Statistics

Status: Mandatory

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Concepts

This study delivers 6 primary concepts and 0 secondary concepts.

Primary concept: Pie Charts (MA-Y6-C020)

Type: Skill | Teaching weight: 3/6

Mastery of pie charts means pupils can read values from a pie chart by using the proportion that each sector represents (expressed as a fraction, decimal, or percentage), construct pie charts by calculating the angle for each sector from data, and evaluate critically whether a pie chart is an appropriate representation for a given dataset. A fully secure pupil connects pie chart interpretation to their fraction, percentage and angle knowledge, recognising that the whole circle represents the total frequency.

Teaching guidance: Introduce pie charts using data sets where the total is 36 (so angles are multiples of 10°) or 100 (so percentages convert directly to angles using the conversion 1% = 3.6°). Before constructing, pupils must understand that the whole circle is 360° and that each sector's angle is calculated as (frequency ÷ total) × 360°. Reading pie charts requires the reverse: finding the frequency from the angle as (angle ÷ 360°) × total. Connect to angle measurement: pupils should measure and draw sectors using protractors. Discuss when pie charts are appropriate (comparing proportions of a whole) and when they are less appropriate (very many categories, or when exact values matter). Key vocabulary: pie chart, sector, angle, proportion, frequency, total, percentage, fraction, circle graph, protractor Common misconceptions: Pupils often read the sector angle as the data value, rather than using it to calculate the proportion. When constructing pie charts, pupils sometimes add frequencies directly rather than converting to angles first. Some pupils assume all sectors in a pie chart represent equal proportions unless clearly different sizes are visible, and fail to read angles carefully with a protractor. The key conceptual understanding to reinforce is that the whole circle = 360° = total frequency = 100%.

Differentiation

Model response (Entry): 50% of 40 = 20 children.

Model response (Developing): Red: (10/36) × 360 = 100°. Blue: (15/36) × 360 = 150°. Green: (5/36) × 360 = 50°. Yellow: (6/36) × 360 = 60°. Check: 100 + 150 + 50 + 60 = 360°.

Model response (Expected): 90° out of 360° = 1/4. 1/4 of 48 = 12 children chose swimming. You cannot compare the two pie charts directly by looking at sector size because they represent different totals — you need to calculate the actual numbers.

Representation stages (CPA)

Primary concept: The Mean as an Average (MA-Y6-C021)

Type: Skill | Teaching weight: 3/6

Mastery of the mean means pupils can calculate the mean of a data set (sum of values ÷ number of values), interpret it as the value each item would take if all items were equal (the 'fair share' or 'levelling' interpretation), and use the mean to compare two data sets. A fully secure pupil understands that the mean may not be a value that appears in the data set, can work backwards from the mean to find a missing value, and knows when the mean is and is not an appropriate measure of average.

Teaching guidance: Introduce the mean through the 'levelling' metaphor: if 5 pupils have different numbers of stickers, the mean is the number each would have if they redistributed stickers equally. Physical or pictorial representations (towers of cubes being levelled) make this concrete. Progress to the calculation procedure (add all values, divide by number of values) and connect this to the levelling process. Extend to finding a missing value given the mean and all other values — this involves working backwards (total = mean × n; missing value = total − sum of known values). Compare the mean with the median and mode briefly to establish that 'average' does not always mean 'the most common' or 'the middle value'. Key vocabulary: mean, average, sum, total, data set, fair share, levelling, missing value, median, mode Common misconceptions: Pupils commonly confuse mean with mode (most frequent) or median (middle value), particularly if they have encountered all three measures without clear differentiation. When finding the mean, pupils sometimes add correctly but then divide by a number other than the count of values (e.g., dividing by the range, or by the largest value). The reverse problem — finding a missing value given the mean — is often approached by guessing rather than by using the total. Explicit recording of the calculation as a sequence of steps prevents most procedural errors.

Differentiation

Model response (Entry): Sum: 4 + 7 + 9 + 8 + 2 = 30. Count: 5. Mean: 30 ÷ 5 = 6.

Model response (Developing): Total must be 5 × 8 = 40. Known total: 6 + 9 + 10 + 7 = 32. Fifth score: 40 – 32 = 8.

Model response (Expected): Group A mean: 35 ÷ 5 = 7. Group B mean: 28 ÷ 4 = 7. Both groups have the same mean, but Group B has more spread.

