Year12 Summary

Year12 Internal summary

MY INQUIRY

END OF TERM3 UPDATE

As91262 (2.7) Calculus Reflection

According to the students’ feedback, most of them enjoyed this topic.

 This reflected in their mock examination results too. However, I am going to continue helping them after school on Friday and term3 break in order to maintain their accuracy and time management skills. I am now looking forward to the external results. 

Calculus Revision As91262(2.7)

Calculus Revision(2.7)

Equation of the tangent lesson

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.

Reflection As91264 (2.14) Apply systems of equations in solving equations

The students finished the internal and questionnaire. Two students gained Merit and one student gained an Excellence. They said that they found the Achieved and Merit questions quite straightforward but had a bit more trouble with the word problems.

Maori Language Week Post No 4

Maori Language Week Post No 3

                                             

Maori Language Week Post No 2

Maori Language Week-Te Wiki o Te Reo Māori 2018-Post No 1

We are excited to celebrate Maori Language Week at Tamaki College.
Our staff here at Tamaki College have whole heap activities planned
to learn and use te reo.
Here is the post No 1.

GO SOLO 2.14 (AS91269)

Achievement(Multi-structural)
The student has applied systems of equations in solving problems.
The student correctly selects and uses methods with systems of equations.
They have demonstrated knowledge of concepts and terms and communicated
using appropriate representations. Anyone of these three situations is required
(1) A proposed fence crosses the drain.
(2)Irrigator crosses the drain.
(3) Irrigator crosses the fence.

forming Achievement with Merit(Relational)

The student has applied systems of equations, demonstrating relational thinking

in solving problems. The student has selected and carried out a logical sequence

of steps. The student has related their findings to the context or communicated their

Thinking of using appropriate mathematical statements.

The student correctly forms the equation for the Irrigator as

and uses the equation of the drain to form a quadratic equation.

This equation is then solved to form the points. The student then indicates

that both points are important as bridges will be needed at both for the irrigator to cross the drain.

OR

Using the equation for the irrigator and the proposed fence the student correctly

forms a quadratic equation.  The student then solves this equation to indicate

that the proposed fence intersects with the irrigator at two points .

The student clearly communicates his/her findings in the context of this problem.

Sensible rounding is required

Achievement with Excellence(Extended Abstract)

The student has applied systems of equations, using extended abstract thinking, in solving problems.

The student has used correct mathematical statements or communicated mathematical insight.

For example:

Using the equation for the irrigator and the proposed fence the student

correctly forms a quadratic equation.  The student then solves this

equation to indicate that the proposed fence intersects with the irrigator at two points

sets of points. Then use discrimination set up to resolve the ranges.

Subject Selection Evening at Tamaki College

Maths week highlights

My Inquiry

End of Term2 update

As91269(2.14) Apply systems of equations in solving problems(internal) -2 credits

Plan:
I am currently teaching Algebra, which is an external topic, and I have covered 2/3 of the content. I have decided to take a pause from teaching this topic to start teaching AS91269. This is because what I have taught so far will be fundamental knowledge for this internal topic. I will continue teaching the rest of Algebra next term after this new topic. 

I have decided to use group  activities so students have repetitive 

practice on where,

• find the points where a straight line and curves meet.
• The curves are Parabolas, circles, and Hyperbolas.
• In each case, they may not meet at all, or they may meet at one or two points.
• Solving the equations of the straight line and curve simultaneously will reduce to a quadratic function.
• Solving will tell where do they meet.
• Finding the discriminant will tell the number points at where they meet.

I will use check, chunk and chew technique to recognise the 

the nature of the graph.

I have decided to spend more time on devising a strategy to

 investigate or solve a problem, identifying relevant concepts in 

context, developing a chain of logical reasoning, or proof and 

forming a generalization. This will be useful for merit and Excellence.

As91261(2.6) Apply algebraic methods in solving problems(4 credits). External

I made the following planning decisions:I began my lesson with a pre-test. I marked it and used the results to guide my teaching approach.I have decided to use group matching activities and jigsaw puzzles, repetitive practice in word problems and ‘Do Now’s for skill practice.I have decided to spend more time with hard factorising, rearranging and word problems during Thursday and Friday after school as these seem to be more difficult areas judging from the pre-test.

I am going to give lots of practice during the holiday break focusing on Expanding brackets, Simplifying, Solving Linear and Quadratics, rearranging and substitution and log rules. Immediately after using these strategies, I am going to ask for their feedback. I hope their feedback will give me insight into how successful these approaches have been. I am going to give them a practice test next term.

