1. Numeracy At PFFNHS PLC November 4, 2010

2. What is Numeracy? Numeracy is the ability to reason with numbers and mathematical concepts A person who is numerate can think and express themselves effectively in quantitative terms Numerate people confidently and effectively use mathematics in real life situations

3. What Role Does Numeracy Play in My Classroom? Math has a role in all subject areas, and is not only relegated to math class What concepts can be looked at in quantitative terms? Debunk the myth that only “math brains” can do math  math is accessible to all! Promote life skills, problem solving, and critical thinking related to numeracy

4. Strands K- 8 Number Sense and Numeration Measurement Geometry and Spatial Sense Patterning and Algebra Data Management and Probability Gr. 9 Applied Math Number Sense and Algebra Linear Relations Measurement and Geometry

5. Opportunities to Focus on Numeracy Number Sense and Algebra Examples Representing numbers and relationships among numbers Magnitude and Place value Positive and negative integers Operations Comparing incomes, e.g how much richer is a billionaire than a millionaire? Ionic charge, measuring temperature, or examining temperature and climate data, income Planning meals, planning events etc.

6. Number Sense and Algebra Example Solving Problems Involving Proportional Reasoning Fractions Percentages Proportions Simplifying Expressions and Solving Equations Recipes- halving and doubling fraction measures Population dynamics Scale factors in art, geography Representing variables in science, using formulas in science Opportunities to Focus on Numeracy

7. Linear RelationsExample Using Data Management to Investigate Relationships Determining Characteristics of Linear Relations Investigating Constant Rate of Change Surveys, fitness data Investigating relationships between variables in science- are they linear or not? Rates, speed, velocity, etc. in science Opportunities to Focus on Numeracy

8. MeasurementExamples Investigating the Optimal Values of Measurements of Rectangles Solving Problems Involving Perimeter, Area, and Volume Investigating and Applying Geometric Relationships Planning and building structures Determining amount of materials needed for a project; quantities of ingredients in cooking Art; star blankets Opportunities to Focus on Numeracy

9. Example- Bioamplification (SNC2L) I asked my students to look at how the concentration of a toxin increased as it moved through the trophic levels of a food chain. The situation:  Each plant in the ecosystem absorbed 1 drop of the toxin.  Insects each ate 25 plants.  Small fish each ate 10 insects.  Large fish ate 5 small fish.  You eat one fish a day for three days.

10. Determine how many molecules of the toxin are in one... a)Plant? b)Insect? c)Small Fish? d)Large fish? e)Human? The Task…

11. How many drops of the toxin are in each plant? Students were able to tell me that each plant had one drop of the toxin The situation:  Each plant in the ecosystem absorbed 1 drop of the toxin.  Insects each ate 25 plants.  Small fish each ate 10 insects.  Large fish ate 5 small fish.  You eat one fish a day for three days.

12. How many drops of the toxin were in each insect? Each insect ate 25 plants. Each plant has one drop of the toxin in it Students were able to tell me that each insect would eat 25 drops of the toxin The situation:  Each plant in the ecosystem absorbed 1 drop of the toxin.  Insects each ate 25 plants.  Small fish each ate 10 insects.  Large fish ate 5 small fish.  You eat one fish a day for three days.

13. How many drops of the toxin were in the small Fish? A lot of students were stumped! They could not tell me how many drops of the toxin were in the small fish I drew a picture on the board to help them visualize the problem I asked one student to share his reasoning: The situation:  Each plant in the ecosystem absorbed 1 drop of the toxin.  Insects each ate 25 plants.  Small fish each ate 10 insects.  Large fish ate 5 small fish.  You eat one fish a day for three days.

14. “Four 25s are 100”“so this is another group of 100” “and this much is 50” “so the total is 250 drops of the toxin.”

15. I was surprised because I thought he would say: “25 times 10 is 250” I asked the class what other ways there were to represent the answer. We discussed their different ways of reaching the answer.

16. How many drops of toxin were in the large fish? So now we know that each small fish had 250 drops of the toxin. Each large fish ate 5 small fish Here are some of the strategies I saw: The situation:  Each plant in the ecosystem absorbed 1 drop of the toxin.  Insects each ate 25 plants.  Small fish each ate 10 insects.  Large fish ate 5 small fish.  You eat one fish a day for three days.

17. 250 +250 1250 250 X 5 1250 500 250 1 250

18. By focusing on the math, I had: – Provided opportunity for students to fill in a gap in their number sense – Provided opportunity for students to move from additive thinking to multiplicative thinking – Demonstrated a mental math strategy – Demonstrated a strategy for problem solving (drawing a picture) – Acknowledged that there can be more than one way to solve a problem

19. Creating Opportunities to Improve Numeracy Group 1 Colleen Darby Lola Shawn Desta Group 2 Scott Kim Angelynn Ashley Darryl Group 4 Tom Craig Nathan Mike Group 3 Robert Kate Brea-ann Sharon