Declarative+and+Procedural+Knowledge+from+year+one+to+nine

__Foundation Year__
Although the Money and Financial Mathematics strand is not found in foundation year it is likely that students will have gained some exposure to money in their home or school contexts. Exposure to coins at this stage would be highly beneficial as it lays the foundation for year one when students are required to begin working with money.

__Year One__
Recognise, describe and order Australain coins according to their value (ACMNA017).

Elaborations

 * ======showing that coins are different in other countries by comparing Asian coins to Australian coins.======
 * understanding that the value of Australian coins is not related to size.
 * describing the features of coins that make it possible to identify them.

__Declarative knowledge__

// Students will know/understand: // DK - that in Australia our currency consists of 5c, 10c, 20c, 50c, $1 and $2 coins DK - what a 5c, 10c, 20c, 50c, $1, and $2 coin looks like. DK - that coins in other countries are different to Australian coins and cannot be used in Australia. DK - that some coins are worth more/less than others (order/sequence). DK - the relative order of the coins. DK - the concept of cents and dollars $1 = 100c. DK - that the size of a coin is not related to its value.

__Procedural Knowledge__ //Students will be able to://

PK - recognise a 5c, 10c, 20c, 50c, $1, and $2 coin. PK - describe features of Australian coins including size, colour and images. PK - differentiate between Australian coins and coins from another currency. PK - match a coin with its value. PK - order coins from least value to greatest and vice versa

__Year Two__
Count and order small collections of Australian coins and notes according to their value(ACMNA034). Elaborations
 * identifying equivalent values in collections of coins or notes, such as two five-cent coins having the same value as one 10-cent coin.
 * counting collections of coins or notes to make up a particular value, such as that shown on a price tag.

__Declarative Knowledge__ // Students will know/understand: //

DK - that in Australian currency there are $5, $10, $20, $50, and $100 dollar notes in general circulation. DK - what a $5, $10, $20, $50, and $100 dollar note looks like. DK - the relative order and value of all Australian coins and notes. DK - that different arrangements of coins and notes can have the same value. Dk - that different collections of coins can make up a particular value.

__Procedural Knowledge__ //Students will be able to:// PK - recognise a $5, $10, $20, $50 and $100 note. PK - describe features of Australian notes including size, colour and images. PK - differentiate between Australian notes and notes from another currency. PK - match a note with its value. PK - recognise the relative order and value of notes. PK - order coins and notes from least value to greatest and vice versa. PK - recognise equivalent values in coins. e.g. 5 x 20c =$1 2 x 50c =$1 PK - count (addition) coins and notes to make up a particular value.

__Year Three__
Represent money values in multiple ways and count the change required for simple transactions to the nearest 5 cents (ACMNA059). Elaborations
 * recognising the relationship between dollars and cents and that not all countries use these demoninations and divisions (for example Japanese Yen).

__Declarative Knowledge__ // Students will know/understand: // DK - that historically in Australia we used 1c and 2c coins, however today these coins are no longer in circulation. DK - that all commercial costs are rounded to the nearest 5 cent value. DK - that there is a relationship between dollars and cents e.g.$1 = 100c. DK - that other countries do not use the same denominations and divisions used in australia e.g. Indonesian Rupiahs. DK - that a value can be represented in multiple ways using different collections of coins and notes.

__Procedural Knowledge__ // Students will be able to: // PK - add two costs to a total in dollars and cents. PK - represent a particular money value in multiple ways using different collections of coins and notes. PK - calculate change due for a payment in whole dollar transactions. PK - round a cost to the nearest 5 cents. PK - count the change due for a payment rounding to the nearest 5 cents.

__Year Four__
Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080).

Elaborations
 * recognising that not all countries use dollars and cents.
 * carrying out calculations in another currency as well as in dollars and cents, and identifying both of them as decimal systems.

__Declarative Knowledge__ // Students will know/understand: //

DK - that some countries do not not use dollars and cents. e.g. Indonesia uses Rupiahs DK - that all commercial costs are rounded to the nearest 5 cent value. DK - that dollars and cents can be shown in decimal form e.g. $1 and 20c can be shown as $1. 20.

__Procedural Knowledge__ // Students will be able to: //

PK - calculate total purchase cost for two or more costs in both dollars and cents. PK - calculate the change due for a total cost from a range of denominations both in coins and notes. e.g.cost is 60 cents - change from $2 PK - calculate the change due for a total cost from a range of denominations in mixtures of coins and notes. e.g. cost is $13. 80 - calculate the change from $20 PK - round a cost to the nearest 5c and calculate change for a single transaction. e.g. total pertrol cost is $44. 98, calculate the change from $50 rounding to the nearest 5 cents. PK - identify dollars and cents as decimal systems. PK - write money quantities in dollars and cents in whole numbers and decimally. PK - enter these quantities into a calculator to carry out calculations. PK - solve money problems with and without digital technologies showing working out.

