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Stage 3 Outcome
A student:
› describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions
MA3-1WM
› selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations
MA3-2WM
› gives a valid reason for supporting one possible solution over another MA3-3WM
› orders, reads and represents integers of any size and describes properties of whole numbers MA3-4NA
Teaching and Learning Activities
Language: Students should be able to
communicate using the following
language: number line, whole number,
zero, positive number, negative
number, integer, prime number,
composite number, factor, square
number, triangular number.
Notes/ Future Directions / Evaluation
Ignition Activities
Greedy Pig
1. To play this game you need an ordinary 6-sided die.
2. Each turn of the game consists of one or more rolls of the die. You keep
rolling until you decide to stop, or until you roll a 1. You may choose to stop at
any time.
3. If you roll a 1, your score for that turn is 0.
4. If you choose to stop rolling before you roll a 1, your score is the sum of all the
numbers you rolled on that turn.
5. Each player has 10 turns.
6. The player with the highest score wins.
There are many variations of this game, the most common being a full class version in
which the teacher rolls the die, and calls out the numbers. All students play using the
same numbers and their score depends on when they elect to ‘save’ their score. If
they save their score any further rolls that turn do not count towards their score. If a 1
is rolled all players who have not saved their score get 0 for that turn and the next turn
starts.
The ones dice can be changed to adding tens, hundreds and thousands by writing on
blank dice. 1 could be changed to any other number as the key number to avoid
rolling.
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Date/
LAC Icons
Calculator Race
Give students a series of addition combinations of various numbers. One group can
add these numbers using pencil and paper another group could use calculators and a
third group could try and solve the problems mentally. Students will come to realise
that the most efficient strategy to solve addition problems varies according to the
difficultly of problems.
Explicit Mathematical Teaching – Integers on the number line
Literacy
Negative Numbers (-)
Positive Numbers (+)
(The line continues left and right forever.)
Integers on the left are smaller than integers on the right.
Examples:
•
•
•
3 is smaller than 8
-1 is smaller than 1
-9 is smaller than -8
Example: John owes $3, Virginia owes $5 but Alex doesn't owe anything, in fact he
has $3 in his pocket. Place these people on the number line to find who is poorest and
who is richest.
Having money in your pocket is positive.
But owing money is negative.
So John has "-3", Virginia "-5" and Alex "+3"Now it is easy to see that Virginia is
poorer than John (-5 is less than -3) and John is poorer than Alex (-3 is smaller than
3), and Alex is, of course, the richest!
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Explicit Mathematical Teaching – Integers and Calculators
Subtracting is the same thing as adding the negative.
So, whenever you subtract, rewrite the subtraction sign as + Then, all the the rules below still apply when performing operations.
Positive + Positive = Positive
Negative + Negative = Negative
The sign for Positive + Negative or Negative + Positive depends on which number
is bigger.
Literacy
Critical and creative thinking
Use a number line to explain the following:
Always subtract and keep the sign of the higher number!
Ask ‘ What if we subtract a larger number from a smaller number on a calculator?
Try these examples on the calculator:
1. 8 - 9 = -1
2. 12 – 15 = -3
3. 19 – 21 = -2
4. 7 – 11 = - 4
Extension
Then ask: ‘What would happen if we took away a negative number from a negative
number?’
Illustrate on number line:
5. -1 – 3 = - 4
6. -11 − 4 = -15
7. -20 – 5 = - 25
Try some calculations of your own.
~3~
Literacy
Explicit Teaching – Primes and Composites
A prime number is a whole number that only has two factors which are itself and one.
A composite number has factors in addition to one and itself.
The integers 0 and 1 are neither prime nor composite.
All even numbers are divisible by two and so all even numbers greater than two are
composite numbers.
Students find all prime numbers between 2 and 100.
Answer:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89
and 97.
Prime Number Challenge:
Great Granddad is very proud of his telegram from the Queen congratulating him on
his hundredth birthday and he has friends who are even older than he is. Great
Granddad was born in the year A (where A is the product of 3 prime numbers), he was
20 years old in the year B (where B is the product of a prime number and a square
number), he was 80 years old in the year C (where C is the product of two prime
numbers) and he celebrated his 100th birthday in the year D (where D is even and the
product of 4 prime numbers). When was he born?
http://nrich.maths.org/828
Literacy
Critical and creative thinking
Explicit Teaching - Square Numbers
A square number is a number that can be arranged in a square pattern. The
patterns of the first three square numbers are depicted below.
Critical and creative thinking
All numbers that end in five are divisible by five; all numbers that end with five and are
greater than five are composite numbers.
The first square number, 1, is shown as a
square containing a single dot. There is 1
row containing 1 dot.
So, there is 1 × 1 = 1 dot in this square
number.
The second square number, 4, is shown
as a square with 2 dots in each side. It is
clear that there are 2 rows each
containing 2 dots.
So, there are 2 × 2 = 4 dots in this square
number.
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The third square number, 9, is shown as a
square with 3 dots in each side. It is clear
that there are 3 rows each containing 3
dots.
So, there are 3 × 3 = 9 dots in this square
number.
Following the pattern above, we can find any particular square number. e.g. The
fourth square number will form a square with 4 rows each containing 4 dots.
So, there are 4 × 4 = 16 dots in the square. Likewise, the fifth square number will
form a square with 5 rows each containing 5 dots.
So, there are 5 × 5 = 25 dots in the square.
2
Note that 5 is often read as '5 to the power 2' and 2 is called the index (or power).
Literacy
Information and communication technology
capability
Critical and creative thinking
Explore square numbers using arrays and grid paper.
Explicit Teaching – Triangular Numbers
A triangular number
Watch the YouTube video below and create a script to explain the formation of
triangular numbers.
http://www.youtube.com/watch?v=8aZqTzH_BD8
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Information and
communication technology
capability
Literacy
Prime or Composite
http://au.ixl.com/math/year-6/prime-or-composite
Information and
communication
technology capability
Literacy
Integers on a number line
http://au.ixl.com/math/year-6/number-lines-with-integers
Information and communication technology
capability
Literacy
Prime or Composite?
http://au.ixl.com/math/year-6/prime-or-composite
http://au.ixl.com/math/year-5/prime-and-composite-numbers
~6~
Information and communication
technology capability
Triangular Numbers
http://www.myteachingplace.com.au/index.php/resources
/years5_6_triangular_square_numbers_root_t_page_1.html
Information and communication
technology capability
Triangular and Square Numbers
http://www.myteachingplace.com.au/index.php/resources/
years5_6_triangular_square_numbers_root_t.html
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