Comparing Graphs: a week of ready-to-teach maths
Five days of lessons for Year 2 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out cards, 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 two card sheets once; the tokens, grids and question cards are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and when.
- 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. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives model answers, so you can walk in and teach it.
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 lesson can also split into a short warm-up and a main session if your timetable runs small blocks.
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 | Picture graphs | Turn a survey into a picture graph: one picture stands for one thing | The picture graph |
| 2 | Bar graphs | Build a column graph and read a height against the scale | The column graph |
| 3 | The same data, two ways | Show one survey as both graphs and check they agree | Side by side |
| 4 | Same and different | Name the common and distinctive features of the two graphs | Side by side |
| 5 | Answer questions from a graph | Find most, least and how many more; choose the right graph | The right graph for the job |
How the week builds
Day 1 turns a survey into a picture graph; Day 2 builds the same counts as a bar graph; Day 3 puts both graphs of one survey side by side; Day 4 names what is the same and what is different; and Day 5 reads a graph to answer questions. It builds on the Year 2 data unit, where data was gathered and first shown in lists and tables, and it opens the way to graphs where one symbol can stand for more than one thing.
Materials for the week (one trip)
- From the classroom: scissors, pencils, coloured pencils, this pack printed.
- Optional counters, stickers or dot stamps for placing on the picture graph; none are essential.
- Cut out once, use all week: the picture tokens and data cards, and the blank graph grids and question cards in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 2 makes and compares graphs. We turn a survey into a picture graph and a bar graph, then compare them: what is the same, what is different, and what each graph tells us.
Try this at home
- Do a tiny survey: how many red, white and other cars pass in five minutes, or the family’s favourite dinners. Tally it as you go.
- Draw it as a picture graph: one square for each one, all rows starting from the same line.
- Ask which has the most, which has the least, and how many more the biggest has than the smallest.
- Find a graph on a cereal box, in a catalogue or in the news, and ask what it tells you.
My graphs this week
Fill one row a day. Tick when you have drawn it and read it.
| Day | My survey | The most | The least | How many more |
|---|---|---|---|---|
| Monday | ||||
| Tuesday | ||||
| Wednesday | ||||
| Thursday | ||||
| Friday |
Printed from the free seegongsik Comparing Graphs teaching pack · seegongsik.com/au/y2/statistics/AC9M2ST02/pack
Picture graphs: one picture, one thing
A picture graph turns a count into something you can see: one picture stands for one thing. Today children run a small survey, then turn the totals into a picture graph and read the most and the least straight off it.
We are learning to
- turn a survey count into a picture graph,
- draw one picture for one thing, all rows starting from the same line,
- read the most and the least from a picture graph.
Success criteria
- I can make a picture graph with one picture for each thing.
- I can say which has the most and which has the least.
You need
The picture tokens and data cards (cut-out sheet 1), one set per pair, or just pencils. The worksheet, one per child. A board for the class graph.
Lesson flow (about 50 minutes)
| 10 min | Count it first Run a quick class survey, such as favourite fruit for fruit break. Tally the answers on the board, then write the totals in a little table. Ask: “Before we can draw a graph, what do we need to know? How many chose each one?” |
| 30 min | One picture each Pairs turn the fruit totals on the worksheet into a picture graph, placing or drawing one token per child in each row, all starting from the same line. Ask: “Each picture stands for one child. If six chose grapes, how many pictures go in the grapes row?” |
| 10 min | Read it back Which row is longest? Which is shortest? Children answer from the graph they built. Ask: “Which fruit has the most pictures? How can you tell so fast?” |
Two half-sessions instead? End Session A once the class survey is tallied. Start Session B by building the picture graph, then read the most and the least.
Watch for these ideas
- Leaving gaps between the pictures, so a shorter row looks longer: one picture per box, every row starting from the same line.
- Drawing one big picture for a whole group instead of one picture for one child.
- Naming the most from the fullest-looking picture instead of counting the squares.
Answers
- The fruit graph: banana has the most with 8, orange has the least with 3.
- Grapes 6. Banana has 5 more than orange (8 and 3). Twenty-two children altogether (5 + 8 + 6 + 3).
