EXPLORING THE TECHNOLOGY

Teacher Works CD Teacher Resources: Page 12/128

Page 6

Teacher Works CD Teacher Resources

5 Minute Check: Page 1/101

Teacher Works CD Teacher Resources

5 Minute Check: Page 1/101

45 minutes

30 minutes

mhpdguest02

mhpd

http://www.mcgraw-hill-pd-online.com/

Student Achievement

30 minutes

A Challenge Problem

20 minutes

DAY 3

Challenge Problem

20minutes

1st 10 minutes: Discuss and come up with a strategy.

Last 8 minutes: Groups will share their strategies with ALL participants.

On Tuesday groups will share their solutions.

My name is FELWAH. I am an owner of a

small CARROT plantation in a

remote desert oasis.

I need your help !!!

FELWAH the HorseIs an owner of a small carrot

plantation in a remote desert oasis.

Handout Booklet: Page 3

Felwah’s harvest, consists of 3000 carrots.

The market place where the stash can be cashed in is 1000 miles away. However, Felwah must walk to the

market, and can only carry up to 1000 carrots at a time. Furthermore, being a horse, Felwah eats one carrot during each and every mile she walks (so Felwah can

never walk anywhere without carrots).

How many carrots can Felwah get to the market?

My name is FELWAH. I am an owner of a small banana plantation in a remote desert

oasis.

I need your help !!!

A Solution

…to the Felwah Horse problem …

…discuss for 15 minutes & we will put closure to it at our next

session…

A Solution to the Felwah Problem

5. travel an additional 333 1/3 miles, you're left with 666 2/3, stash 333 1/3 there (533 1/3 mile point), you have 333 1/3 left

1. Start trip with 1000 carrots

2. Travel 200 miles, you're left with 800 - stash 600 at 200 mile point, keep 200 for 200 mile trip back.

3. Pick up another 1000

4. travel 200 miles, you have 800 left, pick up 200 from stashed, you now carry 1000 and have 400 more stashed.

6. travel back 333 1/3 miles to 200 mile point, you have no bananas left, pick up 200 stashed (leaving 200 still at 200 mile point), go back the other 200 miles.7. pick up another 1000

8. travel to 200 mile point, leaving 800 bananas, pick up remaining 200 stashed

9. with 1000 bananas travel 333 1/3 miles to 533 1/3 mile point, you're left with 666 2/3 bananas.

10. pick up all 333 1/3 that were stashed there

11. you're back at 1000 carrots

12. make remaining 466 2/3 mile trip, 1000-466 2/3 = 533 1/3 carrots left at end.

A spider and a fly are in a 12 meter high room having a 12 meter by 30 meter floor. The spider is on one 12×12 wall halfway between the adjacent walls and 1 meter from the floor. The fly is on the opposite 12 ×12 wall halfway between the adjacent walls and 1 meter from the ceiling. The spider wishes to crawl to where the fly is via the shortest possible route. Find the distance of the shortest possible path.

12 m

12 m

30 m

I want that FLY

2 min

12 m

12 m

30 m

Content: Developing Problem Solving Strategies

Pedagogy: Guiding Students Using Well Chosen Prompts.

Hint 1: Describe the information in terms of TWO dimensions.

12 m

12 m30

m

Shortest Possible Route !

What possible paths areavailable for the spider ?

floor

ceiling

Two Dimensional

Three Dimensional

12 m

12 m

30 m

My Math knowledge will help me

FIND the shortest path.

Is This REALLY The SHORTEST

path ?

floor

30 111

42 mceiling

42

S o l u t i o n

CASE ONE: (a three face solution) is to go to the nearest edge, then across the floor and finally up the opposite wall for a total distance of 1+30+11 = 42.

If we “unfold” the room,

the spider will follow a straight-line

path to the fly.

I want that fly

floor

30 111

42 meters

S o l u t i o n

CASE TWO: (a three face solution) is to go across the wall, NOT the floor nor the ceiling, for a total distance of 43.174...

2210 6 30 6 1864

floor 66 30

10

A New Net

ceiling

S o l u t i o n

CASE THREE: (a four face solution) is to go to the nearest edge, then cut across a corner of the floor, then cut across another corner of the wall, and finally go up the adjacent wall to the opposite point, for a distance of 40.718...

16581166301 22 40.718

floor

30 61

ceiling

40

S o l u t i o n

24

ceiling

side wall

side wall

floor

32

CASE FOUR: (a five face solution) is to go to the nearest edge, then cut across the corner of the floor, then across the side wall and then cut across the corner of the ceiling and finally go to the opposite point, for a distance of 40.

2 26 12 6 1 30 1x

40x

12 m

12 m30

m

Break: Back at 12:30

How are science (and

other cross curricular

topics) embedded

throughout the program?

Handout Booklet:

Pages 1-2

THIRD GRADE

In the Chapter Introductions

THIRD GRADE

Handout Booklet:

Pages 3-4

In Problem Solving Lessons

Handout Booklet:

Pages 7-8

Handout Booklet: Pages 9-

VikHelp Me Explain

How Would You Solve The Problem ?

10

3115

Any

volunteers ?

Help Me Get The Answer Using Sound Mathematical Reasoning

“No Fuzzy Stuff”

10

3115

Help Me Get The Answer Using Sound Mathematical Reasoning

“No Fuzzy Stuff”

10

3115

6th Grade

10

3

1

115

10

311510

10

1147

10

7114

by long division

Mathematical Reasoning“No Fuzzy Stuff”

10

3115

1410

13

1

10

1114

00

3

1

1147

10

1147

10