**Resources**

Powerpoint lesson: Lesson 1 Fractions and Division

Student Worksheet: Lesson 1 Fractions and Division Worksheet

**Discussion**

In this, the first in the sequence of lessons Mr He will deliver on fractions, students focused on the relationship between division and fractions.

The aim of this lesson was for students to identify and apply the links between the * dividend, divisor, numerator and denominator*.

**Taking the concrete to the abstract**

Through the design of the lesson, students started by exploring concrete examples of division such as sharing cakes between a given number of people. They were then required to create a * number sentence* such as:

Through using these number sentences, students identified the links between the dividend, divisor, numerator and denominator. This lead to the generalised definition of a fraction using an algebraic equation and identifying that q can not equal 0.

**Conceptual Variation**

Throughout the lesson, fractions were represented in a wide variety of scenarios such as:

- Dividing food in to groups
- Completing number sentences
- Completing number sentences with algebra
- Identifying fractions from geometric figures

In experiencing the concept within a variety of contexts and representations, students a deeper understanding of the concepts application and actively look for the concept within all scenarios which are provided to them . In looking at algebraic number sentences, students are no longer constrained by specific numbers, but a more generalised application of the concept – deepening the knowledge that the dividend is the numerator and the divisor is the denominator.

**Procedural Variation**

In **Exercise 1** students were provided with an incomplete number sentence, in which the division was given. The aim was for students to be able to complete the sentence by identifying the dividend as the numerator and the divisor as the denominator. Whilst this remained constant in the exercise, the numbers that made up the division were varied. Through completion of this exercise, students will have identified:

- The dividend is the numerator and the divisor is the denominator.
- Even if the dividend is larger than the divisor, the concept is still true
- For any numbers ‘
**n**‘ and ‘**m**‘ a fraction can be formed (where m does not equal 0)

**Exercise 2** then varied the part of the number sentence that students were required to find, guiding students to identify what was missing and then which part of the remaining sentence it linked to. Question 4 asked students to do the opposite of what was required in exercise 1, starting with the fraction and ending in the division statement.

**Key considerations in the design of this lesson**

- Quality, not quantity: Students were required to complete 6 activities in total during the lesson, with each consisting of no more than 5 questions.
- Each question was designed to fulfil a given purpose, with carefully selected variation used to ensure that students experienced the concept in a wide range of scenarios.
- Algebra was embedded within the lesson as a natural consequence of the discussion taking place.
- Key terminology was fundamental to discussion and students were required to use the correct terminology consistently throughout the lesson. Students were also always asked to provide the full number sentence when providing solutions, strengthening the link between division and fractions.