7/27/2019 Lesson Plan Inverse Proportion
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mr-mathematics.com
Figure 1
Lesson Planning Sheet
Title: Inverse Proportion
Learning Objectives:
By the end of the lesson:
All students should be able to derive a formula in the form 1/x
to model inverse proportion.
Most students should be able to derive a formula to model
inverse proportion and use it to calculateunknown values.
Some students should be able to derive and use a formula to
model when one unit is inverselyproportion to the square or cube of
another.
Keywords: Model, Inverse proportion, Varies indirectly, Constant
of Proportionality, Derive, Formula
Learning Activities
Starter/Introduction
Students are challenged to use solve a simple inverse proportion
problem using their
powers of intuition. It is important to have the class describe
their method in order to
develop their mathematical reasoning. Have students work in
pairs to challenge each
other and promote discussion. A pair of students could
demonstrate the solution totheir peers at the front of the
class.
Development
To model an inverse proportion it is important to
ensure students have a secure understanding of
reciprocal functions. Discuss that two
measurements are considered to be inverse
proportion, or vary indirectly when, as one unit
increases the other decreases.
The notation for modelling inverse proportion is
shown to the right in figure 1.
Use the x and y values in the table to highlight
that the y value decreases as the x increases.
When the problem in given in words rather than
as a table it is important for the students to
identify key vocabulary in order to derive the
equation. Underline key words and phrases such as square of,
inversely
proportional or varies indirectly.
The interactive Excel file can be used to provide additional
examples. Use mini-
whiteboards to assess and feedback. When ready, the students
should be able to
work through the problems on the third slide independently.
Feedback solutions
throughout to maintain pace.
Plenary
The plenary is used to consolidate students understanding
between direct and inverseproportion. Ideally, the class would
recognise that cannot be the relationshipsince one increases when
the other decreases. Understanding that k is constant
between the different x and y values indicates that the correct
relationship is
modelled by
Have solutions presented for assessment and feedback.
Resources:
Mini-whiteboards
Interactive Excel
File
Differentiation
More able:
Students could solve problems in a real life context rather than
using data presented in a table.Less Able Students may benefit from
modelling inverse proportions in the form
rather than
.
