HTO + HTO (which show carrying shown clearly and visually) Visual addition using place value disks Suitable for mastery of maths and supporting conceptual understanding of addition with carrying. Subtraction using place value disks (with exchanging/regrouping shown clearly and visually) Suitable for mastery of maths and supporting conceptual understanding of subtraction with exchanging/regrouping. Suitable for any aged child tackling these concepts, particularly useful in Lower Key Stage Two. PPT presentation can be modified/adapted to make other calculations to use as examples.

Mastery Lesson Plans Topic: short multiplication Age group: initially taught in Lower KS2, but could also be used as revision for Y5/6 pupils, before teaching the next stage of multiplication (long multiplication). The UK National Curriculum states that pupils should be fluent in mathematical facts (addition and subtraction within 20 is a vital part of this). This lesson sequence uses many elements of teaching for mastery in order to achieve this fluency: • Small steps – each stage of teaching sequence has been carefully planned to build on pupils’ prior knowledge and understanding. • Balance between factual fluency and conceptual understanding with carefully thought about reasoning questions, which allow pupils to understand concepts at a deeper level. • Procedural Variation – Questions/calculations are chosen carefully in order that as well answering them accurately, pupils will also begin to understand the deeper mathematical structures. As the Japanese say: The answer is only the beginning. • Conceptual Variation – The same mathematical concept is presented and proven in different ways so that pupils can make sense of it. Pack includes: • Smart notebook with resources and question ideas – QUESTIONS/ACTIVITIES: step by step approach to ensure children have a clear conceptual and procedural understanding of short multiplication • PPT (with moving animations) clearly shows concept of regrouping when multiplying.

Representation and Structure, Variation, Coherence, Fluency and Mathematical Thinking Detailed planning for a sequence of lessons covering the transition between fluent short multiplication and long multiplication. Misconceptions, visual images, procedural variation (intelligent practice), carefully designed lesson sequence including fluency, reasoning and problem solving.

Mastery Lesson Plans Topic: addition and subtraction facts to 20. Age group: initially taught in KS1, but could also be used as revision for Y3/4 pupils, before teaching the next stage of addition/subtraction (formal algorithms). The UK National Curriculum states that pupils should be fluent in mathematical facts (addition and subtraction within 20 is a vital part of this). This lesson sequence uses many elements of teaching for mastery in order to achieve this fluency: • Small steps – each stage of teaching sequence has been carefully planned to build on pupils’ prior knowledge and understanding. • Balance between factual fluency and conceptual understanding with carefully thought about reasoning questions, which allow pupils to understand concepts at a deeper level. • Procedural Variation – Questions/calculations are chosen carefully in order that as well answering them accurately, pupils will also begin to understand the deeper mathematical structures. As the Japanese say: The answer is only the beginning. • Conceptual Variation – The same mathematical concept is presented and proven in different ways so that pupils can make sense of it. Pack includes: • Lesson plans (arranged by each small step, rather than by day) • Procedural Variation questions (see NCETM’s definition of intelligent practice) • Smart notebook with resources and question ideas

Lesson showing progression from column addition without regrouping to with regrouping, Representation and structure to support students' understanding.

3ppt files suitable for introducing fractions to pupils in Year 3/4. Could be used as revision for other year groups, or as an example of how to structure teaching towards Mastery approach. The files have been created following the Mastery approach. Reasoning at greater depth, Concrete-pictorial-abstract, procedural variation (intelligently designed questions and activities), small steps to ensure pupils make links between new learning and prior understanding. Supports FLUENCY, REASONING, PROBLEM SOLVING approach. PPT animations reveal answers and images 'on click' for ease of use in the classroom. 1 - Unit fractions - recognise, label, compare unit fractions (1/2, 1/3 1/4 etc) 2- Non-unit fractions - introduces pupils to the concept of two 1/3 recorded as 2/3: recognise, label, compare. 3- Improper fractions - develops children's understanding with visual representations of improper fractions an how they can be recorded as mixed fractions/numbers. The lessons have been carefully designed from a unit plan (handwritten medium term plan) which has been included.

Topic: place value – understanding/representing value of digits (Th H T O) Age group: Aimed at Y4 standard (4 digits), but could also be used as revision for Y3 pupils, as many of the resources can be adapted to represent 3 digits. The UK National Curriculum states that pupils should be fluent in mathematical facts (a deep and clear understanding of place value is vital to this). This lesson sequence uses many elements of teaching for mastery in order to achieve this fluency: • Small steps – each stage of teaching sequence has been carefully planned to build on pupils’ prior knowledge and understanding. • Balance between factual fluency and conceptual understanding with carefully thought about reasoning questions, which allow pupils to understand concepts at a deeper level. • Procedural Variation – Questions/calculations are chosen carefully in order that as well answering them accurately, pupils will also begin to understand the deeper mathematical structures. As the Japanese say: The answer is only the beginning. • Conceptual Variation – The same mathematical concept is presented and proven in different ways so that pupils can make sense of it. Pack includes: • Lesson plans (arranged by each small step, rather than by day) • Smart notebook with resources and question ideas – vast range of images of equipment which can be dragged, edited etc. base ten blocks, place value counters, place value arrows etc.

Planning and two detailed (50+ pages altogether) powerpoint presentations with animations. Lesson plans and sequence follow the Mastery approach which has used best practice used in Singapore, Shanghai,,, Representation and structure, procedural variation, coherently planned lesson sequence. Fluency, reasoning and problem solving Topics covered: Parts and wholes, unit fractions, non-unit fractions, equivalence (simplifying and expanding), ordering and comparing fractions. Ideal (for teaching or revision) for all KS2 classes.

Topic: multiply and divide by ten Age group: Aimed at Y4 standard (4 digits), but could also be used as revision for Y5/6 pupils, as many of the resources can be adapted to represent 3 digits. The UK National Curriculum states that pupils should be fluent in mathematical facts (a deep and clear understanding of place value is vital to this). This lesson sequence uses many elements of teaching for mastery in order to achieve this fluency: • Small steps – each stage of teaching sequence has been carefully planned to build on pupils’ prior knowledge and understanding. • Balance between factual fluency and conceptual understanding with carefully thought about reasoning questions, which allow pupils to understand concepts at a deeper level. • Procedural Variation – Questions/calculations are chosen carefully in order that as well answering them accurately, pupils will also begin to understand the deeper mathematical structures. As the Japanese say: The answer is only the beginning. • Conceptual Variation – The same mathematical concept is presented and proven in different ways so that pupils can make sense of it. Pack includes: • Lesson plans (arranged by each small step, rather than by day) • PPT presentation, with full animations showing effect of multiplying by ten and hundred in memorable visual way, supportive of conceptual understanding. • Smart notebook with resources and question ideas – vast range of images of equipment which can be dragged, edited etc. base ten blocks, place value counters, place value arrows etc.

A fully-editable KS2 Maths arithmetic paper with questions matched to the 2017 paper. Ideal for gap analysis and targeted teaching to prepare students for the arithmetic paper. A revision overview for the reasoning and arithmetic papers is also included. Also included in this are some basic Notebook files with some question types.