1
Idaho State Curriculum Guide Pre-Algebra
Number Sense
Estimation/Accurate Computation
Reasoning/Problem Solving
Measurement
©State of Idaho 2003
Algebra, Functions, & Mathematical Models
Geometry
Data Analysis, Probability, & Statistics
McRel Alignment—8th
ISAT Cut Scores
State Standards
Sample Test Items
New Vocabulary
Number Sense
State
Standard
and
Benchmark
Estimation/Accurate
Computation
Local
Curriculum
Number Sense
337.01a
Place Value,
Expanded
and Standard
Notation
Learning
Continuum
and other
Performance
Objectives
Reasoning/Problem
Solving
Measurement
Sample Assessment and
Sample Quizzes
Algebra, Functions,
& Mathematical
Models
Sample
Sequence
Minimum
Hours
Allotted
Geometry
Data Analysis,
Probability, &
Statistics
Sample Teaching
Strategy
Return to Top
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
For Learning:
Have students choose an amount they’d
like to win in the lottery and write that
number in expanded form from standard
notation. Then exchange expanded forms
with a partner to see if they could convert
to standard form and get the amount their
partner wished for.
Of Learning:
RIT 221-230
RIT 231-240
Use this opportunity to compare
and contrast as to why we may
use standard notation instead of
expanded form, possibly as a
partner activity.
Sample
Resources

2
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
337.01a
Ordering,
Equalities,
and
Inequalities
337.01a
337.02b
Fractions /
Ratio /
Proportion
337.01b
Understand
and use
rational and
irrational
numbers
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Have students list the common simple
fractions as a decimal, and as a percent.
Arrange a list of numbers that are written
as fractions, decimals or percents in
order.
Make chart of common fractions with
decimal equivalents. Look for and explain
the patterns.
Of Learning:
RIT 211-220
RIT 221-230
For Learning:
Use fraction strips to show the meaning of
a fraction.
List the eye color of each student in the
class. Use the data to write the ratio of
blue eyes to brown eyes etc.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy

This may be a good time
research the stock market, noting
that shares recently went to
decimal representation (In 2001 I
believe) from fractional notation.
Possibly integrate with history
and research the crash of 1928
converting some stocks of that
era as decimals used today, and
visa-versa. Throw in percent of
change from 1928 to today.
There are many M&M activities
that could be developed to show
the concept of ratio and
proportion.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
For Learning:
Calculate square roots of 2, 3, 4, and 5 to
the nearest ten-thousandth. Note which
are rational and hypothesize which is the
larger set.
Sample
Resources
Identify the differences between
rational and irrational numbers.
Give examples of each.
M&M activity
http://www.isbe.
state.il.us/ils/cla
ssassess/math/st
ageE/math6A6C
6D10AE.pdf
Real
number
charts
3
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
337.01d
Factorization
/ Divisibility
337.01a
337.01c
Decimals
337.02b
Percents
337.01c
Exponents
and Scientific
Notation
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Sample Assessment and
Sample Quizzes
For Learning:
Have students define and give examples
of prime numbers, composite numbers,
and prime factorization.
For Learning:
On grid paper have students make a
10X10 decimal model. Have the students
then show .3 or .8 on the grid model.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
For Learning:
Have students fill in a chart like this
including the decimal and the percent for
each fraction.
Of Learning:
RIT 211-220
RIT 221-230
For Learning:
Express the national debt in scientific
notation. Calculate how many miles long it
would be if we laid that many dollar bills
end to end.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources
Have the students write a
paragraph describing the
differences between the two
given examples, so that the
students can get a feeling for the
difference between LCM and
GCF
Create a mnemonic device for
each.
Lesson?
Power Point
LCM GCF
Use models to demonstrate
concept.
In pairs or groups, have students
discuss and record situations
where decimals, percents, or
fractions are most appropriate to
use. Research instances of each
making equivalent substitutions
to see if info makes sense.
Create a real world situation,
such as an unmanned mission to
mars, calculating distances using
scientific notation.

4
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
337.01b
Integers
337.01b
Square Roots
337.01a
Absolute
Value
337.01e
Position real
numbers on a
number line
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Write two inequalities involving
-3 and -1
State which number is smaller -3 and -1
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Create number lines to use with
counters to demonstrate that the
number that is further right is the
larger value.
Of Learning:
RIT 221-230
For Learning:
List all the perfect squares between 1 and
625
Estimate
79
Draw a square that has an area of 49
square centimeters
Of Learning:
RIT 221-230
RIT 231-240
For Learning:
Determine between a set of numbers
which has the greater absolute value:
-7, 4, 0, 5.
Drill and practice to memorize
perfect squares between 1 and
625.
Compare absolute value to
distance. Going to grandma’s is
12 miles and 12 miles back.
Neither is a negative number.
For Learning:
Locate a given set of numbers on a
number line.
DMA
Benchmark
Teacher
Observable
ISAT
Of Learning:
RIT 211-220
Create number lines in math
journals for future reference.
Sample
Resources

5
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment and
Sample Quizzes
Estimation and Computation
337.02a
Rational
Numbers
337.02a
Decimals
Learning
Continuum
DMA
Benchmark
Teacher
Observable
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Return to Top
For Learning
Evaluate the following expressions:
½ + 2/3
-5 x 7
12 – 5 7/8
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
For Learning:
Compute batting averages for a given
player or team.
Teacher made assessment covering the
four operations.
Create a travel log taking a
fictitious trip across the U.S. or
integrate with Geography and
countries they’re studying.
Show the meaning of .3 times .8
with a 10x10 grid model.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
RIT 211-220 (Money)
RIT 231-240 (Money)
337.02a
Fractions
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
For Learning:
Using fraction bars, demonstrate through
presentation or illustration a series of
teacher chosen problems with all 4
operations.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Using the stock market, give the
kids $100,000 to “invest” for a
month or so. The students
should tabulate losses and gains
each day – a chance to use
Excel in a technology lesson.
Sample
Resources

6
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
337.02b
recall
common
equivalent
fractions
decimals
percents
337.01a
337.01c
Percents
337.01c
Integers
337.01b
337.02d
Squares and
Square Roots
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
DMA
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
Sample Assessment and
Sample Quizzes
For Learning:
Use of “Mad Minute” type
exercises.
For Learning:
Students should be able to solve all 3
types of percentage problems:
a) 30% of 60 is what number?
b) 12 is 25% of what number?
c) 18 is what % of 72?
Of Learning:
RIT 221-230
RIT 231-240
For Learning:
Use counters to model Addition and
subtraction of integers.
DMA
Benchmark
Teacher
Observable
ISAT
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Teacher
Observable
DMA
For Learning:
Mad Minute type exercises.
Calculate the square root to the hundredth
position.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Drill and practice of common
equivalencies such as 25%, 1/3,
0.5, ¾, etc.
Sample
Resources

Common
fractions chart?
Take a class created survey and
find the percentages of each
answer.
Using percentages of answers to
a survey, have students figure
out how many peers answered in
a particular way.
Create a manipulative system of
green and orange counters to
model positive and negative
numbers to be used to model
addition, subtraction,
multiplication, and division.
Drill and practice.
Use real-world situation showing
how carpenters use Pythagorean
Theorem to make sure walls and
floors are square -- straight.
Power Point
adding integers
Power Point
subtracting
integers
Page 82, 88
Pre-Algebra,
Glencoe 1999.
7
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
337.02c
Order of
operations
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
DMA
337.02e
Select
method of
computation
Teacher
Observable
DMA
337.03a
predict
computation
results
Teacher
Observable
DMA
337.03b
recognize
when
estimation is
appropriate
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Evaluate:
2(16 – 4) ÷ 4 + 6 x 3 =
For Learning:
Given a story problem, describe how you
would solve the problem. Include all
computations and how you would use the
four operations.
For Learning:
Estimate total price for 5 shirts costing
$18. 67 each. (5 x $20)
For Learning:
Explain when/not and why/not doctors and
builders should use estimation.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Create a game using three
number cubes. Have one of the
number cubes 4 – 9, while the
other two are 1 – 6. Make a
board with 64 - 100 chosen
numbers that the object is to get
three or four in a row by using
order of operations to “land” on a
spot.
In groups or pairs, have the
students discuss how they would
handle each situation:
a) Going to the grocery store and
having a fixed amount to spend.
b) Taking a test in school with all
technology available.
c) Describe situations where
pencil and paper is better than
mental math.
Going to the grocery store and
having a fixed amount to spend,
give the kids a list and ask if they
have enough money.
Have students interview adults to
find out when they use
estimation and when they would
never use estimation.
Sample
Resources

