Download File

Warm Up
• Write down objective and homework in
agenda
• Lay out homework (Multi-Step Equations
wkst)
• Homework (Kuta Identity & No Solution wkst)
Unit 1 Common Core Standards
•
•
•
•
•
•
•
•
•
•
•
8.EE.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or
no solutions. Show which of these possibilities is the case by successively transforming the given
equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results
(where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions
require expanding expressions using the distributive property and collecting like terms.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate
system.
A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential
functions.
Note: At this level, focus on linear and exponential functions.
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. Note: At this
level, limit to formulas that are linear in the variable of interest, or to formulas involving squared or
cubed variables.
Unit 1 Common Core Standards
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at
the previous step, starting from the assumption that the original equation has a solution. Construct a viable
argument to justify a solution method.
A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology
to graph the functions, make tables of values, or find successive approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: At
this level, focus on linear and exponential functions.
A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For
example, interpret P(1+r)n as the product of P and a factor not depending on P.
Note: At this level, limit to linear expressions, exponential expressions with integer exponents and
quadratic expressions.
G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and
informal limit arguments.
Note: Informal limit arguments are not the intent at this level.
G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Note: At this level, formulas for pyramids, cones and spheres will be given.
G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles,
e.g., using the distance formula.
Unit 1 Common Core Standards
•
•
•
•
•
•
•
•
•
N-Q.1 Use units as a way to understand problems and to guide the solution of
multi-step problems; choose and interpret units consistently in formulas; choose
and interpret the scale and the origin in graphs and data displays.
N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.
N-RN.1 Explain how the definition of the meaning of rational exponents follows
from extending the properties of integer exponents to those values, allowing for a
notation for radicals in terms of rational exponents. For example, we define 51/3
to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (5 1/3)3
must equal 5.
N-RN.2 Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
Note: At this level, focus on fractional exponents with a numerator of 1.
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.7 Look for and make use of structure.
Warm Up
• Two more than a certain number is 15 less
than twice the number. Find the number.
• Solve for each variable.
• -3v-5+12=17v-22
• x+2=x-2
Warm Up
• Two more than a certain number is 15 less
than twice the number. Find the number.
– X + 2 = 2x – 15, x = -13
• Solve for each variable.
• -3v-5+12=17v-13, v = 1
• 4x+2=x-2, x = -4/3
Vocabulary
• Identities An equation that is true for every
value. "Infinite Solutions"
• No Solution An equation that is never true, no
matter what value you place in for the
variable. "No Solutions"
1.
2.
3.
4.
5.
6.
1) Solve 3x + 2 = 4x - 1
Draw “the river”
- 3x
- 3x
Subtract 3x from
2 = x-1
both sides
Simplify
+
1
+
1
Add 1 to both
sides
3
=
x
Simplify
Check your
3(3)
+
2
=
4(3)
1
answer
9 + 2 = 12 - 1
1.
2.
3.
4.
5.
6.
7.
8.
2) Solve 8y - 9 = -3y + 2
+ 3y
+ 3y
Draw “the river”
11y – 9 =
2
Add 3y to both sides
Simplify
+9
+9
Add 9 to both sides
Simplify
11y = 11
Divide both sides by
11
Simplify
11
11
Check your answer
y=1
8(1) - 9 = -3(1) + 2
Solve
6) 2x + 5 = 2x - 3
1. Draw “the river”
2. Subtract 2x from both
sides
3. Simplify
-2x
-2x
5 = -3
This is never true!
No solutions
Solve
7) 3(x + 1) - 5 = 3x - 2
1.
2.
3.
4.
Draw “the river”
Distribute
Combine like terms
Subtract 3x from both
sides
5. Simplify
3x + 3 – 5 = 3x - 2
3x - 2 = 3x – 2
-3x
-3x
-2 = -2
This is always true!
Infinite solutions
or identity
Be Careful!
• When the solution is ZERO: Zero can be an
answer! Don’t get it confused with no
solution!
• Example: 2x + 3 = 3
• You try: a + 5 = -5a + 5
What is the value of x if 3 - 4x = 18 + x?
1. -3
2.
3.
1
3
Identity
4. No Solution
Answer Now
What is the value of x if
3(x + 4) = 2(x - 1)?
1.
2.
3.
4.
-14
-13
13
14
Answer Now
What is the value of x if
-3 + 12x = 12x - 3?
1.
2.
3.
4.
0
4
No solutions
Infinite solutions
Answer Now
You Try!
•
•
•
•
•
4x + 2 = -2x – 8
5x + 4 = 5(x + 3) - 11
8x + 3 = 3x + 2
6(x-1) = 2x + 6
4(x – 7) = 4x + 3 - 8
You Try! - Answers
•
•
•
•
•
4x + 2 = -2x – 8
5x + 4 = 5(x + 3) - 11
8x + 3 = 3x + 2
6(x-1) = 2x + 6
4(x – 7) = 4x + 3 - 8
•
•
•
•
•
X = -5/3
Identity (all solutions)
X = -1/5
X=3
No Solution
Extra Help!
• http://teachers.henrico.k12.va.us/math/hcpsa
lgebra1/Documents/examviewweb/ev3-4.htm
• http://www.phschool.com/webcodes10/index
.cfm?fuseaction=home.gotoWebCode&wcpref
ix=ata&wcsuffix=0303
• http://www.youtube.com/watch?v=KFBykIQO
8rU&feature=plcp