The following is a selection of elaborations, and parent content descriptors, with a common theme.
conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest (AC9M3ST03)
conducting a whole class statistical investigation into the best day to hold an open day for parents by creating a simple survey; collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best
choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions (AC9M4N07)
recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down and one number up and one number down, and explaining which is the best approximation and why
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M4N08)
recognising the effect of rounding addition, subtraction, multiplication and division calculations, rounding both numbers up, both numbers down, and one number up and one number down; explaining which estimation is the best approximation and why
solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units (AC9M5M02)
using a physical or a virtual “geoboard app” to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter
acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data (AC9M5ST01)
identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made (AC9M5ST02)
interpreting the data represented in a line graph making inferences; for example, reading line graphs that show the varying temperatures or UV rates over a period of a day and discussing when would be the best time to hold an outdoor assembly
solve problems involving the volume and capacity of right prisms using appropriate units (AC9M8M02)
solving practical problems involving volume and capacity; for example, optimal packaging and production
use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (AC9M8M07)
modelling situations involving financial contexts; for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay; comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
solve problems involving the volume and surface area of right prisms and cylinders using appropriate units (AC9M9M01)
finding different prisms that have the same volume but different surface areas, making conjectures as to what type of prism would have the smallest or largest surface area
plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions (AC9M9ST05)
investigating where would be the best location for a tropical fruit plantation by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
solve problems involving the surface area and volume of composite objects using appropriate units (AC9M10M01)
using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a roof top and the optimal shape and dimensions for rainwater storage based on where it will be located on a property; determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression (AC9M10M03)
applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
“…recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down and one number up and one number down, and explaining which is the best approximation and why…”
I feel that I would struggle to do this even in a relevant context, so I can only guess what will happen in the made-up-world of junior secondary textbooks!
(Wondering, seriously, how much of this can actually just be ignored)
All of it.
I suspect there will be a lot of the following:
[Apples] cost [4.83] dollars per [kg]. [Vonada] buys [7.2 kg] of [apples]. Estimate how much [Vonada] pays.
Insert appropriate product, cost per unit, politically correct name, and amount of product purchased.
There might even be a cheese shop.
(And there might even be a student that says Vonada pays 7 dollars because Vonada scans their apples as carrots and carrots are only 0.98 dollars per kg).
Estimation is a skill that seems woefully lacking even in the “more able” students I have worked with over the last decade or so. Give them a Mathematics textbook problem on a made-up scenario: no problem.
Same student in an art class is told to mix 100mL of water per 200g of plaster powder struggles to work out how much they need for 150g of powder.
I’m not entirely sure where it all went wrong and not convinced that calculators are the sole reason (although they probably accelerated the trend)
Indeed. What you’ve identified is a lack of “transfer”:
“Transfer” is a cognitive practice whereby a learner’s mastery of knowledge or skills in one context enables them to apply that knowledge or skill in a different context. Because transfer signals that a learner’s comprehension allows them to recognize how their knowledge can be relevant and to apply it effectively outside original learning conditions, transfer is often considered a hallmark of true learning (Barnett & Ceci, 2002).
I have also found this to be a big problem with students. Particularly within a subject, where many students cannot even transfer skills learnt in one mathematics topic to a later (even the next) topic, let alone to another subject. I’m certain calculators are not the sole reason for this. Perhaps it’s because so many students seem to be ‘rote learners’ …?
A teacher could do worse things than spend a couple of lessons on ‘Fermi problems’: https://en.wikipedia.org/wiki/Fermi_problem
Interesting read. Thanks. Again.
I’ve said this before, but this blog is proving to be more valuable PD than MAVcon…
Um, thanks?
A proof by contradiction (or should that be a contradictory proof), I’m sure. Or is it 100-proof …?
“…Australia, Indonesia, New Guinea and Malaysia…”
Papua New Guinea is the correct name of the country.
Yes, you pointed that out on the draft.
…*Commonwealth of* Australia if we are going to insist on proper titles…
True. Last night I wrote to the Minister for Education, Hon Jason Clare, and pointed out the reference to “New Guinea” in the curriculum. Let’s see if he can fix it.
That’s what inspired you to write to the Minister. Right.
The more I read of their recommendations for the education of young people the more I am convinced they really don’t like kids and do not want them to be educated.
Neither is true, but I understand why it feels that way.
Jack, I think ACARA genuinely cares. It cares in the same way that medieval doctors who performed bloodletting on their patients (to prevent or cure illness) cared.