8
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
337.03c
Determine if
estimate is an
overestimate or
underestimate
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Johnny has $30 for his date with Sally. He
wants to take her to a movie, $7.50 each,
dinner at Pizza Hut, $13.58 pizzas, and
Dairy Queen for $0.99 Blizzards. He
thinks he has enough. Is his estimate of
$30 low, or high, or just right?
Mathematical Reasoning and Problem Solving
338.01a
Use
strategies for
real world
situations
338.01b
Recognize
pertinent
information
338.01c
Make
predictions
and decisions
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Use a real world dealing with an
estimate of travel time to a
location you/ they are heading.
Record the actual time it took to
arrive and indicate whether the
estimate was low, high or just
right.
Return to Top
For Learning:
If paint costs $15 a gallon and covers 300
square feet, how much will it cost to paint
your classroom (give measurements).
As a group, have kids plan a
class party with a set amount of
money.
DMA
For Learning:
Given a problem, identify which
information you need to complete the
problem.
Teacher
Observable
For Learning:
Using a graph, predict what the future
numbers will be.
Tell the kids you have a problem
such as you locked your keys in
the car. Explain it’s your mother’s
birthday and your cat is having
kittens, your spare key is at
home, your daughter dyed her
hair green and so on. Have kids
solve your problem and state
which info was pertinent.
Using research provided by fish
and game, have students work in
groups to predict the salmon run
for the next two years.
Teacher
Observable
DMA
Teacher
Observable
DMA
Sample
Resources

9
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
338.02a
338.02b
338.02c
Use
reasoning
skills to
recognize
problems and
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Sample Assessment and
Sample Quizzes
For Learning:
Knowing how to find the area of a square,
have the students find the surface area of
a cube.
DMA
Teacher
Observable
DMA
Sample Teaching
Strategy
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
For Learning:
Use technology to find the square root of
15,025.
Use Excel to collect data and select the
best way to graphically show results.
Many M&M projects work here.
mathematically.
Teacher
Observable
Minimum
Hours
Allotted
Integrate a unit with Reading and
English where the students write
a proposal/report for a fictitious
company. Maybe a car
dealership is opening a new lot in
town and wants to know what
type of cars to place on the lot.
After giving students a variety of
info, have them explain the
concepts used as well as their
reasoning to solve the situation
for which they formulated their
conjecture and plan of attack and
came up with their conclusions.
express them
338.03a
338.03b
338.03c
Apply
appropriate
technology
and models
to find
solutions to
problems.
338.04a
338.04b
338.04c
Communicate
results using
appropriate
terminology
and methods.
Sample
Sequence
©State of Idaho 2003
For Learning:
Present report using graphs, models,
tables, and a written portion including
proper terminology to show how they
arrived at their conclusion.
Great opportunity for an
interdisciplinary unit between
Math, English, Reading, Science,
and Geography. Maybe a study
on endangered species and
solutions to get them off the
endangered list.
Sample
Resources

10
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment and
Sample Quizzes
Concepts and Principles of Measurement
339.01a-f
339.01d
Understand
and use U.S.
customary
and metric
measurements.
Learning
Continuum
(Length,
Weight,
Volume)
Learning
Continuum
(Time, Temp)
Learning
Continuum
(Area, Perim.,
Circumference)
DMA
Benchmark
Teacher
Observable
ISAT
339.02a
Use rates to
make indirect
measurements
Teacher
Observable
DMA
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Return to Top
For Learning:
Teacher made application test where
students must find area, perimeter,
volume, in multiple converted units, i.e.,
meters and centimeters.
Keep vocabulary up to date in math
journals.
Select and use appropriate units and tools
to make formal measurements as well as
estimates in standard and metric
measures.
Of Learning:
RIT 211-220 (Angle Measure)
RIT 211-220 (Length, Weight, Volume)
RIT 221-230 (Length, Weight, Volume)
RIT 231-240 (Length, Weight, Volume)
As a group project, design and
determine how much lumber
would be needed to build a
doghouse. Include an estimate of
costs and materials. Maybe have
the students include some
measures in both standard and
metric.
Place containers in room with
labels of what size they are, i.e.
e., liter, gallon, quarts, pints, and
cups.
Create a poster with standard
formulas for area, perimeter,
volumes, distance, and
circumference.
RIT 231-240 (Time, Temperature)
RIT 211-220 (Area, Perim, Circum)
RIT 221-230 (Area, Perim, Circum)
RIT 231-240 (Area, Perim, Circum)
For Learning:
If five gallons of ice cream costs $4.50,
how much does 1 quart cost?
Given the weight of a certain
item in the classroom, estimate
the weight of other items.
Sample
Resources

11
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
339.03a
Use
proportions,
ratios and
scales
339.04a
Understand
units and
relations to
one another
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
DMA
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
343.01a
343.01b
343.01c
Patterns,
Sequences,
Functions
DMA
Benchmark
Teacher
Observable
ISAT
Minimum
Hours
Allotted
For Learning:
If 2 inches on the map represents 300 km,
how many kilometers is 75. inches?
For Learning:
Extend the first five numbers in the
Fibonacci sequence and explain the
pattern.
Using what we know about the distance
formula, how might we estimate our travel
time if we need to go 465 miles?
Vocabulary quiz.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Sample Teaching
Strategy
Use nutritional info on the back
of items brought in by students to
find total calories, fat, sugar, etc.
contained in package as well as
cost per ounce, gram, or
whatever measure chosen.
Use map scale to determine
distances.
Enlarge a cartoon to a given
scale.
Determine the reading hours of
an entire class if everyone reads
for twenty minutes.
For Learning:
If you are traveling 60 mph for 4.5 hours,
how far did you travel?
Algebra, Functions, and Mathematical Models
Learning
Continuum
Sample
Sequence
©State of Idaho 2003
Return to Top
Discovery of patterns is fun for
most kids. Give them some
sequences to extend. Have them
explain the pattern.
Demonstrate what we know
about the Pythagorean theorem,
see if one of the classroom wall
is square.
Continue to keep adding
vocabulary to math journals,
continuously correcting improper
terminology usage.
Sample
Resources

12
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
343.02a
Represent data
as graph, table
& mathematical
relationship
343.03a
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
DMA
Use patterns
and functions
to solve
problems
Teacher
Observable
DMA
340.03a
Learning
Continuum
Solving
Equations
and
Inequalities
DMA
Benchmark
Teacher
Observable
ISAT
Sample Assessment and
Sample Quizzes
For Learning:
Given a set of data, organize it in a table
and as a graph. Show the mathematical
relationship that exists.
For Learning:
Illustrate a line graph showing distance
traveled at a constant speed of 60 mph.
For Learning:
Solve x + 6 > 5 and
3y – 9 = 24
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources

Find an article from the paper or
recent magazine, and while the
students are taking notes, hold a
class discussion about what is
being represented and any
mathematical relationship that
exists. Also show an example of
no mathematical relationship.
Use temperature as an example.
Let the x-axis represent time,
while the y-axis represents
temperature. Start at ay time and
temp, assuming constant
increase. If given 6:00 a.m. and
9:30 a.m. predict the temperature
at noon.
Have the students compare and
contrast inequalities with
equality.
Have the students make a
journal entry describing an
instance where they would
equality and inequalities.
Power Point
presentation
one step
equations
with addition
and
subtraction-?
13
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
340.03b
Graph
representation
of linear
equations
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
DMA
Benchmark
Teacher
Observable
ISAT
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
340.02a
Properties
For Learning:
Simplify the expression 4a + 3b – 7 – b +
2a.
For Learning:
Simplify 2(3a + 2c) + a – 4c.
340.02b
Order of
Operations
For Learning:
Graph the equation y = 2x – 4.
DMA
340.02c
Simplifying
Expressions
Sample Assessment and
Sample Quizzes
DMA
Benchmark
Teacher
Observable
ISAT
For Learning:
Identify through matching the expression
and the property it is an instance of.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources

While students take notes, write
an equation on the board.
Demonstrate that to complete the
graph you pick a point for x and
see what y equals thus creating
an ordered pair. Try to get the
students to realize this is nothing
more than substituting for one
value to find the other. Note that
no matter what substitutions are
made, the ordered pairs are
always on the line. Now we only
need two points to make a line.
Relate this to stocking shelves in
a grocery store; we still sort by
item.
A review activity recalling order
of operations works here. Ask
“Why would we not use order of
operations here when we use it
every other time”.
Create another game as we did
the first time we encountered
order of operations.
This is a great jigsaw activity.
Also, you can set up a scavenger
hunt in the classroom where you
have left notes on and
demonstrations of that the kids
have to find and write down in
their journals.
Power Point
Presentation
properties
14
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
340.01a
340.01c
Use Variables
and math
symbols in
expressions,
equations and
inequalities
340.01b
Translate word
problems into
an algebraic
expression
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment and
Sample Quizzes
Teacher
Observable
DMA
For Learning:
As a quiz, given a word phrase, translate
into an algebraic expression and visaversa.
Teacher
Observable
DMA
For Learning:
As a quiz, given a word phrase, translate
into an algebraic expression and visaversa.
Concepts and Principles of Geometry
341.01a
Shapes and
Figures, 2- &
3dimensional
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Minimum
Hours
Allotted
Sample Teaching
Strategy
Let a represent apples, b
represent bananas, c represent
cantaloupe, and g represent
grapes. Ask the students how
these items are sorted at the
store. Reinforce that we keep
apples together and so on, in
reference to addition and
subtraction. I like to refer to
multiplication as a blender. Next,
have them write an expression
for 2 apples, 4 bananas, 6
cantaloupes, and 9 grapes.
While the students take notes
demonstrate that Sara baby-sits
for different periods of time and
wants to write an algebraic
expression to represent how
much she will make if she
charges $4.50 an hour.
Have students write in their math
journals how they could use
algebra like Sara from above did.
Return to Top
For Learning:
Quiz matching pictures and defining
properties to the correct to the correct
two- and three- dimensional object.
Of Learning:
RIT 211-220
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Create a chart listing the types of
one- and two- dimensional
objects. Then classify the objects
using their defining properties.
Finally, draw a picture of the
shapes.
Sample
Resources

