Date:_________________
Name:_________________
Core:__________________
6.2 Solving Equations using Algebra
SHOW YOUR WORK.
The Grade 8 students had an end-of-the year dance. This disc jockey
charged $85 for setting up the equipment, plus $2 for each student who
attended the dance. The disc jockey was paid $197. How many students
attended the dance?
1. Write an equation you can use to solve the problem.
2. Solve the equation.
3. Check your answer and explain how you know it is correct.
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Date:_________________
Name:_________________
Core:__________________
6.3 Solving Equations Involving Fractions
SHOW YOUR WORK.
Five students in Ms. White’s tutorial class after school enjoyed solving
equations. She brought a bag of treats. Ms. White explained that if the 5
students shared the bag of treats equally, then gave one treat each to
the teacher, each student would still have 9 treats. How many treats were
in the bag? Here is the equation Jerry suggested: n/5 – 1 = 9
a) Is Jerry’s equation correct? Explain why or why not?
b) If your answer to part a is yes, solve the equation using algebra. If your
answer to part a is no, correct the equation, then solve the equation using
algebra.
c) Verify the solution.
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Date:_________________
Name:_________________
Core:__________________
6.4 Distributive Property
Which pairs of expressions are equivalent, write yes or no? Explain your
reasoning.
a) 2x + 20 and 2( x + 20 ) ___________
b) 3x + 7 and 10x ____________
c) 6 + 2t and 2( t + 3 ) ___________
d) 9 + x and x + 9 ____________
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Date:_________________
Name:_________________
Core:__________________
6.6 Creating A Table Of Values
Herbie has a mass of 100 Kg. His personal trainer sets a goal for him to lose
2 kg per month until he reaches his goal mass. An equation for this relation
is m = 100 – 2n, where m represents Herbie’s mass in kilograms.
a) Use the equation to create a table of values.
b) At some time, Herbie should have a mass of 60 Kg.
How many months will he have trained?
c) By his birthday, Herbie had trained for 7 months. What was his mass
then?
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Date:_________________
Name:_________________
Core:__________________
6.7 Graphing Linear Relations
Regina plans a marshmallow roast. She will buy 8 marshmallows for each
person who attends, and 12 extra marshmallows in case someone shows
up unexpectedly. Let n represent the number of people who attend. Let
m represent the number of marshmallows Regina must buy. An equation
that relates the number of marshmallows to the number of people is
m = 8n + 12.
a) Create a table of values for the relation.
b) Graph the relation on the back graph paper
c) Describe the relationship between the variables
in the graph.
d) Is the relation linear? How do you know?
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Not Yet Adequate
Adequate
Proficient
Excellent
little understanding; may be
unable to represent,
demonstrate, or explain:
– the relationship between
variables on a graph
– modelling a problem with
a linear equation
– steps used to solve a linear
equation
some understanding;
partially able to represent,
demonstrate, or explain:
– the relationship between
variables on a graph
– modelling a problem with
a linear equation
– steps used to solve a linear
equation
shows understanding; able
to represent, demonstrate,
and explain:
– the relationship between
variables on a graph
– modelling a problem with
a linear equation
– steps used to solve a linear
equation
shows depth of
understanding; in various
contexts; represents,
demonstrates, and explains:
– the relationship between
variables on a graph
– modelling a problem with
a linear equation
– steps used to solve a linear
equation
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Conceptual Understanding
•
Shows understanding of linear
equations and graphing by:
– describing the relationship
between the variables of a
given graph
– modelling a given problem
with a linear equation
– representing the steps used to
solve a given linear equation
visually and symbolically
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)
Not Yet Adequate
Adequate
Proficient
Excellent
Procedural Knowledge
•
Accurately:
– graphs two-variable linear
relations
– solves linear equations
(models, symbols, pictures)
– verifies solutions
limited accuracy; major
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
partially accurate; frequent
minor errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
generally accurate; few
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
accurate and precise; no
errors or omissions in:
– graphing linear relations
– solving linear equations
(models, symbols,
pictures)
– verifying solutions
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and procedures
with partial clarity; may be
incomplete
records and explains
reasoning and procedures
clearly and completely
records and explains
reasoning and procedures
with precision and
thoroughness
Communication
•
Records and explains reasoning
and procedures clearly and
completely, including
appropriate terminology (for
example, ordered pair, linear
relation)