# Free Critical Maths Resources

Critical Maths is a post-16 mathematical thinking curriculum developed by MEI with DfE funding. The resources have been trialled in schools and are freely available.  They are designed to enable students to think about real problems using mathematics.  Many of the resources start by engaging the students in giving an initial opinion and then encourage them to think more deeply and to evaluate their initial thoughts.

To access the Critical Maths resources on the Integral website, please click the button below:

To read more about the project visit Critical Maths or contact Terry Dawson.

## Mapping to All Core Mathematics Qualifications

Using the table below MEI has tried to show how the DfE funded resources, produced as part of the project to develop the ideas expressed in Professor Sir Timothy Gowers' weblog, relate to the content of the new Core Maths qualifications.

Where the specification has a particular system for referencing the content of the course, we have used these codes to identify the statements applicable to each resource. For example "see section C3 item C3.2, S7 item S7.2",  "IQRs1, and CMs6, 7, 10".

In specifications that don't use a system we have attempted to reference the statements using methods such as ; "see section 6, content under the heading probability and risk"  or, "Probability : Understanding that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size" .

Some of the Critical Maths resources may provide partial coverage of the identified statement. For example consider the statement "calculating and interpreting conditional probabilities through representation using expected frequencies with contingency tables, tree diagrams and Venn diagrams", the identified Critical Maths resource covers conditional probabilities as described using tree diagrams only, further examples will be required to cover all of the statement.

AQA City And Guilds Eduqas EDEXCEL OCR
Statistics (6990) Algebra and Graphs (6991) Decision (6994) Using and Applying Maths Maths for Work and Life Quantitative Reasoning Quantitative Problem Solving
Resource Title References refer to AQA specification
sections
References refer to C&G specification
sections
References refer to Eduqas specification
sections
References refer to Edexcel specification
sections
References refer to OCR specification sections
Business and Risk     See section R7,8,9,10 Section 6 See content under the heading probability and risk Probability : Understanding that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size P7 understand and interpret risk; the probability of something happening
multiplied by the resulting cost or benefit if it does; comparison of levels of
risk; application of risk to real-life contexts such as finance, insurance and
CMp1, 2, 8, 9,
CMe6, 7
IQRu7,u8
IQRu7,u8
Decisions with Risk     See section R7,8,9,10 Section 6 See content under the heading probability and risk Probability : Understanding that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size P7 understand and interpret risk; the probability of something happening
multiplied by the resulting cost or benefit if it does; comparison of levels of
risk; application of risk to real-life contexts such as finance, insurance and
IQRu7,u8
CMs2,
CMp4, 7
CMe7
CMs1
IQRu7,u8
Fermi Estimates See section E2 See section E2 See section E2 Section 6 See content under the heading number, ratio and proportion Number : Working with fractions, decimals and percentages in real-life contexts   IQRe1
CMp1, 2, 3,4, 7,
CMp12,13
CMe1-6
IQRe1
SPSe2
Guessing the Answers See sections S4,R4     Section 6 See content under the heading statistics Probability : Understanding that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size A1 infer properties of populations or distributions from a sample, while knowing the limitations of sampling : P1 understand and demonstrate that empirical unbiased samples tend towards
theoretical probability distributions, as sample size increases.
CMs8,10,
CMp7,9
SPSs8
Making Estimates with Limited Data See section E2 See section E2 See section E2 Section 6 See content under the heading number, ratio and proportion Number : Working with fractions, decimals and percentages in real-life contexts   IQRe1
CMp1, 2, 3,4, 7,
CMp12,13
CMe1-6
IQRe1
SPSe2
Percentage Use and Abuse See section F2 See section F2 See section F2 Section 6 See content under the heading Number, ratio and proportion Number: Working with fractions, decimals and percentages in real-life contexts   IQRf5,6
CMn1,
CMp8,10, 14
IQRf5,6
SPSs11
Product Prices       Section 6 See content under the heading number, ratio and proportion     IQRf13
CMp1, 2,6, 8,13
IQRf13
Representative Data       Section 6 See content under the heading statistics Statistics : Evaluating the weaknesses, strengths and suitability of data   IQRs1
CMs6, 7, 10
IQRs1
SPSs12,s26
Random Controlled Trials       Section 6 See content under the heading statistics Statistics : Evaluating the weaknesses, strengths and suitability of data   IQRs1
CMs6, 7, 10
IQRs1
SPSs12,s26
Regression to the Mean         Statistics : Evaluating the weaknesses, strengths and suitability of data   IQRs1
CMs5,
CMp9
IQRs1
SPSs12,s26
Scams     See section R7,8,9,10 Section 6 See content under the heading probability and risk Probability : Enumerating sets and combinations of sets systematically, using
tables, grids, Venn diagrams and tree diagrams
IQRu1,u2
Cms2,
CMp9,
CMe7
IQRu1,u2
Screening     See section R5,R6 Section 6 See content under the heading probability and risk Probability : Calculating and interpreting conditional probabilities through representation using expected frequencies with ….. tree diagrams ….. P4 calculate and interpret conditional probabilities through representation using
expected frequencies with …., tree diagrams ….
IQRu5,u6
CMu1,u2
CMs2
IQRu5,u6
Valid Arguments See section C3 item C3.2, S7 item S7.2     Section 6 See content under the heading statistics Statistics : Recognising correlation and know that it does not indicate causation. A6 recognise correlation and know that it does not indicate causation CMs3,s4,
CMp9
SPSs12,s25
Voting       Topic 1.1 point 3 : Comparing models     CMp11,6,7
How convincing See section C3 item C3.2  and S5,S6     Section 6 See content under the heading statistics Statistics : Evaluating the weaknesses, strengths and suitability of data   IQRs10,s16
CMs8, 9,
IQRs10,s16
SPSs8,s12
SPSh1