15
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
341.01b
Construct and
measure
geometric
shapes
341.01d
Congruency
and Similarity
341.01d
341.01g
Symmetry
and
Transformations
341.01c
341.01h
Geometric
Properties
and
Terminology
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Teacher
Observable
Sample Assessment and
Sample Quizzes
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Minimum
Hours
Allotted
Sample Teaching
Strategy
For Learning:
Use appropriate tools to measure shapes
and angles.
Use rulers, compasses, and
protractors to measure geometric
shapes and angles in the
classroom.
For Learning:
Identify through matching which figures
are congruent and which are similar.
Have students take notes as you
go over similarities and
differences in concepts of
congruence, and symmetry of
shapes. Have students identify
items in the room that are
congruent, similar and/or
symmetric.
Through your demonstration
while students take notes, go
over symmetry and the
transformations rotation,
translation and reflection.
DMA
Learning
Continuum
Sample
Sequence
©State of Idaho 2003
Of Learning:
RIT 211-220
RIT 221-230
For Learning:
Identify which figures share symmetries
and construct their lines of symmetry.
Identify type of transformation.
Of Learning:
RIT 211-220
RIT 231-240
For Learning:
Vocabulary quiz over geometry terms.
Match the description with the figure, i.e.,
a quadrilateral that has only one pair of
opposite sides that are parallel matches
with a trapezoid.
Of Learning:
RIT 211-220
RIT 221-230
RIT 231-240
Have students take notes on
geometry vocabulary. Use
vocabulary to play bingo or
concentration.
Use pinwheel or jigsaw to
learn/teach groups vocabulary
and properties.
Sample
Resources

16
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
341.03a
Coordinate
341.01e
341.02a
Apply formulas
for perimeter,
circumference,
area, and
Pythagorean
theorem
341.01f
Surface area
and volume
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Teacher
Observable
DMA
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Using a city map, have students locate
buildings or intersections using streets as
coordinates.
Of Learning:
RIT 211-220 (Graphing)
RIT 221-230 (Graphing)
RIT 231-240 (Graphing)
For Learning:
Calculate the area and perimeter of a
basketball court and it’s center circle as
well as it’s key.
Using the Pythagorean theorem, calculate
the missing side.
For Learning:
Given a figure with measurements given,
calculate surface area and volume.
Data Analysis, Probability, and Statistics
342.01a
342.01b
Analyze and
make
conclusions
drawn from
tables charts
and graphs
Teacher
Observable
DMA
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Create a game similar to
“Battleship”.
Relate to Geography and latitude
and longitude (recall).
Create a poster with standard
formulas for area, perimeter,
volumes, distance, the
Pythagorean theorem, and
circumference.
Construct a cylinder, pyramid,
rectangular prism, cube, etc.,
and calculate surface area
and volume.
Return to Top
For Learning:
Quiz over the interpretation of a graph,
table, and a chart.
Using graphs, charts, or tables
found in the paper, hold a class
discussion over what the info is
trying to present as the students
take notes.
Sample
Resources

17
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
342.02a
Collect
organize, and
display data
342.04a
Probability &
Prediction
342.04b
342.05b
Language of
probability
342.04c
342.05c
Recognize
equally likely
outcomes
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Teacher
Observable
DMA
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Have the students create a survey. They
are to collect the results, organize and
display the data as an individual project.
For Learning:
Quiz on basic simple probabilities such
as:
What is the probability that you will roll
an even number on a six-sided number
cube.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Have students collect and
display data by surveying the
actual number of chocolate chips
in a cookie.
There are many M&M activities
that can be used here also.
Find the probability of drawing a
jack of hearts in a standard deck
of cards.
Of Learning:
RIT 221-230
For Learning:
Give a quiz over the vocabulary used in
probability.
For Learning:
Quiz over probability of rolling a 5 on a
number cube and the probability of a
spinner landing on a certain number or set
of numbers.
Use vocabulary to play bingo or
concentration.
Have the students bring coins, or
they can use two sided counters,
and let each flip the coin 50 times
recording each result. Then survey
the class and see how many, if
any, had 25 of each. Next, add all
students’ results and see if overall
heads and tails were even. Ask
why or why not.
Sample
Resources

18
Idaho State Curriculum Guide Pre-Algebra
State
Standard
and
Benchmark
342.05a
Combinations
and
Permutations
342.03a
Statistics
342.03b
Range,
frequency
and
distribution
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Learning
Continuum
DMA
Benchmark
Teacher
Observable
ISAT
Teacher
Observable
DMA
Sample Assessment and
Sample Quizzes
For Learning:
Have students model the theoretical
probability of rolling a 7 with two six sided
number cubes.
Of Learning:
RIT 221-230
For Learning
Have students compute an individual
mean, median, mode, and range of
grades in a particular course.
Of Learning:
RIT 221-230
RIT 231-240
For Learning:
Given a set of data, create a frequency
distribution chart.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Have five students volunteer and
come to the front of the class. To
demonstrate permutations, have 3
chairs and see how many ways the
kids can be arranged where order
matters. Using the same kids and
chairs, demonstrate how many
ways the kids can be grouped
where order doesn’t matter,
combinations.
Survey the students about their
father’s age, moms don’t like us to
know. Collect and organize the
data to demonstrate finding the
mean, median and mode.
Maybe use a jigsaw method to
have students discover and teach
each other about mean, median
and mode.
Bring lists of professional sports
teams or leagues and have the
kids work in groups or individually
to organize the data into a
frequency distribution. While you’re
demonstrating with one set of data,
have the students working with
another set.
Sample
Resources

19
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
APPROVED ISAT PROFICIENCY SCORES
Return to Top
Approved by the State Board of Education March 6, 2003
READING
Basic
Proficient
Advanced
2
174
182
193
3
185
193
204
4
192
200
211
5
198
206
217
6
203
211
222
7
207
215
226
8
210
218
229
9
213
221
232
10
216
224
235
LANGUAGE
Basic
Proficient
Advanced
2
176
184
197
3
186
194
207
4
193
201
214
5
200
208
221
6
204
212
225
7
207
215
228
8
211
219
232
9
213
221
234
10
214
222
235
MATH
Basic
Proficient
Advanced
2
174
185
201
3
185
196
212
4
194
205
221
5
202
213
229
6
208
219
235
7
214
225
241
8
222
233
249
9
229
240
256
10
231
242
258
PROFICIENCY LEVELS DEFINITIONS
Approved by the State Board of Education March 6, 2003
ADVANCED: Exceeds Standards
Back to Top
The student demonstrates thorough knowledge and mastery of skills that allows him/her to function
independently above their current educational level.



The student demonstrates a comprehensive understanding of all relevant information relevant to
the topic at level.
The student demonstrates comprehension and understanding of knowledge and skills above his/her
grade level.
The student can perform skills or processes independently without any significant errors.
20
Idaho State Curriculum Guide Pre-Algebra
PROFICIENT: Meets Standards
©State of Idaho 2003
Back to Top
The student demonstrates mastery of knowledge and skills that allow them to function independently on all
major concepts and skills related to their educational level.


The student demonstrates a comprehensive understanding of all information relevant to the topic, at
level.
The student can perform skills or processes independently without any significant errors.
BASIC: Below Standards
Back to Top
The student demonstrates basic knowledge and skills usage but cannot operate independently on concepts
and skills related to his/her educational level. Requires remediation and assistance to complete tasks without
significant errors.


The student has an incomplete knowledge of the topic and/or misconceptions about some
information.
The student requires assistance and coaching to complete tasks without errors.
BELOW BASIC: Critically Below Standards
Back to Top
The student demonstrates significant lack of skills and knowledge and is unable to complete basic skills or
knowledge sets without significant remediation.


