Organising and Displaying Data: a week of ready-to-teach maths

Five days of lessons for Year 5 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus 25 survey cards from one class (three of them wrong, to be found), dot plot cards to match to their shapes, 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. Print the survey cards and the dot plot cards once per pair. Book devices with a spreadsheet for Day 3 if you can.
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. The big idea of the week: the kind of data decides how to show it. Categories (nominal, or ordinal when they have an order) go in a column graph; counted numbers go in a dot plot. Data is checked before it is used, and a display is described by its mode, the most common value, and its shape.

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.

How the week builds

One class survey runs through the week: Day 1 names its kinds of data, Day 2 checks and tallies it, Days 3 and 4 show it, and Day 5 reports on it. It builds on Year 4’s pictographs and column graphs (AC9M4ST01), and it leads to Year 6, where two sets of data are compared by mode, range and shape (AC9M6ST01).

Materials for the week (one trip)

• From the classroom: rulers, coloured pencils, scissors, sticky notes for a class dot plot, devices with a spreadsheet if you have them, this pack printed.
• Print once per pair: the survey cards (Day 2) and the dot plot cards (Day 4).

Words for the word wall

data, variable, categorical, nominal, ordinal, numerical, frequency table, tally, column graph, scale, dot plot, mode, shape

Dear families

This week in maths, Year 5 collects data to answer a question, checks it for mistakes, and shows it in tables, column graphs and dot plots. We describe data by its mode, the most common value, and by its shape: where it bunches up and where it trails off.

Try this at home

• Ask family and friends one question, such as how many hours they slept. What answer came up most often?
• Find a graph in a newspaper or online. Does it have a scale and labels? What does it show?
• Spot an answer that cannot be right, such as 30 hours of sleep. How would you check it?

Questions I asked this week

Fill one row a day. Write the question and the most common answer.

Printed from the free seegongsik Organising and Displaying Data teaching pack · seegongsik.com/au/y5/statistics/AC9M5ST01/pack

What kind of data?

Data answers a question, and its kind decides what to do with it. Categorical data sorts answers into groups: nominal when the groups have no order, like favourite sport, and ordinal when they do, like how spicy you like food: mild, medium or hot. Numerical data is counted or measured; counted data such as goals scored this season is discrete, whole numbers only. A good survey question says exactly what to answer, with choices or units.

We are learning to

• tell nominal and ordinal categorical data from numerical data,
• write a clear survey question for each kind,
• answer a survey so that the answers can be counted.

Success criteria

• I can say what kind of data a question will give.
• I can write a survey question with clear choices or units.

You need

The worksheet, one per child, and scissors to cut off the survey slips. A box to collect the slips for Day 2.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by writing questions.

Watch for these ideas

• Calling an answer categorical because it is written in words, such as ‘three’.
• Calling a numbered label numerical. A jersey number or a postcode names something; it is not an amount.
• Forgetting that ordered groups (ordinal) have to stay in their order.

Answers

• Part A: 1 numerical, 2 nominal, 3 nominal, 4 ordinal, 5 numerical, 6 nominal, 7 ordinal, 8 numerical.
• Part B: questions vary. Check that each gives the kind asked for and says exactly what to answer, for example ‘Which fruit do you like best: apple, banana or orange?’ Part C: the class’s own answers.

What kind of data?

A. Is the data nominal, ordinal or numerical?

B. Write a survey question that gives...

C. Our class survey

Answer, then cut along the dashed line and post your slip in the box.

Collect and check

Data is checked before it is used. An answer that cannot be right, an answer that does not fit the question, or a student counted twice would all change the counts, so those answers are set aside. Then a frequency table lists each answer with its count, tallied in bundles of five, and the counts must add up to the number of answers kept.

We are learning to

• check data for answers that cannot be right and for double entries,
• organise data in a frequency table with tally marks,
• check that the counts add up.

