Alberta Regional Professional Development Consortia

High School Mathematics Institute #1 hosted by Calgary Regional Consortium

January, 2010 with Dr. Peter Liljedahl

Outline and Discussion Guide

Clip Number / 1
Description / Introduction to Course Sequences
Possible Questions /
  • Which course sequence(s) will be recognized by universities and colleges?
  • Which course sequence(s) will be recognized by NAIT or SAIT?
  • Which course sequence(s)will be recognized by trades (Registered Apprenticeship Program)?

Clip Number / 2
Description / Transition from Grade IX to Grade X. The following flowchart is taken from the Alberta Program of Studies Mathematics 10 to 12 with Achievement Indicators, 2008

Possible Questions / What are the pre-requisites for M10Common and M10-3
Clip Number / 3
Description /
  • Discussion of what needs to change, how we look at curriculum, and what makes students stop thinking.

Possible Questions and activities /
  • Consider beginning with a 2 X 2 grid rather than 3 X 3
  • See following activity. Construct required grid on classroom floor with masking tape . Use people to represent X and each O to model the question.
  • What needs to change in the classroom?
  • How does the new program of studies look at curriculum?
  • What processes can teachers implement that will make students think?
  • What do teachers do that allows students to opt out of thinking?

Clip Number / 4
Description / How do we get students to think, take risks and collaborate?
Possible Questions /
  • What will assessment look like?
  • What will the classroom setting look like? Consider board work, group work, evaluation (partner quizzes, etc)
  • Consider various models for utilization of results from partner quizzes—do you agree that these marks should be ‘discarded’?

Clip Number / 5
Description / Questions can be presented textually, modelled physically or stated orally.
THE WINE SNOB –
I like wine – but I'm a bit of a snob! I won't drink wine that has been exposed to light more than 10 times. I drink 1 bottle of wine a day. To help reduce the trips to the store I have bought a BIG wine chest and a SMALL wine chest that protects my bottles from the light. The question is – how often do I have to go to the wine store?
Ideal work space
  • Whiteboards or windows
  • Tables with manipulatives (if needed)
Clarifying points
  • The wine comes home from the wine store in boxes.
  • The boxes do not fit into the wine chests.
  • When I open a wine chest ALL of the bottles in the chest are exposed to light.
  • I will drink bottles that have been exposed to light up to 10 times.

Other possible questions that have more than one solution.
CATS AND RATS – If 6 cats can kill 6 rats in 6 minutes, how many cats are needed to kill 100 rats in 50 minutes?
Ideal work space--Whiteboards or windows
Clarifying points --You can't have fractional cats or rats.
Possible extension--There is more than 1 correct answer! To find more answers think about how the cats may or may not be working together.
5TH NUMBER – Write down two whole numbers. Now write down a third number that is the sum of the first two. Write down a fourth that is the sum of the previous two. Finally, write down a fifth number that is the sum of the previous two (eg. 3, 45, 48, 93, 141). What do the first two numbers have to be in order for the fifth number to be 100?
Is there more than one solution?
Ideal work space--Whiteboards or windows
Clarifying points
  • The numbers do not have to be in ascending order.
  • Repeat numbers are permitted.
Extension
  • Find multiple representations for your solution.
  • Keep in mind that there are multiple answers to these ‘non-standard’ questions, depending upon interpretation.