By: Robin Kapoor, Kin Wong, Dayana El-Rafehi

 Activity #1: Jelly Bean  Activity #2: A rule to remember  Context: Numeracy  Historical Background  Activity #3: Numeracy in other subjects  Backward Design  Unit Plan  Lesson Plans  Activity #4: Mole Fun  Discussion

Numeracy is the knowledge of the basic number skills and the ability to apply those skills in contexts that require high levels of literacy to interpret situations and make judgements - Advert English Dictionary Numeracy is the mathematics for effective functioning in one's group and community, and the capacity to use these skills to further one's own development and that of one's community. Numeracy is a critical awareness which builds bridges between mathematics and the real world, with all its diversity - John Dingwall

 Distinction between numeracy and mathematics was sharply drawn in the 18 th and 19 th centuries ◦ Numeracy – a concrete skill embedded in the context of real-world ◦ Mathematics – abstract, formal subject of study  precollege work did not emphasize mathematics (ie. Harvard University did not even require basic arithmetic for admission until 1802)  Around 1800, there was an increased exposure to arithmetic which consisted of the study of practical skills aimed at boys planning to go into economics (practiced real life problems)

 instead of learning abstract rules capable of generalization in the real world, students memorized the solution to each and every problem that is encountered  after the War of 1812, some educational theorists proposed entirely new ways to teach arithmetic  this new way of teaching introduced many people, males and females, to the basics of “quantitative literacy”.  It was not till 1998 that the term “numeracy” became common currency

“Mathematical literacy is particularly important for careers in science and technology, which ultimately enhance the capacity of the Canadian economy for innovation” -Human Resources and Development Canada

There was a statistically significant difference between the estimated average combined mathematics scores of 15-year-old boys and girls in both 2003 and In 2003, boys had an estimated average score (541) that was 11 points higher than the score for girls (530). In 2006, the gap between the two genders remained relatively constant, at only 14 points; boys achieved an estimated average score of 534 while girls achieved a score of 520. Scores for both genders decreased between 2003 and NATIONAL PICTURE:

than the Canadian average.

INTERNATIONAL PICTURE:

 An increasing number of jobs require employees to handle data, work with spreadsheets, and interpret statistics.  been estimated that businesses spend more each year on improving employees' numeracy skills than the government spends on maths education in schools.  poor levels of numeracy are a greater barrier in the workplace than low levels of literacy

 Numeracy for everyday life (e.g., budgeting, time management, games/sports, health related, and household tasks).  Numeracy for community, for civic participation, and for understanding social and political issues.  Work related numeracy, including measuring, scheduling, tracking/monitoring, and managing revenues and expenditures.  Numeracy for personal organization, in matters such as money, time, and travel.  Numeracy for knowledge and further learning (needed for further study in disciplines and trades requiring mathematics).

 Each table group is given a subject (History, Science, Arts, English, Music, Phys-ed, etc)  Brainstorm, as a group, how numeracy is used/involved in these courses.

Mole Counting

 What is Avogadro’s favourite soda drink?  Who is Avogadro’s favourite rapper?  What is Avogadro’s favourite summer fruit?

“A Mole Is A Unit“A Mole Is A Unit”

Chemistry Grade 11: Quantities in chemical reactions Overall Expectations D1: analyse processes in the home, the workplace, and the environment sector that use chemical quantities and calculations, and asses the importance of quantitative accuracy in industrial chemical processes D2: investigate quantitative relationships in chemical reactions, and solve related problems D3: demonstrate an understanding of the mole concept and its significance to the quantitative analysis of chemical reactions Big Ideas Relationships in chemical reactions can be described quantitatively The efficiency of chemical reactions can be determined and optimized by applying understanding of quantitative relationships in such reactions Essential Question How has our knowledge of the quantitative relationships in chemical reactions used in the home, the workplace and the environmental sector? Guiding Questions Why is a balanced chemical reaction essential? What type of information could be extracted from a balanced chemical reaction? Based on your knowledge on the mole concept, how would you optimize the synthesis of a product in a chemical reaction?

DAY 1 HOOK: The Dozen Lab Introduction to Mole concept DAY 2 Introduction to Avogadro’s number- conversions between number of particles and number of moles Video-Mole Day Class work-Dozen vs. Mole DAY 3 Molar Mass and Moles (conversions between molar mass and moles) ACTIVITY: chalk lab Class work-Worksheet DAY 4 Mass and Molecules (mass to particles; particles to mass) LAB: The bubble gum lab Class work- textbook work DAY 5 QUIZ PART ONE: Percent Composition & Hydrates Self taught Lab, then debrief of what they learned DAY 6 PART 2: Lab continuation Empirical & Molecular Formulae Class work- textbook work DAY 7 & 8 Introduction to Stoichiometry Class work- worksheets DAY 9 Demo: limiting reagent Limiting Reagents and Excess Reagents Class work- textbook work DAY 10 LAB : Limiting Reagents Lab Class work- textbook work DAY 11 WORK PERIOD DAY 12 Demo: Percentage yield Class work-Preparation for lab DAY 13 Lab: Percent Yield DAY 14 Review: Mole Race DAY 15 UNIT TEST

