Systems of Equations As91587(3.15) CTD

Raise Māori student achievement through the development of cultural visibility and responsive practices across the pathway as measured against National Standards and agreed targets for reading Years 1-10 and NCEA years 11-13. As a CoL leader within the school. I  am more interested in inquiring about student learning and my own practice.

I really enjoy teaching this topic with Geogebra as students clearly enjoy the practicality of the tasks. Learners also dealt with planes in 3D (not straight lines), which added to the complexity and excitement of the work.
Here are my instructions for learners to follow:

Achievement Criteria:
(1)   Form new equation
       Use GC-If answer=unique solution.
(2) Geometrical interpretation –Draw using Geogebra.
(3) Change of equation into context/write a conclusion.

Merit/ Excellence Criteria:
(1)   Form new equation
Prove algebraically-you must attempt by hand
Use GC-If answer=maths error
There are -Multiple solutions (dependent solutions) or No solutions (inconsistent)
0= Number means No solutions (inconsistent)
0=0 means multiple solutions (dependent solutions)
(2) Geometrical interpretation -Draw, Explain parallel, not parallel
(3) Put a change of equation into context/write conclusion.




Learners found the achievement section straight forward as they were able to use Graphics calculators/3D calculators in solving equations. The formation of questions were also manageable with the guidance of Dr Janni.

However, learners found Merit and Excellence sections more challenging as these equations had to be solved by hand and there were six different scenarios’s to choose from. In order to make this simpler, I got an idea from a chart in a calculus scholarship textbook. I then passed this chart and thinking on to my students and colleagues who found it incredibly useful in breaking equations down.

In order to solidify algebraic understanding, I also encouraged students to collaborate on practice questions using a whiteboard to avoid careless mistakes. I also continually link everything back to SOLO taxonomy and wrote headings for each exercise to clarify where exactly we are at in equations.

Feedback: The HOD Mrs Singh came to observe one of my lessons and is happy with the progress made by students. 

Next step: learners have completed their internal and it is under marking. 

Reference: Scholarship Calculus AMA book.

Cluster Create Staff Meeting session 1

#1.  Raise Māori student achievement through the development of cultural visibility and responsive practices across the pathway as measured against National Standards and agreed targets for reading Years 1-10 and NCEA years 11-13. As a CoL leader within school. I  am more interested in inquiring about student learning and my own practice

Last week we had our Manaiakalani Cluster Create session meeting at Tamaki College.

It has been an excellent opportunity to learn and how to facilitate learning, introduce cooperative and inquiry.

It also helped to learn and explore new practices relevant to Mathematics.

Introduction session: conducted by Dorothy Burt and I found it very useful.

During the first session: 

I attended "how to create a digital magazine cover using tools that learners have access to" by   Lenva Shearing.

The session I attended was useful because it enables me to create impressive digital magazine with well-designed layout for all my students.

During the second session:

Our Mathematics department planned to run 3 different create sessions during that time.  

Here is the session I have presented.

Next step: I will going to incorporate sphero activity to year13 in Kinematics.

Introduction to Linear programming

• #1.  Raise Māori student achievement through the development of cultural visibility and responsive practices across the pathway as measured against National Standards and agreed targets for reading Years 1-10 and NCEA years 11-13. As a CoL leader within school. I  am more interested in inquiring about student learning and my own practice.

Linear programming and Applications

Introduction

In the past few lessons, we have been forming inequalities out from word problems and drawing inequalities to find feasible regions.

It’s a method that is often used in companies to help them maximise profits or minimise costs under constraints. This method was developed during WWII to solve military logistics e.g. number of soldiers, airplanes and weapons.
My learners' engagement is very high at present as they are working with online tool demos for graphing
and the problems are very practical.
I hope this assessment will shift their achievement towards a better grade(Merit or Excellence)

Video watch
.



Applications





Student work

Linear Programming

Chocolatier Burie wants to make chocolates that are handmade and machine
made. They have employees who works no more than 1296 hours per week
and machines that can run up to 1824 hours per week.

Handmade chocolates require 18 hours of labour and 6 hours of machine
time while machine made chocolates require 4 hours of labour and 12 hours
of machine time. With handmade chocolates, they earn a profit of $89 per
batch and with machine made chocolates, they earn a profit of $55 per batch.

How many batches of handmade and machine made chocolates should be
made to achieve maximum profit on a weekly basis?

5 Graph constraints

Next step: I am going to use the KWL chart to find their weaknesses and strengths.

Year 13 Inquiry - Rate of change - Lollipop activity

How does licking change things? Using Lolli Pops, measuring tapes and dental floss to investigate

#1.  Raise Māori student achievement through the development of cultural visibility and responsive practices across the pathway as measured against National Standards and agreed targets for reading Years 1-10 and NCEA years 11-13. As a CoL leader within school I  am more interested in inquiring about student learning and my own practice.

Investigation questions

(1) What is the volume of the lollipop?
(2) How many licks to the center?
(3) How long until it has gone?
(4) What is the relationship between Time, Radius, Volume, Circumference and surface area?

Let’s investigate those relationships starting with the easy to measure (circumference) and also estimate how long it will take until the lollipop is no more!

We had guesses, ranging from 10 minutes through to 35 minutes.

Gathering Data:handed out one lollipop per pair of students, along with some dental floss for measuring circumference. We set our timer for 30 seconds and began sucking and capturing data!

They also have a  handout for tracking the circumference over the 30 seconds intervals.   

Analyzing data: We first looked at the Time vs Radius relationships? 

LollyPop Table (Radius)

Time (seconds)	Circumference (cm)	Radius (cm)	First differences of radius (cm/30 seconds)	First differences of radius (cm/ second)	Instantaneous rate of change at time ____
0	9.0	1.43
			-0.16	-5.33 x 10-3
30	8.0	1.27
			-0.08	-2.67 x 10-3
60	7.5	1.19
			-0.08	-2.67 x 10-3
90	7.0	1.11
			-0.03	-1.00 x 10-3
120	6.8	1.08
			-0.11	-3,67 x 10-3
150	6.1	0.97
			-0.09	-3.00 x 10-3
180	5.5	0.88
			-0.08	-2.67 x 10-3
210	5.0	0.80
			-0.04	-1.33 x 10-3
240	4.8	0.76
270	4.8	0.76
			-0.04	-1.33 x 10-3
300	4.5	0.72
			-0.04	-1.33 x 10-3
330	4.3	0.68
			-0.02	-6.67 x 10-3
360	4.1	0.65
			-0.09	-3.00 x 10-3
390	3.5	0.56
			-0.04	-1.33 x 10-3
420	3.2	0.51
			-0.03 -0.08	-1.00 x 10-3
450	3.0	0.48		-2.67 x 10-3
480	2.5	0.40	-0.05	-1.67 x 10-3
510	2.2	0.35	-0.10	-3.33 x 10-3
540	1.6	0.25	-0.25	-8.33 x 10-3
570	0	0

Using DESMOS

Conclusion:

(1) What is the volume of the lollipop? 

     V = 4/3πr3

C = 9.0cm

r = C/2π

r = 9/2π

r = 1.43cm (2dp)

V = 4/3πr3

V = 4/3π(1.43)

V = 12.25cm3

(2) How many licks to the center? 300 seconds
(3) How long until it has gone? 570 seconds.
(4) What is the relationship between Time, Radius, Volume, Circumference and surface area? We are going to move onto this next week.