Reflection Trigonometry 2.4(AS91259-internal -3 credits)

The students finished the Trigonometry internal and

Questionnaire. One of them gained an Excellence and two of them gained a merit.

They said that they found the achieved questions quite straightforward

but circular part challenging. I did lots of practice after school.

They enjoyed Check, Chunk and Chew method.

KWL Chart Strategy

Completing the “K” portion of the chart increases student comprehension by engaging their prior knowledge; they begin the unit already thinking about and connecting with the topic. The “W” section of the chart is a road map that helps students become active learners and gives them ownership of the learning objective. Completing the “L” activity at the close of the unit reinforces what they have learned.

Chunk, Check and Chew Strategy

I found this strategy very effective to teach Trigonometry

(1)I begin Trigonometry unit of information with a preview activity and follow that with an initial presentation of a chunk of critical information. This part of the lesson takes about ten to twelve minutes.

(2) After presenting a “chunk,” giving students a task to do with a partner or group to actively process the new information. The techniques in this guide will give you many ways to engage your students in this kind of cognitive processing.

 (3) Following the processing, I gave another chunk of new information. This chunk was a form of brief ppt/video to the critical information with a partner. Students have specific kinds of processing in which they will engage once each information-input segment has occurred.

(4)  I  repeated the above cycle until all of the chunks of critical information for a lesson or unit have been introduced and processed.

(5) I instructed students to review the critical information chunks from the day and think about whether anything they learned in a previous lesson connects with their new learning. Then ask them to engage in some kind of summarizing activity to connect the various information chunks.

Here is the Link

GO SOLO for As91259(2.4) Trigonometry

Apply trigonometric relationships in solving problems.

Achievement
Students will demonstrate competency in at least two different methods 
 listed 

           Length of an arc of a circle,

           Area of a sector of a circle,   Sine rule, Cosine rule,
         Area of a triangle

Merit

Students will demonstrate competency in at least two different methods and 

use at least one type of relational thinking across their solutions. 

Solve problems and model situations that require them to apply 

trigonometric relationships, including the sine and cosine rules, 

in two and three dimensions

solves problems that can be modelled by trigonometric relationships

uses the area formula for triangles and the sine and cosine rules 

to  solve problems

uses radian measure

Excellence

Students will demonstrate competency in at least two
different methods and use extended abstract thinking across 
their solutions and answer question
 fully relating to the problem.
Arc length and area of sector problems:
-semi-circular cross-section troughs
-security light coverage-radar overlapping areas

Chunk,Chew,Check technique CCC

CHUNK = INPUT Students acquire new information 
in varied ways.

CHEW = PROCESSStudents make sense of new
information in varied ways.

CHECK = OUTPUT Students show what they have
learned in varied ways.

I found this technique useful for Trigonometry

Term 2 Plan Trigonometry 2.4(AS91259-internal -3 credits)

Term2-Topic 1-Trigonometry-Apply trigonometric relationships 

in solving problems

Actions and Reflections

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

I have been working my way through trigonometry (2.4) with my 12MAC class.

I have chosen 3 Maori students for my enquiry.

I began my lesson with a pre-test which I marked to use as a guide to my teaching

approach.

This is a topic where I am going to use the graphics calculator and resource sheet.

I am going to apply the Chunk, Chew, and Check strategy to teach this topic and send

online lessons. I will use this technique to work out the sides/angles, calculate circular

 shapes using sine rule, cosine rule.

 I have decided to spend more time devising a strategy to investigate or solve a problem,

 identifying relevant concepts in context, developing a chain of logical reasoning and

working backward with trig formulae. This will be useful for merit and excellence questions.

Immediately after using these strategies, I am going to ask for their feedback. I hope their

feedback will give me insight into how successful these approaches have been.

I am going to give them a practice test (herb gardens).

I have started after school support sessions on Thursdays and Fridays to give more one to

one support to students in order to improve their external results.

Also at the end of the topic, I am going to give the students a questionnaire with the following

 questions;

I really enjoy this unit/ I didn’t enjoy this unit, I found this useful/not useful and comment

Reflection

As91264(2.9) Inference -

The students finished the Statistical Inference/ second internal and

Questionnaire. Two of them gained Excellence and one gained a merit.

They said that they found the achieved questions quite straightforward

but had a bit more trouble with the contextually based Excellence part.

They worked hard during class time and Friday after school to maintain

Their grade as well as time-bound. Also, I found the checkpoint very

useful in giving them feedback. The tick box helped me in terms of marking.

.

Here is the feedback:

They enjoyed the Calculus topic (previous) better than Statistics topic(this).

Therefore I am planning to replace this topic with Graph 2.2 (4credits) next

year.