Success criteria

• I can find the answers that must be set aside and say why.
• I can make a frequency table whose counts add up to the number of answers kept.

You need

The survey cards (cut-out sheet 1), one set per pair, cut out. The class’s survey slips from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Counting a card twice or missing one. Sort the cards into piles first, then count each pile.
• Setting aside an answer that is unusual but possible, such as a big family.
• Leaving out a value with a count of 0, so the table jumps.

Answers

• Part A: card 14, 0 people at home cannot be right: the student lives there; card 19, ‘rocket’ is not a way to get to school; card 23, a second card for student 6. That leaves 22 of 25 cards.
• Part B: walk 8, car 7, bus 4, bike 3; total 22. Part C: 1 people 0, 2 people 2, 3 people 4, 4 people 8, 5 people 5, 6 people 2, 7 people 1, 8 people 0; total 22.

Collect and check

A. Check the cards. Which must be set aside, and why?

Card ______ because ____________________________________________

Card ______ because ____________________________________________

Card ______ because ____________________________________________

B. How do you usually get to school?

Use only the cards you kept.

C. How many people live in your home?

Column graphs

A column graph shows categorical data: one column for each category, its height read against a scale up the side that starts at 0 and climbs in equal steps. Nominal categories can go in any order, often tallest first; ordinal categories keep their own order, so the reading graph runs from ‘not at all’ to ‘a lot’. A spreadsheet draws the same graph from a table: categories in one column, counts beside them, then insert a column chart.

We are learning to

• draw a column graph with a scale, a title and labels,
• keep ordinal categories in their order,
• make the same graph in a spreadsheet.

Success criteria

• I can draw a column graph that someone else can read exactly.
• I can explain why ordered categories keep their order.

You need

Rulers and coloured pencils. The kept survey cards and the Day 2 worksheet. Devices with a spreadsheet if you have them.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by drawing the graph.

Watch for these ideas

• A scale that starts at 1, or has uneven steps, so the columns mislead.
• Columns of different widths, or no gaps between the categories.
• Putting ordinal categories in order of size instead of in their own order.

Answers

• Parts A and B: not at all 3, a little 5, quite a lot 8, a lot 6; the columns in this order, against a scale from 0 to 10.
• Part C: 1. yes; walk, car, bus and bike have no order, so any order is right. 2. the answers go from least to most enjoyment; shuffled, the graph would hide that pattern.

Column graphs

A. How much do you enjoy reading? Tally the cards you kept.

B. Draw a column graph of the reading data

Write a title and label each column. The scale is drawn for you.

Title: ________________________________________________

C. Does the order matter?

1. Could the columns of a travel graph (walk, car, bus, bike) go in any order? Why?

2. Why must the reading columns stay in their order?

Dot plots, mode and shape

A dot plot shows numerical data: one dot for each answer, stacked over its value on a number line. The mode is the value under the tallest stack. The shape says where the dots bunch up and where they trail away, and it is told in context: what it says about the people who answered.

We are learning to

• draw a dot plot of numerical data,
• find the mode,
• describe the shape of the data in the context of the question.

Success criteria

• I can draw a dot plot and find its mode.
• I can say where the data bunches and where it trails off, and what that means.

You need

Sticky notes and a number line on the board. The Day 2 worksheet. The dot plot cards (cut-out sheet 2), one set per pair, cut out.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Giving the number of dots in the tallest stack as the mode, instead of the value under it.
• Leaving out values with no dots, which squashes the number line and hides gaps.
• Describing the shape without the context, as in ‘it goes up and down’.

Answers

• Part A:

  Part B: 4; more homes in this class have 4 people than any other number.
• Part C: A 2, B 4, C 3, D 1. Part D: most homes have 3 to 5 people and 4 is the most common; a few have 2, and a few have 6 or 7, so the dots bunch around 4 and trail off further to the right.

Dot plots, mode and shape

A. Draw a dot plot of how many people live in each home

Use your Day 2 table: one dot for each card you kept.

