Directions: For each standard below, answer the questions
and provide an explanation for your solution. In order to get a score of a 4,
you must provide an explanation of what your solution means and how you got it.
Standard 1.0: Students identify and use the arithmetic
properties of subsets of integers and rational, irrational, and real numbers,
including
closure properties for the four basic arithmetic operations where applicable.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Prove, or give a counter example:
the average of two rational numbers is a
rational number
|
How did you go about this problem? |
|
Standard 2.0: Students understand and use such operations
as taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional
power . They understand and use the rules of exponents.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Find the reciprocal:
|
When might you use this in Algebra 1? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Simplify
|
In what order did you do this problem? After you
have done the problem, what do you notice? |
|
Standard 3.0: Students solve equations and inequalities
involving absolute values.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Solve for x:
3|x| + 2 = 14
|
Write out the steps you took to solve the problem |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Solve for x:
|2x - 1| = 9
|
Explain the process you went through to get your
solution(s) |
|
Standard 4.0: Students simplify ex pressions before solving
linear equations and inequalities in one variable, such as 2(2x – 5) + 4 (x – 2)
= 12.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Simplify and solve:
3 (x – 1) – 2(x + 1) = 2x |
What might have been an error that a lot of
students
made in this problem? |
|
Standard 5.0: Students solve multi-step problems,
including word problems, involving linear equations and linear inequalities in
one variable and
provide justification for each step.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
A 22 cm piece of licorice has a bite
taken out of
it. The first piece left over is twice the size of
the bitten piece and the second left over piece is
two cm longer than the bitten piece. How long is
each piece of licorice? |
Explain what your original expression or equation
means |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Is the solution below correct or
incorrect?
-3 (x + 2) – 4(x – 1) = -8x + 3
-3x + -6 – 4x + 4 = -9x + 3
-7x + -2 = -9x + 3
-15x = 1 |
Explain why it is correct, or identify where the
mistake was made |
|
Standard 6.0: Students graph a linear equation and compute
the x- and y- intercepts. They are also able to sketch the region defined by the
linear inequality.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Find the x and y intercepts of the
linear equation:
 |
What does x-intercepts mean? Where else do we see
this in algebra 1? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Use the grid below to graph the line:
-3x + 2y = - 12 |
What information did you have to find in order to
graph the line? Why? |
|
Standard 7.0: Students verify that a point lies on a line,
given an equation of the line. Students are able to derive linear equations by
using the
point- slope formula .
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Is the point (-1,1/6) a solution to
the linear
equation 2x + 6y = -1? |
What does your answer mean in terms of the graph ? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Write an equation for a line that
contains the
point (2. – 4) and has a slope of ½ |
Explain your process |
|
Standard 8.0: Students understand the concepts of parallel
lines and perpendicular lines and how their slopes are related. Students are
able to
find the equation of a line perpendicular to a given line that passes through a
given point.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Are the two lines below parallel?
and 4y – x = 3 |
What did you need to know about parallel lines to
be
able to answer this question? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Write the equation for the line that
goes through
the point (4, 3) and is perpendicular to the line
below:
 |
Explain the process you had to go through to get
your
equation |
|
Standard 9.0: Students solve a system of two linear
equations in two variables algebraically and are able to interpret the answer
graphically.
Students are able to solve a system of two linear inequalities in two variables
and to sketch the solution set.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Solve the system below
y = x – 1
2x + 3y = 12 |
Which method did you use to solve the system,
what
does your answer mean graphically? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Solve the system below
2x + 3y = 4
6x + 9y = 12 |
Which method did you use to solve the system,
what
does your answer mean graphically? |
|
Standard 10.0: Students add, subtract , multiply, and
divide monomials and polynomials . Students solve multi-step problems, including
word
problems, by using these techniques.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Below is a quadratic function in
factored form,
change it to standard form
y = (3x – 1) (x + 2) |
Once you have an equation in standard form, what
can
you easily find? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
A swimming pool is twice as long as
it is wide, if
you add one foot to both its length and its width,
what will the new area be? |
Draw a picture that explains your answer |
|
Standard 15.0: Students apply algebraic techniques to
solve rate problems, work problems, and percent mixture problems.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Kami has some nickels and some dimes.
The
value of the coins is $1.65. There are 12 more
nickels than there are dimes. How many of each
does Kami have? |
Explain the process you went through to solve
this
problem. |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
A train leaves Santa Monca traveling
east at 80
km/h. An hour later, another train leaves Santa
Monica on a parallel track at 120 kn/h. How far
from Santa Monica will the two trains meet? |
Explain how you set the problem up. |
|
Standard 16.0: Students understand the concepts of a
relation and a function, determine whether a given relation defines a function,
and give
pertinent information about given relations and functions.
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Find the domain and range of the
relation below |
Is the relation a function? How do you know? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Find the domain and range of the
relation below
{ (2, 4) (-2, 6) (3, 1) (4, 1) ( 3, 2) } |
Is the relation a function, how do you know? |
|
Standard 21.0: Students graph quadratic functions and know
that their roots are the x-intercepts
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Find the solution to the factored
form of the
quadratic below:
y = (-2x +1) (4x + 16) |
What does this tell us about the graph of the
quadratic? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
Find the x-coordinate of the vertex
y = -2x2 + 8x - 2 |
How would you use this information to find the y
coordinate of the vertex? |
|
| Problem/ Your Solution |
Explanation |
Mark (teacher feedback) |
| Where on the graph does y = 0? |
Explain how this relates to the first problem on
this
page. |
|
Challenge problems: For those of you that want to take
them on…here is a glance at what’s ahead.
5) Factor the polynomial (break it into two binomials that multiply together to
get the trinomial
a. 3x2 – 4x + 8
b. 4x2 + 8x + 36
c. 9x2 – 12x + 24
d. 2x2 + 20x – 4
e. x2 + 10x - 2
