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# Multiplicative Reasoning - A model for professional development

Created on 01 February 2016 by ncetm_administrator
Updated on 04 April 2016 by ncetm_administrator

# Example lessons

Below are examples of three of the 15 lessons contained within the Teaching Units.

Examples of some of the problems contained in these, and other, lessons can be seen here.

Unit 1 - Deepening understanding of fractions
Lesson 1B(i): Parts of a shape

In this lesson we think of fractions as parts of a whole, and make use of geometric representations such as shaded parts of a region (as well as using the standard numerical symbolisation). Students have the opportunity to estimate fractions in a qualitative way but there is also scope for increasingly analytic approaches.

Unit 2 - Understanding and identifying proportional contexts
Lesson 2A(ii): Percentages on the bar model

In this lesson students continue to work with the bar model, as a follow-on from the work begun in lesson 2A(i).

The context of a computer download bar is used to introduce the percentage bar. Students experience a range of other contexts, but unlike the contexts chosen for lesson 2A(i), here the contexts do not immediately conjure up a rectangular image if you were to represent them pictorially.

Students are encouraged to develop their use of the percentage bar to answer a wide range of percentage questions including finding a percentage of something, percentage reduction, reverse percentage problems and expressing one amount as a percentage of another.

Unit 3 - Application to a range of proportional problems.
Lesson 3A: Exploring multiplicative structures

In this lesson students explore proportional relationships from some given data, identifying and using structures to calculate additional values related to the data.

They gain experience of determining appropriate mathematical operations to apply and to which quantities, in a given situation.

Students also have the opportunity to both pose and answer their own and given questions.