EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4 week unit of work in secondary school
mathematics
Your name: Leo Hui
School, grade & course: Burnaby South Secondary School, Grade 11 Pre-Calculus
School, grade & course: Burnaby South Secondary School, Grade 11 Pre-Calculus
Topic of unit (NOTE: This should be a unit
you will actually be teaching on practicum!):
Systems
of Equations and Inequalities
Preplanning questions:
(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)
This topic is included in the curriculum because it is the
foundation of many mathematical concepts and examples. The advanced topics
like trigonometry, differentiation and integration are built upon the
knowledge of setting and solving mathematical equations. For example, if students
do not have the prior knowledge of systems of equations, it is difficult for
them to understand the equations of tangent lines in trigonometry. It is
important for students to learn it because they need to have the knowledge of
systems of equations to understand the concepts and solves problems in subjects
like physics and chemistry, and many real-world problems can be described in
equations and then solved using mathematical methods. Students can also transform
their problems to mathematical equations and solve them. Also, this topic is intrinsically
interesting, useful and beautiful because students can solve equations
graphically (i.e., using intersections of lines and curves) and use equations
or inequalities to create interesting shapes or patterns, and this can raise
students’ interest to learn this topic.
|
(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)
A student mathematics project is planned to serve as a
demonstration of how to apply systems of equations in daily life. The topic
is called “Start your own business”. The purpose of this project is to ask
students to budget their own businesses with the use of linear or quadratic
equations to determine the break-even point. The schedule of the project is:
The project will be assessed by a
rubric related to content, accuracy, creativity and communication.
|
(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)
To evaluate what and how students
learn from this unit, I will use 2 types of assessment: formative and
summative. For formative assessment, in-class worksheets and take-home assignments
from the textbook are the basic tools to check the learning performance of
students. I will also include some activities like group discussions and Kahoot
in lessons to observe how students understand the basic concepts of linear and
quadratic equations, e.g., x-intercepts, y-intercepts, real roots, or no roots.
For summative assessment, I will use 2 unit tests to evaluate the overall
student learning of equations and inequalities respectively. A group
project is also designed to ask students to apply systems of equations to solve problems in their daily life, and then students are
required to present the projects during a lesson. Their performance will be
assessed by a rubric related to content, accuracy, creativity and
communication.
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
|
Review
of linear and quadratic equations
|
2
|
Plotting
of linear and quadratic equations
|
3
|
Solving
systems of equations graphically
|
4
|
Solving
systems of equations algebraically
|
5
|
Solutions
of linear-quadratic and quadratic-quadratic equations
|
6
|
Application
of systems of equations in the real world
|
7
|
Unit
test for the system of equations
|
8
|
Linear
inequalities in two variables
|
9
|
Quadratic
inequalities in one variable
|
10
|
Quadratic
inequalities in two variables
|
(11)
|
Application
of linear and quadratic inequalities in the real world
|
(12)
|
Unit
test for the system of inequalities
|
Lesson Title: Solving systems of equations graphically (Lesson 3)
Created by: Leo Hui
Subject: Pre-Calculus 11
Grade: 11 Block:
3
Stage 1 – Desired Results
|
|||
Big Idea(s): what students will understand (at a conceptual level, see connections to and
between ideas, goes beyond the classroom learning)
- Functions allows us to model
contextualized situations, including financial ones.
Essential Question(s):
- How do we plot linear and
quadratic equations?
- How can we solve equations
graphically?
|
|||
Curricular
Competencies: what students
will do (activities to deepen
understanding / product)
- visualize to explore and illustrate mathematical
concepts and relationships
|
Content
Competencies: what students
will know
(basic knowledge, definitions, theories, laws)
(this is often right/wrong, yes/no)
- how to solve graphically problems that
involve systems of linear-quadratic and quadratic-quadratic equations in two
variables
|
||
Stage 2-Learning
Plan
|
|||
Potential
Barriers to Success
(Might
include: engagement, motivation, organization, language ability,
exceptionalities, reading level etc.)
