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Algebra 1: Learning Targets
CHAPTER 6
As the chapter moves along, place a check mark by those things that you have mastered.
___
I can define variable(s) to represent unknown(s) in a word problem.
___
I can represent a word problem with one or two equations.
___
I can solve a system of equations using Substitution.
___
I can solve a system of equations using Elimination.
Review topics:
1. I can solve a system of equations using Equal Values.
2. I can use generic rectangles to multiply two polynomials.
3. I can set up a proportion to represent a situation.
4. I can solve an equation involving a proportion.
5. I can solve linear equations containing one or two variables.
Algebra 1: Learning Targets
At the end of Chapter 7 you will be able to:
Semester 2 (12 days)
As the chapter moves along, place a check mark by those things that you have mastered.
___
I understand that growth rate and slope are the same.
___
I can determine the growth rate of a line using growth triangles on the graph.
___
I can find the slope of a line without graphing using
___
I understand that horizontal lines have a slope of 0.
___
I understand that the slope of a vertical line is undefined.
___
I understand that parallel lines have the same slope.
___
I understand that perpendicular lines have slopes that are opposite reciprocals. (e.g. 2/3
 -3/2)
___
I can find x- and y-intercepts of a line without graphing.
___
I can write the equation of a line given its slope and a point, without graphing.
___
I can write the equation of a line given two points, without graphing.
___
I can find the slope of a line when its equation is given in standard form. (i.e. Ax+By=C)
y
.
x
Algebra 1: Learning Targets
At the end of Chapter 8 you will be able to:
Semester 2 (14 days)
As the chapter moves along, place a check mark by those things that you have mastered.
___ I understand that rewriting the area of a rectangle from a sum to a product is called factoring.
___ I can factor expressions having a common factor.
___ I can factor quadratic expressions using generic rectangles and diamond problems.
___ I understand that the graphs of the quadratic equations that we will study are parabolas.
___ I understand that standard form of the equation of a parabola is y = ax2 + bx + c.
___ I understand that factored form of the equation of a parabola is y = a(x – d)(x – e) where d and e are the xintercepts of the graph.
___ I can make a table from a quadratic equation.
___ I can make a quadratic equation from a table.
___ I can make a quadratic equation from its graph.
___ I can make a quadratic equation from the x-intercepts and one other point on the parabola.
___ I can find the line of symmetry of a parabola from a graph.
___ I can find the line of symmetry of a parabola from a table.
___ I can find the line of symmetry of a parabola from the equation in factored form.
___ I understand that the vertex is always on the line of symmetry.
___ If a table shows symmetry, then I can find the x-coordinate of the vertex.
___ I can locate the vertex of a parabola from its graph.
___ I can use the equation and the x-coordinate of the vertex to find its y-coordinate.
___ I understand that y = ax2 + bx + c has infinitely many solutions.
___ I understand that ax2 + bx + c = 0 has zero, one, or two solutions.
___ I understand that the solution(s) to ax2 + bx + c = 0 correspond to the x-intercepts (roots) of the parabola
y = ax2 + bx + c and that there can be zero, one, or two solutions/x-intercepts.
___ I know how to solve equations like ax2 + bx + c = 0 by factoring and using the Zero Product Property.
___ I understand that some quadratic expressions can not be factored.
___ I can solve equations like ax2 + bx + c = 0 using the Quadratic Formula.
___ I understand that the Quadratic Formula must be used to solve equations containing expressions that can not
be factored.
Algebra 1: Learning Targets
At the end of Chapter 9 you will be able to:
Semester 2 (10 days)
As the chapter moves along, place a check mark by those things that you have mastered.
___ I understand that < means “is less than” and > means “is greater than or equal to”
___ I understand that inequalities such as x > 4 or -3 < x < 10 have infinitely many solutions.
___ I understand that solutions to inequalities having one variable can be represented on a number line using
boundary point(s) and shading.
___ I understand that the boundary point for a solution set of an inequality such as 2x + 3 < 11 is found by
solving the equation 2x + 3 = 11.
___ I understand that I must test some value in the inequality, other than the boundary, to determine the direction
to shade on the number line to represent the complete solution to the inequality.
___ When graphing solutions on a number line, I understand that the symbol ○ (open circle) is used to show that
the boundary point is not included in the solution set. It is used with inequality symbols < and >.
___ When graphing solutions on a number line, I understand that the symbol ● (closed circle) is used to show
that the boundary point is included in the solution set. It is used with inequality symbols < and >.
___ I understand that |x| is read “the absolute value of x” and tells how far x is from 0 on a number line.
___ I understand that solutions to inequalities having two variables can be represented on an (x,y) graph using
boundary line and shading.
___ I understand that the boundary line for a solution set of an inequality such as 2x + 3y < 12 is the line having
equation 2x + 3y = 12.
___ I understand that I must use the inequality to test some point not on the boundary line to determine which
side of the boundary line to shade.
___ When graphing solutions on an (x,y) graph, I understand that the symbol - - - (dotted line) is used to show
that points on the boundary line are not included in the solution set. It is used with inequality symbols
< and >.
___ When graphing solutions on an (x,y) graph, I understand that the symbol ___ (solid line) is used to show
that points on the boundary line are included in the solution set. It is used with inequality symbols < and >.
___ I understand that in a system of inequalities, the solutions are those points that make all of the inequalities
true.
___ I can find solutions to a system of inequalities by graphing each boundary line, testing points from each
region, and shading the region(s) containing points whose coordinates satisfy all of the inequalities.
___ I understand that some inequalities (or systems of inequalities) have no solution.
Algebra 1: Learning Targets
At the end of Chapter 10 you will be able to:
Semester 2 (16 days)
As the chapter moves along, place a check mark by those things that you have mastered.
___ I understand that a number divided by itself such as
x
equals 1 unless the denominator is 0.
x
___ I can find values to exclude because they would make the denominator be 0.
___ I understand that a rational expression looks like a fraction such as
x 3
.
x4
___ I can simplify a rational expression in which the numerator and denominator contain identical factors.
___ I understand that I cannot simplify a rational expression unless the numerator and denominator are in
factored form. YOU CANNOT CANCEL TERMS!
x2
1
IS NOT EQUAL TO
x4
2
___ I can multiply rational expressions and write the product in simplest form.
___ I can divide rational expressions and write the quotient in simplest form.
___ I can eliminate fractions in equations by multiplying both sides by a common denominator.
___ I can make equations easier to solve by multiplying or dividing both sides by a common factor.
“Rewriting”
___ I can recognize when two equations are equivalent and understand that they have the same solution.
___ I can solve equations by “Undoing” the operations in reverse order.
___ I can solve equations by using the “Looking Inside” method.
___ I can solve absolute value equations like |2x – 6| = 14.
___ I can solve perfect square equations like (x – 4)2 = 25.
___ I can find both boundary points for an absolute value inequality and graph its complete solution.
___ I can rewrite a quadratic equation from standard form into perfect square form by Completing the Square.
___ I understand that xn means that there are n factors of x.
___ I can simplify products of exponential expressions.
Example: (x2)(x3) = x5
___ I can simplify quotients of exponential expressions.
Example:
___ I can simplify powers of exponential expressions.
Example: (x2)3 = x6
___ I understand that x0 = 1.
___ I understand that x-n =
1
.
xn
x8
 x3
5
x