The student has critical deficiencies of relevant knowledge of topic and/or misconceptions about
some information.
The student cannot complete any skill set without significant assistance and coaching.
21
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
State Standards—8th Grade Math
Return to Top
336.
MATHEMATICS STANDARDS – GRADE 8, SECTIONS 337 THROUGH 343.
The samples associated with the content standards are meant to illustrate meaning and to represent possible areas of
application. They are not intended to be an exhaustive list, but are samples of applications that would demonstrate
learning.
337.
BASIC ARITHMETIC, ESTIMATION, AND ACCURATE
COMPUTATIONS.
Rationale: An understanding of numbers and how they are used is necessary in the everyday world. Computational skills and procedures should be
developed in context so the learner perceives them as tools for solving problems.
Standard – The student will:
Understand and use
numbers.
01.
a.
Return to Place Value
Content Knowledge and Skills:
Read, write, order, and compare
real numbers (integers, fractions,
decimals, percents, ratios) and
absolute values.
Return to Ordering
Return to NS: Decimals
Return to Fraction/ Ratio/
Proportions
Return to Absolute Value
Return to EC: Percents
Return to Use Rational
Numbers
b.
Understand and use real numbers,
both rational and irrational.
i.
ii.
iii.
iv.
v.
vi.
i.
ii.
Return to NS: Integers
Samples of Applications:
Interchange fractions, decimals, or percents, to
determine pricing markup or markdown.
Use fractions to increase or decrease recipes.
Use percentages to computer taxes and
commissions.
Use decimals to computer interest problems.
Use ratios to compute sports averages (batting
averages).
Which has greater absolute value, -5 or 2?
Explain that irrational numbers neither terminate
nor repeat when written in decimal form.
Calculate the square root of a number to the
thousandths.
Return to NS: Square Roots
Return to EC: Squares and
Square Roots
c.
Return to NS: Decimals
Return to Exponents
Return to EC: Percents
Show a sense of magnitudes and
relative magnitudes of real
numbers (integers, fractions,
decimals) using scientific notation
and exponential numbers.
i.
ii.
Express distances in our solar system using
scientific notation.
Order a list of fractions, decimals, and exponential
numbers.
Return to EC: Integers
Return to Factorization /
Divisibility
d.
Develop and apply number theory
concepts.
i.
Identify prime factorization, greatest common
factors and least common multiples.
Return to Position Numbers
on Number Line
e.
Understand the position of real
numbers on a number line.
i.
ii.
Locate a given set of real numbers on a number line.
Accurately identify positive and negative integers
on a thermometer.
22
Idaho State Curriculum Guide Pre-Algebra
02.
Perform
computations
accurately.
a.
Consistently and accurately
add, subtract, multiply, and
divide rational numbers.
b.
Instantly recall common
equivalent fractions,
decimals, and percents.
c.
©State of Idaho 2003
i.
Plan a road trip. Record and calculate gas
mileage, food and lodging expenses.
Evaluate numerical
expressions using the order
of operations.
i.
Find the surface area of a cylinder.
d.
Understand and use
exponents.
i.
Solve problems using exponential growth,
for instance, Sally tells 3 friends a secret.
The next day those 3 friends tell 3 other
friends. If this pattern continues for 5 days,
how many friends will hear the secret?
e.
Select and use an
appropriate method of
computation from mental
math, paper and pencil,
calculator, or a combination
of the three.
f.
Use appropriate vocabulary.
a.
Use estimation to predict
computation results.
b.
Recognize when estimation
is appropriate and
understand the usefulness of
an estimate as distinct from
i.
Estimate the population of people at the
mall on any given date.
Explain why or when exact answers might
be necessary.
Return to EC: Rational
Numbers
Return to EC: Decimals
Return to EC: Fractions
Return to Fraction/ Ratio/
Proportions
Return to Recall Common
Equivalents
Return to NS: Percents
Return to Order of
Operations
Return to EC: Squares and
Square Roots
Return to Select Method of
Computation
03.
Estimate and judge
reasonableness of
results.
Return to Predict
Computation Results
Return to Recognize
Appropriate Estimation
ii.
23
Idaho State Curriculum Guide Pre-Algebra
c.
Return to Determine if
Estimate is Over or Under
d.
338.
an exact answer.
Determine whether a given
estimate is an overestimate
or underestimate.
i.
©State of Idaho 2003
Estimate driving time to a given destination
and compare to actual time (given
particular miles per hour).
Use appropriate vocabulary.
MATHEMATICAL REASONING AND PROBLEM SOLVING.
Rationale: These processes are essential to all mathematics and must be incorporated in all other mathematics
standards.
Standard – The student
will:
01. Understand and
use a variety of
problem-solving
skills.
Content Knowledge and Skills:
a.
Samples of Applications:
Use a variety of strategies,
including common
mathematical formulas to
compute problems drawn
from real-world situations.
i.
i.
Given a problem, identify essential
information.
i.
After finding the area of square, find the
surface area of a cube.
ii.
iii.
Return to Use Strategies in
Real Life
Return to Recognize
Pertinent Information
b.
Recognize pertinent
information for problem
solving.
Return to Make Predictions
and Decisions
c.
Make predictions and
decisions based on
information.
Use reasoning
skills to recognize
problems and
express them
mathematically.
a.
Use a variety of methods,
such as words, numbers,
symbols charts, graphs,
tables, diagrams, and
models, to explain
mathematical reasoning and
concepts.
b.
Apply solutions and
strategies to new problem
situations.
02.
Return to Use Reasoning
Skills
Return to Use Reasoning
Skills
Determine amount of interest earned in a
savings account.
Compute amount of paint needed for a
bedroom.
Given $500 to plan a year-end class party
using several committees, develop a budget
for the party.
24
Idaho State Curriculum Guide Pre-Algebra
Return to Use Reasoning
Skills
03.
Apply appropriate
technology and models
to find solutions to
problems.
c.
Formulate conjectures and
justify (short of formal
proof) why they must be or
seem to be true.
i.
a.
Understand the purpose and
capabilities of appropriate
technology use as a tool to
solve problems.
i.
Use technology to find the square root of
5,281.
b.
Use computer applications
to display and manipulate
data.
i.
Display and compare the frequency of
various M&M colors using computer
applications.
c.
Select appropriate models to
represent mathematical
ideas.
a.
Use a variety of methods,
such as words, numbers,
symbols, charts, graphs,
tables, diagrams, and
models, to communicate
mathematical information.
i.
Write an explanation on how to solve a
problem.
Display results of a problem in graphic
form.
Return to Use Technology
Return to Use Technology
Return to Use Technology
04.
Communicate
results using
appropriate
terminology and
methods.
©State of Idaho 2003
ii.
ii.
Debate the following: If people like cheese
and mice like cheese, then people are mice.
On a crisp autumn day, the 1st four students
to class are wearing shorts. What will be
the possible attire of the rest of the students
in the class? Explain.
Return to Communicate
Results
b.
Use appropriate vocabulary
to communicate
mathematical information.
c.
Use appropriate notation.
Return to Communicate
Results
Return to Communicate
Results
339.
CONCEPTS AND PRINCIPLES OF MEASUREMENT.
Rationale: The first step in scientific investigation is understanding the measurable attributes of objects.
Standard – The student
will:
Content Knowledge and Skills:
Samples of Applications:
25
Idaho State Curriculum Guide Pre-Algebra
01.
Understand and
use U.S. customary
and metric
measurements.
a.
Select and use appropriate
units and tools to make
formal measurements
using both systems.
ii.
Return to Measurement
Return to Measurement
02.
03.
04.
Select and use the appropriate tool to measure the
length of a school building, the length of a
classroom, the length of a thumbtack and the
length of a student’s shoe.
Measure the interior angles of a triangle.
b.
Apply estimation of
measurement to real-world
and content problems
using actual measuring
devices.
c.
Recognize the differences
and relationships among
measures of perimeter,
area, and volume
(capacity) in both systems.
i.
Model length, area, and volume using various
manipulatives (string, tiles, and cubes).
d.
Solve problems involving
length, perimeter, area,
volume (capacity), weight,
mass, and temperature.
i.
Design and determine how much lumber would be
needed for an average size doghouse.
Design a laser alarm system using numerous
mirrors as reflection points.
e.
Convert unit of
measurement within each
system.
f.
Use appropriate
vocabulary.
Apply concepts of
rates and other
derived or indirect
measurements.
a.
Use rates to make indirect
measurements.
Apply the concepts
of ratios and
proportions.
a.
Apply dimensional
analysis.
i.
©State of Idaho 2003
Return to Use Rates
Understand and use
proportions, ratios, and
scales.
Return to Use Proportions
a.
Understand units and
their
relationship to one another
and to real-world
ii.
i.
ii.
i.
ii.
iii.
i.
Use formulas and appropriate procedures for
solving measurement problems, for instance,
distance equals rate * time.
Given the weight of 1 gallon of water, calculate
the weight of water in the swimming pool.
Use proportions to find the height of a flagpole.
Use map scale to determine distances.
Enlarge a cartoon to a given scale.
