Mystery Number...  it is greater than 546 tenths  when you divide it by 35.6, the quotient is a whole number  there is an 8 in the tenths place  it is less than 20,000 hundredths

 another story problem or a mathematical task?  determining cognitive demand  when to use high cognitive demand tasks

On the Greenway trail there are posts marking every quarter (1/4) mile. Jamie began jogging at the starting post. She jogged until she reached the post marked 3/4 mi., where she began to walk. She began jogging again at the 1 mi. post, where she continued to jog until she reached the one and a half mi. post. She walked until she reached the one and three- fourths mi. mark; then she jogged to the 2 mi. post where she turned around and jogged the entire way back to the start post. How far did Jamie jog? Explain how you know.

___ + ___ =.39 ___ x ___ = 20 ___ - ___ =.039 ___ ÷ ___ = 320

 require complex, non-algorithmic thinking  require justification and explanations for solutions and methods used  procedures cannot be followed mindlessly  require exploration & understanding of mathematical concepts, processes, or relationships  require considerable cognitive effort

 algorithmic  reproducing previously learned facts, rules, procedures, or formulas  focused on producing correct answers  require no explanation or explanations focus solely on the procedure used

1, = 1, = 1,369 1, = 1,309 1, = 1,304 1, = 1,294 How do you know 275 was subtracted from 1,569?

The festival committee gave out prizes to the people in the entrance line according to their position in line. Every 9th person in line got a free wristband for unlimited rides, and every 6th person in line got a free cotton candy. In what position in line was the first person to receive both a wristband AND a ticket for cotton candy? How do you know?

Start with any fraction... add 3/4 subtract 1/8 subtract 5/8 What do you notice about the number after the final step? What types of numbers will this work for?

How does the use of high cognitive demand tasks align with Investigations?

A variety bag of Halloween candy has 393 candies. If you can determine how to share them equally among the entire class, you will each receive your fair share of the candies.

23 x 10 = = = = = = = = = 2

A rectangular garden has dimensions of 10 x 40, which is an area of 400 square feet. You could enclose this garden with 100 feet of fencing. Suppose you wanted to enlose another garden with 100 feet of fencing. What are the length and width of the garden with the greatest area you could enclose? Explain your thinking.

Each marble has the same mass. The containers are equal in mass. What is the mass of an empty marble container? Explain how you know.

The Swim Club charges a $50 membership fee plus $40 per month. The Cool Pool Club charges a $175 membership fee plus $20 per month. Which is the better deal? Explain your thinking.

"...a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity.

...but if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a task for, and some means of, independent thinking." Polya, 1973/1945

Friel, S. (2009). Powerpoint Presentation Greenes, C., Dacey, L. S., Spungin, R. (1999). Hot math topics. Dale Seymour Publications: Parsippany, NJ. various volumes and ages. Sellers, P. (2010). The trouble with long division. Teaching Children Mathematics, p