Your name: Hai Qi (Sukie) Liu
School, grade & course: Southpointe Academy, Grade 9, Mathematics
Topic of unit (NOTE: This should be a unit you will actually be teaching on practicum!):
Linear Relations
Preplanning questions:
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)
Under the curricular competencies from the BC’s curriculum for mathematics 9, students are expected to “use tools or technology to explore and create patterns and relationships, as test conjectures” and to “connect mathematical concepts to other areas and personal interests” (BC’s Curriculum). I find the unit of linear relations being closely related to these two competencies. In learning about this unit on linear relations, students will develop a sense of how different aspects of life are related in the world we live in. For example, we can use linear relations to explain interest earned, purchase costs, patterns, and how human body parts are related. What’s interesting and useful about this topic is that many real-life scenarios can be understood through linear relations in math.
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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)
Students will work on an in-class activity focusing on linear relationships in the real world. Looking at the in-class activity as a reference, students will have to conduct research on a current issue from the real world that they are interested in, and pose a question in a way that allows them to find data to quantify the relationship. Students will have to submit a report that includes the following components:
A short introduction providing background information on the topic A question posed about the relationship between a dependent and independent variable for the topic Hypothesis and a brief explanation about the topic’s relationship A data table organizing the data collected for the dependent and independent variables A properly labeled scatter plot showing the relationship between your variables that you collected data for A trend-line showing the overall relationship between the data on the scatter plot A discussion of the answer to your question concerning the relationship including reasons for the results you have found Going beyond the data to make a meaningful prediction about your social issue using your trend line and scatter plot Discussion of any other factors that affect the confidence of your answer to the question you posed about your social issue Your final conclusion as the answer to the question you posed concerning your social issue
Students will be evaluated based on Introduction, Data, Results, Conclusion, and Report Presentation. |
(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) Since I am teaching in an IB school following the MYP curriculum, teachers are required to assess the prescribed subject-group objectives using assessment criteria for each subject group. In mathematics, students will be assessed based on four criteria, knowing and understanding (A), investigating patterns (B), communicating (C), and applying mathematics in real-life contexts (D). Each criterion will have achievement levels from 1-8 with unique descriptors under each band of levels. In the summative assessment for this unit, students will be assessed in criteria A and D. Hers is a list of formative and summative assessments for this unit: Formative assessment: - pizza worksheet; - exercise questions assigned from note packages; - IXL practice; Summative assessment: - written test assessing criteria A and D
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Elements of your unit plan:
a) Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.
Lesson | Topic |
1 | Introduction to Linear Relations Part 1 |
2 | Introduction to Linear Relations Part 2 |
3 | Slope and y-intercept |
4 | Graphing Linear Relations |
5 | Unit Project (formative task): Part 1 |
6 | Unit Project (formative task): Part 2 |
7 | Unit Project: Part 2 continued + Review session |
8 | IXL Practice on Linear Relations |
9 | Summative Task 1 |
10 | Summative Task 2 |
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b) Write a detailed lesson plan for three of the lessons which will not be in a traditional lecture/ exercise/ homework format. These three lessons should include at least three of the following six elements related to your mathematical topic. (And of course, you could include more than three!)
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 - Lesson 1
b) Arts and mathematics
c) Indigenous perspectives and cultures
d) Social/environmental justice - Lesson 5 and 6
e) Open-ended problem solving in groups at vertical erasable surfaces (“thinking classroom”) - Lesson 5
f) Telling only what is arbitrary, and having students work on what is logically ‘necessary’ - Lesson 1, 5, and 6
Be sure to include your pedagogical goals, topic of the lesson, preparation and materials, approximate timings, an account of what the students and teacher will be doing throughout the lesson, and ways that you will assess students’ background knowledge, student learning and the overall effectiveness of the lesson. Please use a template that you find helpful, and that includes all these elements.
Unit project:
Part 1. Can the Earth Sustain Itself?
There are over 7.8 billion people living on the Earth as of the year 2020, with China and India topping the list with over 1 billion people each. Experts predict that if the population continues to grow at the current rate, the world’s population will reach 10 billion by 2050.
A question that many have asked is whether the Earth will be able to sustain such a large population in terms of food production? Even in the 18th century, a famous professor by the name of Thomas Malthus made a very famous prediction that population would outrun food supply eventually.
