Download 3m + 13 = 5m + 6

Additional Algebra Skills Needed
to Solve Equations
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21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson:
•
Spend AT LEAST 30 minutes studying the
Lesson Overview, Teacher Notes on each
slide, and accompanying worksheets.
•
Set up your projector and test this PowerPoint file to make
sure all animations, media, etc. work properly.
•
Feel free to customize this file to match the language and
routines in your classroom.
*1st Time Users of 21st Century Lesson:
Click HERE for a detailed description of our project.
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Lesson Overview (1 of 4)
Lesson Objective
OBJECTIVE: Students will be able to efficiently solve equations
by thoughtful selection of first moves, eliminating fractional
coefficients and distributing negative signs.
LANGUAGE OBJECTIVE: Students will discuss with a partner
potential solution moves in order to better understand the
reasoning for selecting a particular first move.
Lesson Description
This is the second in a series on basics of solving equations.
This lesson covers some more sophisticated ideas involved in
solving equations. Students explore selecting a first move
where they come to understand the value in scanning and
assessing options before taking action to find the most
efficient means of solving. They will develop skill in
distributing a negative sign using distributive property and in
eliminating fractional coefficients by multiplying by the
denominator of the fraction. These skills enable students to
add sophistication to their equation solving skills.
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Lesson Overview (2 of 4)
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Lesson Vocabulary
Distributive property, negative, coefficient, constant,
denominator
Materials
independent class work, homework, exit slip, powerpoint,
calling sticks
Common Core
State Standard
8EEc7b - Solve linear equations with rational number coefficients,
including equations whose solutions require expanding
expressions using the distributive property and collecting like
terms. http://www.corestandards.org/
Lesson Overview (3 of 4)
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Scaffolding
The frequent turn-and-talk strategy used throughout the lesson is a
method utilized to aid student understanding by giving them time to
think and to hear the thinking of others besides the teacher. This is a
great strategy for both ELL students and for students with learning
differences. The work is scaffolded with many opportunities for
guided practice and color coding for each new move.
Enrichment
Students seeking additional challenges will find challenging work on
both the class work and homework worksheets. Here is some
challenging online practice:
http://www.algebralab.org/practice/practice.aspx?file=algebra1_33.xml
Online
Resources for
Absent
Students
http://www.algebra-class.com/solving-algebra-equations.html
Good LearnZillion lessons on this topic:
https://learnzillion.com/lessonsets/560-solve-linear-equations-inone-variable
https://learnzillion.com/lessonsets/560-solve-linear-equations-inone-variable
Lesson Overview (4 of 4)
Before and After
The work of solving equations has been built upon through
previous grades and also the ratios and proportions 8th grade unit.
In 6th grade for example students have solved basic equations and
they have created equivalent expressions using the distributive
property and combining like terms. The work is solidified in 7th
grade using numbers in any form (decimals, fractions, and negative
numbers) and relying more heavily on the properties of the
operations. This lesson follows algebra work looking at
expressions and graphs and the previous lesson titled Introduction
to Solving Equations covers basics of solving equations. Later
lessons will move into solving systems of equations and reasoning
about the shape and characteristics of the graph of a line by
looking at an equation, often requiring manipulations first –
manipulations that this lesson provides the skills for.
Topic Background A nice history of solving equations can be found here:
http://faculty.etsu.edu/gardnerr/Galois/history-of-equations.htm
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Warm Up
OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection
of first moves, eliminating fractional coefficients and distributing negative signs.
LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves
in order to better understand the reasoning for selecting a particular first move.
Evaluate.
Simplify.
j
1 2
¸ =
6 3
l 5(n + 6 + 2p) =
k
2 1
¸ =
3 6
m -3(2x + 4) =
Answers
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Agenda
Agenda:
OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection
of first moves, eliminating fractional coefficients and distributing negative signs.
LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves
in order to better understand the reasoning for selecting a particular first move.
1) Warm Up – basic skills review - YOU
2) Mini-Lesson #1 – Picking a First Move - ME
3) Mini-Lesson #2 – Shortcut for a Fractional Coefficient – ME
4) Guided Practice – practice solving equations – US
5) Mini-Lesson #3 – Distributing a Negative Sign – ME
6) Guided Practice – practice solving equations – US
7) Independent Practice – practice solving equations – YOU
8) Assessment – Exit Ticket - YOU
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Launch
Mini-lesson #1: Picking a First Move
Ex. 1
3m + 13 = 5m + 6 Solve using the symbolic method.
Did you get m = 7/2 or 3½ for a solution?
What was your first move?
Turn and Talk:
Take turns speaking with a partner to share your
first move. Was it the same? If not, ask your
partner why he or she chose that move first.
Agenda
10
Launch
There is more than 1 first move from which to choose.
Ex. 1
3m + 13 = 5m + 6
3m
+
13
=
5m
+
6
-
OR
3m
+
13
=
5m
+
6
-
3m
3m
5m
5m
13 = 2m + 6
-2m + 13 = 6
-6
-6
- 13 - 13
Will there be 2 different solutions? Let’s find out!
7 = 2m
-2m = -7
st
Either 1 move can
2 2
-2 -2
7/2 = m
be used to get the
same result.
m = 7/2
Agenda
11
Launch
There is more than 1 first move from which to choose.
