__POTW #1 HINTS:__

Notice that there 64 little squares, but there is also one very large square(the whole checkerboard) and there are a number of different sized squares such as 2 x 2, 3 x3 etc...

**the squares can also overlap one another**

THE HANDSHAKE PROBLEM: TRY TO MAKE AN ORGANIZED LIST

1 PERSON - 0 HANDSHAKES

2 PEOPLE - 1 HANDSHAKE

3 PEOPLE - 3 HANDSHAKES

4 PEOPLE - 6 HANDSHAKES

ETC...

SEE IF YOU CAN DISCOVER A PATTERN

I WOULD ALSO LIKE YOU TO USE A DIAGRAM TO PROVE YOUR ANSWER

__POTW #2 Hints:__

Remember that you only have one of each, and you do not have to use all of the coins. For example, you could buy an item for $0.11 by using a dime and a

penny. You could buy an item for $1.30 by using a loonie, a quarter and a

nickel.

__POTW #3 Hints:__

1 topping would mean 1 type of pizza could be made.

2 toppings would mean 3 types of pizzas could be made. For example, if the 2 toppings were ham and mushroom, the types of pizzas that could be made would be:

1) ham

2) ham and mushroom

3) mushroom

If we added another topping such as onion, then the following pizzas could be made:

1) ham

2) ham, mushroom

3) ham, mushroom, onion

4) ham, onion

5) mushroom

6) mushroom, onion

7) onion

Hints for POTW # 4:

Keep trying different combinations. I suggest using a labeled diagram to help. Adam and Larry will have to cross the bridge together at some point.

__POTW #5 Hints:__

Start with a simpler problem. For example find the smallest # that is divisible by 1,2,3,4,5 and 6. Then use multiples of that # until you find one that is divisible by 7. Then continue in a similar manner until you have a # that is also divisible by 8, 9, and 10. Be sure to realize that if some # is divisible by 2 and 3 it will also be divisible by 6 and if a number is divisible by 2 and 5 already it will also be divisible by 10.

__POTW #19 Cody's aquarium for his sea turtle named Mrs. V.__

a)carefully show all of your work

b) check the units carefully(hours for one hose, seconds for another, and minutes for the third)

c) convert them all to a common unit of time (ex. 1 litre per second means 60 litres per minute)

__Problem of the week #8 Fractions__

a) Try to determine what fraction of the tank 12 litres is.

b) What is the difference between 2/3 and 1/2?

__Problem of the week #9 Fractions__

You need to find out what one-fourth of one-half would be. Using a diagram may help.

__Problem of the week #11 FRACTIONS__

a)Find a common denominator for 9, 3, and 6.

b) Determine what fraction is left from one whole after adding the fractions for each of the three older children.

Problem of the week #12 Rectangles

Find a common denominator (LCM) for 4, 5, and 10

__Problem of the Week #13__ "Total Rectangles"

Hints: a) Rectangles can be differnt sizes

b) Solve simpler problems first and then set up a chart to help you discover the rule/pattern

ex. 1 small rectangle = 1 total rectangle

2 small rectangles = 3 total rectangles

3 small rectangles = 6 total rectangles

c) Be sure to use diagrams to help prove your answer.

__Problem of the week #14__ Gauss Problem

Hints: a)Make a t-chart and look for a pattern when you add 1 + 2 =, then 1+2+3, then 1+2+3+4

b) try to put pairs of numbers together to make the problem easier

Hint, Hint ex. 1 + 99, 2 + _, 3 + _, etc...

__Problem of the Week #15__ "Round Robin Tournaments"

HInts: a) Solve a simpler problem first. How many games are needed for a two, three, and

four team tournament? Use an organized list:

ex. Team A vs Team B, Team A vs Team C, Team B vs Team C

b) Make a chart with the data you have discovered. ex. T-chart

c) Look for any patterns in your T-chart.

d) Attempt to show the necessary games with diagrams. ex. For a 3 team tournament use

a triangle to connect all 3 teams, for 4 teams use a square, etc...

__Problem of the Week #5__ "The Pond Problem"

Hints: a) Set up a chart with the dates

b) Consider working backwards

__Problem of the Week #4 __"Peterson's Pizza Parlour"

Hints: a) Use an organized list

b) solve a simpler problem first

ex. How many combinations are possible with 1, 2 or 3 toppings?

c) Look for a pattern

__Problem #1 Checkerboard__

Hints: a)The answer is not 64

b) A 1 x 1 square has 1 square in total, but a 2 x 2 square does have 4 squares in fact there are 5 squares in total. There are 4 small squares and 1 large square for a total of 5.

c) A 3 x 3 square will have 14 squares in total. 9 small, 4 medium, and 1 large

__Problem #2 Earn $1000000000__

It will take an average of three seconds to count and say each number from one to one billion.

Please guess/estimate first, and then calculate how many seconds, minutes, hours, days or years it will take.

Start with a simpler problem.

a)Find a common denominator for 9, 3, and 6.

b) Determine what fraction is left from one whole after adding the fractions for each of the three older children.

Problem of the week #12