Determine the reading hours of an entire class if
everyone reads 20 minutes.
26
Idaho State Curriculum Guide Pre-Algebra
Return to Understand Units
340.
©State of Idaho 2003
applications.
CONCEPTS AND LANGUAGE OF ALGEBRA.
Rationale: Algebra is the language of mathematics and science. Through the use of variables and operations, algebra allows students
to form abstract models from contextual information.
Standard – The student
will:
01. Use algebraic
symbolism as a
tool to represent
mathematical
relationships.
Content Knowledge and Skills:
Samples of Applications:
a.
Understand and use
variables in expressions,
equations, and
inequalities.
i.
If B represents the number of boys in the class,
and G represents the number of girls in the
class, write an equation and solve it in the
number of students in the classroom.
b.
Translate simple word
statements and story
problems into algebraic
expressions and equations.
i.
Given that the price of gas is changing each
week, write an algebraic expression to
represent the cost of purchasing 10 gallons of
gas.
Return to Use Variables
Return to Translate Word
Problems
c.
Return to Use Variables
02.
Evaluate algebraic
expressions.
a.
Understand and use the
following properties in
evaluating algebraic
expressions: commutative,
associative, identity, zero,
inverse, distributive, and
substitution.
i.
Evaluate expressions such as 2x + y when
given values for x and y.
b.
Understand and use the
order of operations in
evaluating basic algebraic
expressions.
i.
Explain why order of operations is important
when evaluating expression such as: 3 + 2 * 8.
c.
Simplify algebraic
expressions.
i.
Simplify expressions such as: 3a + 4b – 5a +
6b –7.
a.
Solve one- and two-step
equations and inequalities using
inverse operations.
i.
Solve equation such as: 12x – 5 = 31.
b.
Explore graphical representation
i.
Use technology to create a graph of linear
Return to Properties
Return to Order of
Operations
Return to Simplify
Expressions
03.
Solve algebraic
equations and
inequalities.
Use symbols (<, >, =, , ,
) to express relationships.
Return to Solving Equations
27
Idaho State Curriculum Guide Pre-Algebra
Return to Graph Linear
Equations
341.
to show simple linear equations.
©State of Idaho 2003
relations.
CONCEPTS AND PRINCIPLES OF GEOMETRY.
Rationale: The study of geometry helps students represent and make sense of the world by discovering
relationships and developing spatial sense.
Standard – The student
will:
01. Apply concepts of
size, shape, and
spatial
relationships.
Content Knowledge and Skills:
a.
Precisely describe,
classify, and understand,
relationships among types
of one-, two-, and threedimensional objects using
their defining properties.
b.
Construct and measure
various angles and shapes
using appropriate tools.
Return to Geometric
Properties/Terminology
c.
Understand and apply
fundamental concepts,
properties, and
relationships among
points, lines, planes,
angles, and shapes.
Return to Congruency/
Similarity
d.
Recognize and apply
congruence, similarities,
and symmetry of shapes.
e.
Return to Shapes and
Figures
Return to Construct /
Measure Shapes
i.
Compare measurements of opposite and
alternate angles in a parallelogram.
Apply formulas for
perimeter, circumference,
and area to polygons and
circles.
i.
Calculate the area of a center circle of a
basketball court.
f.
Understand the concept of
surface area and volume
(capacity).
i.
Construct a cylinder and calculate its surface
area and volume (capacity).
g.
Explore and model the
effects of reflections,
translations, and rotations
on various shapes.
i.
Create a tessellation using a combination of
reflection, translation or rotation showing
movement on a plane.
Return to Symmetry /
Transformations
Return to Apply Formulas
Return to Surface Area
Return to Symmetry /
Transformations
Samples of Applications:
28
Idaho State Curriculum Guide Pre-Algebra
Return to Geometric
Properties/Terminology
02.
Apply the
geometry of right
triangles.
h.
Use appropriate
vocabulary.
a.
Investigate right triangle
geometry using the
Pythagorean Theorem.
i.
ii.
©State of Idaho 2003
Investigate the relationships among the 3 sides
of a right triangle of a Pythagorean triple.
Determine the length of a handicap access
ramp given the height and length of the incline.
Return to Apply Formulas
03.
Apply graphing in
two dimensions.
a.
Use the coordinate plane
as it relates to real-world
applications.
Return to Coordinate
342.
DATA ANALYSIS, PROBABILITY AND STATISTICS.
Rationale: With society’s expanding use of data for prediction and decision-making, it is important that
students develop an understanding of the concepts and processes used in analyzing data.
Standard – The student
will:
01. Understand data
analysis.
Content Knowledge and Skills:
a.
Return to Analyze Charts
Return to Analyze Charts
02.
Collect, organize,
and display data.
Apply simple
statistical
measurements.
Return to Statistics
i.
ii.
b.
Explain and justify
conclusions drawn from
tables, charts, and graphs.
c.
Understand and use
appropriate vocabulary.
a.
Collect, organize, and
display data with
appropriate notation in
tables, charts, and graphs
(scatter plots, line graphs,
bar graphs, pie charts).
i.
Choose and calculate the
appropriate measure of
central tendency – mean,
median, and mode.
i.
Return to Use Data
03.
Analyze and interpret
tables, charts, and graphs
(scatter plots, line graphs,
bar graphs, pie charts).
Samples of Applications:
a.
ii.
iii.
ii.
iii.
Analyze and interpret bar graphs and pie charts
in magazines or newspapers.
Given a scatter plot, choose a line of best fit.
Collect and display data by surveying the
actual number of chocolate chips in cookies.
Survey and graphically display music
preference categories.
Identify the usefulness and/or limitations of
surveys.
Compute an individual mean grade in a
particular course.
Find the median student height in a classroom.
Find the most common shoe size in your class.
29
Idaho State Curriculum Guide Pre-Algebra
b.
Return to Range,
Frequency, Distribution
04.
Understand basic
concepts of
probability.
a.
Explore the significance
of range, frequency, and
informal distribution.
i.
Model situations of
probability using
simulations.
i.
ii.
ii.
Return to Probability /
Prediction
Understand and use the
language of probability.
c.
Recognize equally likely
outcomes.
i.
Document frequency of heads and tails when
flipping a coin 100 times.
a.
Make predictions based on
experimental and
theoretical probabilities.
Understand and use
appropriate vocabulary.
i.
Find the theoretical and experimental
probability of throwing a pair of 6 sided
number cubes and getting a sum of 7.
Conduct statistical
experiments and interpret
results using tables, charts,
or graphs.
i.
Graphically display the results of 40 spins of a
4-quadrant spinner; explain the results.
or decisions based
on data.
Return to Language of
Probability
Calculate range and distribution of professional
basketball salaries.
Create a frequency distribution chart of
professional basketball salaries.
Find the probability of drawing a jack of hearts
in a standard deck of cards.
Use a spinner to represent the number of points
scored by a 75% free throw shooter in a
basketball game
b.
Return to Language of
Probability
Return to Recognize
Outcomes
05. Make predictions
©State of Idaho 2003
b.
Return to Combinations/
Permutations
c.
Return to Recognize
Outcomes
343.
FUNCTIONS AND MATHEMATICAL MODELS.
Rationale: One of the central themes of mathematics is the study of patterns, relationships, and functions.
Exploring patterns helps students develop mathematical power.
Standard – The student
will:
01. Understand the
concept of
functions.
Content Knowledge and Skills:
a.
Samples of Applications:
Extend patterns and
identify a rule (function)
that generates the pattern
using real numbers.
i.
Use functional
relationships to explain
how a change in one
quantity results in a
change in another.
i.
ii.
Extend the 1st five numbers in the Fibonacci
sequence and explain the rule.
Explain how the amount of sales tax depends
on the cost of the item.
Return to Pattern,
Sequence, Function
b.
Return to Pattern,
Sequence, Function
ii.
Find the number of pencils needed for a
classroom if each student must have 3 pencils.
Explain how the number of pencils needed will
change as the number of students’ change.
Using what we know about a 3, 4, 5, right
triangle, prove a corner of a room is square or
30
Idaho State Curriculum Guide Pre-Algebra
not square.
c.
Return to Pattern,
Sequence, Function
Understand and use
appropriate vocabulary.
©State of Idaho 2003
31
Idaho State Curriculum Guide Pre-Algebra
02.
Represent
equations,
inequalities, and
functions in a
variety of formats.
Return to Represent Data
03. Apply functions to
a variety of
problems.
Return to Use Patterns and
Functions
©State of Idaho 2003
a.
Represent a set of data in a
table, as a graph, and as a
mathematical relationship.
i.
Collect data on the temperature of hot water as
it cools over time and organize and display the
results in several forms, including tables and
graphs.
a.
Use patterns and functions
to represent and solve
problems.
i.
Illustrate on a line graph distance traveled at a
constant speed of 55 miles per hour.
33
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
RIT Below 150-160
Algebraic o  for answer to equation
(151-160)
Concepts
Return to
Top
RIT 161-170
o ( ) used in equations
RIT 191-200
 if-then, product, sum
o variables, exponents
(signs / symbols)
inequality, if-then
statement, term in
sequence, square
numbers, negative
coefficient
o I=pxrxt
o <, > symbols
RIT 201-210