Representation stages (CPA)

Primary concept: Introduction to Probability (MA-Y6-C025)

Type: Knowledge | Teaching weight: 2/6

Mastery at Year 6 level means pupils understand that the likelihood of an event can be described on a scale from impossible (0) to certain (1) and that simple equally likely outcomes can be listed and counted to determine the probability of an event. A fully secure pupil can place events on a probability scale using appropriate vocabulary, list all outcomes of a simple experiment (such as rolling a die or tossing a coin), and express the probability of a specific outcome as a fraction of the total number of equally likely outcomes.

Teaching guidance: Introduce probability through familiar games and experiments. Use a probability line (from 0 to 1 or from 'impossible' to 'certain') on which pupils place event cards. Conduct simple experiments — rolling dice, drawing coloured counters from a bag — and compare experimental results with theoretical probabilities to establish that probability describes long-run relative frequency. Systematic listing of all possible outcomes using a sample space diagram or list is the key skill; emphasise the need to be exhaustive and to avoid double-counting. Connect fractions work to probability: the probability of getting a 3 on a fair die is 1/6, where 1 is the number of favourable outcomes and 6 is the total number of equally likely outcomes. Note: while probability is not a named Year 6 statutory domain, it is explicitly covered in the non-statutory guidance and forms an important bridge to KS3. Key vocabulary: probability, likelihood, certain, impossible, even chance, unlikely, likely, outcome, equally likely, sample space, event, fraction Common misconceptions: Pupils often believe that outcomes in a random experiment must alternate (the 'gambler's fallacy': 'I've had three tails so the next must be a head'). They may also incorrectly assume that all events are equally likely (a die is more likely to show a 6 than any other number, some pupils think, because 6 is a special number). When listing outcomes, pupils commonly miss some possibilities or count the same outcome twice. Using a structured sample space grid or tree diagram prevents incomplete listing.

Differentiation

Model response (Entry): Rolling a 7: impossible. Getting heads: even chance. Sun rising: certain.

Model response (Developing): Total counters: 3 + 5 = 8. P(red) = 3/8.

Model response (Expected): P(blue) = 90/360 = 1/4 = 0.25 = 25%.

Representation stages (CPA)

Primary concept: Describing and Comparing Data Distributions (MA-Y6-C026)

Type: Skill | Teaching weight: 3/6

Mastery means pupils can describe the overall distribution of a data set — its range, any clusters or gaps, whether data is spread widely or bunched together — and compare two data sets by considering both their measures of average and their spread. A fully secure pupil understands that comparing two groups requires examining both the typical value (mean, median or mode) and how spread out the data is (range), and can articulate what a difference in mean or range implies about the groups being compared.

Teaching guidance: Use real data sets from meaningful contexts: comparing heights, journey times, test scores of two groups. Ask pupils to make comparisons before introducing vocabulary, then formalise the language of distribution. Ensure pupils understand that range alone does not describe a distribution adequately — two data sets can have the same range but very different spreads. Use back-to-back stem-and-leaf diagrams or side-by-side dot plots for comparison. Require pupils to write comparative statements in the form 'On average, Group A... because..., however Group B has a greater/smaller spread because...'. Connect to the statistics objectives for pie charts and line graphs introduced in Year 6. Key vocabulary: distribution, range, spread, cluster, gap, compare, average, mean, median, mode, data set, outlier Common misconceptions: Pupils commonly compare two data sets using only the mean, ignoring the spread. They may confuse range (a measure of spread) with average. Some pupils state comparisons without referring to the context — 'Group A has a higher mean' without explaining what this means for the groups being compared. Requiring contextualised conclusions addresses this weakness.

Differentiation

Model response (Entry): Range = 11 – 3 = 8. The data is spread over 8 units.

Model response (Developing): Team A: mean = 4, range = 4. Team B: mean = 4, range = 7. Same average, but Team B is more spread out — their scores are less consistent.

Model response (Expected): Most scores cluster between 67 and 72. There are two outliers: 45 (low) and 95 (high). Mean = 488/7 ≈ 69.7. The mean is reasonably representative because it is in the cluster, but the two outliers pull it slightly. The median (70) might be more representative.

Representation stages (CPA)

Primary concept: Median and Mode as Averages (MA-Y6-C027)

Type: Knowledge | Teaching weight: 2/6

Mastery means pupils can identify the mode (the value that occurs most frequently) in a data set and find the median (the middle value when data is ordered) for both odd and even counts of values, and can explain why the mean, median and mode can give different values for the same data set. A fully secure pupil understands when each average is most appropriate to use — the mode for categorical data, the median when there are extreme outliers, the mean when the data is relatively evenly spread — and interprets measures of average critically rather than applying them mechanically.

