Statistics

KS2

MA-Y3-D007

Interpreting and presenting data using bar charts, pictograms and tables, and solving one-step and two-step questions from data including 'how many more?' and 'how many fewer?'.

National Curriculum context

In Year 3, the statistics curriculum builds on the KS1 work of recording, interpreting and comparing simple data by requiring pupils to interpret and present data using scaled bar charts and pictograms, where each unit represents more than one item. The non-statutory guidance clarifies that pupils should ask and answer questions, including two-step questions, using information presented in bar charts, pictograms and tables. Solving questions such as 'How many more?' and 'How many fewer?' requires pupils to perform subtraction calculations on data values, connecting statistics directly to the calculation domains. This increasingly sophisticated engagement with data prepares pupils for the more complex graphical work with line graphs and pie charts encountered in Years 4 and 5.

2

Concepts

2

Clusters

1

Prerequisites

2

With difficulty levels

AI Facilitated: 2

Lesson Clusters

1

Interpret and construct scaled bar charts and pictograms

introduction Curated

Scaled charts are the Year 3 entry point for statistics, requiring pupils to understand one symbol/bar represents more than one item. Foundational representation skill.

1 concepts Patterns
Scaled bar charts and pictograms
2

Solve one-step and two-step questions using information from data

practice Curated

Moving from reading charts to reasoning from data and answering multi-step questions is the key statistical thinking progression in Year 3.

1 concepts Evidence and Argument
Solving one-step and two-step questions from data

Teaching Suggestions (1)

Study units and activities that deliver concepts in this domain.

Interpreting and Presenting Data

Mathematics Practical Application
Pedagogical rationale

Y3 statistics introduces scaled axes for the first time, which is a multiplication concept applied in a data-handling context. Previously, children used 1:1 pictograms; now each symbol or bar division represents multiple items. This requires confident use of the 2, 5, and 10 times tables to read and create charts. Two-step comparison questions ('How many more did X have than Y?') combine subtraction with data reading, making this an excellent domain for reasoning and problem-solving.

CPA Stage: pictorial → abstract NC Aim: reasoning and problem solving
Interlocking cubes (for building physical bar charts) Counters (for concrete data sorting before charting)
Bar charts (with scaled axes in 2s, 5s, or 10s) Pictograms (with keys showing 1 symbol = 2 or 5 items) Tally charts and frequency tables Carroll diagrams and Venn diagrams for sorting data
Fluency targets: Read values accurately from a bar chart with a scaled axis; Interpret a pictogram key and calculate totals for each category; Answer 'how many more/fewer' questions by finding the difference; Draw a bar chart with an appropriate scale for a given data set
Solving one-step and two-step questions from data Scaled bar charts and pictograms

Prerequisites

Concepts from other domains that pupils should know before this domain.

Formal columnar addition from Number - Addition and Subtraction
MA-Y3-C014

Domain Vocabulary

21 terms across 2 concepts (21 domain-specific)(4 shared)

Domain-specific (21)
Concept
T3

altogether(adverb)

The total when everything is combined; the result of adding all amounts together.

T3

axis(noun)

A reference line on a graph or chart used for plotting data; the horizontal is the x-axis, vertical is the y-axis.

T3

bar chart(noun)

A graph that uses rectangular bars of different heights to compare quantities across categories.

Shared by 2 concepts

T3

data(noun)

Information collected and recorded, often as numbers, that can be sorted, compared, and displayed.

Shared by 2 concepts

T3

difference(noun)

The result of subtracting one number from another; how much more or less one number is than another.

T3

fewer than(phrase)

A smaller number of countable items when comparing two groups.

T3

frequency(noun)

The number of times a particular value or event occurs in a set of data.

T3

interpret(verb)

To read and make sense of information presented in graphs, charts, tables, or diagrams.

Shared by 2 concepts

T3

key(noun)

A legend on a pictogram or chart explaining what each symbol represents.

T3

label(noun)

Words or symbols added to a graph, diagram, or shape to identify parts and make it easier to read.

T3

more than(phrase)

A greater amount; having a larger value.

T3

one-step(adjective)

A problem requiring only a single calculation to find the answer.

T3

pictogram(noun)

A chart that uses pictures or symbols to represent data, where each symbol may represent one or more items.

Shared by 2 concepts

T3

present(verb)

To display or show data, calculations, or results in a clear, organised way.

T3

question(noun)

A mathematical problem to be solved or answered.

T3

represents(verb)

Stands for or shows; used when a symbol, picture, or expression stands for a value.

T3

scale(noun)

The numbered markings on a measuring instrument or the axis of a graph, showing regular intervals.

T3

symbol(noun)

A written mark used to represent a mathematical operation or relationship (e.g. +, -, ×, ÷, =).

T3

table(noun)

A way of organising data or numbers in rows and columns for easy reading and comparison.

