(1) Why do we teach this unit to secondary school
students? Research and talk about the following: Why is this topic included
in the curriculum? Why is it important that students learn it? What learning do
you hope they will take with them from this? What is intrinsically interesting,
useful, beautiful about this topic? (150 words)
In our technologically
advanced era, the accessibility of statistics has drastically improved,
fostering a widespread appreciation for its applications. As society
increasingly relies on data-driven insights, a fundamental understanding of
statistical and probabilistic concepts becomes essential for society
development (especially economic development) and informed decision-making. By
recognizing this, the BC government decide to adapt the curricula to emphasize
data analysis skills and the practical application of probability in real-life
scenarios. I hope that through my unit plan design, students can learn basic
information that is useful to them from data, which can help them make
decisions in their future lives. By recognizing both individual details and
overarching information, I hope them can cultivate abstract thinking skills
essential for adapting to complex societal situations. The goal is to train
students in a way of thinking that will help them handle different situations
in society more effectively.
Unit Plan Template
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Course: Math
Grade 9 |
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Unit:
Probability and Statistics |
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Big Idea(s): |
|
·
Analyzing the validity, reliability, and representation
of data enables us to compare and interpret. |
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Curricular
Competencies: |
Content: |
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Reasoning and analyzing ·
Use reasoning and logic to explore, analyze, and
apply mathematical ideas ·
Estimate reasonably ·
Use tools or technology to explore and create
patterns and relationships, and test conjectures ·
Model mathematics in contextualized experiences Understanding and solving ·
Apply multiple strategies to solve problems in both
abstract and contextualized situations ·
Develop, demonstrate, and apply mathematical
understanding through play, inquiry, and problem solving ·
Visualize to explore mathematical concepts Communicating and representing ·
Use mathematical vocabulary and language to
contribute to mathematical discussions ·
Explain and justify mathematical ideas and decisions ·
Communicate mathematical thinking in many ways Connecting and reflecting ·
Connect mathematical concepts to each other and to
other areas and personal interests ·
Use mathematical arguments to support personal
choices ·
Incorporate First Peoples worldviews and
perspectives to make connections to mathematical concepts |
· Probability
and Statistics · population
versus sample, bias, ethics, sampling techniques, misleading stats · analyzing
a given set of data (and/or its representation) and identifying potential
problems related to bias, use of language, ethics, cost, time and timing,
privacy, or cultural sensitivity · using
First Peoples data on water quality, Statistics Canada data on income,
health, housing, population
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(2) A mathematics project connected to this unit:
Plan and describe a student mathematics project that will form part of this
unit. Describe the topic, aims, process and timing, and what the students will
be asked to produce, and how you will assess the project. (250 words)
Unit
Project Artifact of Probability and Statistics
Option
1: Designed Game Analysis
Objective:
In this option, your task is to analyze a game and report the results along
with the calculations involved. Game including: rolling dice, pull cards, draw
marbles from bag. Your report should detail the rules of the game, the expected
outcomes, and the actual results obtained through experimentation. Calculate
probabilities, expected value, and any relevant statistical measures to analyze
the game's outcomes. Discuss any surprises or patterns observed and reflect on
the significance of your findings.
Option
2: Candy Statistics
Objective:
Choose a type of candy (M&Ms, Skittles, jelly beans, or other complex
candies) as your subject for statistical analysis. Acquire a sample and conduct
a detailed statistical examination. Record data on color distribution, or
flavour distribution. Utilize statistical tools to analyze your findings,
including measures of central tendency, dispersion, and probability. Present
your results in a clear and organized manner, using statistical and probability
terms. Reflect on the implications of your analysis, considering any patterns
or variations observed.
Guidelines
of Project Artifact:
1. Clearly
outline the objectives of your chosen option.
2. Provide
a step-by-step description of your methodology.
3. Include
calculations, charts or tables or graphs to support your analysis.
4. Use
statistical and probability terms appropriately.
5. Present
your findings in a well-organized written format.
6. Reflect
on the significance of your results and any unexpected observations.
7. The
artifact can be: written report, poster, power-point slides, recorded video
The
project will only be marked based on: clarity (how you present your experiment
and results), credibility (correctness of concepts and calculations), and
rationality (logical appropriateness in applying mathematical
concepts/calculations).
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Assessment: (Evidence of students demonstrating achievement in
Big Idea(s), Curricular Competencies, Content, and Language Objectives) |
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· Assignments · In class
participation · Quizzes · Unit project artifacts
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(3) Assessment and evaluation: How
will you build a fair and well-rounded assessment and evaluation plan for this
unit? Include formative and summative, informal/ observational and more formal
assessment modes. (100 words)
Formative assessment
will involve in-class participation, enabling ongoing feedback and
understanding of group progress. The unit project artifacts will be assessed
base on math concepts application and problem-solving skills, providing
insights into applied knowledge and skills. Summative assessment will include
quizzes and assignments, offering a snapshot of understanding, and assignments,
measuring proficiency against set standards. This combination of informal
observation through participation and project artifacts, along with more formal
assessments like the mark of quizzes and assignments, ensures a well-rounded
evaluation that caters to diverse learning styles and effectively gauges
student achievement in the unit.
