Unit Plan: Who is healthier
‘In how many different ways can you write an equation?’.
Clouding the picture
Split the class into groups and give each group a marker pen and some sugar paper
Ask the students to draw the diagram below
As the students if “3x + 4” could be written in a different way.
(e.g as 2x + x + 4)
Ask them to complete the diagram writing all of the ways that 3x + 4 can be written down. Importantly ask them to put these to categories as below. The final picture should look like the one overleaf
Clouding The Picture cont……
Now extend to quadratic expressions For example
or…
This is then an excellent way of introducing “completing the square.
Unit Plan: Planning A Holiday
The Gym Problem
’A local gym charges £5 a session but members may pay an annual fee of £100 and then pay £2.50 per session.’
What would you advise?
Lesson Plan: The Gym Problem
Introduce problem:
’A local gym charges £5 a session or members may pay an annual fee of £100 and then pay £2.50 per session.’ What would you advise?
Pairs or small groups investigate and prepare a presentation.
Questions to ask:
How are you going to break the problem down?
What maths are you going to use?
What is the best way to present your findings?
What are you basing your choice on?
How could this be expressed algebraically?
How do the graphs help you?
How does each part relate to the problem?
Focus on establishing the meaning of the variables (s = number of sessions and C = total cost per year, in £) and thus the meaning of the intersection of, say, C = 5s and C =100 + 2.5s and its connection with the solution of
5s = 100 + 2.5s.
What would happen if...?
1) The annual fee changes, for example, it goes up to £120: or what happens if the cost per session changes, etc.
– How does this affect your choice?
– What happens to the position of the graph?
– How is it expressed algebraically?
Draw out the connection between
– steepness (gradient), the variable cost in the problem and the coefficient of x in the equation;
– the intercept on the graph, the fixed-cost part of the problem and the constant in the equation.
Presentations:
Choose one or two well-developed presentations that focus on different key points.
Develop problem further:
Investigate the effect of changes to different aspects of the problem on the equations, their graphs, the
point of intersection and algebraic solution. Establish why it’s a straight-line graph (equal steps – cost per session).
SACRED HEART CATHOLIC COLLEGE RICH TASKS BOOKLET JUNE 08