T3

total(noun)

The amount you get when everything is added together.

T3

two-step(adjective)

A problem requiring two separate calculations to find the answer.

Concepts (2)

Scaled bar charts and pictograms

skill AI Facilitated

MA-Y3-C040

In Year 3, bar charts and pictograms use scales where one bar unit or one symbol represents more than one item (e.g. each symbol = 5, each 1 cm on a bar chart = 10 children). Pupils must read the scale key, multiply appropriately to find values, and use these values to answer questions. Mastery means pupils can read scales on bar charts (including values between marked intervals) and pictograms (including half-symbols when one symbol represents 2 or more), and can present data in these formats.

Teaching guidance

Start with scales of 2 or 5 before moving to 10 or 100. For pictograms, use concrete half-symbols (a picture cut in half) before the abstract representation. Always read the key first. Practise reading values that fall between marked scale intervals. Creating their own bar charts and pictograms from given data is as important as reading them — the act of choosing a suitable scale builds understanding. Use real data from classroom surveys to make the work meaningful.

Vocabulary (12 terms)
axis T3 new — A reference line on a graph or chart used for plotting data; the horizontal is the x-axis, vertical is the y-axis.
bar chart T3 new — A graph that uses rectangular bars of different heights to compare quantities across categories.
data T3 — Information collected and recorded, often as numbers, that can be sorted, compared, and displayed.
frequency T3 — The number of times a particular value or event occurs in a set of data.
interpret T3 new — To read and make sense of information presented in graphs, charts, tables, or diagrams.
key T3 — A legend on a pictogram or chart explaining what each symbol represents.
label T3 new — Words or symbols added to a graph, diagram, or shape to identify parts and make it easier to read.
pictogram T3 — A chart that uses pictures or symbols to represent data, where each symbol may represent one or more items.
present T3 new — To display or show data, calculations, or results in a clear, organised way.
represents T3 new — Stands for or shows; used when a symbol, picture, or expression stands for a value.
scale T3 — The numbered markings on a measuring instrument or the axis of a graph, showing regular intervals.
symbol T3 — A written mark used to represent a mathematical operation or relationship (e.g. +, -, ×, ÷, =).
Common misconceptions

Pupils read the numerical label on the scale as the value (reading 2 on a scale of 5 as '2 items' rather than '10 items'). Half-symbols in pictograms are often misread as zero rather than half the represented value. Pupils may not realise they need to consult the key before reading the chart, treating each bar unit as worth 1.

Difficulty levels

Entry

Reading a pictogram where each symbol represents 1 item, and reading a bar chart with a scale of 1.

Example task

This pictogram shows favourite fruits. Each apple symbol = 1 child. How many children chose banana?

Model response: There are 5 banana symbols, so 5 children chose banana.

Developing

Reading a pictogram where each symbol represents 2 items, including interpreting half-symbols, and reading bar charts with a scale of 2 or 5.

Example task

In this pictogram, each star symbol = 2 votes. The row for 'Pizza' shows 4 full stars and a half star. How many votes for Pizza?

Model response: 4 full stars = 4 x 2 = 8 votes. Half star = 1 vote. Total = 9 votes.

Expected

Reading and interpreting scaled bar charts and pictograms where each unit represents 5 or 10, and presenting data in a bar chart with a chosen scale.

Example task

A bar chart shows the number of books read. The scale goes up in 5s. The bar for 'March' reaches to the line between 15 and 20. How many books were read in March?

Model response: The bar is halfway between 15 and 20. Halfway between 15 and 20 is 17 or 18. Looking carefully, it appears to be at the midpoint, so about 17 or 18 books.

Greater Depth

Choosing an appropriate scale for data and creating a bar chart or pictogram, justifying the scale choice.

Example task

These are the results of a survey: Red 35, Blue 20, Green 15, Yellow 30. Draw a bar chart. What scale will you use? Why?

Model response: I will use a scale of 5 because all the values are multiples of 5, which makes the bars easy to draw accurately. The y-axis goes from 0 to 35 in steps of 5.

CPA Stages

concrete

Collecting real data from class surveys, physically building scaled bar charts using stacking cubes (where each cube represents more than 1), and laying out pictograms with picture cards where each card represents a set number

Transition: Child reads and builds scaled bar charts and pictograms correctly, interpreting half-symbols and values between marked intervals

pictorial

Drawing scaled bar charts and pictograms on paper with correct axis labels, keys and scales, reading values from charts including those between marked scale points

Transition: Child draws scaled charts with correct labels, keys and scales, and reads intermediate values accurately

abstract

Interpreting charts and tables from descriptions or partially given data, choosing appropriate scales for data sets, and reasoning about the advantages of different chart types

Transition: Child selects appropriate scales for given data, interprets charts from descriptions without seeing them, and reasons about chart type choices

Delivery rationale

Primary maths (Y3) with concrete stage requiring physical manipulatives (stacking cubes (Unifix), pictogram picture cards). AI delivers instruction; facilitator sets up materials.

