EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4 week unit of work in secondary school
mathematics
Name:
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Brenda
Jin
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School
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David
Thompson Secondary
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Grade
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10
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Subject
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FMP
10
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Topic
of unit
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Chapter
6: Solving a Linear System
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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 chapter extends from the linear equation, moves to the graph and solve linear system, also includes the arithmetic sequences, thus, learning this will help students to understand and deal with more complicated linear relations. Linear equations are an important tool in science and many everyday applications. They allow
scientist to describe relationships between different sets of two variables
in the physical world, make predictions, calculate solution (the intersection
point of linear system), and make conversions, among other things. Graphing
linear equations helps make trends visible.
I hope students
could develop algebraic and graphical reasoning through the study of the relations. They could learn to solve problems that involve systems of linear
equations in two variables, graphically and algebraically, also could use
their understanding of linear functions to develop the properties of
arithmetic sequences and series, then solve related problems. It is very
useful, and it is vital in multiple areas of science in general, and it’s
easy to solve and practical in everyday life.
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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)
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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)
The
assessment and evaluation include homework check, practice test, quiz, unit
test and project, 5 parts, each part weight 16%, 4%, 20%, 40% and 20%,
respectively.
（add paragraph to explain the reasons. why and how?）
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Elements of your unit plan:
a) Give a numbered list of the topics of the 12
lessons in this unit in the order you would teach them.
Lesson
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Date
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Topic
and description
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Assignment
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Handout
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1
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March
6
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Opener,
and group work/6.1 solving linear system by graphing (A)
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2
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March
10
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6.1-part
B and 6.2 solving linear system by addition (A)
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3
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March
12
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6.2-part
B,
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4
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March
30
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Quiz
6.1-6.2, 6.3 solving linear systems by addition (A)
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5
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April
1
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6.3
solving linear systems by substitution (B)
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6
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April
3
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6.4
problem-solving with two variables,
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7
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April
7
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Review
and quiz 6.1-6.4
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8
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April
9
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6.5
arithmetic sequence
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9
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April
15
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6.6
arithmetic series
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10
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April
17
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Review
and practice test
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11
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April
21
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Chapter
test
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12
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April
23
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Review
chapter test, Project: Draw a bridge in Aboriginal area with linear system
equations.
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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!)
Subject: FMP 10
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Grade: 10
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Date:
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Duration: 76 minutes
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Lesson Overview
(What this lesson is
about)
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Students do a problem-solving activity
related to the linear system, understand the history of the linear system, review
related terms and learn about isolate variable in an equation.
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Class Profile
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Total: 26 students
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Big
Idea(s)
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·
Using algebra to generalize relationships through abstract thinking.
·
Connect the topic with history.
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Curricular
Competencies
(What the students
will do)
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Develop thinking strategies to solve the problem,
and explore, analyze, and apply mathematical ideas using linear equations.
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Content Objectives
(What the students
will know)
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By the end of the lesson, students should be
able to:
Knowledge:
Explain the following terms: (a) coordinate
system (rectangular coordinate system; (b) ordered pair; (c) linear equation;
(d) slope intercept, slope,
y-intercept; (e) point of intersection; (f) system of linear equations,
linear system; (g) Solution (to a system of linear equations), one solution,
no solution and infinite solution; (h) consistent system, independent
equations; (i) inconsistent system; (j) consistent, dependent equation.
1.
Solving a linear system by
graphing.
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Materials
and Equipment Needed for this Lesson
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Scientific Calculators, project, laptop, whiteboard markers, Grid
paper
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Lesson Stages
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Students do: Learning Activities
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Teacher Do
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Time Allotted
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1.
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Warm-up activity
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1.
Students work in groups
2-3/group
2.
Each group write on their answer on the board.
3.
Discuss the solutions.
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Project the
practice question and manage group activity.
See Warm-up
practice sheet
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20 minutes
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2.
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Presentation part A
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1.
Students discuss and talk
about the history of linear equations, linear system equations.
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Ask students
about what they know about the history of linear equations, linear system equations. (see skeleton notes)
Review mathematics history with linear system
equation.
The procedure for solving simultaneous linear
equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.
Systems of linear equations arose in Europe
with the introduction in 1637 by René Descartes of coordinates in geometry.
In fact, in this new geometry, now called Cartesian geometry, lines and
planes are represented by linear equations, and computing their intersections
amounts to solving systems of linear equations.
The first systematic methods for solving
linear systems used determinants, first considered by Leibniz in 1693. In
1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.
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5 minutes
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Presentation part B
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Students work with pairs to figure out the
definition and examples (10 minutes)
Explain
their understanding and correct their mistakes.
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1.
Hand out the vocabulary sheet
2.
Check the understanding
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15 minutes
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Presentation part C
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Listen and
take notes
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1.
Explain the definition of linear systems, with the warmup practice.
(see skeleton notes)
2.
Solving a linear system by graphing. (see, skeleton notes)
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15 minutes
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Practice
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Ask students
to write down the example, and try to solve it
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Guide the students
to solve the problem, (see skeleton notes)
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5 minutes
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Independent
Work
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Ask a student
to practice an example.
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Check and
correct them.
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5 minutes
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4.
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Assignment
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Pg. 144 #1-3, 5 (all), 4(b, e), 6(b, e, h, j, l)
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10
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5.
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Closure
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Summary:
In this
class, we learned about how to definition of the linear system and solving it
by graphing.
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2 minutes
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After class
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Continue the assignment
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