input, output, table,
associative, equation
o , 
RIT 231-240

RIT 171-180
regression equation,
varies inversely as the
square, slope of parallel
lines, solution to system,
factor (used with
equations)
 sign
o – used as negative
RIT 211-220

RIT 241-250

RIT 181-190
commutative, solve,
square numbers, input,
output, number sequence
RIT 251-260

parabola, intercepts,
number of solutions,
simultaneous equations,
counterexample, solution
set, sin A, cosine, tangent,
discriminant, imaginary
solutions, difference of
two squares, read solution
set from graph, factor
completely
RIT 221-230

absolute value,
evaluate, quotient
o square root symbol,
%, absolute value
symbol
RIT 261-300
34
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
RIT Below 150-160
Compu- (Below 150)
 and
tation
Return
to Top
RIT 161-170
o $, decimal point
o +, =, (151-160)
 equals, facts
o x (multiplication symbol)
RIT 191-200



“Solve for n”
estimate, round, closest to,
sum, of (used as in “½ of
36”)
o square root symbol
RIT 211-220
 smallest, tenth
o – as a negative, + as a
positive
RIT 241-250
decimal fractions,
opposite
RIT 181-190
 closest, how many
o division symbol (both
forms)
RIT 201-210
difference, not true,
power of 10, rounded,
thousands
o ¢, %
RIT 231-240

RIT 171-180
RIT 251-260

sum of opposites
RIT 221-230

product, divide, most,
if – then, compute,
lowest terms
RIT 261-300
35
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
Geometry
RIT Below 150-160

shape, circle, same as
RIT 161-170

matches, triangle,
square, corners, cone,
closed, inside
RIT 171-180

congruent, figure
RIT 181-190

o
Return
to Top
RIT 191-200

o
symmetrical, parallel, intersecting,
diagonal, pair, angle, cylinder,
outside, inside, sphere, faces,
corresponding, point, intersect,
outside, axis of symmetry, line
segment, pentagon
symbol for parallel lines
RIT 201-210

o
RIT 231-240
intersection,
quadrilaterals, octagon,
parallelogram,
pyramid, isosceles,
right angle, diameter,
right angle, geometric,
perpendicular, plane
 for triangle, angle
symbol
RIT 241-250
RIT 211-220

o
symmetrical, perpendicular, ray,

vertex, rotation, triangular prism,
corresponding parts,
supplementary, acute angle,
transformation
 - congruent symbol,  - double o
arrow symbol for similarity,  - pi
symbol, ABC – to label triangle
RIT 251-260
symmetry, point, sides,
rectangle, cube, straight,
line segment, shortest
line AB (with double arrow
over AB), line segment AB
(with segment line over
AB)
RIT 221-230
radius, polygon,
circumference, trapezoid,
rectangular box,
equilateral, similar, obtuse
angle, straight angle, slide
angle symbol, label for line
– L1
RIT 261-300
36
Idaho State Curriculum Guide Pre-Algebra

transformation, hypotenuse, edge,
isosceles, scalene triangle, similar
trapezoids, alternate interior
angles, sum of angles in triangle

o
symmetrical halves,
diameter, radius, angle
bisector, tangent,
corresponding parts of
congruent triangles,
Pythagorean theorem,
corresponding angles,
complementary angles,
construction
sign for parallel lines

©State of Idaho 2003
slope, non-vertical and non
horizontal, midpoint, endpoint,

rotational symmetry, reflected,
perpendicular bisector, similar
triangles, similar trapezoids,
similar cylinders, conditional,
counterexample, conclusion of inthen statement, interior of angle,
exterior angle of regular polygon,
interior angle of regular polygon,
sum of angles in triangle equals
180 degrees, congruent angles,
adjacent angles, vertical angles
postulate (261-270)
HL (271-280)
37
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
Measurement
Return to
Top
RIT Below 150-160

o
longest, shortest, how
tall, kilometer, meter,
time (151-160)
C for Celsius, cm for
centimeter
RIT 161-170

o
RIT 191-200

o
height, width,
parallelogram, square,
rectangle, triangle, year,
ton, seconds, kilogram,
distance, miles, liter
mm = millimeter, a.m. and
p.m., hr = hours, min =
minutes
o
rectangular house, height
and base, algebraic
expression, rows and
columns, checking
account, car purchase,
commission, simple
interest
F = 9/5 C + 32, formula
for finding volume of a
pyramid

o
RIT 201-210

o
RIT 231-240

how long, names of days of
week, next, names of months,
pennies, centimeter, inches
degree symbol, : for time –
1:00, face of quarter, dime,
penny, and nickel
RIT 171-180
right angle, circumference,
minutes, decades, milligrams,
gram, cubic feet, volume,
liters, length, weight,
kilometers, millimeters, mass
ft for feet, mL = milliliters,
right angle symbol, symbol for
line segment, 
doubled and tripled,
rectangular solid, cylindrical
tank, algebra tiles, inscribed,
time-and-a-half, sales tax,
discount

o
RIT 211-220

o
RIT 241-250

line segment, area, square units,
perimeter, days, week, set, coins,
thermometer, temperature, pounds,
ounces, pints, quarts
$, decimal point for cents, F =
Fahrenheit, lb = pounds, sq = square
units, cent sign, recognize back of
penny, nickel, dime, and quarter
RIT 181-190
yards, measure of angle, degrees,
protractor, centuries, below zero,
Celsius, rectangular solid, rectangular
prism, decades, ounces
” = inches, yd = yards, b = base, h =
height, r = radius, s = side, angle
symbol, - for negative, + for positive,
d = distance, tsp = teaspoon, pt = pint,
gal = gallon, qt = quart, c = cup
RIT 221-230

o
RIT 251-260

o
circumscribed, distance formula
formula for finding volume of a
cone, formula for volume of a cube,
formula for finding volume of a
rectangular solid
about, length, estimate,
perimeter, change, quarter,
dollars, dozen, units, feet,
yard, grams, meters, cups,
gallons, nickel, pennies,
dime, tablespoon, hours,
minutes, degree
m = meters, g = grams
reasonable, formula,
segment BC, pi, radius
squared, diameter, metric
units, quarts, gallons,
rectangular box, base, rate
oz = ounces, C =
circumference
RIT 261-300

rate of interest, successive
discounts (271-280)
38
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
Number
Sense
RIT Below 150-160

how many
o
 for answer
RIT 161-170

Return to
Top
RIT 191-200

o
thirds, fourths, rounded,
thousands, exponential form,
mixed number, improper
fraction, lowest common
denominator, percent,
expanded form, prime,
factor, proportion
use of dot as a multiplication
symbol
ones, tens, hundreds,
thousands, numeral,
ordinal numbers through
eleventh, counting
RIT 171-180

even numbers, same as,
fewest
o < and > signs, = sign
RIT 201-210

o
RIT 231-240
missing number, pentagon,
simplest fraction, biggest,
hundredths, one less,
decimal numeral, squared,
divisible, inequality,
expanded numeral,
equivalent, point, standard
numeral, sequence
+ used as positive symbol, used as negative symbol
RIT 241-250

Base ten, prime factors
RIT 181-190

first, second, third,
etc., odd, one-fourth,
one-half, reduce,
fractions, order,
divisible, round,
smallest, largest,
lowest terms, greatest
common factor, least
common multiple,
closest, units, set,
digit, greater than,
greatest
RIT 221-230

always true, proportion,
multiply, between, tens
digit, standard numeral,
ratio
RIT 211-220

o
counting number, portion,
fractional part, lowest terms,
reciprocal, order, scientific
notation, prime factorization,
not prime, factor tree,
common multiples, greatest
common denominator,
equivalent, nearest dollar
square root symbol
RIT 251-260
RIT 261-300

infinite non-repeating
decimal (261-270)
39
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
RIT Below 150-160
RIT 161-170

Reasoning
and
Problem
Solving
how many, not, in all,
altogether
RIT 171-180

Return to
Top
RIT 191-200

o
terms, meter, millimeters, kilogram, feet,
yards, unit of measurement, height,
thousands, hundreds, tens, table, graph,
length, width, rectangular, area, square
inches, exactly, coins, numeral, even,
change, average, opposite, percent,
subtrahend, addend, formula, circle,
diameter, operation, total, fact, fraction,
surfaces, cube, temperature, first – fifth
(ordinal names), difference, equivalent
tally marks, =, - as an integer sign, %, C,
 for answer
RIT 201-210

equation, product,
increased, number
line, information not
needed, division,
estimate, odd, prime,
cube, pattern,
geometric patterns,
extra information
o rxt=d
RIT 231-240

regression equation
RIT 241-250

matrix
product, number
sentence, problem, how
many more, multiples,
greater than, left, how
much, money, answer,
about, outside, inside,
shape, calendar, picture
RIT 211-220