Teaching guidance: Build on the formal treatment of the mean introduced in the Year 6 statistics domain by contrasting it with median and mode using the same data sets. Use data with outliers to show how the mean is pulled away from the centre while the median is not, making the median a more representative average for skewed data. Use categorical data to illustrate the mode (e.g., most popular colour, most common shoe size). For the median, emphasise the procedure: order all values, count to find the middle position. With an even count, the median is the mean of the two middle values — though this can be introduced as an extension. Discuss which average would be used in real contexts: average house price (median), average shoe size (mode), average test score (mean). Key vocabulary: median, mode, mean, average, representative, ordered, middle value, frequency, outlier, appropriate Common misconceptions: Pupils frequently confuse median and mode, particularly since both can be described as 'middle' in informal terms. When finding the median, pupils often forget to order the data first, producing incorrect results. With an even number of values, pupils may choose one of the two middle values arbitrarily rather than averaging them. Some pupils believe the mode is always the most appropriate average regardless of context.

Differentiation

Model response (Entry): The mode is 3 because it appears 3 times, more than any other value.

Model response (Developing): Ordered: 2, 3, 5, 7, 8, 11. Even count (6 values): median is the mean of the 3rd and 4th values = (5 + 7) ÷ 2 = 6.

Model response (Expected): Mode = 5 (most common). Median = 5. Mean = 52/9 ≈ 5.8. The mean is pulled up by the outlier (12). The mode or median (both 5) better represent the typical shoe size.

Representation stages (CPA)

Primary concept: Interpreting and Constructing Statistical Charts and Graphs (MA-Y6-C028)

Type: Skill | Teaching weight: 3/6

Mastery means pupils can read, interpret and construct a range of statistical representations including pie charts, line graphs, bar charts and tables, moving fluently between the data and its representation to answer questions and draw conclusions. A fully secure pupil understands the purpose of each representation (pie charts for proportions, line graphs for change over time, bar charts for comparing discrete categories), can identify when a representation is misleading or inappropriate, and can select the most suitable representation for a given data set and purpose.

Teaching guidance: Ensure all four representations are treated as a connected repertoire rather than isolated skills. Pose questions that require pupils to choose which representation to use, justifying their choice. Include misleading graphs (truncated y-axes, unequal intervals) and ask pupils to identify and explain why they are misleading — this deepens understanding of what features of a graph convey accurate information. For pie charts, connect explicitly to angle (total = 360°) and fraction/percentage equivalences. For line graphs, discuss what the gradient (steepness of the line) means in context (rate of change). Use digital tools to create and modify graphs, discussing how changing the scale changes the visual impression. Key vocabulary: pie chart, line graph, bar chart, table, frequency, proportion, scale, axis, title, misleading, representation, interpret, construct Common misconceptions: Pupils commonly read individual data points from a line graph rather than interpreting the trend or rate of change. They frequently confuse discrete and continuous data, applying bar charts to continuous data or histograms to discrete data. When constructing graphs, pupils often neglect titles, axis labels, and appropriate scales. The most important conceptual gap is between reading a graph and using a graph to compare, predict or identify patterns.

Differentiation

Model response (Entry): 8 children chose fish. [Reads from the top of the 'fish' bar to the y-axis]

Model response (Developing): [Draws bar chart with y-axis going up in 2s from 0 to 16, bars at correct heights, labelled axes and title]

Model response (Expected): Starting the y-axis at 995 exaggerates the visual difference between bars. A rise from 998 to 1002 looks like a doubling when the y-axis starts at 995, but it is actually a tiny change relative to the total.

Representation stages (CPA)

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Thinking lens: Scale, Proportion and Quantity (primary)

Key question: How big, how many, or how much — and how does that change how we think about it? Why this lens fits: Probability language (certain, likely, unlikely, impossible) and early probability as a fraction both require proportional reasoning — expressing likelihood as a number between 0 and 1 connects distributional description to the probability scale. Question stems for KS2:

How many times bigger is this than that?

What fraction of the whole is this part?

Which unit of measurement fits best here? Why?

If we doubled the amount, what would change?

Secondary lens: Evidence and Argument — Comparing two distributions requires constructing an evidence-based argument using averages and range — 'Group A performed better on average, but Group B was more consistent' is a statistical claim that must be justified from the data.

