Progression Step 4:

 

Progression Step 4 in the Curriculum for Wales Mathematics and Numeracy Area (typically for ages 11–14, or Year 7–9) focuses on deepening conceptual understanding, increasing fluency, and applying logical reasoning to more abstract concepts. It emphasizes building on prior learning to tackle complex problems, including financial literacy, advanced measurement, and data handling.

 

Key Areas of Learning (Progression Step 4):

• Number System & Relationships: Learners explore relationships within the number system, including working with larger numbers, negative numbers, fractions, decimals, and percentages.
• Algebraic Reasoning: This involves recognizing, copying, generating, and describing rules for patterns and sequences, using symbolic notation to represent relationships.
• Geometry & Measurement: Learning focuses on calculating with 2D and 3D shapes, exploring angle relationships, and using compound measures.
• Statistics & Probability: Learners collect, represent, and interpret data, understanding the role of probability in making decisions.
• Financial Literacy: Understanding budgeting, managing money, and making informed financial decisions.
• The Five Proficiencies: Learning is structured around conceptual understanding, communication using symbols, fluency, logical reasoning, and strategic competence.

 

Hwb resources for Progression Step 4.

 

Skills list for Progression Step 4:

 

The number system:

- I can read and write numbers of any size.

- I can use the terms cube, cube root and reciprocal.

- I can show awareness of the need for standard form and its representation on a calculator.

- I can use and interpret numbers in standard form within calculations.

- I can use rounding to estimate and check answers.

- I can present answers to a given number of decimal places or significant figures.

- I can make and justify estimates and approximations of calculations.

- I can choose the appropriate degree of accuracy to present answers.

 

Relationships within the number system:

- I can use equivalence of fractions, decimals and percentages to select the most appropriate one for a calculation.

- I can recognise that some fractions are recurring decimals, e.g. 1/3 is 0.333333.....

- I can use powers and understand the importance of powers of 10.

 

Calculation:

- I can use the four operations and the connections between them, e.g. apply division as the inverse of multiplication.

- I can use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places.

- I can use appropriate strategies for multiplication and division, including application of known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6.

- I can use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06.

- I can use the order of operations including brackets and powers.

- I can calculate a percentage increase or decrease.

- I can express one quantity as a percentage of another.

- I can calculate percentages of quantities using non-calculator methods where appropriate.

- I can use ratio and proportion including map scales.

 

Financial Literacy:

- I can calculate using foreign money and exchange rates.

- I can make informed decisions relating to discounts and special offers.

- I can carry out calculations relating to VAT, saving and borrowing.

- I can appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing.

- I can understand the advantages and disadvantages of using bank accounts, including bank cards.

- I can understand the risks involved in different ways of saving and investing.

- I can use and understand efficient methods of calculating compound interest.

- I can describe why insurance is important and understand the impact of not being insured.

 

Measurement:

- I can represent and use compound measures, using standard units.

- I can read and interpret scales on a range of measuring instruments.

- I can demonstrate an understanding of the relationship between a formula representing a measurement and the units used.

- I can use the common units of measure, convert between related units of the metric system and carry out calculations.

- I can use rough metric equivalents of imperial units in daily use.

- I can interpret fractions of a second appropriately.

- I can use timetables and time zones to calculate travel time.

- I can convert temperatures between appropriate temperature scales. 

 

Shape and Space:

- I can find circumferences of circles using my understanding of π.

- I can calculate the areas of two-dimensional simple and compound shapes, including circles.

- I can apply the formulae for the volume of simple prisms.

 

Angle:

- I can measure and draw angles.

- I can apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale.

 

Collecting Data:

- I can collect own data for a survey, e.g. through designing a questionnaire.

- I can plan how to collect data to test a simple hypotheses.

- I can collect both quantitative and qualitative data.

 

Representing Data:

- I can select and construct appropriate charts, diagrams and graphs with suitable scales.

- I can construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate.

- I can construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, choosing an appropriate scale.

- I can construct graphs to represent data including scatter diagrams to investigate correlation.

 

Interpreting Data:

- I can interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading.

- I can interpret mathematical information; drawing inferences from graphs, diagrams and data, including discussion on limitations of data.

- I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain.

- I can use mean, median, mode and range to compare data (continuous and discrete), and can choose the most appropriate average.

- I can explore trends and extreme values (outliers) for data sets.

- I can examine results critically, select and justify choice of statistics, recognising the limitations of any assumptions and their effect on the conclusions drawn.