- The class survey and the graph built from it vary: check one picture per child, every row starting from the same line.
Make a picture graph
Here is a fruit survey from Room 2. Draw one picture for each child, one picture in each box. Start every row from the same line. Then read your graph.
| Fruit | How many children |
|---|---|
| apple | 5 |
| banana | 8 |
| grapes | 6 |
| orange | 3 |
Draw the picture graph
Each box holds one picture. One picture stands for one child.
Read your graph
Which fruit has the most? ____________
Which fruit has the least? ____________
How many children chose grapes? ____
How many more children chose banana than orange? ____
How many children were in the survey altogether? ____
Bar graphs: read the height
A bar graph, also called a column graph, swaps the row of pictures for one solid bar. The number is no longer a crowd of pieces but a height you read against a scale. Today children build bars for the same survey and learn to read the top of a bar across to the numbers.
We are learning to
- build a bar graph from a survey, one bar for each thing,
- colour each bar to the right height using the scale,
- read how many by looking at the top of the bar, not the pieces.
Success criteria
- I can colour a bar to the right height for each number.
- I can read how many by looking at the top of the bar.
You need
The blank bar-graph grid (cut-out sheet 2) or the worksheet grid. Coloured pencils. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | From pictures to bars Show yesterday’s picture graph. Run a finger up each row and cap it with a solid bar the same height. Ask: “If we join the pictures into one solid bar, how tall should the banana bar be?” |
| 30 min | Colour the bars Pairs colour a bar for each fruit up to the right number on the grid, then read each height back against the scale on the side. Ask: “The top of the banana bar is level with which number on the side?” |
| 10 min | Read the scale Cover the numbers on a finished bar; children read its height from the scale alone. Ask: “You cannot see the count. How does the scale still tell you how many?” |
Two half-sessions instead? End Session A after the bars are coloured. Start Session B with reading the scale.
Watch for these ideas
- Reading the bar from the wrong line: the height is measured from zero at the base, not from where the colour happens to start.
- Counting the grid squares one by one instead of reading the number the top lines up with.
- Drawing bars of different widths: only the height carries the number, not the width.
Answers
- For the fruit survey the banana bar is tallest at 8 and the orange bar shortest at 3.
- Apple 5. Grapes top lines up with 6. Grapes has 1 more than apple (6 and 5).
- Coloured bars vary a little in neatness: check each reaches the right line and starts from zero.
Colour the bars
Here is the same fruit survey. Colour a bar for each fruit up to the right number. Start every bar at the bottom line. Then read your graph.
| Fruit | How many children |
|---|---|
| apple | 5 |
| banana | 8 |
| grapes | 6 |
| orange | 3 |
Colour the bar graph
Colour from the bottom line up. The number on the side tells you how high to stop.
Read your graph
How tall is the banana bar? ____
Which bar is the shortest? ____________
How many children chose apple? ____
How many more chose grapes than apple? ____
Which number does the top of the grapes bar line up with? ____
The same data, two ways
A picture graph and a bar graph can show the very same survey. They look different, but they must tell the same story. Today children put both graphs of one fruit survey side by side and check that they agree.
We are learning to
- show one survey as a picture graph and as a bar graph,
- read the count for each thing from both graphs,
- check that the most, the least and the order are the same in both.
Success criteria
- I can find the same count in both graphs.
- I can show that both graphs give the same most and least.
You need
The picture graph from Day 1 and the bar graph from Day 2, or the worksheet, which shows both. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Two graphs, one survey Lay the picture graph and the bar graph next to each other on the board. Ask: “These look different. Are they about the same fruit survey, or two different ones?” |
| 30 min | Check they agree Pairs read the count for each fruit off both graphs and write them in the table. The two numbers in each row must match. Ask: “The picture graph says banana is 8. What does the bar graph say for banana?” |
| 10 min | Same winner Which fruit is the most in each graph? Which is the least? They line up. Ask: “Could one graph say banana wins and the other say orange? Why can that never happen?” |
Two half-sessions instead? End Session A after the table is filled. Start Session B with the most and the least.