RIT 181-190

add, subtract, multiply,
divide, rate, kilometers,
hours, between, equals,
cost, time, less than,
closest to, equation, weigh,
minutes, pieces, dozen,
cups, inches, pounds,
miles, sum, dime, nickel,
pennies, quarter
o +, $, decimal point for
cents, ¢
RIT 221-230
decimals, fractions, what 
shape, hour, minutes,
gallons, average,
probability, graph,
squares
o %
o
RIT 251-260
mortality, odometer, magic
square, deducted, less than
twice, addends, less than
sum, rectangle, diameter,
radius, label (units), area,
perimeter
I = prt
RIT 261-300
40
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “SubGoal”
RIT Below 150-160

Data
Analysis,
Statistics
and
Probability
Return to
Top
RIT 161-170
RIT 191-200

average, bar graph,
percentage
o %
vertex, fractional part,
amount of sales,
translation, matrix,
possibility, mean salary,
coordinates of points

RIT 201-210

RIT 231-240

probability
RIT 171-180
least often, how many
ways, ordered pairs,
coordinates, distance
formula
RIT 241-250

coordinate, Venn
diagram, greatest
decrease, endpoints,
midpoint
chance
RIT 181-190

RIT 211-220

dice, arranged, highest
mean
RIT 251-260
most often
RIT 221-230

even numbers, mean,
median, integer,
intersection, table,
frequency, origin,
quadrant
RIT 261-300
41
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
RIT 211-220
©State of Idaho 2003
RIT 221-230
RIT 231-240
Algebra
Solving
Equations,
Simplifying
Expressions,
Order of
Operations
Return to Guide




Solve decimal equations (one step,
addition and subtraction)
Solve integer equations (one step,
multiplication and division)
Evaluate expressions using the order of
operations (may include parentheses or
exponents)
Solve quadratic equations







Solve for missing addends in an
addition or subtraction sentence
Use boxes or other symbols to stand for
any number in expressions or equations
Solve whole number equations with
one variable (multiplication and
division)
Solve integer equations (one step, all
four operations)
Solve equations involving more than
one operation
Solve one-step linear equations in one
variable using addition, subtraction,
multiplication, and division with
integer solutions
Simplify numeric expressions by
applying properties of rational numbers
(e.g. identity, inverse, distributive,
associative, commutative)
Write an algebraic expression to model a
situation
 Evaluate an algebraic expression for
given values
 Explore equivalent ratios involving
missing variables
 Use the correct order of operations to
evaluate numeric and algebraic
expressions
 Simplify and evaluate expressions that
include positive and negative integral
components
 Simplify polynomials by combining
like terms
 Use the rules of exponents to multiply
and divide monomials
 Solve simple linear equations and
inequalities over the rational numbers
 Create a table of (x, y) values for the
given linear equation and graph the
function
42
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Patterns,
Sequences,
Functions

RIT 211-220
Use logic to solve a problem
involving a function table


Return to Guide


Properties

Return to Guide
©State of Idaho 2003
RIT 221-230
Complete a function table according 
to a rule
Recognize and continue a number

pattern and/or geometric
representation (e.g. Fibonacci
sequence, triangular numbers)

State a rule to explain a number
pattern, including arithmetic
progression
Investigate geometric patterns and
relationships and describe them
algebraically
RIT 231-240
Using whole numbers, complete a
function table based on a given rule
Graph linear functions, noting that
the vertical change (change in yvalue) per unit of horizontal change
(change in x-value) is constant
Identify linear equation for a
straight line
Understand the properties of
integers: commutative, associative,
identity, zero property of
multiplication, distributive property
of multiplication over addition, and
inverse property of addition
Data Analysis, Probability, and Statistics

Solve problems involving
arrangements
Data Analysis

Return to Guide

Read and interpret information from 
a graph
Interpret Venn Diagrams
Make predictions from a graph
Combinations
and
Permutations

Use a tree diagram to determine the
number of possible outcomes of an
event
Solve problems involving combinations
and permutations
Interpret data given in horizontal
and vertical bar graphs to solve
problems
Read and interpret information in a
table
 Read and interpret information from
a graph
Return to Guide

43
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Probability and
Prediction

RIT 211-220
Investigate experimental probability
of an event using a coin or spinner


©State of Idaho 2003
RIT 221-230
RIT 231-240
Investigate experimental probability Determine the number of possible
outcomes of an event
of an event using a coin or spinner
Predict outcomes using probability
Return to Guide
Statistics
Return to Guide

Know the concepts of mode,
median, and mean; compute and
compare them in simple examples
to demonstrate that these measures
of central tendency may differ for a
given set of data

Calculate range, mode, median, and
mean
44
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
RIT 211-220
©State of Idaho 2003
RIT 221-230
RIT 231-240
Estimation and Computation
Decimals

Return to Guide



Add decimals through hundredthousandths with a calculator
Multiply a decimal by a decimal,
factors to thousandths
Divide a decimal by a whole
number and vice versa
Compute basic operations with
monetary amounts up to and
including $20.00

Subtract whole numbers and
decimals to the hundredths place
(same number of digits)


Write a number sentence to solve
one-step word problems involving
the operations of addition,
subtraction, and multiplication of
fractions and decimals





Subtract decimals through hundredthousandths with a calculator

Multiply a decimal by multiples of
10, 100, or 1000

Divide a whole number (or decimal)
by a decimal to thousandths



Add whole numbers and decimals
to the hundredths place (same
number of digits)
Subtract decimals to the hundredths
place (not the same number of
digits)
Subtract decimals to thousandths,
vertically and horizontally, with and
without regrouping
Subtract a decimal from a whole
number
Multiply a decimal by a decimal,
factors to thousandths place
Divide a decimal by a whole
number and vice versa
Divide a whole number (or decimal)
by a decimal to thousandths place
Compute and count change greater
than $20.00
45
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Fractions

Return to Guide




RIT 211-220
Add fractions with like
denominators, answer in lowest
terms
Add mixed numbers with unlike
denominators with regrouping
Multiply a whole number by a
fraction
Divide a fraction by a fraction
Divide a mixed number by a whole
number or a fraction





Integers
Return to Guide
Percents
Return to Guide






Add integers with like signs
Add integers with unlike signs
Add several integers
Multiply integers with unlike signs
Divide integers with unlike signs

©State of Idaho 2003
RIT 221-230
Add and subtract fractions with like
denominators; change improper
fractions to mixed numbers
Subtract fractions having unlike
denominators, answer in lowest
terms
Add and subtract whole numbers,
fractions and mixed numbers
Use estimation to solve problems
involving mixed numbers
Divide a whole number, fraction or
mixed number by a mixed number
Divide integers, like signs
RIT 231-240
Add fractions having unlike denominators with
answer reduced to lowest terms
 Subtract fractions having unlike
denominators with answer reduced to
lowest terms
 Add and subtract mixed numbers with like
denominators with regrouping
 Add and subtract mixed numbers with
unlike denominators with regrouping
 Add and subtract whole numbers, fractions,
and mixed numbers
 Multiply a fraction by a fraction; answer in
lowest terms
 Multiply mixed numbers
 Divide a fraction by a fraction
 Divide a mixed number by a whole number
or a fraction
 Multiply three factors using fractions,
mixed numbers, and whole numbers in any
combination, answer in lowest terms
 Divide a whole number, fraction, or mixed
number by a mixed number






Find the percent one number is of
another (20 is what % of 90)
Find a number from a percent (4 is
9% of what number)


Add integers with unlike signs
Add several integers
Multiply integers with like signs
Divide integers with like signs
Find the percent one number is of
another (8 is what % of 20?)
Find a number from a percent (20 is
45% of what number?)
46
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Squares

RIT 211-220
Calculate the square of any number
less than 100

©State of Idaho 2003
RIT 221-230
Evaluate expressions using square
roots

Return to Guide
Whole Numbers

Divide a 3-digit or 4-digit number
by a 1-digit number
Use multiplication as a check for
division
Multiply by multiples of 10 and 100
with an emphasis on mental math
Divide a 4-digit number by a 2-digit
number

Return to Guide


Identify similar figures (same shape, may or
may not be the same size)


Identify congruent polygons and
their corresponding sides and angles
Identify congruent triangles
according to corresponding parts
(SSS, SAS, ASA)

Graph ordered pairs in all four
quadrants (coordinate geometry)




