|---|
The five columns are the five days: drawing columns, reading a graph, picture graphs, keys, and comparing and choosing.