Watch for these ideas
- Thinking two graphs that look different must be about different data.
- Reading a different winner from each graph because the pictures or bars were counted carelessly.
- Believing a taller-looking bar beats a longer row when the two counts are actually equal.
Answers
- Both graphs give apple 5, banana 8, grapes 6, orange 3. Every row matches.
- Banana is the most and orange the least in both graphs.
- Largest to smallest in both: banana, grapes, apple, orange. Yes, the graphs agree.
Do they agree?
Here is one fruit survey drawn two ways. Read each fruit from both graphs. Do the numbers match?
Picture graph
Bar graph
Check they agree
| Fruit | Picture graph | Bar graph | Same? |
|---|---|---|---|
| apple | |||
| banana | |||
| grapes | |||
| orange |
Read both graphs
Which fruit is the most in the picture graph? ____________ In the bar graph? ____________
Which fruit is the least in each graph? ____________
Do both graphs give the same most and the same least? Yes □ No □
What is the same, what is different
Yesterday two graphs of one survey agreed on the counts. Those are the common features: the facts every honest graph must share. Today children name the distinctive features too, what each kind of graph does its own way, and sort statements into same and different.
We are learning to
- describe common features: what is the same in both graphs,
- describe distinctive features: how a picture graph and a bar graph differ,
- sort a statement into same-in-both or different.
Success criteria
- I can name one thing that is the same in both graphs.
- I can name one thing that is different about how they show the data.
You need
The picture graph and the bar graph from Days 1 to 3, on the board or in front of each pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Same or different? Read statements aloud and have children point left for same, right for different, such as the counts, uses pictures, the winner, uses a scale. Ask: “Is the winner a same thing or a different thing between the two graphs?” |
| 30 min | Two sentences Pairs sort the worksheet statements, then write one same sentence and one different sentence about the fruit graphs. Ask: “Finish these: The graphs are the same because... The graphs are different because...” |
| 10 min | Share and sort Groups read a sentence; the class decides if it is a common feature or a distinctive one. Ask: “Does this sentence talk about the facts, or about how the graph looks?” |
Two half-sessions instead? End Session A after the sort. Start Session B by writing the two sentences.
Watch for these ideas
- Calling a difference in the counts when it is really a difference in how the graph looks: the counts never change.
- Thinking one graph is right and the other wrong, when both are correct.
- Only ever spotting what is different and missing what the two graphs share.
Answers
- Same in both: banana has the most; the counts are 5, 8, 6 and 3; orange has the least.
- Different: one graph uses pictures; one graph uses a scale on the side; you can count each child one by one on the picture graph.
- Sentences vary. Banana has 5 more than orange in both graphs (8 and 3), because the counts are a common feature.
Same and different
Look back at your picture graph and your bar graph of the fruit survey. Tick where each sentence belongs.
| Sentence | Same in both | Different |
|---|---|---|
| Banana has the most. | ||
| One graph uses pictures. | ||
| The counts are 5, 8, 6 and 3. | ||
| One graph uses a scale on the side. | ||
| Orange has the least. | ||
| You can count each child one by one. |
Write it yourself
One thing that is the same in both graphs:
One thing that is different about the two graphs:
One more
How many more children chose banana than orange? Picture graph ____ Bar graph ____
Answer questions from a graph
Now the graphs go to work. Children read a graph to answer real questions: which is the most, which is the least, how many more, how many altogether. They also decide which kind of graph best answers a question.
We are learning to
- answer most, least and how-many-more questions from a graph,
- work out how many there are altogether,
- choose the graph that best answers a question.
Success criteria
- I can find the most, the least and how many more from a graph.
- I can say which graph suits a question and why.
You need
The read-the-graph question cards (cut-out sheet 2), a graph from the week or the worksheet graph, and the worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Quick reads Show the playground-games graph; children answer most and least on their whiteboards. Ask: “Which game has the most? Show me. Which has the least?” |
| 30 min | Question cards Pairs draw a read-the-graph card (most, least, how many more, how many altogether) and answer it from the graph, writing a number sentence where they can. Ask: “How many more chose handball than skipping? What take-away tells you?” |
| 10 min | Which graph? Pose a job; children hold up picture or bar for the graph that suits it. Ask: “If a hundred children answer next time, which graph still fits on the page?” |
Two half-sessions instead? End Session A after the quick reads. Start Session B with the question cards.