- not engaged in learning
|
What will you
do? (differentiation/adaptations)
(not enough to just list obstacles w/o thinking of how to address
them)
- introduce an online software, GeoGebra, for students to try
- integrate an in-class activity/game into the lesson to motivate students to learn |
||
Resources /
Materials Required / Technology
- a notebook for showing an online
software (GeoGebra), a projector, iPads for students, vertical erasable white boards and markers
|
|||
Stage 3 – Assessment Evidence
|
|||
- in-class worksheets about linear and quadratic
equations
- an in-class activity with the use of vertical
erasable boards to see how students understand the solving of linear-quadratic
equations
|
|||
Stage 4 – Teaching Plan
|
|||
Time:
|
Teacher Does:
|
Students Do:
|
|
10 mins
|
- Review the previous lesson about plotting linear
and quadratic equations using Kahoot
- Introduce an online software, GeoGebra, that will
be used later in the lesson to engage students in learning
|
- Play Kahoot about questions of x-intercepts,
y-intercepts, slopes and roots.
|
|
15 mins
|
- Explain how to solve linear-linear
equations graphically with examples
- Show how to use GeoGebra to solve linear-linear
equations
|
- Take notes of how to solve linear-linear equation
system
- Try GeoGebra |
|
15 mins
|
- Explain how to solve linear-quadratic
equations graphically with examples
- Show how to use GeoGebra to solve linear-quadratic
equations
|
- Take notes of how to solve linear-quadratic
equation system
- Try GeoGebra |
|
10 mins
|
- Give an in-class worksheet and then check the
answers with students after they finish.
|
- Do an in-class worksheet about solving linear and
quadratic equation systems graphically
|
|
15 mins
|
- Ask students to group in teams, give an activity about drawing 3 different linear-quadratic equation systems that contain no
solutions, 1 solution and 2 solutions respectively on vertical erasable white
boards and evaluate the students' learning by checking their answers afterward.
|
- Group themselves into teams, draw 3
linear-quadratic equation systems required by the teacher and then present
the 3 systems to the class.
|
|
10 mins
|
- Summarize what they have learnt in the lesson
- Inform students what they will learn in the next
lesson
|
||
Homework /
Teacher Preparation for next class
- Assignment from the textbook
|
|||
Lesson Title: Quadratic inequalities in one variable (Lesson 9)
Created by: Leo Hui
Subject: Pre-Calculus 11
Grade: 11 Block:
3
Stage 1 – Desired Results
|
|||
Big Idea(s): what students will understand (at a conceptual level, see connections to and
between ideas, goes beyond the classroom learning)
- Functions allows us to model
contextualized situations, including financial ones.
Essential Question(s):
- How do we solve quadratic inequalities
in one variable?
|
|||
Curricular
Competencies: what students
will do (activities to deepen
understanding / product)
- visualize to explore and illustrate mathematical
concepts and relationships
|
Content
Competencies: what students
will know
(basic knowledge, definitions, theories, laws)
(this is often right/wrong, yes/no)
- how to solve problems involving
quadratic inequalities in one variable
|
||
Stage 2-Learning
Plan
|
|||
Potential
Barriers to Success
(Might
include: engagement, motivation, organization, language ability,
exceptionalities, reading level etc.)
- not engaged in learning
|
What will you
do? (differentiation/adaptations)
(not enough to just list obstacles w/o thinking of how to address
them)
- integrate a current issue (e.g., environmental
justice) into the lesson to motivate students to learn
|
||
Resources /
Materials Required / Technology
- a notebook, a projector, videos
about environmental justice (https://www.youtube.com/watch?v=dREtXUij6_c, https://www.youtube.com/watch?v=30xLg2HHg8Q)
|
|||
Stage 3 – Assessment Evidence
|
|||
Formative (before/during)
- in-class worksheets about quadratic inequalities
in one variable
|
|||
Stage 4 – Teaching Plan
|
|||
Time:
|
Teacher Does:
|
Students Do:
|
|
10 mins
|
- Review the lesson about finding roots of quadratic
equations
|
- Answer the questions given by the teacher
|
|
15 mins
|
- Give a lecture about how to solve quadratic
inequalities using 3 methods (graphing, test points and case analysis) with
examples
|
- Take notes of how to solve quadratic inequalities
using the 3 methods
|
|
15 mins
|
- Play a video about environmental justice and then
introduce one of the causes of environmental injustice is the transportation
of wastes to the low-income regions or countries
- ask students to think about the ways of treating
wastes
|
- Brainstorm different ways of treating wastes and
present their ideas on poster papers.
|
|
10 mins
|
- Introduce a new technique called gasification
which converts solid wastes to fuels and show a quadratic inequality to
estimate the cost of this waste treatment will be $C/kg or less in t years
from the present.