__Year Five__
Create simple financial plans (ACMNA106).

Elaborations __ Declarative Knowledge __
 * creating a simple budget for a class fundraising event
 * identifying the GST component of invoices and receipts

// Students will know/understand: // DK - the concept and value of saving money. DK - the concept and value of budgeting. DK - the concept of lending/ borrowing money. DK - the concept of adding interest when borrowing/lending. DK - that a financial plan/budget is useful for small and large scale events e.g. a shopping trip or a school fete. DK - that there is and 10% Goods and Services Tax (GST) on most goods and services transactions in Australia. DK - that GST is a Value Added Tax (VAT).

__Procedural Knowledge__ // Students will be able to: // PK - create a simple saving plan PK - create a simple budget. PK - create a financial plan for a class event identifying potential costs. PK - locate and identify the GST component in a receipt or tax invoice.

__Year Six__
Investigate and calculate percentage discounts of 10 %, 25 % and 50% on sale items, with and without digital technologies (ACMNA132).

Elaborations __Declarative Knowledge__ // Students will know/understand: // DK - that a sale item can either have an set amount deducted from it or a percentage discount technologies. DK - the importance of being able to calculate the percentage discount without digital DK - the equivalence of percentage values and their decimal representation. e.g. 20% = 20 out of 100 = 20/100 = 0.20  DK - the key word "of" in maths implies multiplication e.g. find 10% of $55 means 10% x $55 =0.10 x $55 =$5.50
 * using authentic information to calculate prices on sale goods.

__Procedural Knowledge__ //Students will be able to:// PK - identify recall an instance when they recieved a percentage discount. PK - identify circumstances where a percentage discount must be carried out without digital technologies. PK - calculate a percentage of a quantity with and without digital technologies. PK - calculate percentage values of money quantities for 10%, 25%, and 50% without technologies showing working out. PK - calculate percentage calculations for 10%, 25%, and 50% of money values using a calculator. PK - calculate the sale or discounted price after a percentage discount is applied. e.g. find the sale price for a shirt priced at $45 if there is a 20% discount (by subtracting the discount from the original price).

__Year Seven__
Investigate and calculate best buys with and without technologies (ACMNA174).

Elaborations


 * applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g.

__Declarative Knowledge__

//Students will know/understand://

DK - the concept of unitary price

e.g. the cost per single item, per kg, per metre, per hour etc.

DK - that a best buy can be calculated by comparing the unitary price of two of more goods/services.

e.g comaring the cost of two brands of apple

DK - that the term best buy in this situation is dependant purely on the monetary value, there are other factors which ultimately determine a best buy, such as quality.

__Procedural Knowledge__

//Students will be able to://

PK - calculate unitary prices for a range of quantities and situations

e.g. 6.5 metrtes of material cost $23, find the cost per metre.

e.g. David works for 12 hours and is paind $102, find the hourly rate of pay.

PK - make comparative calculations on similair costings to make best buy decisions.

e.g what is better; a carton of 24 cans of lemonade for $18 or a carton of 30 cans of lemonade for $21?

PK - make comparative calculations with and without digital technologies showing working out.

__Year Eight__
Solve problems involving profit and loss, with and without digital technologies (ACMNA189).

Elaborations


 * expressing profit and loss as a percentage of cost or selling price, comparing the difference
 * investigating the methods used in retail stores to express discounts

__Declarative Knowledge__

//Students will know/understand://

DK - what the terms profit and loss mean.

DK - the difference between an absolute/fixed discount and a percentage discount.

__Procedural Knowledge__

//Students will be able to://

PK - calculate both profit and loss using subtraction.

PK - identify/provide example of absolute and percentage discounts.

PK - calculate what percentage one quantity is of another.

PK - calculate percentage profit or loss and compare.

PK - differentiate between a fixed and percentage discount.

PK - calculate the percentage of an fixed cash discount.

PK - calculate the cash value of a percentage discount.

PK - make comparison between a percentage and fixed cash discount.

e.g. what is better $20 off the price or 10% off the price?

__Year Nine__
Solve problems involving simple interest (ACMNA112).

Elaborations


 * understanding that financial decisions can be assisted by mathematical calculations.

__Declarative Knowledge__

//Students will know/understand://

DK - that simple interest is a fee paid by a borrower to the lender.

DK - that simple interest is a fixed percentage of the original borrowed amount (principle).

DK - that the standard formula for calculating interest is: Interest = Principle x Rate x Time.

DK - that the interest rate must be converted to a percentage before working out the interest

e.g 15% interest rate is 0.15

__Procedural Knowledge__

//Students will be able to://

PK - calculate simple interest using the following formula (Interest = Principle x Rate x Time).

PK - calculate the total repayments (principle + interest).

PK - calculate periodic payments on a loan in weeks, months and years.

PK - find 'unkowns' in simple interest calculations

e.g. unknown principle, interest rate and time period.

PK - calculate an interest rate relative to a time period

e.g. 6% per annum = 0.5 % per month or 2% per quarter = 8% per annum.

PK - appreciate through applied skills the value of mathematical calculations in making financial decisions