Addition and Subtraction 23, Money and Financial Maths 9_Guided and Independent Investigations
(Year 3) ACMNA054, ACMNA055, ACMNA059, NSW MA2-5NA
Add and subtract money with up to four digits using mental strategies, including rounding total to the nearest 5 cents, then give change.
GUIDED INVESTIGATION
Children learn how to investigate the concept by following teacher’s
instructions until they are ready to investigate the concept independently.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their current level of
understanding informing both themselves and the teacher of their current level of
understanding
Resources: playing cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. have a pack of playing cards
3. flip cards and make numbers
as money to add and subtract
as guided by the teacher
4. record their number sentence
and solution strategy
What language could we use to ask
questions and explain?
What could we do?
What language could we use to explain?
Children:
 My numbers are ...
1. sit in pairs
 I added / subtracted my numbers as
2. have a pack of playing cards
money by …
3. flip cards and make numbers as
money to add and subtract that are
neither too easy nor too
challenging
4. record their number sentence and
solution strategy
• How can we add money on a number line?
REFLECTION Before, during and after lessons, children discuss then
record responses to reflection questions to inform themselves and the teacher • How can we subtract money on a number line?
• How are adding and subtracting whole numbers and money related?
of their current level of understanding.
 What numbers did you add /
subtract as money?
 How did you add / subtract
the numbers as money?
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Email: [email protected]
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CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative assessment
data for both the child and the teacher.
‘Doing’ mathematics is not enough and is not a good indicator of understanding.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,
Select cards to make
money to add, using
mental strategies.
Select cards to make
money to subtract,
using mental strategies.

In pairs, children select cards to make money amounts to add using mental strategies. Mental strategies include;
keeping one number whole, and partitioning the other number using friends of 10 and place value (This develops and
uses deep understanding of non-standard place value as children add multiple place values across a single place value.
For example, when adding $9.00 to $38.69, children are not simply adding 2 single-digit numbers of dollars, they are
adding a single-digit number of dollars to a number with 10 dollars, 1 dollars, 10 cents and 1 cents. This they develop
and use their understanding of non-standard place value.)

partitioning both numbers into place values, and adding each place value separately (This uses only standard place
value and so limits understanding of non-standard place value as children simply add within place values.)

compensation (This develops and uses deep understanding of place value as children round numbers to place values to
make addition more efficient.)

In pairs, children select cards to make money amounts to subtract using mental strategies. Mental strategies include
►
►
keeping one number whole, and partitioning the other number using friends of 10 and place value, (This
develops and uses deep understanding of non-standard place value as children subtract multiple place values
across a single place value. For example, when subtracting $9.00 from $38.69, children are not simply
subtracting 2 single-digit numbers of dollars, they are subtracting a single-digit number of dollars from a number
with 10 dollars, 1 dollars, 10 cent and 1 cents. This they develop and use their understanding of non-standard
place value.)
partitioning both numbers into place values, and adding each place value separately (This uses only standard
place value and so limits understanding of non-standard place value as children simply add within place values.
Partitioning both numbers into place values is confusing when the digit we are subtracting is greater than the
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
►
digit we are subtraction from, for example, $38.69 – $9.23 because we are subtracting 9 dollars from 8 dollars.
This also may lead some children to subtract inappropriately, for example, when subtracting $9.23 from $38.69,
they may record $8 - $9 but calculate $9 - $8 instead, (this may also stem from someone having incorrectly told
them that 'you take the small number away from the larger number'!)
compensation (This develops and uses deep understanding of place value as children round numbers to place
values to make subtraction more efficient.
Addition, first to
$50.00 or $100.00
wins.

In pairs, children take turns to flip 3 or 4 cards to make a three-digit or a four-digit number as a money amount and add,
keeping a running total. First player to reach $50.00 or $100.00 wins.
Subtraction, first to 0
wins.

In pairs, children take turns to flip 3 or 4 cards to make a three-digit or a four-digit number as a money amount and
subtract from $100.00 or $50.00, keeping a running total. First player to reach 0 wins.
Select a card, decide to
add it as a $10 or $1 or
10c or 1c, aiming to
reach a target number.

In pairs, children select a card. They decide whether to add it as a 10 dollar, a 1 dollar, a 10 cent or a 1 cent. They take
turns to repeat this 5 times with 5 different cards. The child closest to $100.00, or a predetermined target number after
5 additions wins. NB: Both children could use the same card as their friend, but one may choose to add it as a 10 cent,
while their friend may choose to add it as a 10 dollar.
Select a card, decide to
subtract it as a $10 or
$1 or 10c or 1c, aiming
to reach a target
number.

In pairs, children select a card. They decide whether to subtract it from $100.00 (or $50.00 etc) as a 10 dollar, a 1 dollar,
a 10 cent or a 1 cent. They take turns to repeat this 5 times with 5 different cards. The child closest to 0, or a
predetermined target number after 5 subtractions wins. NB: Both children could use the same card as their friend, but
one may choose to subtract it as a 10 cent, while their friend may choose to subtract it as a 10 dollar.
Make 3 or 4 digit
numbers, add/subtract
its value from the total,
first player to 0 or
1000 wins.

In pairs, children start with $50.00. In turn children flip 3 or 4 cards to make a three- or four-digit number. If more cards
red, they subtract its value from their total. If more cards black, they add its value to their total. If the same number
cards are red as black, the child chooses whether to add or subtract. The first player to either 0 or 10 000 wins.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Select a card, decide to
add/subtract as a
thousand, a hundred, a
ten or a one.

In pairs, children start with $50.00. In turn children flip a card. They decide whether to use the card as a thousand, a
hundred, a ten or a one. If the card is black they subtract its value from their total. If the card is red, they add its value
to their total. The first player to either 0 or $100.00 wins.
Use a calculator to add
three and four-digit
numbers as money.