Overview, Expectations and Rationale 1. Big Ideas:  Understanding the significance of Avogadro’s Number is chemistry  Understanding conversions between moles and number of atoms, particles, or molecules 2. Ministry Expectations: Overall  D3. Demonstrate an understanding of the mole concept and its significance to the quantitative analysis of chemical reactions

Specific  A1.12 use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI and imperial units)  A1.13 express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures  D2.1 use appropriate terminology related to quantities in chemical reactions, including, but not limited to: Stoichiometry, percentage yield, limiting reagent, mole, and atomic mass [C]  D3.2 describe the relationships between Avogadro’s number, the mole concept, and the molar mass of any given substance

Overview, Expectations and Rationale 1. Big Ideas:  Relationships in chemical reactions can be described quantitatively  The efficiency of chemical reactions can be determined and optimized by applying an understanding of quantitative relationships in such reactions

2. Ministry Expectations: Overall  D1. Analyze process in the home, workplace, and the environment sector that use chemical quantities and calculations and assess the importance of quantitative accuracy in industrial chemical processes  D2. Investigate quantitative relationships in chemical reactions, and solve related problems;  D3. Demonstrate an understanding of the mole concept and its significance to the quantitative analysis of chemical reactions

Developing Skills of Investigation and Communication:  D2.1 use appropriate terminology related to quantities in chemical reactions, including but not limited to: stoichiometry, percentage yield, limiting reagent, mole and atomic mass [C]  D2.3 solve problems related to quantities in chemical reactions by performing calculations involving quantities in moles, number of particles and atomic mass [AI]  D2.5 calculate the corresponding mass, or quantity in moles or molecules, for any given reactant or product in a balanced chemical equation as well as for and other reactant or product in the chemical reaction [AI] Understanding Basic Concepts:  D3.2 describe the relationships between Avogadro’s number the mole concept, and the molar mass of any given substance  D3.4 explain the quantitative relationships expressed in a balanced chemical equation, using appropriate units of measure (e.g. moles, grams, atoms, ions, molecules)

 Brainstorm- ◦ the importance of numbers in our daily lives (where are numbers used/required) - the mole and Avogadro's number-how does the mole relate to daily lives  Chalk activity- ◦ Students can gather class data (input data on table on board) and analyze the gathered data

Overview, Expectations and Rationale 1. Big Ideas:  Definite proportions of substances can be calculated, and the relationship between Avogadro’s number, the mole concept, and the molar mass of any given substance. 2. Ministry Expectations: Overall  D2. Investigate quantitative relationships in chemical reactions, and solve related problems.  D3. Demonstrate an understanding of the mole concept and its significance to the quantitative analysis of chemical reactions

Specific  D2.1 use appropriate terminology related to quantities in chemical reactions, including, but not limited to: stoichiometry, percentage yield, limiting reagent, mole and atomic mass  D2.3 solve problems related to quantities in chemical reactions by performing calculations involving quantities in moles, number of particles, and atomic mass  A1.1 formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research  A1.5 conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data  A1.11 communicate ideas, plans, procedures, results, and conclusions orally, in writing, and/or in electronic presentations, using appropriate language and a variety of formats (e.g., data tables, laboratory reports, presentations, debates, simulations, models)  A1.12 use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI and imperial units)  A1.13 express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures

 For this lesson one could change the’ mini-lab’ to “guess the weight of each substance and win a prize” ◦ The teacher could explain how all of the different compound are one mole each (the teacher would write down all of the substances on the blackboard) ◦ This will motivate and encourage students to participate by actually estimating a weight through direct observation of the various substances ◦ this could illustrate to students the importance of estimations in science which is a crucial part of numeracy

 Each table will be provided with one handout  As a group work on solving the problems given  After having completed the questions, check answers with teachers circulating  One person from the group is responsible for coming up to board and writing down the appropriate words on worksheet that corresponds to the answers obtained  Words will form a sentence  Fastest group to correctly obtain a sentence will win a prize

 To graduate from high school, students needs to have 3 credits in mathematics. Is this too few/much?  How can you alleviate the math/numeracy fear that some teachers may have?  Should the government implement an EQAO test for the grade 12s not as a requirement for graduation, but for the post- graduate school/workplace to assess the student’s capability in mathematics?  Is math inborn?

 Cohen, Patricia (2001). The Emergence of Numeracy. In: Steen, L.A. (Ed.) Mathematics and Democracy, The case for Quantitative Literacy. USA: NCED, The Woodrow Wilson National Fellowship Foundation.  Dingwall, John. (2000). Improving Numeracy In Canada  McCarthy, L and Zawojewski, J.S. (2007). Numeracy in Practice. Principal Leadership (Middle School Ed., 7(5),