Company Tax Rates Versus Personal Tax Rates

28 04 2018

This article prompted me to investigate current company tax rates. They’re currently 27.5-30% without a tax free threshold.

I then investigated personal income tax rates. A person earning $37000 and hence at the bottom of the 19% bracket pays 9.7% of each dollar earned.

A person earning $87000 and hence at the bottom of the 37% bracket pays 22.8% of each dollar earned.

A person earning $180000 and hence at the bottom of the 45% bracket pays 30% of each dollar earned. I was not able to find what proportion of tax payers this would be.

I then went in search of past personal tax rates because I could recall the top bracket being 66.7%.

This is what I found for the 1971-72 financial year.


The Plight of a Farmer

13 04 2018

The drought in the country is making it very hard for the farmers.

My brother has a Dorper stud. Dorpers often have multiple births. He scans for twins and separates those ewes into a different paddock before lambing. He currently needs to feed the stock every day. The ewes are lambing. When he feeds the ewes, the lambs get separated from their mother. This puts them in danger of being taken as an easy feed by one of the 11 hungry eagles waiting in the trees in the paddock. There are hungry foxes around too. 

In a better season the stock would be grazing and ewes with new lambs would keep apart more. The season is warmer than normal for this time of year. The ewes are coming into water every day and staying near the water during some of the day too. In a better year they would water every second day.

His query is how to best tackle this issue.

Lambing occurs over about 6 weeks although the bulk of the lambs will fall within 2-3 weeks. There are options in the future to try to have the lambs fall closer together, so whatever strategy is put into place, the manpower involved is required for a shorter timeframe. Each lost lamb has the potential of selling for about $120 in 4 months time. 

Does he install some sort of flexible fencing or yard system and separate the ewe and twins as soon as they are born, for a couple of days. And then put them into a smaller paddock with less sheep and lambs for another few days before releasing them back to the main mob? This raises the issue of feed and water, besides the cost involved.

Then there’s a system called smart shepherd.

Or a virtual fence

I asked my brother if he could count the new lambs in the mob and track that each day to get a perspective of the duration and number of separate paddocks required. I received a video of maybe 200 frolicking lambs having the time of their life racing around. In short, it’s too hard to count them.

But such numbers do exist for the stud which one would assume would fairly accurately mimic the main mob. So a simulation of the situation could be developed. 

The main mob has 400 ewes. The stud 119.

Here’s the stud story.

Date Number Lambs Number Ewes that lambed
13-Mar 6 4
14-Mar 5 4
15-Mar 2 2
16-Mar 0 0
17-Mar 4 4
18-Mar 0 0
19-Mar 7 5
20-Mar 3 2
21-Mar 4 2
22-Mar 3 2
23-Mar 0 0
24-Mar 0 0
25-Mar 0 0
26-Mar 9 5
27-Mar 13 11
28-Mar 14 12
29-Mar 12 8
30-Mar 7 4
31-Mar 13 9
1-Apr 4 3
2-Apr 6 4
3-Apr 17 12
4-Apr 6 6
5-Apr 0 0
6-Apr 2 2
7-Apr 0 0
8-Apr 2 2
11-Apr 1 1
12-Apr 3 2
Total 143 106

There’s no definitive answer but students could still investigate the pricing of the alternatives (maybe in terms of the value of lambs) and then make a justified plan according to their opinion.


The 400-year-old Kepler Conjecture that your local greengrocer knows how to solve

22 06 2017

This afternoon the second meeting of the “Mathematics Matters @ UTS” Club will occur. 

I intend to share this article with those attending, as I endeavour to foster the enthusiasm I hold for many things mathematical.

Dan Meyer spoke on Fake World Maths at NCTM this morning

18 04 2015

The presentation was most entertaining and informative.

Dan demonstrated modeling using the decisions involved in making a  local delivery company as efficient as possible. He outlined the criteria used to decide which drivers were more likely to have an imminent accident and shared the monetary saving made by just shaving 1 mile off the route of each driver per day. It just goes to show that lots of lite bits can amount to huge results.
He then analyzed the modelling questions in textbooks which need to 

In reality the questions mostly only allow the students to perform operations and interpret results. The only questions validated were probability questions. 

Teachers need to fill the gaps of such questions and set the scene and then ask the students what information they need to solve the problem without giving the information, initially.
He showed a brilliant video on 2 ways of climbing a set of stairs and estimating the time taken to complete the second climb. 
He encouraged estimation with calculation to validate the processes used. 
He then showed this (as given to a primary class) 

who were then shown


in order to guess the total number of cheese balls present. When told they were wrong a conversation ensued as to which assumption lead to the faulty logic. 

He made reference to the Estimation 180 website for information for further problems and suggested we use our phones to video situations such as peeling a potato in order to get data to estimate the time taken to peel a bag of potatoes etc. He also suggested that we use the curiosity of others to ask different questions about the real world and hence raise the interest and confidence in maths.

Thank you Dan for stimulating us to reexamine and change the questions we ask and provide in our classroom. 

Multi Dimensional Mathematics by Jo Boaler and Conrad Wolfram

10 02 2015

This post details the dimensions of Mathematics and what students miss in the classroom. Enjoy.


Distance Problem From a Recent Drive

19 04 2014

Bega is 35km from Merimbula and Tathra is 26km from Merimbula. If Tathra is 19km from Bega, how is this so?


Slurpee for $2.90

8 09 2012

My classes were all talking about 7-eleven’s Slurpees on Wednesday. Once we knew the diameter could be up to 23cm and the depth 28 cm I set them to calculating the capacity of a cylinder compared to a square prism. It made for a practical interlude to the lesson in both Year 11 and Year 9.