Children use a calculator to add three- and four-digit numbers as money amounts, then check. Children explain their
strategy to a friend.
Use a calculator to
subtract a three or
four-digit number as
money.

Children use a calculator to subtract a three- or four-digit number as money amounts, then check. Children explain their
strategy to a friend.
Add money amounts
together, player with
highest/lowest total
wins.

In pairs, children flip 10 cards. They each secretly select 6 of the numbers to make 2 three-digit numbers as money
amounts to add together or 8 cards to make 2 four-digit numbers as money amounts to add together. They each add
their numbers as money amounts. They child with the highest / lowest total wins.
Subtract money
amounts together,
player with
highest/lowest total
wins.

In pairs, children flip 10 cards. They each secretly select 6 of the numbers to make 2 three-digit numbers as money
amounts to subtract, or 8 cards to make 2 four-digit numbers as money amounts to subtract. They each subtract their
numbers as money amounts. The child with the highest / lowest total wins.
Try to make 2 threedigit numbers add to an
answer in a target $10,
$1 or a 10c.

In pairs or small groups, children select 6 or 8 cards. Each child tries to make 2 three-digit numbers or 2 four-digit
numbers as money amounts to add with an answer in a target 10 dollar, a 1 dollar or a 10 cent. For example, the
numbers 4, 5, 8, 2, 3 and 1, and the target 1 dollar is $6.00. A child could make the three-digit numbers, $1.32 + $4.85,
or $2.58 + $4.13 etc.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
Try to make 2 threedigit numbers to
subtract to an answer in
a target $10, $1 or a
10c.

In pairs or small groups, children select 6 or 8 cards. Each child tries to make 2 three-digit numbers or 2 four-digit
numbers as money amounts to subtract with an answer in a target 10 dollar, a 1 dollar or a 10 cent. For example, the
numbers 4, 5, 8, 2, 3 and 1, and the target dollar is $3.00. A child could make the three-digit numbers, $5.34 -$1.82, or
$4.58 - $1.32 etc.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
5
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Select cards to make money amounts to add using mental strategies.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Select cards to make money amounts to subtract using mental strategies.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Take turns to flip 3 or 4 cards to make a three-digit or a four-digit number as a
money amount and keep a running total.
First player to reach $50.00 or $100.00 wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Take turns to flip 3 or 4 cards to make a three-digit or a four-digit number as a
money amount and subtract from $100.00 or $50.00, keeping a running total.
First player to reach 0 wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Take turns to select a card.
Decide whether to add it as a 10 dollar, a 1 dollar, a 10 cent or a 1 cent.
Repeat this 5 times with 5 different cards.
The child closest to $100.00, or a predetermined target number after 5 additions
wins.
NB: You could use the same card as your friend, but you may choose to add it as a
10 cent, while your friend may choose to add it as a 10 dollar.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Take turns to select a card.
Decide whether to subtract it from $100.00 (or $50.00 etc) as a 10 dollar, a 1 dollar,
a 10 cent or a 1 cent.
Repeat this 5 times with 5 different cards.
The child closest to 0, or a predetermined target number after 5 subtractions wins.
NB: You could use the same card as your friend, but you may choose to subtract it as
a 10 cent, while your friend may choose to subtract it as a 10 dollar.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Start with $50.00.
Take turns to flip 3 or 4 cards to make a three- or four-digit number.
If more cards red, subtract its value from your total.
If more cards black, add its value to your total.
If the same number cards are red as black, choose whether to add or subtract. T
The first player to either 0 or 10 000 wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Start with $50.00. In turn children flip a card.
Decide whether to use the card as a thousand, a hundred, a ten or a one.
If the card is black subtract its value from your total.
If the card is red, add its value to your total.
The first player to either 0 or $100.00 wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Use a calculator to add three- and four-digit numbers as money amounts, then
check.
Explain your strategy to a friend.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Use a calculator to subtract a three- or four-digit number as money amounts, then
check.
Explain your strategy to a friend.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Flip 10 cards.
Each secretly select 6 of the numbers to make 2 three-digit numbers as money
amounts to add together or 8 cards to make 2 four-digit numbers as money
amounts to add together.
Each add your numbers as money amounts.
They child with the highest / lowest total wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Flip 10 cards.
Each secretly select 6 of the numbers to make 2 three-digit numbers as money
amounts to subtract, or 8 cards to make 2 four-digit numbers as money amounts to
subtract.
Each subtract your numbers as money amounts.
The child with the highest / lowest total wins.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Select 6 or 8 cards.
Each child tries to make 2 three-digit numbers or 2 four-digit numbers as money
amounts to add with an answer in a target 10 dollar, a 1 dollar or a 10 cent.
For example, the numbers 4, 5, 8, 2, 3 and 1, and the target 1 dollar is $6.00. A child
could make the three-digit numbers, $1.32 + $4.85, or $2.58 + $4.13 etc.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Money using Mental Strategies
ADDITION AND SUBTRACTION 23, MONEY AND FINANCIAL MATHEMATICS 9 Add and subtract money with up to four digits using mental
strategies, including rounding total to the nearest 5 cents, then give change.
Sit with a friend.
Select 6 or 8 cards.
Each child tries to make 2 three-digit numbers or 2 four-digit numbers as money
amounts to subtract with an answer in a target 10 dollar, a 1 dollar or a 10 cent.
For example, the numbers 4, 5, 8, 2, 3 and 1, and the target dollar is $3.00. A child
could make the three-digit numbers, $5.34 -$1.82, or $4.58 - $1.32 etc.
http://www.alearningplace.com.au