Solving one-step and two-step questions from data

skill AI Facilitated

MA-Y3-C041

Data questions range from one-step (reading a single value directly from a chart) to two-step (reading values from a chart and then performing a calculation, e.g. finding how many more). In Year 3, pupils are explicitly required to solve two-step questions such as 'How many more children chose football than swimming?'. Mastery means pupils can identify which operation to use after reading the relevant values from a chart or table, and can answer both one-step and two-step questions accurately.

Teaching guidance

Teach pupils to first identify what they need to find, then identify which data values they need, then perform the calculation. Model think-alouds: 'I need to find how many more — that's a subtraction. I need to read the value for football (40) and the value for swimming (25). 40 – 25 = 15, so 15 more children chose football.' Use a range of question types: how many altogether (addition), how many more/fewer (subtraction), how many times as many (multiplication). Connect explicitly to the calculation domains.

Vocabulary (13 terms)
altogether T3 — The total when everything is combined; the result of adding all amounts together.
bar chart T3 — A graph that uses rectangular bars of different heights to compare quantities across categories.
data T3 — Information collected and recorded, often as numbers, that can be sorted, compared, and displayed.
difference T3 — The result of subtracting one number from another; how much more or less one number is than another.
fewer than T3 — A smaller number of countable items when comparing two groups.
interpret T3 — To read and make sense of information presented in graphs, charts, tables, or diagrams.
more than T3 — A greater amount; having a larger value.
one-step T3 new — A problem requiring only a single calculation to find the answer.
pictogram T3 — A chart that uses pictures or symbols to represent data, where each symbol may represent one or more items.
question T3 — A mathematical problem to be solved or answered.
table T3 — A way of organising data or numbers in rows and columns for easy reading and comparison.
total T3 — The amount you get when everything is added together.
two-step T3 new — A problem requiring two separate calculations to find the answer.
Common misconceptions

Pupils often read values correctly but then choose the wrong operation: for 'how many more', they may add rather than subtract. For two-step questions, pupils may answer only the first step and stop. When totalling all categories, pupils may read an axis value rather than add up all the bars.

Difficulty levels

Entry

Answering one-step questions by reading a single value directly from a bar chart, pictogram or table.

Example task

A bar chart shows favourite colours. How many children chose blue?

Model response: The bar for blue reaches 12 on the scale. 12 children chose blue.

Developing

Answering 'how many more' or 'how many fewer' questions that require reading two values and subtracting.

Example task

The bar chart shows: Football 25, Swimming 15, Tennis 10. How many more children chose football than tennis?

Model response: Football: 25. Tennis: 10. 25 - 10 = 15. Fifteen more children chose football.

Expected

Solving two-step questions from data, such as finding a total and then comparing, or combining categories before answering.

Example task

A table shows pets: Dogs 18, Cats 12, Fish 8, Rabbits 7. How many more children have dogs or cats than fish or rabbits?

Model response: Dogs + Cats = 18 + 12 = 30. Fish + Rabbits = 8 + 7 = 15. Difference: 30 - 15 = 15 more.

Greater Depth

Interpreting data to answer reasoning and explanation questions, including 'is it true that...' and 'explain why'.

Example task

A pictogram shows: Monday 20, Tuesday 15, Wednesday 25, Thursday 10, Friday 30. A pupil says 'More than half the total ice creams were sold on Wednesday and Friday.' Is this true? Show your working.

Model response: Total = 20 + 15 + 25 + 10 + 30 = 100. Wednesday + Friday = 25 + 30 = 55. Half of 100 = 50. 55 > 50, so yes, more than half were sold on Wednesday and Friday.

CPA Stages

concrete

Answering one-step and two-step questions from physical data displays (cube towers, object pictograms), physically comparing towers or groups to find differences and totals

Transition: Child reads data displays and answers two-step questions by identifying the correct operation (add for 'altogether', subtract for 'how many more'), not just reading a single value

pictorial

Answering one-step and two-step questions from drawn bar charts, pictograms and tables, recording the reading and calculation steps on paper

Transition: Child systematically reads values, identifies the operation needed, calculates and writes the answer for any two-step data question

abstract

Solving multi-step data questions mentally, choosing the correct operations from question language, and explaining which data values are needed and why

Transition: Child interprets 'how many more', 'altogether', 'how many fewer' and 'times as many' correctly, selects the right operation, and solves without needing to see the chart

Delivery rationale

Primary maths (Y3) with concrete stage requiring physical manipulatives (data display (cube bar chart), pictogram with physical objects). AI delivers instruction; facilitator sets up materials.