Develop computational fluency
with division facts
Divide multi-digit numbers using a
calculator
Introduce the math strategy of
compatible numbers in estimating
for all four operations
RIT 231-240
Identify perfect squares in a list of
numbers and calculate the positive
square root of a perfect square
Divide a 2-digit number or a 3-digit
number by a 1-digit number with
remainder
 Divide multi-digit numbers using a
calculator
Geometry
Congruency and
Similarity
Return to Guide
Coordinate
Return to Guide


Find location of coordinates on a
number line
Locate the vertex on a coordinate
grid
47
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Geometric
Properties and
Terminology

Return to Guide

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RIT 211-220
Identify points, lines, line segments,
rays, and angles
Identify angles: right, obtuse, and
acute
Identify when two intersecting lines
are perpendicular
Identify properties of similar figures
Measure angles using a protractor
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Shapes and
Figures, 2- and
3-Dimensional
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Identify faces, edges, and corners
(vertices) on solid figures
Contrast open and closed figures
Identify polygons: triangle,
quadrilateral, pentagon, hexagon,
and octagon
Identify quadrilaterals: square,
rectangle, parallelogram, trapezoid,
rhombus
Analyze solid figures: triangular
pyramid and rectangular pyramid
(faces, edges, and vertices)
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©State of Idaho 2003
RIT 221-230
Identify the center, radius and
diameter of a circle
Measure angles using a protractor
Classify angles: supplementary and
complementary
Classify angles: adjacent, vertical,
corresponding, and supplementary
Find the missing angle
measurement in a triangle when two
angles are known
Analyze circles: center, chord,
diameter, radius, arc, semicircle,
and circumference
Analyze solid figures: rectangular
prism, triangular prism, triangular
pyramid, square, pyramid (faces,
edges and vertices)
Classify polygons by sides and
angles
RIT 231-240
Classify triangles by sides (equilateral,
isosceles, and scalene) and angles
(acute, obtuse, and right)
 Classify polygons by sides and
angles
 Identify and discriminate between
regular and irregular polygons
 Find the missing angle
measurement in a triangle when two
angles are known
 Solve word problems involving
similar polygons
 Identify the base angles of a triangle
 Know the definition of the
hypotenuse of a triangle
 Calculate the circumference of a
circle using the formula
48
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Symmetry and
Transformations
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RIT 211-220
Identify types of transformations
(rotation)
©State of Idaho 2003
RIT 221-230
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RIT 231-240
Understand meaning and
representation of a dilation
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Measurement
Area, Perimeter, 
Circumference
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Length, Weight,
Volume
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Calculate the area of irregular
shapes
Understand the effects of changing
dimensions on perimeter and area
Measure length to the nearest
millimeter, centimeter, meter, and
kilometer
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Time,
Temperature
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Measure length with metric
measures (centimeter)
Measure length with customary
measures (inch)
Select the appropriate unit of
measure for length, area, and
volume
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Compute word problems with time
and calendars
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Number Sense
Absolute Value
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Find the perimeter of a square or
rectangle using the formula
 Find the perimeter of polygons
 Calculate the area of a
parallelogram and rectangle
 Calculate the area of a triangle
Find the volume of a pyramid
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Definition and application of
absolute value
Convert from Celsius to Fahrenheit
Subtract Fahrenheit temperatures
49
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Decimals
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Exponents and
Scientific
Notation
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Factorization /
Divisibility
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RIT 211-220
Round monetary amounts to the
nearest single coin or bill which
could be used to pay for a purchase
up to and including $20.00
Write the decimal equivalent of a
fraction and label as repeating or
terminating
Round decimals to nearest whole
number, tenth, or hundredth
Write a terminating decimal as a
fraction or mixed number
Round decimals to nearest whole
number, tenth, hundredth, or
thousandth
Identify and order decimal and
fractional coordinates on a number
line
Order of “powers”
Write a whole number or a decimal
in scientific notation
Write a number expressed in
scientific notation in standard form
Understand and use rules of
divisibility
Identify the greatest common factor
of two whole numbers: list the
factors or prime factorization
Identify the greatest common factor
and least common multiple of two
whole numbers
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©State of Idaho 2003
RIT 221-230
Identify and order decimal and
fractional coordinates on a number
line
Relate fractions to decimals
Write a decimal or mixed decimal
for a fraction (2/3=0.66)
RIT 231-240
Write a decimal or mixed decimal for a
fraction
 Write a whole number or a decimal
in scientific notation (negative
exponents)
Identify and use powers of 10
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Identify the least common
denominator for 3 or more
fractions: list the multiples or prime
factorization
Evaluate expressions using the
order of operations that include
exponents
Find products by applying rules for
exponents
50
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Fractions, Ratio, 
and Proportions
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RIT 211-220
Write improper fractions from
picture presentations
Change a fractional numeral to its
simplest form (lowest terms)
Compare and order fractions and
mixed numbers
Identify and order decimal and
fractional coordinates on a number
line
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Integers
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Ordering
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Percents
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Identify the greater or lesser of 2
integers
Order integers on a number line
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Compare and order fractions with
the same denominator and with
different denominators
Order decimals to thousandths;
identify the greater or lesser of two
decimals to thousandths
Express a fraction as a decimal and
as a percent
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©State of Idaho 2003
RIT 221-230
Model and write numerical
fractions
Change a fractional numeral to its
simplest form (lowest terms)
Understand the concept of ratio
using concrete and pictorial models
Determine if a pair of ratios is equal
or not equal using the equivalent
fractions method
Write the missing number in 2
equivalent ratios
Solve proportions using the cross
product method
Understand the meaning of integers
Order a set of integers from least to
greatest
Place numbers in correct order on a
number line
Write a ratio (fraction) as a percent
and a percent as a ratio (fraction):
denominators of 100
RIT 231-240
Define ratio
 Write ratios in a variety of ways
51
Idaho State Curriculum Guide Pre-Algebra
ISAT “Sub-Goal”
Place Value
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RIT 211-220
Understand and identify the place
value and value of each digit in
numerals through the billions
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©State of Idaho 2003
RIT 221-230
Match word names to numerals to
the hundred thousands in decimals
RIT 231-240
Write numerals in expanded form
through the billions
 Understand and identify place value
and value of each digit in numerals
through the hundred billions
Choose and use an appropriate problem
solving strategy: Draw a picture, Make
a model, Guess and test, Make a list,
Make a table, Find a pattern, Work
backwards, Solve a simpler problem,
Draw a diagram, or Write an equation
Write and solve an equation using
ratios, given a word problem
Write and solve an equation for a word
problem
Solve simple interest problems
(amount x rate x time)
Use estimation to determine if
solutions to word problems are
reasonable
Use logic to predict outcomes
 Work backwards to solve problems
 Solve multi-step problems involving
computation
 Find correct mathematical expressions
to represent word problems
 Find simple interest earned
 Find commission and total pay
 Find missing numbers in a diagram by
using patterns
 Use map scales to solve problems
 Solve if-then logic problems
 Solve complex word problems
involving ratio, percent, discount, sale
price, rounding and estimation,
averaging, length, volume, rate,
calendars, probability, money, and time
 Given the answer to a problem,
determine the question
 Formulate expressions and equations to
model problem solving situation
Mathematical Reasoning and Problem Solving
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Mathematical
Reasoning and
Problem Solving
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Solve practical word problems
involving perimeter and area of a
square, rectangle or triangle
Solve practical problems involving the
mean (average) of a set of numbers
Solve one- and two-step word
problems involving any combination of
basic operations on whole numbers,
decimals, and fractions
Determine the discount price and sale
price
Choose and use an appropriate problem
solving strategy: Draw a picture, Make
a model, Guess and test, Make a list,
Make a table, Find a pattern, Work
backwards, Solve a simpler problem,
Draw a diagram, or Write an equation
Calculate the cost of one item or the
unit cost using a proportion
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52
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
53
Idaho State Curriculum Guide Pre-Algebra
Sample Test Items
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RIT 211-220: Algebraic Concepts
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RIT 221-230: Algebraic Concepts
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RIT 231-240: Algebraic Concepts
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RIT 211-220: Computation
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RIT 221-230: Computation
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©State of Idaho 2003
54
Idaho State Curriculum Guide Pre-Algebra
RIT 231-240: Computation
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RIT 211-220: Geometry
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RIT 221-230: Geometry
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RIT 231-240: Geometry
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RIT 211-220: Measurement
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©State of Idaho 2003
55
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
RIT 221-230: Measurement
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RIT 231-240: Measurement
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RIT 211-220: Number Sense and Numeration
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RIT 221-230: Number Sense and Numeration
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RIT 231-240: Number Sense and Numeration
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56
Idaho State Curriculum Guide Pre-Algebra
©State of Idaho 2003
RIT 211-220: Problem Solving
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RIT 221-230: Problem Solving
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RIT 231-240: Problem Solving
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RIT 211-220: Statistics, Probability, & Graphing
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RIT 221-230: Statistics, Probability, & Graphing
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RIT 231-240: Statistics, Probability, & Graphing
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