Today, there are many countries whose people are starving due to poor soil and drought conditions. In many countries, rice and wheat are the food basics of life and when these disappear, people are in trouble. The table below shows an estimate of the total population of the world and an estimate of the total annual global rice and wheat production for the respective year.
Year | Populations (millions) | Food (million tonnes) |
1975 | 4064 | 1128 |
1980 | 4434 | 1159 |
1985 | 4840 | 1327 |
1990 | 5281 | 1417 |
1995 | 5708 | 1337 |
2000 | 6115 | 1443 |
2005 | 6513 | 1588 |
2010 | 6923 | 1560 |
2015 | 7341 | 1636 |
2020 | 7800 | 1600 |
Activity
1. What is your hypothesis as to the relationship between food production and the world’s population? Explain your reasoning.
2. Plot the data on the scatter plot as accurately as you can.
3. What does the scatter plot you created tell you about the relationship between food production and the population of the world?
4. Why do you think the relationship you described in Q3 exists?
5. Sketch a trend-line through the data points and explain the value of this line when examining the relationship between the dependent and independent variables
6. Plot your trend-line on the graph and use it to make your own prediction about how much food will have to be produced to sustain the world’s population in the year 2050. Do you think the Earth can sustain such a population? State your assumptions.
7. List three factors other than food production that affect the world’s population.
8. Why do you think this is an important social issue for everyday people in Canada? How can we help to sustain the world’s population? Explain.
Part 2. The challenge
Now that you have examined relationships in the real world, it is time to take charge and choose your own relationship to analyze.
Choose a current issue from the real world that you are interested in or would like to learn more about. A simple working definition of a social issue for this project is any issue that has an effect on a person, city, country, the world, wildlife, the environment, etc.
Here are some ideas to get you thinking about a specific topic.
Is there a relationship between a country’s wealth (GDP) and the amount of money that donate to developing countries?
Is there a relationship between a city’s unemployment rate and the number of food shelters in the city?
Is there a relationship between the population of a city and the number of people that own hybrid automobiles?
Is there a relationship between the number of students that would use public transportation and price of a bus ticket?
Once you have an idea about a social issue that interests you, the difficult part will be posing a question in a way that allows you to find data to quantify the relationship. Try to pose a question that doesn’t have an obvious answer as this will make your topic interesting.
The Deliverables
You must submit a report that includes the following as part of your final project:
A short introduction providing background information on your topic and sparking the audiences’ interest.
A question posed about the relationship between a dependent and independent variable for your topic
Your hypothesis and a brief explanation as to your gut feeling about your topic’s relationship
A data table organizing the data that you collected for your dependent and independent variables
A properly labeled scatter plot showing the relationship between your variables that you collected data for
A trend-line showing the overall relationship between the data on the scatter plot
A discussion of the answer to your question concerning the relationship including reasons for the results you have found
Going beyond the data to make a meaningful prediction about your social issue using your trend line and scatter plot
Discussion of any other factors that affect the confidence of your answer to the question you posed about your social issue
Your final conclusion as the answer to the question you posed concerning your social issue
Title | Introduction to Linear Relations Pt 1 | Grade | 9 | Date | TBA |
TC | S. Liu | Subject | Mathematics | Time | 70 mins |
Learning Intentions | Understand (big idea or SOI) | Know (content) | Do (skills) |
Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations. | Two-variable linear relations, using graphing, interpolation, and extrapolation two-variable continuous linear relations; includes rational coordinates horizontal and vertical lines graphing relation and analyzing interpolating and extrapolating approximate values spirit canoe journey predictions and daily checks
| Use reasoning and logic to explore, analyze, and apply mathematical ideas making connections, using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences
Use mathematical vocabulary and language to contribute to mathematical discussions
Connect mathematical concepts to each other and to other areas and personal interests
Finding patterns and understanding relationships |
Assessment | At the start (formative) | At the end (formative or summative) |
Task/Activity: understanding relationship | Task/Activity: Homework |
What I am looking for:
Students thinking about the relationships in our everyday life. Also connecting these relationships to our topic of linear relation. | What I am looking for:
Finding patterns, generating table of values, plotting values on graphs, writing equations to represent the linear relationship. |
Differentiation | Adaptations for ELL, SEN, different learners, etc. |
This lesson may be delivered in person or remotely. Students can write directly on the pdf file or the print-out version of the notes. Visuals are included in the notes to make questions and concepts more explicit. Students present problems to discuss in class with varying degrees of difficulty and types. Students take turns to teach each other. The exercise will give students the experience of listening to their peers explain problems, or teaching them the problem. they could agree, disagree, question or help each other navigate to the solution of the problems.
