Download Lesson on Solving Linear Equations File

Melissa Bancroft
Educ 224
3 – 5 Day Lesson Plan
Scott Plummer
Sept. 8, 2013
1: Introduction
This Pre-Algebra unit will focus on solving linear equations. Students will solve
equations in one variable. Students will solve proportion and percent problems. Students will
rewrite equations in two or more variables.
This unit will take about 5 days to complete. Class meets five days a week for 50
minutes a class period. The unit will have 3 lesson plans. I have allowed an extra class period to
use as quiz day and a review day for the unit test.
Objectives:
Students will be able to:







Solve one-step equations using algebra.
Solve two-step equations.
Solve equations by combining like terms.
Solve equations using the distributive property.
Solve equations with variables on both sides.
Solve equations with grouping symbols.
Solve real-world problems.
2: Lesson Plan 1
Subject and Grade Level: Equations, Pre-Algebra,
NE Mathematics Standards: MA 8.3.1.b Describe relationships using algebraic expressions,
equations, and inequalities (e.g., two-step, one variable)
A: Student Objective(s): Students will solve one-step equations using algebra.
B: Opening Activity: Key vocabulary: Equations - something that says that two things are the
same, using mathematical symbols. Variable - a symbol for a number that we do not know yet.
Linear equation - is an equation in one variable that can be written in the form ax + b = 0 where
a and b are constants and a / 0. Solution - is a number that when substituted for the variable
results in a true statement. Use this activity from www.thinkfinity.com to help demonstrate
keeping equations balanced: Activity: Balance Scale Using Numbers
C: Developing Activity: Solve 4x + 8 = 20.
4x = 12 subtract 8 from each side.
x = 3 divide each side by 4.
The solution is 3.
Check x = 3 in the original equation 4x + 8 = 4(3) + 8 = 12 + 8 = 20.
Solve 7x + 13 = 9x -5
13 = 2x -5 subtract 7x from both sides
18 = 2x add 5 to each side
9 = x divide each side by 2
Check 7x + 13 = 9x -5
7(9) + 13 = 9(9) -5
63 + 13 = 81 - 5
76 = 76
Substitute 9 for x.
Multiply
Solution checks.
D: Closing Activity: Solve an equation using the distributive property.
Solve 3(5x - 13) = -2( -x + 7) -12x
15x - 39 = 2x - 14 -12x distributive property
15x - 39 = -10x -14
25x - 39 = -14
combine like terms
Add 10x to each side
25x = 25
Add 39 to each side
x = 1
Divide each side by 25.
The solution is 1.
Check 3(5(1) - 13) = -2(-1 + 7) -12 (1) Substitute 1 for x
3( -8) = -2 (6) -12
-24
= -24
Simplify
Solution checks.
E: Evaluation: Give worksheet on solving equations. Give time in class to work, checking for
understanding. Give additional worksheets to students that need more practice. Grade
worksheet.
F: Materials: White board, white board markers, worksheet.
Lesson Plan 2
Title: Equations
Lesson focus: Solving Multi-Step Equations
Subject and Grade level: Pre-Algebra
NE Mathematics Standards: MA8.3.3.c Solve multi-step equations involving rational numbers.
A: Student Objectives: Students will solve multi-step equations. Students will solve equations by
combining like terms. Students will solve equations using the distributive property.
B: Opening Activity: Key vocabulary: like terms, reciprocal, and distributive property. We have solved
one-step and two-step equations. Recall solving one-step equations. Watch video as reminder of how
to solve equations.
http://www.youtube.com/watch?v=0BsoWvWXOMM
Solve
x+9=2
x = -7
Subtract 9 from both sides.
Recall solving two-step equations.
Solve
3x + 7 = 19
3x = 12 Subtract 7 from both sides.
x = 4 Divide both sides by 3.
C: Developing Activity:
Solve an equation by combining like terms.
Solve 8x - 3x - 10 = 20
5x - 10 = 20 Combine like terms.
5x = 30
Add 10 to both sides.
x = 6 Divide both sides by 5.
Solve an equation using the distributive property.
Solve 7x + 2 ( x+6) = 39
7x + 2x + 12 = 39 Distribute 2 through x+ 6.
9x + 12
9x
= 39 Combine like terms.
= 27
Subtract 12 from both sides.
x =3
Divide each side by 9.
D: Closing Activity:
Describe and correct the error in solving the equation. Present incorrect problem.
5x - 3( x - 6) = 2
5x - 3x - 18 = 2
2x - 18
= 2
2x = 20
x
= 10
Have students solve and explain the error.
E: Evaluation: Assign homework from textbook 4-34 even. Grade randomly selected problems.
F: Materials: White board, white board markers, textbook.
Lesson Plan 3
Title: Equations
Lesson Focus: Solving equations with variables on both sides
Subject and Grade Level: Pre-Algebra
NE Mathematics Standards: MA 8.3.3.c Solve multi-step equations involving rational numbers.
A: Student Objectives: Students will solve equations with variables on both sides.
Students will solve equations with grouping symbols.
Students will solve real-world problems.
B: Opening Activity: Key vocabulary: identity.
We have solved equations with variables on one side. Recall solving
2v + 5v - 8 = 13
7v - 8 = 13 Combine like terms.
7v = 21 Add 8 to both sides.
v = 3 Divide both sides by 7.
C: Developing Activity: Solve an equation with variables on both sides.
Solve 7 - 8x = 4x - 17
7 - 8x + 8x = 4x - 17 + 8x Add 8x to both sides.
7 = 12 x -17
Simplify both sides.
24 = 12x
Add 17 to both sides.
2 = x
Divide each side by 12.
Solve an equation with grouping symbols
Solve
9x - 5 = 1/4 (16x + 60)
9x - 5 = 4x + 15 Distributive property.
5x - 5 = 15 Subtract 4x from both sides.
5x = 20 Add 5 to both sides.
x=4
Divide each side by 5.
D: Closing Activity: Solve a real-world problem.
Find the length and the width of the picture frame described.
The length is 12 inches more than the width. The perimeter is 7 times the width.
Let w = width
l = 12 + w. The length is l
P = 7w.
The perimeter is P.
Formula for perimeter is 2 l + 2 w = P.
Using substitution
2(12 + w) + 2w = 7w
24 + 2w + 2w = 7w distributive property
24 + 4w = 7w Combine like terms
24
= 3w Subtract 4w from both sides.
8
= w Divide both sides by 3.
The width is 8 inches. The length is 12 + w = 12 + 8 = 20.
The picture frame has length 20 inches and width 8 inches.
Watch video to further understanding of solving real world problems.
http://www.youtube.com/watch?v=xKH1Evwu150
E: Evaluation: Assign homework from textbook. 4 - 44 even. Grade randomly selected
problems.
F: Materials: White board, white board markers, and textbook.
4: Summative Assessment
During the 5 days, I will give a quiz to help reinforce the information we are learning. I will have a class
period the day before the unit test for review and to correct any homework to be turned in for partial
credit. I will give a test at the end of the unit.
5: Description of Assessment Plan
A Pre-test will be used to see what prior knowledge my students have for solving equations. Each lesson
will reinforce objectives. Homework assignments will be given daily from each section. A class period is
scheduled before the unit test for review of the unit. Students will be able to rework any problems from
the 3 sections during the review period for partial credit added back to their grade. I will be available to
my students before and after school for any additional help or review.