1. Problem solving Div. one and two
St. Pat’s, Tuesday November 29, 2016
Day Four

2. Math Prayer
Lord teach me to number my days
And graph them according to your ways
Trusting you to base me in my plan
To complement your perfect diagram
Subtract the points you do not want from me
But add the values you have set for me
Divide the dividends I possess accordingly
So I can multiply them systematically.
Draw the lines I have to follow
Guide me properly with your arrow
Because sometimes I tend to be irrational
Yet all the while you want me to be rational.
Well I learn that life is like a slope
With its ascends and descends that I must cope
Going through such a wonderful formula
Is just like solving problem in algebra
Life is indeed an infinite equation
Perfected by your eternal computation
And only a minuscule projection
Give thanks and praise your Almighty creation
Amen

3. Let’s begin with a problem
Horizontal surface with manipulatives
Wolf, Sheep, and Cabbage
 You need to move the wolf, sheep, and cabbage to the opposite shore by rowing them over one at a time in a boat. It gets more difficult though because when you are not around, the wolf will eat the sheep, the sheep will also do the same when alone with the poor little cabbage. How do you do this?

4. What makes a good problem great?
Low floor High ceiling
Accessible to all/success for all
Multiple strategies
Possibly multiple solutions
Thinking/problem solving/collaborating/persevering
How we present it, how we ask questions, how we don’t show, how we don’t tell, how we teach…

5. Speed dating
Share your favourite problem solving experience from your classroom

6. Let’s look at some problems…

7. Moving colours
Give each student a coloured circle (or use different shapes) red or yellow (or other colors) that you have prepared. There should be equal numbers or one more of one of the colors.
Ask students, “How many students have red circles and how many have yellow circles.” Encourage them to get up and move around the room to work this out.
More possible questions:
“How can we show that we have an equal number of each color or more of one color than the other color?”
“How many students can fit in a row on the carpet?”
“How many rows will we have?”
“What would be the best arrangement?”

8. Three block towers
How many ways can we make a tower with three blocks, with four blocks, with five blocs….?

9. Ice cream scoop
Your favourite ice-cream shop has 10 flavours of ice-cream.
How many different 2-scoop cones can you make with 10 flavours? What about 12 flavours?
What about “n” flavors?

10. Snap it
Each child makes a train of connecting cubes of a specified number.
On the signal “Snap,” children break their trains into two parts and hold one hand behind their back.
Children take turns going around the circle showing their remaining cubes.
The other children work out the full number combination.

11. How close to 100?
This game is played in partners. Two children share a blank 100 grid.
The first partner rolls two number dice.
The numbers that come up are the numbers the child uses to make an array on the 100 grid.
They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible.
After the player draws the array on the grid, she writes in the number sentence that describes the grid.
The second player then rolls the dice, draws the number grid and records their number sentence.
The game ends when both players have rolled the dice and cannot put any more arrays on the grid.
How close to 100 can you get?
Variation
Each child can have their own number grid. Play moves forward to see who can get closest to 100.

12. Squares to stairs How do you see the pattern growing?
Extension question ideas:
How many squares are in a different figure?
Can you use 190 squares to continue the pattern?
How can you figure out how many total squares are in any figure?
If you have 1,478 squares, can you make a stair-like structure using all of the squares?

13. RESOURCES https://www.youcubed.org/tasks/
RESOURCES

14. Working groups/collaboration
Kindergarten -
Grade one -
Grade two -
Grade Three -
Grade four -
Grade five -
Grade six -

15. Let’s finish with a problem!
Can you get all of the dark green frogs to the right of the empty spot and all of the light green frogs to the left of the empty spot? The frogs move by either “hoping” or “sliding” forwards to a vacant spot.
Note: A frog can only slide into a vacant spot next to it OR can only hop over one other frog to land in an open spot.
Or this one -

16. Can we problematize the curriculum?
Teaching through problem solving as a pedagogical approach…
let’s talk about this next time!