Unit Plan

 

(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

 

Course: Math Grade 9

 

Unit: Probability and Statistics

 

Big Idea(s):

·       Analyzing the validity, reliability, and representation of data enables us to compare and interpret.

 

Curricular Competencies:

Content:

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

 

(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).

 

 

Assessment: (Evidence of students demonstrating achievement in Big Idea(s), Curricular Competencies, Content, and Language Objectives)

·       Assignments ·       In class participation ·       Quizzes ·       Unit project artifacts

 

(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.

 

 

 

Sequence	Topic	Tasks / Activities	Resources / Materials
1	Introduction to Statistics	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

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
LESSON COMPONENTS:
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.
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.
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.
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.
Closure (10 mins)	Complete handouts and assign homework Work block for the rest Remind for coming quiz
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: Introduction of Probability

 

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
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
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.
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.
LESSON COMPONENTS:
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
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