Transcript Supporting the learning needs of high achieving students

Supporting the learning needs of
‘high achieving students’.
Exploring mathematical patterns with
cards, circles and grids
Mā te huruhuru
ka rere te manu.
It is the feathers which enable
the bird to fly.
Consider….
x x x
x x
x x x
Mt Tawarewa
How did that work?
Ideas to share?
"Choose any two digit number, add together both digits and then
subtract the total from your original number. When you have the
final number look it up on the chart and find the relevant symbol. "
mysticalball
The Fish Tank
You have a fish tank containing 200
fish and 99% of them are guppies.
You will remove guppies until 98% of
the remaining fish are guppies. How
many will you remove?
Using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 once and
only once.
Where can they be placed so that the horizontal
sum equals the vertical sum.
1
9
2
7
3
8
6 5 4
Some foundation work
• Calculate
a) 5 × 7
b) 19 × 21
c) 299 × 301
Do you see a pattern?
What about:
a) 24 × 26
b) 119 × 121
c) (n − 1 )(n + 1)
Let’s try 14 × 16
10 × 10
4 × 10
(n − 1 )(n + 1) = n2 - 1
Take a number
Take a number
Square that original number
Cube that original number
Add five times the original number and add this
to the cube of the original number
What do you notice?
10 playing cards
Watch the demonstration…
How can you do order the pack so that you can
replicate this?
What is the least consecutive …
• What is the least number of consecutive
natural numbers so that adjacent numbers
are:
a) 2 units apart
b) 3 units apart
c) 4 units apart
d) n units apart.
There’s a grid over there!
How long does it take to paint the
house?
If Sally can paint a house in 4 hours and John can paint the
same house in 6 hours, how long will it take for both of them
to paint the house together?
1 house
1
2
4
6
Answer
• Sally can paint 1/4 of a house per hour.
John can paint 1/6 of a house per hour.
Let's say the answer is t hours for the total job.
Then (1/4)t + (1/6)t = 1
(1/4 + 1/6)t = 1
(6/24 + 4/24 )t = 1
(10/24)t = 1
t = 24/10 hours = 2.4 hours
•
If Sally can paint a house in 4 hours, then she can paint 1/4 of a house in 1 hour.
If John can paint a house in 6 hours, then he can paint 1/6 of a house in 1 hour.
Let x be the number of hours it would take them to paint the house.
Working together, they can paint 1/x of the house in one hour, so
1/ + 1/ = 1/
4
6
x
Multiply by LCD, so 12x (1/4 + 1/6 = 1/x)
3x + 2x = 12
5x = 12
x=2.4 hours.
Also, 40% of 60 minutes is 24 minutes. Final answer = 2 hours and 24 minutes.
A third painter…
What if Wirimu can paint a house in 5 hours and he was able
to assist Sally and John, how long will it take for the three of
them to paint the house together?
1 house
1
2
4
6
Looking for patterns.
Draw / display
examples to give you
some ideas
Plotting points on a graph to
display your examples
Making links
Graphically
Numerically
What type of graph is it?
Straight Line
Linear?
Other?
Algebraically generalising
What is the rule?
Generating a
numerical
pattern /
sequence
Questions?