Day 4: Bridging when adding decimals

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In this lesson, the class builds on the previous day’s work by learning to bridge with decimals. The teacher begins by creating a context for the use of decimals by having the students measure different items with a ruler and then find their combined length. Throughout this lesson, the teacher continues to use research-backed pedagogical practices by systematically teaching new procedures in small steps, explicitly teaching and modelling both the procedures and the use of manipulatives to represent problems, asking lots of questions to check the students’ understanding, and using concrete, visual, and abstract representations to support students’ understanding.

Learning to bridge when adding decimals

The following pedagogical strategies are evident in the video:

  • Using concrete representations to support students’ conceptual understanding
  • Using correct mathematical language to consolidate students’ understanding of concepts
  • Providing fully worked examples to build students’ conceptual and procedural understanding
  • Integrating concrete and visual representations to help develop flexible thinking

This lesson on bridging with decimals begins with the students taking measurements with a ruler. This places the use of decimals in context by demonstrating when students would use and add decimals. It is also an opportunity to practise and consolidate their knowledge of measurement (for example, the teacher asks ‘where do we measure from on a ruler?’). When the teacher sets an addition problem, the class confidently uses number lines to solve the problem. This demonstrates the way that the week’s lessons have helped to consolidate the students’ understanding of both the strategy of bridging and the use of number lines to represent their working visually.

The teacher also models how to use physical materials (in this case, base tens blocks) to represent decimals, and reinforces the students’ understanding of place value by using the materials to explore the relationship between ones, tenths, and hundredths. Throughout the session, the teacher continues her practise of constantly asking the students to explain their thinking. This allows her to check their understanding, as well as contributing to the students’ sense of themselves as capable of explaining and expressing their mathematical knowledge.

Practising bridging when adding decimals

You will observe the teacher enacting the following strategies in the video:

  • Asking questions to enhance students’ understanding
  • Integrating multiple representations to develop flexible thinking
  • Guiding student practice to ensure efficient learning
  • Modelling example problems to support learning

In this video, the teacher works with a small group of students to provide additional challenge by adding numbers involving hundredths. She starts with guided practice and then moves on to having the students practise independently, in line with the principles of explicit teaching. It is exciting that when she offers the students the choice of another similar problem or a more challenging one, they enthusiastically ask for more challenge. This shows how effective an explicit, systematic approach to teaching maths can be in developing students’ self-concept as mathematicians.

As she has done in previous lessons, she reminds them to use their number knowledge to estimate whether or not they will need to bridge through a whole number, and reinforces the fact that they can draw on their basic facts knowledge (for example, using their knowledge that 8 + 2 = 10 to solve 0.8 + 0.2). She also makes a point of writing up two different approaches to solving the problem that students have used: one student has bridged to the nearest tenth, while another has bridged to the nearest whole number. She writes both approaches on a number line on the board, so that the class can see explicitly how they both reach the same correct answer.