How should I identify the key point of a Mathematics lesson?
Each lesson should have a simple, clear outcome, which helps to form the building blocks of an objective. This key point should be identified by considering what we want the pupils to be able to understand/do/know confidently by the end of lesson? For example, in Year 3, over a series of lessons, one objective is for pupils to be able to add a single digit to a three-digit number. In order to achieve this, pupils must first be provided with opportunities to add a single digit to a three-digit number without ‘bridging over ten’ e.g. 272 + 6. The key point of this part of the objective is to identify that the only change will be of the digits in the ‘ones’ place-value column. Pupils will achieve this through the exploration and evaluation of a variety of concrete, pictorial and abstract representations. In the next series of lessons, pupils will then move on to adding a single digit to a three-digit number with bridging over ten e.g. 275 + 8. This skill draws on their previous experience and knowledge of key ‘small facts’ at Y1. Again, pupils will achieve this through the exploration and evaluation of a variety of concrete, pictorial and abstract representations.
How will pupils develop their fluency skills?
Pupils will be provided with a daily opportunity to develop, practise and consolidate their fluency skills in order to identify and apply ‘small facts’. This will help them to make connections to the wider contexts of Maths. The teaching and learning of key facts will be used in conjunction with the Fluency progression document* and will be tracked throughout school. *This is currently being developed by the Core Maths Team.
How do I avoid pupils making the same mistakes over again?
Misconceptions will be directly targeted using the Power Maths Teaching Guide and provide opportunities for pupils to encounter, discuss and solve them.
How can I use effective questioning to strengthen and deepen understanding?
The use of precise, targeted and probing questioning during lessons will ensure that pupils develop technical proficiency and think deeply about mathematical concepts. Throughout each lesson plan, Power Maths provides effective question prompts that support and challenge pupils. Teachers will supplement these using ‘How’ and ‘Why’ question starters to aid the extraction of deeper responses. ‘If you know this, what else do you know?’ helps pupils make connections to other concepts. Using questioning forms part of our planning evidence for the specific cohort we are teaching and should be included on our lesson materials. See ‘Maths Questioning Template’ for further examples.
How will pupils access concrete, pictorial and abstract learning?
(All pupils will need to access each stage but some may progress quicker than others to the abstract)
Concrete
This is the first step in learning and is a crucial foundation in supporting and embedding conceptual understanding. We will provide the most appropriate manipulatives for all pupils to use. Place value counters, place value charts, dienes apparatus, multi-link, strips of papers and washing lines are just some of the examples that will be available to pupils in their Maths Boxes (table-top resource boxes). When used as part of everyday practice, pupils will develop the confidence to use them purposefully to make representations of their learning. Power Maths also provides a list in each lesson of resources to aid pupils understanding. The examples in the ‘Discover’ section of Power Maths can be used to create a physical demonstration of a representation
Pictorial
Pupils should be introduced to a variety of representations at each stage of their learning. These include: part-whole models, tens frames, drawing of objects (e.g. dinosaurs with spots on), subitisation, arrays, bar modelling, number lines, partitioning and extended column methods (e.g. using place value counters or dienes to make a column addition). Isolating these images for pupils to discuss and interpret using the Power Maths online textbook and tools section as well as ‘screenshotting’ them is essential. Pupils should be given the opportunity to represent these pictorial concepts (e.g. through journaling). Teachers should develop a working wall to capture a variety of representations that are used and discussed within the lesson. This allows pupils to make reference to them as they progress through the unit. Teachers will be provided with flipchart paper to record these collective responses.
Abstract
Pupils will use abstract methods as an efficient way of representing their in-depth understanding of concepts and calculation methods. Importantly, pupils should be able to relate abstract methods back to pictorial and concrete representations, explaining how they link together. Pupils will be given the opportunity to evaluate different methods and identify which method/representations are most efficient or best to use. We will also adhere to the Power Maths Calculation Policy.
Support
How will pupils be supported in lessons?
Pupils will be well supported during lessons in a variety of ways. These include sitting in mixed ability pairings with a carefully selected Learning Partner. Each lesson will provide opportunities for Learning Partner activities and discussion to take place during the first phase of the lesson. The deployment of Teacher and Teaching Assistant support will be carefully considered to target and monitor pupils who may require additional support. The ‘strengthening’ activities in the Power Maths program provide opportunities for pupils to receive pre-teaching and same-day intervention sessions. Each classroom’s mathematical environment will also play a key role in supporting pupils. ‘Working walls’ will be used to support learners with current representations, vocabulary, steps to success etc. Displays will be fluid and interactive, changing regularly to reflect current learning.
Challenge
How will I provide opportunities to challenge and deepen pupils’ understanding?
Pupils working at greater depth or who have the potential to work at greater depth will also be challenged in lessons in a variety of ways. These include the use of targeted questioning to deepen their understanding. Working with Learning Partners offers pupils working at greater depth the opportunity to explain their mathematical thinking to others, whilst assisting them. Pupils will be signposted to challenge tasks within the ‘Think Together’ section, as well as accessing the ‘deepening’ resources in Power Maths. Furthermore, pupils will be able to access additional learning materials using the ‘Build a Sequence’ resources.
Resources
How can I resource Mathematics in my classroom?
All pupils will have access to concrete and pictorial resources stored in table-top resource boxes. These boxes will be regularly adapted, depending on the theme of the lesson. Teachers will receive flipchart paper or an equivalent to capture representations, discussion points and agreed steps to success to enable pupils to refer to them. To ensure pupils have adequate concrete materials, an inventory and wish list will be used to monitor resources throughout the school. We acknowledge that in order for pupils to gain the most out the Power Maths program, our long–term goal is to provide them with shared access to a textbook (one between two). Pupils in Reception and Years 1 to 3 will work directly from pupil books. Pupils in Years 4 to 6 will transfer questions and answers in an appropriate fashion into squared Maths books.
