Comparing and Analysing Displays: a week of ready-to-teach maths

Five days of lessons for Year 4 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out display cards, a class dot plot, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the display cards once for Day 2, and print or project the class dot plot for Day 3.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. 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 the answers. Year 4 moves from making displays to judging them: which display answers a question best, what shape the data makes, how spread out it is, and whether a display tells the truth.

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.

Dot plots and variation

A dot plot puts one dot for each value above a number line, stacked like a column. It shows every value, so it is the clearest way to see the shape and the spread of numerical data. In this pack variation means how spread out the values are: close together is little variation, far apart is a lot.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 judge displays: what each one shows well and what it hides. Days 3 and 4 read what a display reveals about a whole data set, its shape and its variation. Day 5 puts it all to work spotting displays that mislead. It builds on making pictographs and column graphs (AC9M4ST01).

Materials for the week (one trip)

• From the classroom: rulers, coloured pencils, scissors, and this pack printed.
• Optional: sticky notes or counters to build a class dot plot on the board.
• Cut out once: the display cards. Print or project once: the class dot plot.

Words for the word wall

display, frequency table, tally chart, pictograph, column graph, dot plot, scale, axis, effective, shape, peak, spread, variation, highest, lowest, misleading

Dear families

This week in maths, Year 4 judges data displays: which one answers a question best, what the data looks like, and whether a graph could be misleading.

Try this at home

• Find a graph in a newspaper, a website or an advertisement. What is it trying to show?
• Check where the scale of a graph starts. Does it start at 0?
• Record a family score each day, such as minutes of reading. Are the numbers close together or spread out?
• Ask: would a table or a graph show this better, and why?

Displays I looked at this week

Fill one row a day. Write where you saw a display and one thing it showed.

Printed from the free seegongsik Comparing and Analysing Displays teaching pack · seegongsik.com/au/y4/statistics/AC9M4ST02/pack

One data set, five displays

The same data can be shown in many ways, and each display is good at something different. A frequency table gives exact numbers; a tally shows how the data was counted; a pictograph is quick to read for small numbers; a column graph and a dot plot show at a glance which category is biggest. Children compare five displays of one survey and say what each does well and what it hides.

We are learning to

• compare different displays of the same data,
• say what a display shows well and what it hides,
• choose a display to answer a question.

Success criteria

• I can say which display answers a question fastest, and why.
• I can name one thing a display hides.

You need

The worksheet, one per child, and coloured pencils.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three questions; start Session B with the last two.

Watch for these ideas

• Thinking the five displays show different data because they look different.
• Choosing the most colourful display rather than the one that answers the question.
• Reading an exact value off a bar that stops between the lines of the scale.

Answers

• 1 the frequency table; 2 the column graph and the dot plot (the pictograph too); 3 26 children, quickest by adding the table; 4 soccer, with 8.
• 5 answers vary: the graph shows the differences by height at a glance, which the table hides; the table gives exact numbers the graph only shows by its scale. 6 the tally chart and the dot plot, with a mark or dot for every child.

One data set, five displays

A. Our favourite sport: the same survey, shown five ways

B. Use the displays.

The right display

No display is best for everything. The best display is the one that answers the question being asked: a table for exact numbers, a tally for counting answers as they come in, a column graph or a dot plot for comparing at a glance and seeing the spread, a pictograph for young readers. A display also needs a title, axis labels and a fair scale before anyone can use it.

We are learning to

• match a question to the display that answers it best,
• judge whether a display is effective,
• explain our choice of display.

Success criteria

• I can choose a display for a question and say why it is the best one.
• I can say what a display is missing.

You need

The display cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the card match; start Session B with Part B.

Watch for these ideas

• Always choosing the column graph, whatever the question.
• Thinking a display without a title or labels is fine because the numbers are there.
• Thinking a tally chart is a finished display rather than a way of counting.

Answers

• Part A: 1 frequency table; 2 tally chart; 3 column graph (or dot plot); 4 dot plot (or column graph); 5 pictograph.
• Part B: it has no title, no label on either axis, so we cannot tell what was counted or who answered. Part C: a column graph or a dot plot; the white bar is the tallest, with 9 cars.

The right display

A. Which display does each job best? Write it.

Choose from: frequency table, tally chart, pictograph, column graph, dot plot.

B. This display is not finished. What is missing? Why does it matter?

C. Cars passing the school: draw the display you think is best, and say why.

The shape of the data

A dot plot of numerical data makes a shape. The dots may rise to a peak in the middle, pile up at one end, or stay flat and even across all the values. Describing the shape sums up the whole data set in a few words: most homes have 4 people, and very few have 2 or 6. Children build a class dot plot, describe the shapes of three dot plots, then draw and describe one of their own.

We are learning to

• read and draw a dot plot,
• describe the shape of a set of data,
• say what the shape tells us.

Success criteria

• I can draw a dot plot from a list of numbers.
• I can say whether data peaks in the middle, bunches at one end or stays flat.

You need

The class dot plot (cut-out sheet 2) on the board, and a sticky note or counter per child. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the dot plot to draw.