Ex. 1
3m + 13 = 5m + 6
3m
+
13
=
5m
+
6
3m
3m
13 = 2m + 6
OR
3m
+
13
=
5m
+
6
5m
5m
-2m + 13 = 6
Are there any other first moves?
Turn and Talk: Discuss with your partner. See if you
can work together to find all the possible first moves.
Agenda
12
Launch
3m + 13 = 5m + 6
- 13
- 13
3m = 5m + -7
3m + 13 = 5m + 6
-6
-6
3m + 7 = 5m
3m + 13 = 5m + 6
3m
+
13
=
5m
+
6
-
3m
+
13
=
5m
+
6
-
3m
5m
5m
-2m + 13 = 6
3m
13 = 2m + 6
Turn and Talk:
Is there
move first
that steps.
is better to use?
These
are allone
thefirst
possible
Why do you
one isinbetter
than the
others?
Dothink
theythat
all result
the same
solution?
Agenda
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Launch
3m + 13 = 5m + 6
3m + 13 = 5m + 6
- 13
- 13
-6
-6
3m = 5m + -7
3m + 7 = 5m
- 5m - 5m
- 3m
- 3m
-2m = -7
7 = 2m
-2
-2
2 2
These two first moves are similar.
7/2 = m
m = 7/2
3m + 13 = 5m + 6
- 3m
- 3m
13 = 2m + 6
-6
-6
7 = 2m
2 2
7/2 = m
3m + 13 = 5m + 6
- 5m
- 5m
-2m + 13 = 6
- 13 - 13
-2m = -7
-2 -2
m = 7/2 Agenda
Some
Somepeople
peoplemight
mightsay
saythat
thatthe
thecalculations
calculationsare
areeasier
easierififyou
youdo
do
not
nothave
haveto
todivide
divideby
byaanegative.
negative. You can avoid this if you do not
14 create a negative with your first move.
Launch
This order of moves is the way most solutions will
be presented in examples. Although it is important
to realize that there are many possible first moves.
3m + 13 = 5m + 6
- 3m
- 3m
13 = 2m + 6
-6
-6
7 = 2m
2 2
7/2 = m
In general, a preferable order of
moves would minimize the need to
calculate with negative numbers,
fractions, or decimals.
Agenda
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Launch
Mini-lesson #2: Shortcut for a fractional coefficient.
Ex. 2
8 + ¼b = 5
–8
–8
¼b = -3
¼ ¼
Solve for b. Check your answer.
Why is subtracting 8 a better first
We
know
thatsubtracting
¼ is attached
move
than
¼b?to the b
by multiplication and the way to
undo a coefficient is to divide by the
coefficient. But there is a faster way
to undo this coefficient because it is
a fraction.
Agenda
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Launch
How to cancel the fractional coefficient
8+ b=5
–8
–8
b = -3
1
4
1
4
1
4
1
4
-3 ÷14 =
1
4
:
8+ b=5
–8
–8
4( b) =(-3)4
1
4
1
4
b = -12
-3  4 =
1
- 3  4=
1 1
-12
b = -12
Remember that when you divide
by a fraction you multiply by the
reciprocal. So if you multiply both
sides by 4 you will cancel the 14 .
Agenda
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Practice: Solve for the variable, substitute to check
1.) -6 + x = -5
2.)
1
3
3.) 0 = 4 +
n
5
x + 9 = - x + 12
This is the same as
Answers
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1
2
1
4
1
n
5
Agenda
Practice
Mini-lesson #3: Distributing a negative sign.
Ex. 3
14 = – (p – 8)
14 = – p + 8
–8
–8
6 = -p
-1 -1
-6 = p
Let’s review the
Wait, what happened?
distributive property:
-(p) = -1(p) = -p
2(x – 5)
-(-8) =2x-1(-8)
– 10 = +8
Now, solve for p.
Agenda
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Practice: Solve for the variable, substitute to check
4.) -8 = –(x + 4)
6.) –(y – 2) +
5
2
5.) 12 = – (-6x – 3)
= 3(y + 1)
Answers
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Agenda
Practice: Independent Class work
Answers
24
Next blank section
Agenda
Practice: Class worksheet
Exit Slip
26
Go to Answers
Agenda
Practice: Class worksheet
Exit Slip
28
Go to Answers
Agenda
Practice: Class worksheet
Exit Slip
30
Go to Answers
Agenda
Exit Slip
Agenda
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21st Century Lessons
The goal…
The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in
urban and turnaround schools, by bringing together teams of exemplary educators
to develop units of high-quality, model lessons. These lessons are intended to:
•Support an increase in student achievement;
•Engage teachers and students;
•Align to the National Common Core Standards and the Massachusetts curriculum
frameworks;
•Embed best teaching practices, such as differentiated instruction;
•Incorporate high-quality multi-media and design (e.g., PowerPoint);
•Be delivered by exemplary teachers for videotaping to be used for professional
development and other teacher training activities;
•Be available, along with videos and supporting materials, to teachers free of charge via the
Internet.
•Serve as the basis of high-quality, teacher-led professional development, including mentoring
between experienced and novice teachers.
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21st Century Lessons
The people…
Directors:
Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee
Ted Chambers - Co-director of 21st Century Lessons
Tracy Young - Staffing Director of 21st Century Lessons
Leslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and Advancement
Wendy Welch - Curriculum Director (Social Studies and English)
Carla Zils – Curriculum Director (Math)
Shane Ulrich– Technology Director
Marcy Ostberg – Technology Evaluator
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