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Sequence |
Topic |
Tasks
/ Activities |
Resources
/ Materials |
|
1 |
Introduction
to Statistics
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Introduce
statistics history, background Understand
the meaning of why use statistics Introduce
basic concepts of statistics. Provide
worksheet of vocabulary puzzle to get familiar with statistics terms |
·
Slides ·
Projectors ·
Whiteboard
markers/erasers ·
Handouts ·
Vocabulary
puzzle |
|
2 |
Introduce
descriptive statistics measures. |
Introduce
the terms: mean, median, and mode Handout
of: How to calculate each measure Understanding
when to use each measure |
·
Projectors ·
Whiteboard
markers/erasers ·
Questions
worksheet |
|
3 |
Practice
in mean, median and mode |
Definition
and calculation of the mean, median, and mode Examples
and practical applications through worksheets and graphics Understanding
the relation between the data and table |
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers |
|
4 |
Dive
deeper in mean and median Understand
the concept of mode and its applications.
|
Definition
and calculation of the median Explore
the median as an alternative measure of central tendency. Comparing
mean and median When to
use the median Definition
and calculation of the mode When to
use mode |
·
Slides ·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers |
|
5 |
Half
unit Overview Probability
Basics |
Overview
on mean, median, mode Quiz of
statistics
|
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers ·
Vocabulary
puzzles ·
Quizzes |
|
6 |
Introduce
basic concepts of probability.
|
History
background of probability Definition
of probability Simple
probability examples Probability
as a fraction |
·
Slides ·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers |
|
7 |
Rule
of probability
|
How to
find probability Addition
rule Multiplication
rule Complementary
events |
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers ·
Textbooks |
|
8 |
Application
of probability
|
Problem-solving
and application of mean, median, mode, and probability concepts Practical
exercises and examples Quizzes
on probability Distribute
topics unit project: Group work presentation of designed game/statistics
real-life scenarios: 1)
Draw
different colour marbles from bags 2)
Draw
cards from a deck of card 3)
Statistics
on colours of M&Ms 4)
Statistics
on colours of Skittles 5)
Rolling
dice game probability 6)
Flip
coin statistics/game |
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers ·
Quizzes |
|
9 |
Explore
the statistics and probability in game
|
Students
will be collaborating on designed games, doing experiments, statistics, math
concept application exploration. |
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers ·
Cards ·
M&Ms ·
Skittles ·
Dices ·
Wheels ·
Coins ·
Bag
of coloured balls |
|
10 |
Unit
Project Presentation
|
Final
Unit Project Artifact Presentation |
·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers |
These
elements should be thoroughly integrated into the lessons (i.e. not an add-on
that
the
teacher just tells!)
a) History of this mathematics
b) Arts and mathematics
c) Indigenous perspectives and cultures
d) Social/environmental justice
e) Open-ended problem solving in groups at vertical erasable
surfaces (“thinking classroom”)
f) Telling only what is arbitrary, and having students work on what
is logically ‘necessary’
Lesson
Title: Dive deeper into mean and median
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Grade: |
9 |
Concepts/Themes/Topics: Mean
and median |
|
|
Duration: |
80 min |
||
|
Resources/Materials: · Slides · Worksheet · Projectors · Whiteboard
markers/erasers |
Objective: Students will understand and be able to calculate the mean and median
of a set of data with a better understanding in real life application |
||
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LESSON COMPONENTS: |
|||
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Beginning (5~10 mins) |
Prepare students ready for the class Warm up: Asking students what they learnt mean and median from last
class, ask students to write and draw on board Introduce the statistics underneath in mean and median. |
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Part 1 (15 mins) |
(Presentation and practice) Explain by examples (normal distributed/bell shaped bar chart and
skewed distributed chart) that why we need different measure in statistics. |
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Part 2 (25 mins) |
(Practice) Calculate mean and median - Use handout with practice
questions to teach students how to find the mean by adding up all the numbers
and dividing by the total count and how to find the median by ordering the
numbers and identifying the middle value. Adaptation：d) Social/environmental
justice – statistics will be related with water consumption, car ownership,
income of different countries: increase
awareness of resources distribution, social/environmental justice - Work through examples
together on the board. |
||
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Part 3 (20~25 mins) |
(Activity - an extension of the new
content) Group Activity: - Divide students into small
groups. - Provide each group with a
set of data to find the mean and median. - Circulate to assist and
answer questions. |
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Closure (10 mins) |
Complete handouts and assign homework Work block for the rest Remind for coming quiz |
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Assessment |
Assess students through their participation in the group activity,
completion of the worksheet, and their ability to explain the concepts, completion
of assignment and correctness for selected questions. |
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Lesson
Title: Introduction of Probability
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Grade: |