B. The mode

The mode is   ______   people. What does it tell you about this class?

C. Match the dot plot cards to the shape cards

D. Describe the shape of the people-at-home data

Where do the dots bunch up? Where do they trail off? What does that say about the homes?

Report on the data

A display is read back by matching each column or stack to the scale, and checked before it is trusted: a title, labels, a scale that starts at 0 and climbs in equal steps, and the right kind of graph for the data. A short report answers the question in context: the mode, the shape, and anything surprising, such as a mode that is still less than half of all the answers.

We are learning to

• read values back from a table, a column graph and a dot plot,
• check whether a display can be trusted,
• write a report that answers the question with the mode and the shape.

Success criteria

• I can read a display exactly and spot one that misleads.
• I can write a short report about data, in its context.

You need

The Day 2, 3 and 4 worksheets. Mini whiteboards for the quiz. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Trusting a graph without checking where its scale starts.
• A report that lists numbers without answering the question.
• Saying ‘most of the class’ for the mode when it is less than half of the answers.

Answers

• Part A: 1. at 2, not 0. 2. no: bike is 3 and walk is 8, but the columns start at 2, so bike looks far smaller. 3. a title. Part B: 1. 22. 2. walk. 3. no, 8 of 22 is less than half. 4. 4.
• Part C: reports vary. A good one names the mode of each question in context, notes the shape of the people-at-home data, and says how many students answered.

Report on the data

A. Check this graph of the travel data

B. Read the survey

1. How many students are in the survey after the checking?   ______

2. Which way to school is the mode?   ______

3. Did more than half of the students answer with the mode? How do you know?   ______________________

4. What is the mode of people at home?   ______

C. Write a report

How do the students in this class get to school, and how many people live in their homes? Write three or four sentences. Use the mode and the shape of the data.

Survey cards: one class’s answers

One set per pair (Day 2). Each card is one student’s answers to three questions: how they get to school, how much they enjoy reading, and how many people live in their home. Some cards must be set aside before counting.

Teacher note: there are 24 students in this class. The cards to set aside and why are on the Day 2 plan.

Dot plot cards and shape cards

One set per pair (Day 4). Cut out all eight cards and match each dot plot to the card that describes its shape.

Teacher note: each dot plot has exactly one shape card. The matches are on the Day 4 plan.

What we know: Organising and Displaying Data

Work on your own.

1. Write nominal, ordinal or numerical for each.
   a. how many teeth you have lost   __________

   b. favourite fruit   __________

   c. how tired you are: not at all, a little, very   __________
2. A survey asked ‘How many hours did you sleep last night?’ Circle the answer that must be a mistake.
   9 26 8 10
3. Make a frequency table of these favourite seasons: summer, winter, summer, autumn, spring, summer, winter, summer, spring, autumn, summer, winter.

   summer	autumn	winter	spring

4. How many more chose mango than banana?   ______
   How many answered altogether?   ______
5. A graph shows ‘How often do you play outside?’: never, sometimes, often, every day. Why should its columns stay in this order?
6. Goals scored by a team in each game. What is the mode?   ______
7. Describe the shape of the goals dot plot.
8. Which display suits each: a column graph or a dot plot?
   a. favourite fruit   ______________    b. goals in each game   ______________

Answers and marking guide

Answers

1. a. numerical; b. nominal; c. ordinal
2. 26: there are only 24 hours in a day
3. summer 5, autumn 2, winter 3, spring 2; total 12
4. 7 − 4 = 3; 20 altogether
5. the answers have an order, from least to most often; shuffled, the graph would hide that
6. 2 goals
7. bunched from 1 to 3 goals, highest at 2, with a tail to the right (1 game of 6)
8. a. a column graph (categories); b. a dot plot (counted numbers)

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by naming the kind of data first and reading every display against its scale.

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: kinds of data, checking data, column graphs, dot plots and the mode, and reporting.