Optimisation Lesson

Go SOLO 91262(2.7) Calculus

Achievement

Understand the relationship between a function (equation) and the  *  graph of the gradient function (derivative)  *  area between the graph and the x axis (integral)

Understand the symbols   dy/dx, f’(x), f"(x) and dx

Differentiate expressions that have integer exponents like 3x2 and 4/x2

Find the gradient at a given point of a graph if given the equation of the graph

Find the point on a graph that has a given gradient if given the equation of the graph

Integrate expressions that have integer exponents like 3x2 and 4/x2

Find the equation of a curve if I am given the gradient function

Merit

Find turning points

Identify what type of turning point and when a function is increasing or decreasing

Find the equation of a tangent to a curve

Solve kinematics problems (velocity, acceleration)

Interpret my solution into words related to the problem

Excellence

Optimisation problems

Kinematics

Rates of change

Form equations for optimization and area problems, kinematics and rates of change

Plan

As 91262(2.7 ) Apply calculus methods in solving problems

Achievement		with Merit	Achievement with Excellence
·      Apply calculus methods in solving problems.		·      Apply calculus methods, using relational thinking, in solving problems.	·      Apply calculus methods, using extended abstract thinking, in solving problems.

I have been working my way through Calculus (2.6, External) with my 12MAC class.

I chose 3 Maori students.

I made the following planning decisions:

 I used the check, chunk and chew technique to recognize find the gradient if a function at

 a given ‘x’ value, Sketch the gradient function, Given the derivative f’(x) and a point (x,y),

 find the original function f(x).

 I decided to spend more time Find the equation of the tangent line, Find a point on a curve 

when given a gradient, Find the coordinates of the turning points on a graph, Find the rate

 of change of a function at a given time, Find the maximum/minimum values of a given 

function, Kinematics problems – finding speed from a distance function, Find the function f(x)

 when given f’(x) is given.

And optimizing applications – using calculus to find the maximum. Use the second derivative to determine the nature of turning points, Identify the ‘x’ values where a function is increasing or decreasing, Kinematics problems – finding the distance from a speed function. This will be useful for merit and excellence questions.

(1)  I have started after school Friday after school to give more one to one support to students in order to improve their External results.

(2)  Also at the end of the topic, they sat  Mock Examinations.

As 91262(2.7) Calculus

Who invented Calculus? Here is the answer.

Reflection As91261(2.6) Algebra(External)

According to the students’ feedback, most of them found the Achieved questions straightforward but found the Merit and Excellence questions in a contextual based situation quite difficult. This was reflected in their Mock examination results. So, I am going to continue helping them after school on Friday and during the term3 break. I. I am now looking forward to the external results. 

As91261 Algebra Revision for Mock Examination

My students and I planned this term(3) very carefully to avoid the last
minute rush. We finished the 1/3 of the Algebra after the last internal(2.14)
and made them to practice past papers for homework. Here is the video.

GO SOLO As91261(2.6) Algebra

Achieve

Apply algebraic methods in solving problems:

• selecting and using methods
• demonstrating knowledge of algebraic concepts and terms
• communicating using appropriate representations.

Manipulate algebraic expressions
Expand brackets up to 3 factors
Factorising expressions including quadratics
Use fractional and negative indices 
Change the subject of the formula  
Use elementary properties of logarithms 
Simplify rational expressions.

Solve equations involving. 
Multi-step linear equations or inequations,      eg 3(2x − 5) = 5x + 7
Quadratics that can be factorised      eg 2x² − 11x = 21  
Polynomials in factorised form   eg 3x²(x − 7)(2x + 6) = 0 
Simple logarithmic and exponential     eg Log₂x = 2,  2^x = 64 
Forming and solving linear/linear simultaneous equations.

Merit

Relational thinking involves one or more of:

• selecting and carrying out a logical sequence of steps
• connecting different concepts or representations
• demonstrating an understanding of concepts
• forming and using a model;

and also relating findings to a context, or communicating thinking using 

appropriate mathematical statements

Solve problems involving equations.
Assessment will be based on a selection from: 
- quadratics requiring the use of the quadratic formula 
- linear/non-linear simultaneous equations  
- exponential eg 13^4x-5 = 6.
non-linear equations may be given as appropriate to the complexity of the problem.
Students will be expected to solve problems in context.

Excellence

Extended abstract thinking involves one or more of:

• devising a strategy to investigate a situation
• identifying relevant concepts in the context
• developing a chain of logical reasoning, or proof
• forming a generalisation;

and also using correct mathematical statements, or communicating

 mathematical insight.

Choose algebraic techniques and strategies to solve problems.
Where appropriate, interpretation of a solution will be expected and

 may involve the nature of the roots of a quadratic.