Watch for these ideas

• Describing single values only (“there are 9 at 4”) instead of the whole shape.
• Spacing the dots unevenly, so the stacks cannot be compared.
• Leaving out a value with no dots, which changes the shape.

Answers

• Part A: 1 a peak in the middle, tallest at 4; 2 bunched at one end, tallest at 0; 3 flat and even, every stack 4 or 5.
• Part B: 0: 3, 1: 8, 2: 5, 3: 1, 4: 1 dots; bunched at one end, tallest at 1. Part C: answers vary.

The shape of the data

A. Describe the shape of each dot plot. Ring one.

B. Draw a dot plot of these answers. Then describe its shape.

Brothers and sisters: 1, 2, 1, 0, 1, 3, 2, 1, 1, 0, 2, 1, 4, 1, 2, 0, 1, 2

C. Sketch a dot plot that peaks in the middle. What data could it show?

Variation

Variation is how much the values differ. Two data sets can have the same total and still vary very differently: the Hawks scored 28 goals in 8 games, always 3 or 4; the Owls also scored 28, from 0 up to 8. Children draw both teams as dot plots on the same line, compare the lowest and highest values, and say which team is more consistent.

We are learning to

• describe how much a set of data varies,
• compare the variation of two data sets,
• use the lowest and highest values to talk about spread.

Success criteria

• I can say which of two data sets varies more, and how I know.
• I can explain why two sets with the same total can look very different.

You need

Coloured pencils (two colours). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the dot plots; start Session B with Part B.

Watch for these ideas

• Thinking the set with the bigger total must vary more.
• Looking only at the highest value, not at how far it is from the lowest.
• Thinking a set with large variation is wrong or badly collected.

Answers

• Part B: the Hawks lowest 3, highest 4; the Owls lowest 0, highest 8; both 28 goals; the Owls vary more; the Hawks are more consistent, scoring at least 2 every game, while the Owls scored fewer than 2 in 3 games.
• Part C: 1 B, 2 A, 3 B.

Variation

A. Goals in 8 games. Draw a dot plot for each team.

B. Compare the teams.

C. Which set varies more? Ring A or B.

Displays that mislead

A display can show the right numbers and still tell the wrong story. A scale that starts above 0 makes a small difference look huge; a scale with uneven gaps squashes some bars and stretches others; bigger symbols make one row of a pictograph look like more. Children find what is wrong with three displays, redraw one fairly, and finish with the self-check quiz.

We are learning to

• check the scale of a graph before reading it,
• explain how a display can mislead,
• redraw a misleading graph so that it is fair.

Success criteria

• I can find what is misleading in a display and say why.
• I can redraw a graph with a scale that starts at 0 and goes up evenly.

You need

Rulers and coloured pencils. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the redraw.

Watch for these ideas

• Comparing the heights of the bars without reading the scale.
• Thinking a display must be true because the numbers on it are true.
• Not noticing when the gaps on a scale are different sizes.

Answers

• Part A: 1 the scale starts at 20, so shop B (24) looks twice as big as shop A (22); 2 the gaps jump 1, 1, 3, 5, so Cam’s 10 looks only a little more than Bo’s 5; 3 both days are 4 books, but Tue’s symbols are bigger.
• Part B: a scale from 0 in fives; the two bars end at 22 and 24 and look almost the same. Part C: answers vary.

Fair scale for Part B: 0, 5, 10, 15, 20, 25.

Displays that mislead

A. Each display misleads. What is wrong with it?

B. Redraw graph 1 fairly: start the scale at 0 and go up in fives.

C. Which display would you use to show your class survey to the principal? Why?

Display cards

One set per pair, for Day 2. Cut out the ten cards. Match each job to the display that does it best.

Teacher note: A column graph (or dot plot); B pictograph; C frequency table; D dot plot (or column graph); E tally chart.

Our class dot plot

Print once, or project it, for Day 3. Each child adds one dot, or a sticky note, above the number of letters in their first name.

What we know: Displays

1. Which display shows exact numbers best? Ring one: column graph · frequency table · dot plot
2. Which display shows at a glance which category is the biggest? __________________
3. Describe the shape of this dot plot. __________________________
4. Which dot plot shows more variation, A or B? ____

   A

   B
5. In dot plot A, what are the lowest and highest values? ____ and ____
6. What is misleading about this graph? __________________________________
7. Blue is 43 and red is 41. Is blue about twice as big as red? Why? ______________________
8. Why does a display need a title and labels? ________________________________________

Answers and marking guide

Answers

1. The frequency table.
2. A column graph (a dot plot or a pictograph also works).
3. Bunched at one end: most of the data is at 4, the high end.
4. B: its values spread right across the line; A’s stay close together.
5. 2 and 4.
6. The scale starts at 40, not 0, so the difference looks much bigger than it is.
7. No: blue is only 2 more than red.
8. So the reader knows what was counted and what each bar or dot stands for.

A quick three-level guide

Eight questions, three ideas. A child at standard chooses a display to suit a question, describes the shape and variation of a data set, and checks the scale before believing a graph.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: comparing displays, choosing a display, shape, variation, and misleading displays.