9 |
Concepts/Themes/Topics: Probability |
|
|
Duration: |
80 min |
||
|
Resources/Materials: · Worksheet · Projectors · Whiteboard
markers/erasers |
Objective: Students will understand and be able to calculate the probability and
use experimental data to compare such that they will have a better
understanding of probability in real life application |
||
|
LESSON COMPONENTS: |
|||
|
Beginning (10~15 mins) |
Prepare students ready for the class Hook activity: Play gambling wheel game, determine different rules of
winning, let whole class guess if I win or lose transfer topics from
statistics to probability. Adaptation：a) History of this
mathematics – Introduce the history of probability: first was designed for analyze
game: increase awareness of mathematics
underneath real-life all the time and math are developing |
||
|
Part 1 (15 mins) |
(Presentation and practice) Different game analyze: flip coin, pull from deck of card, roll the
fair dice, gambling wheel, pull marbles from bag, etc. Introduce the definition of probability |
||
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Part 2 (20~30 mins) |
(Activity - an extension of the new
content) Group Activity: - Divide students into small
groups and provide each group with a dice. - Ask students to record
different size of trials (10, 20, 40, 60, 100), practice the mean, median,
mode, compare the result with theoretical probability. Adaptation：f) Telling only what is
arbitrary, and having students work on what is logically ‘necessary’ – by analyzing real
experiential data, student work on understanding why there is a theoretical
probability, distinguish the difference between theoretical probability and
sample probability: increase
awareness of relation between statistics and probability |
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|
Part 3 (10-15 mins) |
(Practice) Let each group present their result Calculate probability - Use handout with practice
questions to teach students how to find the probability. - Work through examples
together on the board. |
||
|
Closure (10 mins) |
Complete handouts and assign homework Review the key concepts of probability. - Ask students to share how
they would explain these concepts to a classmate. - Address any lingering
questions. |
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Assessment |
Assess students through their participation in the group activity,
completion of the worksheet, and their ability to explain the concepts, completion
of assignment and correctness for selected questions. |
||
Lesson
Title: Explore the statistics and
probability in game
|
Grade: |
9 |
Concepts/Themes/Topics: Probability
and Statistics Unit Project |
|
|
Duration: |
80 min |
||
|
Resources/Materials: ·
Worksheet ·
Projectors ·
Whiteboard
markers/erasers ·
Cards ·
M&Ms ·
Skittles ·
Dices ·
Wheels ·
Coins · Bag of coloured balls |
Objective: Students will understand and be able to calculate the mean and median,
mode of a set of data and make connection with probability. |
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LESSON COMPONENTS: |
|||
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Beginning (5 mins) |
Prepare the classroom ready for students and distribute unit project
experiments items |
||
|
Part 1 (10 mins) |
(Presentation) Give the guideline to students: 1. Clearly outline the objectives of
your chosen option. 2. Provide a step-by-step description of
your methodology. 3. Include calculations, charts or
tables or graphs to support your analysis. 4. Use statistical and probability terms
appropriately. 5. Present your findings in a
well-organized written format. 6. Reflect on the significance of your
results and any unexpected observations. 7. The artifact can be: written report, poster,
power-point slides, recorded video The project will only be marked
based on: clarity (how you present your experiment and results), credibility
(correctness of concepts and calculations), and rationality (logical
appropriateness in applying mathematical concepts/calculations).
Adaptation：c) Indigenous perspectives and cultures – Provide choice and flexibility in learning activities so that different
aspects of learners’ whole selves can be attended to. |
||
|
Part 2 (60 mins) |
(Group Project Experiment and Exploration) - Set group work on their
own project in different tables, circulating and helping students 1)
Draw
different colour marbles from bags 2)
Draw
cards from a deck of card 3)
Statistics
on colours of M&Ms 4)
Statistics
on colours of Skittles 5)
Rolling
dice game probability 6)
Statistics
on flavors of complexed jelly beans Adaptation： c) Indigenous perspectives and cultures – Learning is experiential and
relational:
support learner’s
understanding of their own learning processes and how to apply various
processes in different contexts; provide as many authentic experiential
learning, opportunities as possible. Help learners understand their own
learning processes and how they build understanding on previous learning
experiences. e) Open-ended problem solving in groups at vertical erasable
surfaces (“thinking classroom”) – by experimenting themselves, student work
on applying math concepts into open ended real-life problem: explore the math concepts and
analyze the real-life problems by students themselves |
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|
Closure (5 mins) |
Ask whole class to clean and help peers to set the classroom back to original
positions. Adaptation：c) Indigenous
perspectives and cultures – Learning
is holistic and relational: increase sense of place, the environment they
are studying - Ask students to share how
they would explain these concepts to a classmate. - Address any lingering
questions. |
||
|
Assessment |
Assess students through their participation in the group project
activity |
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