- Use this example to display the application of
quadratic inequalities to help people solve environmental problems
|
- Take notes of this example
|
|
15 mins
|
- Give an in-class worksheet and then check the
answers with students after they finish.
|
- Do an in-class worksheet about quadratic inequalities
|
|
10 mins
|
- Summarize what they have learnt in the lesson
- Inform students what they will learn in the next
lesson
|
||
Homework /
Teacher Preparation for next class
- Assignment from the textbook
|
|||
Lesson Title:
Application of linear and quadratic inequalities in the real world (Lesson 11)
Created by: Leo
Hui
Subject: Pre-Calculus 11
Grade: 11 Block:
3
Stage 1 – Desired Results
|
|||
Big Idea(s): what students will understand (at a conceptual level, see connections to and
between ideas, goes beyond the classroom learning)
- Functions allows us to model
contextualized situations, including financial ones.
Essential Question(s):
- How do we apply linear and
quadratic inequalities in daily life?
|
|||
Curricular
Competencies: what students
will do (activities to deepen
understanding / product)
- visualize to explore and illustrate mathematical
concepts and relationships
|
Content Competencies: what students will know
(basic knowledge, definitions, theories, laws)
(this is often right/wrong, yes/no)
- how to solve problems that involve
linear and quadratic inequalities in two variables
- the application of inequalities in daily
life
|
||
Stage 2-Learning
Plan
|
|||
Potential
Barriers to Success
(Might
include: engagement, motivation, organization, language ability,
exceptionalities, reading level etc.)
- not engaged in learning
|
What will you
do? (differentiation/adaptations)
(not enough to just list obstacles w/o thinking of how to address
them)
- integrate an in-class activity/game into the
lesson to motivate students to learn
|
||
Resources /
Materials Required / Technology
- a notebook, a projector, iPads
for students, poster papers and markers
|
|||
Stage 3 – Assessment Evidence
|
|||
Formative (before/during)
- in-class worksheets about linear and quadratic inequalities
- an in-class drawing activity to see how students
can apply linear inequalities to create areas of different shapes or patterns
(i.e., art)
|
|||
Stage 4 – Teaching Plan
|
|||
Time:
|
Teacher Does:
|
Students Do:
|
|
5 mins
|
- Review the previous lesson about quadratic inequalities
in 2 variables
- Introduce a drawing activity that students will do
in the lesson to engage students in learning
|
- Play Kahoot of questions about 3 methods of
solving quadratic inequalities
|
|
5 mins
|
- Briefly revisit the solving and plotting of linear
inequalities with examples
|
- Do examples together with the teacher
|
|
10 mins
|
- Put the plotting of linear and quadratic
inequalities together and explain with examples and the use of GeoGebra
|
- Do examples together with the teacher
- Try GeoGebra
|
|
10 mins
|
- Show daily examples of using linear and quadratic
inequalities
|
- Take notes about the application of linear and
quadratic inequalities
|
|
15 mins
|
- Give an in-class worksheet and then check the
answers with students after they finish.
|
- Do an in-class worksheet about linear and
quadratic inequalities
|
|
20 mins
|
- Ask students to group in teams, using linear and
quadratic inequalities to create areas of different shapes or patterns they
want (e.g., using 2 vertical linear inequalities and 2 horizontal linear inequalities
to create an area of a square or a rectangle) on poster papers and evaluate the students' learning by checking their answers afterward.
|
- Group themselves into teams, design areas of
different shapes using linear and quadratic inequalities on poster papers and
then present their shapes or patterns to the class
|
|
10 mins
|
- Summarize what they have learnt in the lesson
- Inform students that they will have a unit test in
the next lesson
- Talk about the scope of the test
|
||
Homework /
Teacher Preparation for next class
- Assignment from the textbook
|
|||