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Preparation | Materials/Resources | Organization (setup, pre-made things, classroom management, etc.) |
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Learning Engagements | Opening (provocation, APK/S, mental set) | Time |
Ask students: What is relationship? A linear relationship? Give examples of linear relationships in real life. Any history of relationship you can think of/relate to? | 10 min |
Strategy |
| Time |
Class discussion
Student-inquiry
Introduce “scatterplot” and “trend-line”
Work with students
Student Inquiry
Pair Work | Students work Explore This 1 individually. Ask students to answer the following questions 
Students try 3 examples of linear patterns from this website https://www.geogebra.org/m/xmjstebu
Students work on Example 1 and Example 2 individually, then go over the solutions as a class.
Ask “what is a scatterplot?” Provide an example of a scatterplot Introduce the “trend-line”, draw the trend-line on scatterplot
Work on Example 3 with students. 
Talk about “independent variable” and “dependent variable” Then create table of values for Sam, ask students to create table of values for Karen and Jonathan. Students will plot the table of values from above. Students will write an equation for each of the plotted graphs above
Students work on “Linear vs Non-Linear” and “Example 4” in pairs Ask some pairs to present their solutions to the class 
| 5 min
5 min
15 min
6 min
10 min
15 min |
Closure / Resolution | Time |
Assign homework exercises to be submitted with notes #1, 4, 6 from https://courseware.cemc.uwaterloo.ca/42/assignments/1107/12
| 5 min |
Where do you think students will struggle in the lesson? What will you do to counter this? |
Students may need more time to digest and understand the relationship between the given variables. students will talk and learn from each other in pair works. Students will be assigned practice questions to check on their understanding
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Title | Unit Project Part 1 | Grade | 9 | Date | TBA |
TC | S. Liu | Subject | Mathematics | Time | 70 mins |
Learning Intentions | Understand (big idea or SOI) | Know (content) | Do (skills) |
Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations. | Two-variable linear relations, using graphing, interpolation, and extrapolation two-variable continuous linear relations; includes rational coordinates horizontal and vertical lines graphing relation and analyzing interpolating and extrapolating approximate values spirit canoe journey predictions and daily checks
| Use reasoning and logic to explore, analyze, and apply mathematical ideas making connections, using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences
Demonstrate and apply mental math strategies
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Use mathematical vocabulary and language to contribute to mathematical discussions
Connect mathematical concepts to each other and to other areas and personal interests
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Assessment | At the start (formative) | At the end (formative or summative) |
Task/Activity: Ask: “What have we learned in this unit so far?” | Task/Activity: Can the Earth Sustain Itself |
What I am looking for: Quick recap of what we have been talking about in the last four lessons. | What I am looking for: Students will be given a real-life context problem examining relationship with a current world issue. Students are expected to interpret the data and answer the questions with the given data. |
Differentiation | Adaptations for ELL, SEN, different learners, etc. |
Students with IEP can work in the student resource centre with resource teachers This lesson may be delivered in person or remotely. Students can write directly on the pdf file or the print-out version of the notes. Students present problems to discuss in class with varying degrees of difficulty and types. Students take turns to teach each other. The exercise will give students the experience of listening to their peers explain problems, or teaching them the problem. they could agree, disagree, question or help each other navigate to the solution of the problems. Students will finish today’s exercise for homework if they don’t finish it in class.
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Preparation | Materials/Resources | Organization (setup, pre-made things, classroom management, etc.) |
| Handout will be premade and given to students at the beginning of class Graph paper will be provided if lesson is delivered at school Students will be asked to have graph paper ready if lesson is taught remotely
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Learning Engagements | Opening (provocation, APK/S, mental set) | Time |
Quick recap of what we covered so far Ask students to shout out what we have covered so far in this unit | 3 min |
Strategy |
| Time |
Work on “Can the Earth Sustain Itself” together as a class
Student-inquiry | Ask students to read the introduction paragraphs to interpret the situation presented. There are over 7.8 billion people living on the Earth as of the year 2020, with China and India topping the list with over 1 billion people each. Experts predict that if the population continues to grow at the current rate, the world’s population will reach 10 billion by 2050. A question that many have asked is whether the Earth will be able to sustain such a large population in terms of food production? Even in the 18th century, a famous professor by the name of Thomas Malthus made a very famous prediction that population would outrun food supply eventually.
