AC9M1ST02 • Year 1 Maths

Representing and Comparing Data

Collected data can be represented with one-to-one displays where each mark or symbol stands for one response. Frequencies help compare categories.

Learning goals

Collected data can be represented with one-to-one displays where each mark or symbol stands for one response. Frequencies help compare categories.

Learning routine: Use collected data → Make display → Count frequencies → Compare → Discuss

Success looks like

  • Make one-to-one displays
  • Count frequencies
  • Compare categories
  • Discuss findings
  • Use evidence
Concept model and worked application

One symbol means one response

apple: ●●●banana: ●●orange: ●●●●

Because each dot means one person, orange has the highest frequency.

Compare using frequencies, not guesses

mostleastsame asdifference

Use the display to support what you say about the data.

Explain your thinking: Say what each part of the model represents, then explain why the answer or conclusion follows.

Read a one-to-one display

Use one symbol for each response and compare category frequencies.

Worked example

A picture display shows four circles for walking to school and two circles for cycling. Each circle represents one child.

Travel to school: each circle represents one child
MethodChildren
Walking● ● ● ●
Cycling● ●
  1. Read the key: one circle means one child.
  2. Count four walkers and two cyclists. Line up the first two circles in each row to compare.
  3. There are two more walkers than cyclists, and six children altogether.

Watch for this mistake: Bigger pictures do not represent more children. In a one-to-one display, count the symbols and keep them the same size.

Try it, then explain

  1. A display shows 3 square symbols for cats and 5 for dogs. One square means one pet. How many more dogs than cats?

    Hint

    Match three symbols from each group.

    Answer and explanation

    2 more dogs.

  2. Two categories each have four symbols. What can you conclude?

    Hint

    Compare the counts, not the labels.

    Answer and explanation

    Both categories have the same frequency: four each.

Australian Curriculum elaborations

These curriculum examples extend the central model into varied contexts. They are learning contexts, not extra definitions to memorise.

E1

creating a pictograph with objects or drawings; discussing the possible categories for the pictograph, arranging the objects or drawings into the categories, then reflecting on the chosen categories and deciding whether they were helpful

Try and explain: Make a one-picture-per-child display for four apples, two pears and one banana as favourite-fruit responses. How many pictures are needed?

Answer and teaching point

Seven pictures in three labelled categories. Keep symbols the same size and use one picture for each response.

E2

translating data from a list or pictorial display into a tally chart to make counting easier; describing what the tally chart is showing, by referring to the categories; using skip counting by fives to compare the numbers within each category and explaining how the tally chart answers the question

Try and explain: Convert dog, cat, dog, dog, cat, bird into a tally chart. Which category has the greatest frequency?

Answer and teaching point

Dog has 3, cat 2 and bird 1. Dog has the greatest frequency because it has the most recorded responses.

E3

recognising that when there is no data for a particular category you may choose whether or not to include it in your data display, and use a zero or blank for that category depending on the purpose of the data collection or presentation; for example, creating a birthday calendar for the class and discussing that there are no students born in May and therefore there are no names listed

Try and explain: No child in a class has a birthday in June. A birthday chart includes June. What should its count be?

Answer and teaching point

Zero. No names or marks in that labelled month can show zero, but a written 0 makes the meaning especially clear.

E4

representing data with objects and drawings where one object or drawing represents one data value; describing the displays and explaining patterns that have been created using counting strategies to determine the frequency of responses

Try and explain: One-to-one rows show six circles for walking and four for cycling. How many more children walk?

Answer and teaching point

Two more. Match four circles from each row; two walking circles remain unmatched.

E5

discussing what data frequency means in terms of the total count for a particular category and relating the highest frequency to being the most popular category in the collected data

Try and explain: A vote has art 7, music 5 and drama 7. Is there one most popular option?

Answer and teaching point

No. Art and drama tie for the highest frequency, with seven votes each.

E6

exploring First Nations Australian children’s instructive games; for example, Kolap from Mer Island in the Torres Strait region, recording the outcomes, representing and discussing the results

Cultural safety: Use a community-approved source, name the specific Nation or community where the source does, and avoid presenting diverse First Nations knowledges as one generic tradition. Follow local cultural and intellectual property protocols before inviting community participation.

Common misconceptions and traps
  • Symbols worth different amounts — In a one-to-one display, every symbol must mean one response.
  • Comparing by picture size — Compare by frequency, not by how big a drawing looks.
  • Claim without evidence — Use the data display to support the finding.
Guided learning activities

Build a display

Use counters to show data with one counter per response.

Model: one counter = one vote

Compare categories

Find which category has the most, least or same number.

Model: most / least / equal

Discuss finding

Say one finding using evidence from the display.

Model: Dog has 3 more than cat.

Revision Notes

Key idea: Collected data can be represented with one-to-one displays where each mark or symbol stands for one response. Frequencies help compare categories.

Remember

  • Make one-to-one displays
  • Count frequencies
  • Compare categories
  • Discuss findings
  • Use evidence

Quick questions

  • What does one-to-one display mean?
  • Which category has the most dots?
  • How do you find the difference between two categories?
  • State one finding from a data display.

Return to the concept model if an answer is uncertain. Use the model to explain, not just to guess.

Official curriculum reference

AC9M1ST02: represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings

Australian Curriculum Version 9.0

Practice, test and teacher resources

Use the Practice Sheet for written or hands-on work, Practice for supported feedback, and Test when the student is ready to demonstrate independent mastery.

🎥 Optional Video Lesson

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Back to the lesson

Before you watch:

  • Pause after each worked example.
  • Try the examples yourself.
  • Return to the SkillrHub lesson before continuing.
Recommended: Data

Scratch Garden — Read a picture display and compare how many are in each category.

As you watch: Check what one picture stands for before comparing the rows.

Load video player Loads YouTube in this lesson. See the video notice below.

Try it: Draw one fruit picture for each answer in your survey. Which category has more, and by how many?

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Curriculum equivalents: Victoria, NSW and international

Curriculum equivalents for Representing and comparing data

Mapped skill: represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

RegionCurriculum frameworkClosest level or code
AustraliaAustralian Curriculum v9.0AC9M1ST02 · Year 1
VictoriaVictorian Curriculum F–10 Version 2.0 — MathematicsVC2M1ST02 · Level 1
New South WalesNSW Mathematics K–10 Syllabus (2022)MA1-DATA-02 · Stage 1
United States (USA)Common Core State Standards for MathematicsGrade 1
Canada (Ontario)Ontario Curriculum — MathematicsGrade 1
United Kingdom (England)National Curriculum in England — MathematicsYear 2, Key Stage 1
IndiaNCERT / CBSE — MathematicsClass 1

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.

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Topic reference: AC9M1ST02 — Representing and Comparing Data

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