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Session structure: Practical Application + Secondary Data Analysis

This study uses 2 vehicle templates:

Practical Application (main structure)

A hands-on sequence where pupils apply knowledge and skills to solve a practical problem or create a functional outcome. Begins with a real-world context, builds skills through rehearsal, guides design or planning, supports making or problem-solving, and concludes with evaluation against success criteria.

context → skill_rehearsal → design → make_or_solve → evaluate Assessment: Practical outcome (solution, product, program) evaluated against defined success criteria, with written or verbal explanation of the process and decisions made. Teacher note: Use the PRACTICAL APPLICATION template: set a real-world context or problem that requires pupils to apply knowledge and skills. Rehearse the key skills needed through guided practice. Support pupils in designing their approach, carrying out the practical task, and evaluating their outcome. Encourage them to explain what worked well and what they would improve. KS2 question stems:

What skills will you need to solve this problem?

What is your plan, and why did you choose this approach?

How well did your solution work?

What would you change if you did it again?

Secondary Data Analysis

An enquiry using existing published data sets rather than first-hand collection. Pupils frame an enquiry question, select and evaluate appropriate data sources, process and present data using statistical or graphical methods, analyse patterns and anomalies, evaluate reliability, and present findings.

question_framing → data_selection → processing → analysis → evaluation → presentation Assessment: Data analysis report including processed data presented in appropriate formats, statistical analysis where relevant, interpretation of findings, and evaluation of data reliability and limitations.

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Mathematical reasoning skills (KS2)

These disciplinary skills should be woven through teaching, not taught in isolation:

Checking and verifying results — Use inverse operations, estimation or an alternative method to check whether a result is reasonable, and adjust working when an answer does not make sense in context.

Problem solving with unfamiliar and complex structures — Formulate and solve problems that require choosing from a wide range of mathematical knowledge, devising strategies for problems with no immediately obvious method, and persevering through multi-stage solutions in unfamiliar contexts.

Mathematical proof — Understand and apply the concept of mathematical proof, distinguishing between evidence, conjecture and proof, constructing simple proofs by exhaustion or direct argument, and recognising why a finite number of examples cannot prove a universal statement.

Critical evaluation and error analysis — Critically evaluate the validity of mathematical arguments and solutions presented by others, identifying errors in reasoning or calculation, explaining why a result is or is not correct, and constructing counter-examples to disprove false claims.

Algebraic reasoning and generalisation — Express generalisations symbolically using algebraic notation, reason about the properties of unknown quantities, and use algebra to prove or disprove conjectures about numbers and geometric relationships.

Estimation, checking and reasonableness — Use rounding, inverse operations and known facts to estimate answers before calculating, check the reasonableness of results in context, and identify errors in worked examples by comparing expected and actual outcomes.

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Vocabulary word mat

Prior knowledge (retrieval plan)

Pupils should already know the following from earlier units:

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Assessment alignment (KS2)

KS2 test framework content domain codes assessed by this study:

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Scaffolding and inclusion (Y6)

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Knowledge organiser

Core facts (expected standard):

Pie Charts: Interpreting pie charts to find missing values and comparing pie charts that represent different-sized groups.

The Mean as an Average: Using the mean to compare two data sets and understanding that the mean may not be a value in the data set.

Introduction to Probability: Calculating probabilities of single events as fractions, decimals or percentages, and understanding that all probabilities sum to 1.

Describing and Comparing Data Distributions: Describing distributions using language of clusters, gaps and spread, and making justified comparisons between data sets.

Median and Mode as Averages: Explaining when each average (mean, median, mode) is most appropriate and selecting the best one for a given data set.

Interpreting and Constructing Statistical Charts and Graphs: Choosing the appropriate chart type for different data, identifying misleading features in given charts, and drawing conclusions from data.

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Graph context

Node type: MathsTopicSuggestion | Study ID: MTS-Y6-009 Concept IDs:

MA-Y6-C020: Pie Charts (primary)

MA-Y6-C021: The Mean as an Average (primary)

MA-Y6-C025: Introduction to Probability (primary)

MA-Y6-C026: Describing and Comparing Data Distributions (primary)

MA-Y6-C027: Median and Mode as Averages (primary)

MA-Y6-C028: Interpreting and Constructing Statistical Charts and Graphs (primary)

Cypher query:

``cypher

MATCH (ts:MathsTopicSuggestion {suggestion_id: 'MTS-Y6-009'})

-[:DELIVERS_VIA]->(c:Concept)

-[:HAS_DIFFICULTY_LEVEL]->(dl)

RETURN c.name, dl.label, dl.description

``

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Generated from the UK Curriculum Knowledge Graph — zero LLM generation.