Today, there are many countries whose people are starving due to poor soil and drought conditions. In many countries, rice and wheat are the food basics of life and when these disappear, people are in trouble. The table below shows an estimate of the total population of the world and an estimate of the total annual global rice and wheat production for the respective year.
Students examine the data individually. Ask students for any findings they see in these data. 
Students answer Q1 individually. 1. What is your hypothesis as to the relationship between food production and the world’s population? Explain your reasoning.
Students work on Q2 – Q4. They are allowed to work and discuss with their peers, but each student has to write their own response. 2. Plot the data on the scatter plot as accurately as you can. 3. What does the scatter plot you created tell you about the relationship between food production and the population of the world? 4. Why do you think the relationship you described in Q3 exists?
For Q5, review and go over the “trend-line” with students together as a class. 5. Sketch a trend-line through the data points and explain the value of this line when examining the relationship between the dependent and independent variables
For Q6, plot the trend-line on the graph. Ask students to make predictions. 6. Plot your trend-line on the graph and use it to make your own prediction about how much food will have to be produced to sustain the world’s population in the year 2050. Do you think the Earth can sustain such a population? State your assumptions.
Students continue to work on Q7 and Q8. 7. List three factors other than food production that affect the world’s population. 8. Why do you think this is an important social issue for everyday people in Canada? How can we help to sustain the world’s population? Explain.
| 5 min
5 min
3 min
15 min
10 min
10 min
10 min |
Closure / Resolution | Time |
Ask students to share their answer for Q8. Mention about the second part of the project which we will start next class.
| 10 min |
Where do you think students will struggle in the lesson? What will you do to counter this? |
The concept of a “trend-line” is quite new to the students. I believe I will need more time to explain this to ensure students’ understanding. Some students might struggle on deciding which would be the dependent and independent variables.
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Title | Unit Project Part 1 | Grade | 9 | Date | TBA |
TC | S. Liu | Subject | Mathematics | Time | 70 mins |
Learning Intentions | Understand (big idea or SOI) | Know (content) | Do (skills) |
Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations. | Two-variable linear relations, using graphing, interpolation, and extrapolation two-variable continuous linear relations; includes rational coordinates horizontal and vertical lines graphing relation and analyzing interpolating and extrapolating approximate values spirit canoe journey predictions and daily checks
| Use reasoning and logic to explore, analyze, and apply mathematical ideas making connections, using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences
Demonstrate and apply mental math strategies
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Use mathematical vocabulary and language to contribute to mathematical discussions
Connect mathematical concepts to each other and to other areas and personal interests |
Assessment | At the start (formative) | At the end (formative or summative) |
Task/Activity: Unit Project part 1
| Task/Activity: Unit project part 2 |
What I am looking for: | What I am looking for: Students will make connections to the real-world context Students will analyze relationships on social or environmental issues happening in the real world. students will demonstrate research skills and apply a mathematical understanding of the relation to the real world
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Differentiation | Adaptations for ELL, SEN, different learners, etc. |
Students with IEP can work in the student resource center with resource teachers This lesson may be delivered in person or remotely. Students do individual research for a topic in this activity. Their choice can be influenced by their interest, culture, personal life, and research skills.
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Preparation | Materials/Resources | Organization (setup, pre-made things, classroom management, etc.) |
| Students will need to bring their computers for research purposes Handout will be premade and given to students at the beginning of class Graph paper will be provided if the lesson is delivered at school Students will be asked to have graph paper ready if the lesson is taught remotely |
Learning Engagements | Opening (provocation, APK/S, mental set) | Time |
Remind students of Part 1 of this unit project we did last class, ask students if they have any other questions from this exercise.
Go over questions students may have from the previous exercise. | 10 min |
Strategy |
| Time |
Introduce the unit project
Question time
Individual work time | Using Part 1 as an example, introduce part 2 of the unit project that involves research.
Go over instructions and criteria for this task. Answer students’ questions.
Students will research on a topic that invovles relationships in the real world.
| 20 min
30 min
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Closure / Resolution | Time |
Check in with students. Students should have a topic decided by the end of class. | 10 min |
Where do you think students will struggle in the lesson? What will you do to counter this? |
I think students will struggle with finding topics for this project. Students are allowed to have similar topics as long as they are analyzing relationships with different dependent and independent variables. |
