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# Mathematics

### Objectives in mathematics:

Mathematics, the world’s most useful subject.

Mathematics makes our life orderly and prevents chaos.

Qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract and spatial thinking, critical thinking, problem-solving abilities and even effective communication skills.

Mathematics is the birthplace of all invention, without which the world cannot move a millimetre.

Be it a chef or a farmer, a carpenter or a mechanic, a shopkeeper or a doctor, an engineer or a scientist, a musician or a magician, everyone needs mathematics in their day-to-day life.

Key Stage 3 - Working mathematically at Ibstock Community College

Through the mathematics content, pupils will be taught to:

Develop fluency

Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots.

Select and use appropriate calculation strategies to solve increasingly complex problems

Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Substitute values in expressions, rearrange and simplify expressions, and solve equations.

Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].

Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.

Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.

Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.

Identify variables and express relations between variables algebraically and graphically.

Make and test conjectures about patterns and relationships; look for proofs or counter-examples.

Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.

Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.

Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.

Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.

Begin to model situations mathematically and express the results using a range of formal mathematical representations.

Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Develop Mastery

Maths teaching for mastery rejects the idea that a large proportion of people ‘just can’t do maths’.

All pupils are encouraged by the belief that by working hard at maths they can succeed.

Pupils are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time, as happens in Shanghai and several other regions that teach maths successfully. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind.

If a pupil fails to grasp a concept or procedure, this is identified quickly and early intervention ensures the pupil is ready to move forward with the whole class in the next lesson.

Lesson design identifies the new mathematics that is to be taught, the key points, the difficult points and a carefully sequenced journey through the learning. In a typical lesson pupils sit facing the teacher and the teacher leads back and forth interaction, including questioning, short tasks, explanation, demonstration, and discussion.

Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.

It is recognised that practice is a vital part of learning, but the practice used is intelligent practice that both reinforces pupils’ procedural fluency and develops their conceptual understanding.

Significant time is spent developing deep knowledge of the key ideas that are needed to underpin future learning. The structure and connections within the mathematics are emphasised, so that pupils develop deep learning that can be sustained.

Key facts such as multiplication tables and addition facts within 10 are learnt to automaticity to avoid cognitive overload in the working memory and enable pupils to focus on new concepts.