In this lesson, the class applies their understanding of the strategy of bridging to solving problems with fractions. Throughout the lesson, the teacher ensures that the class has a sound conceptual understanding of fractions, supporting this with the use of concrete representations and checking their understanding of mathematical terms in relation to fractions.

Learning to bridge when adding fractions

The pedagogical strategies featured in this video include:

• Using concrete representations to support students’ understanding of maths concepts
• Integrating multiple representations to develop students’ ability to think flexibly
• Checking student understanding at every step to support them to master new material
• Focusing on correct mathematical language to ensure sound understanding of mathematical concepts and procedures

This lesson begins with a review of the previous day’s learning. The teacher reminds the class that they are using the strategy of bridging to solve problems, and tells them that today’s lesson will involve the same strategy but a different type of number – fractions. She begins by checking the students’ conceptual understanding of fractions, using a multipack of crisps to model the concept of a whole divided into parts, and Numicon blocks to provide a concrete representation of fractions. At the same time she is checking their use of the language of fractions – for example, she is careful to correct a student who says ‘six thirds’ instead of ‘three sixths’. She also explicitly ensures that the class understands the terms ‘mixed number’ and ‘improper fraction’, as well as their understanding that the different representations of the same number are equivalent (in this example, she ensures that they understand that 1 ³⁄₆ = ⁹⁄₆). This is important because the students need a sound conceptual understanding of fractions in order to work with them fluently.

Practising bridging with fractions

The evidence-informed approaches you will notice in this video include:

• Using concrete representations to build conceptual understanding
• Asking questions to check for student understanding and ensure they are learning new material effectively
• Providing fully worked examples to support students’ conceptual and procedural understanding
• Asking questions to check for conceptual and procedural understanding
• Guiding student practice to support their procedural learning
• Talking to students about their learning and confidence, which helps build their academic self-concept and mathematical identity

In order to consolidate their conceptual understanding of fractions, the teacher begins this session by having all the students ‘build’ the fractions in the practice problem using manipulatives (Numicon blocks), and then add them. She also explicitly models making improper fractions with materials, both to support their conceptual understanding of fractions and to ensure that the students understand how to use the materials correctly. In the next part of the session, the students practise representing the fractions with Numicon blocks and then writing the numerals on whiteboards in order to build their conceptual understanding by integrating concrete and abstract representations. Only once this foundational work has been done does the teacher move on to subtracting fractions.

You might notice a student use the expression ‘tidy number’ when bridging, which is a hangover from a previous approach to teaching bridging. Throughout this week’s lessons, the teacher makes a deliberate effort to move on from the use of this term, replacing it with specific mathematical terms such as ‘whole number’ and ‘multiple of ten/one hundred’. She similarly encourages the students to use the term ‘subtract’ rather than the more colloquial ‘take away’. The research on effective maths teaching emphasises the need to use and ensure students understand the language of mathematics, and this is a good example of the teacher explicitly replacing generic language with specific mathematical vocabulary and ensuring students understand its meaning.

Towards the end of this video, the teacher checks in with the students to see how they are feeling about the maths work they have been doing in the lesson, and suggests some courses of action if they are not feeling confident (such as asking for help from the teacher or a peer). Paying attention to how students feel about maths, and normalising the use of help-seeking, helps to build their mathematical identities.

Focusing on the language of mathematics

In this video you will observe the teacher:

• Exploring mathematical vocabulary to ensure clarity and understanding
• Asking many questions to continually check the students’ understanding

In this short video, the teacher invites the students to spend the final part of the lesson focusing on and exploring their understanding of the language of mathematics. The class explores the terms ‘fraction’ and ‘whole number’, offering explanations and providing examples. This helps to further develop their conceptual understanding as well as building their fluency in using mathematical vocabulary.