By: Robin Kapoor, Kin Wong, Dayana El-Rafehi
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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
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Distinction between numeracy and mathematics was sharply
drawn in the 18th and 19th 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)
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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
NATIONAL PICTURE:
INTERNATIONAL PICTURE:
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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
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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).
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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
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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”
Chemistry Grade 11: Quantities in chemical reactions
Overall Expectations
Essential Question
Big Ideas
• Relationships in chemical
D1: analyse processes in the
reactions can be described
home, the workplace, and the
quantitatively
How has our knowledge of
environment sector that use
•The efficiency of chemical
the quantitative
chemical quantities and
reactions can be determined
relationships in chemical
calculations, and asses the
and optimized by applying
reactions used in the
importance of quantitative
understanding of quantitative
home, the workplace and
accuracy in industrial chemical
relationships in such reactions
the environmental sector?
processes
D2: investigate quantitative
relationships in chemical
reactions, and solve related
problems
D3: demonstrate an
understanding of the mole
concept and its significance to
Guiding Questions
the quantitative analysis of
•Why is a balanced chemical reaction essential? What type
chemical reactions
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 numberconversions 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
DAY 7 & 8
PART 2:
Introduction to Stoichiometry
Lab continuation
Class work- worksheets
Empirical & Molecular
Formulae
Class work- textbook
work
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 14
Review: Mole Race
DAY 15
UNIT TEST
DAY 12
DAY 13
Demo:
Lab: Percent Yield
Percentage yield
Class work-Preparation
for lab
Overview, Expectations and Rationale
1. Big Ideas:
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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
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A1.12 use appropriate numeric, symbolic, and graphic modes of
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A1.13 express the results of any calculations involving data
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D2.1 use appropriate terminology related to quantities in chemical
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D3.2 describe the relationships between Avogadro’s number, the
representation, and appropriate units of measurement (e.g., SI and
imperial units)
accurately and precisely, to the appropriate number of decimal
places or significant figures
reactions, including, but not limited to: Stoichiometry, percentage
yield, limiting reagent, mole, and atomic mass [C]
mole concept, and the molar mass of any given substance
Overview, Expectations and Rationale
1. Big Ideas:
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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
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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:
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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:
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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)
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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
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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
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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
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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
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To graduate from high school, students needs to
have 3 credits in mathematics. Is this too few/much?
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How can you alleviate the math/numeracy fear that
some teachers may have?
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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?
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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. 1-36
McCarthy, L and Zawojewski, J.S. (2007). Numeracy in
Practice. Principal Leadership (Middle School Ed., 7(5), 3237