Watch for these ideas
- Answering how many more by naming the bigger number instead of the difference between the two.
- Forgetting to add every category when finding how many there are altogether.
- Thinking one kind of graph is always best, rather than matching the graph to the question.
Answers
- Most is handball with 7; least is skipping with 2; soccer 5.
- Handball has 5 more than skipping (7 - 2 = 5). Eighteen children altogether (4 + 7 + 5 + 2).
- A hundred answers suit a bar graph and its scale; exact one-by-one counting suits a picture graph; the winner shows up fast in either.
Read the graph
Here is a survey of favourite playground games. Read the bar graph to answer the questions. Write a number sentence where you can.
Answer from the graph
- Which game is the most popular? ____________
- Which game is the least popular? ____________
- How many children chose soccer? ____
- How many more chose handball than skipping? ____ (number sentence: ____ - ____ = ____)
- How many children answered altogether? ____
- If a hundred children answered next time, which graph would fit the page better: a picture graph or a bar graph? ____________
Picture tokens and data cards
Cut out the cards. Use the picture tokens to build a picture graph, one token for one thing. Write your survey categories on the blank label cards, and show each count with a number card. One set per pair is plenty.
Picture tokens (one token, one thing)
Teacher note: these are the squares from “The picture graph” on screen; one token stands for one child or one thing.
Number cards
Label cards (write your own)
Write a category on each card, such as apple, banana or a colour, to name the rows of your graph.
Blank grids and question cards
Cut along the dashed lines. Use the blank picture grid and the blank bar grid to make your own graphs. Use the question cards to ask a partner about any graph on the wall.
Blank picture graph
Write a label in the dashed box, then draw one picture per box. Start every row from the same line.
Blank bar graph
Write a label in each dashed box, then colour a bar up to its number, starting at the bottom line.
Read-the-graph question cards
Teacher note: these are the jobs from “The right graph for the job” on screen, turned into cards for a partner game.
What we know: Comparing Graphs
Work on your own. This is a picture graph of the shells a class found at the beach. Count the squares.
- In this picture graph, one square stands for how many shells? ____
- Which shell did the children find the most of? ____________
- Which shell did the children find the least of? ____________
- How many spiral shells did they find? ____
- How many more fan shells than spiral shells? ____
- How many shells did they find altogether? ____
- A bar graph shows how many by the ____________ of each bar.
- The same shells are also drawn as a bar graph. Does the bar graph show the same shell as the most? Circle one: yes / no
Answers and marking guide
Answers
- One. Each square stands for one shell.
- Fan (7).
- Round (2).
- 4 spiral shells.
- 3 more (7 - 4 = 3).
- 19 altogether (6 + 7 + 4 + 2).
- The height of the bar (read the top against the scale).
- Yes: fan is the most in both graphs, because two graphs of one survey share the same counts.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Read a value (Q1, Q4) | counts the squares with help | reads a count straight from the graph (spiral is 4) | reads any row and explains that one square is one shell |
| Most and least (Q2, Q3) | points to the longest row | names the most (fan) and the least (round) | puts all four shells in order, most to least |
| How many more, altogether (Q5, Q6) | compares two rows | finds how many more (3) and the total (19) | writes the number sentences 7 - 4 = 3 and 6 + 7 + 4 + 2 = 19 |
| Read and compare graphs (Q7, Q8) | knows a bar shows how many | reads a bar by its height and says the two graphs agree | explains why the most must be the same in both graphs |
Eight questions, four ideas. A child at standard reads the graph for most, least, how many more and the total, and knows two graphs of one survey agree.
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 | Picture graph | Bar graph | Two ways | Same and different | Reads and answers |
|---|---|---|---|---|---|
The five columns are the five days: make a picture graph, make a bar graph, show one survey two ways, name same and different, and answer questions from a graph.