Download Language Arts Curriculum Guide Template

Idaho State Expanded Curriculum Guide Math 5th Grade
Number Sense
Estimation/Accurate Computation
Reasoning/Problem Solving
Measurement
©State of Idaho 2003
Algebra, Functions, & Mathematical Models
Geometry
Data Analysis, Probability, & Statistics
McRel Alignment
State Standards
ISAT Cut Scores
Sample Test Items
New Vocabulary
Number Sense
State
Standard
and
Benchmark
Estimation/Accurate
Computation
Local
Curriculum
Number Sense
307.01.a
307.02.c
Whole
Numbers
Learning
Continuum
and other
Performance
Objectives
Reasoning/Problem
Solving
Measurement
Sample Assessment
and Sample Quizzes
Sample
Sequence
Algebra, Functions,
& Mathematical
Models
Minimum
Hours
Allotted
Geometry
Data Analysis,
Probability, &
Statistics
Sample Teaching
Strategy
Return to Top
Learning
Continuum
Math
Benchmark
Teacher
Observable
For Learning:
Students will write, compare, and
order whole numbers trough billions
on math sheet given by the instructor.
Explain how to compare two
numbers. (Compare the values of the
same place, and always start with the
greatest place value.)
Play Roman numeral Bingo
Practice rounding numbers to a give
place value up to billion
Of Learning:
RIT 201-210
RIT 211-220
Students math roman numeral to it’s
equivalent Arabic number
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
307.01.b
Place Value,
Expanded
and Standard
Notation
307.01.b
307.01.e
Ordering,
Equalities,
and
Inequalities
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Teacher will read a six to ten digit
number to students and they will write
that number using correct place
value.
Students will be given a number in
the billions and they will rewrite that
number using expanded notation.
Of Learning:
RIT 201-210
RIT 221-230
For Learning:
Students will arrange a set of
decimals and/or fractions in order
from least to greatest
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Demonstrate using place value
neighborhood the relationship
between units, thousands, millions
and billions.
Show students how to write a 6 to 10
digit number using expanded
notation.
Demonstrate how to order a set of
decimals from least to greatest.
Follow the procedure for ordering
whole numbers. Work from left to
right. If number contains a whole
number order it first then start at
tenths place and work to the right in
order to arrange decimals.
Give students a card with a fraction
with a common denominator or a
different denominator and have them
line up in order.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
307.01.e
Fractions /
Ratio /
Proportion
307.01.f
307.02.a
307.01.d
Factorization
/ Divisibility
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a set of 10 flash cards student
will write down 20 proper fractions to
be reduced. Student will also include
a answer key for fraction set.
Show students 6 green cubes and 8
red cubes. Students will show on an
answer sheet three different ways to
write the ratio of green to red cubes.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
For Learning:
Students will use a factoring tree to
factor a teacher given large number.
Students will divide a two or three
digit number by a one or two digit
number with zeros in the quotient.
Students will write down the answers
to the 100 harder multiplication and
division facts in a timed test.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Using unfix cubes demonstrate how
to reduce fractions by grouping with
sets of two, three, etc.
Demonstrate to students how you can
use unfix cubes to write ratio
problems.
Have students create pictures to
represent improper fractions
Review daily in Daily Oral Math type
practice
Show students that in order to factor
numbers we need to know both prime
and composite numbers.
Show students how to make a factor
tree when factoring larger numbers.
Demonstrate the steps in
dividing a three and four digit number
by a one-digit number.
Demonstrate the steps in dividing a
three and four digit number by a onedigit number.
Sample
Resources

Daily oral math
Mountain math
http://www.mou
ntainmath.com/produ
cts_math.shtml
Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
307.01.c
307.01.d
307.01.e
Decimals
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a picture of a set of objects the
student will write a fraction for the set,
reduce the fraction to its lowest form,
and then write its decimal form.
Given a list of decimals students will
put the list in order from least to
greatest.
Students will change a list of
decimals to fractions and order them
from greatest to least.
Learning
Continuum
Percents
Math
Benchmark
Teacher
Observable
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
For Learning:
Create a quiz grid with numbers on
the front. Each number represents a
questions. Form teams. Players take
turns picking numbers and answering
questions.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Integers
Learning
Continuum
For Learning:
Math
Benchmark
Of Learning:
RIT 221-230
Teacher
Observable
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Demonstrate using a picture of a set
of objects how to write a fraction for
the set of objects, reduce the fraction
and write its decimal form.
On the board write 3.21, 3.34, 3.05,
and 3.29. Demonstrate how to
compare the numbers by first
rewriting them vertically with their
decimal points aligned. Show
students how the fraction equivalents
would also be ordered.
Place a fraction, decimal, and percent
on the wall in different places around
the room. Give the students cards
with equivalent fraction, decimal, or
percent on it and have them go stand
under the different form of their
number.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Exponents
and Scientific
Notation
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a list of number the student
writes them in scientific notation.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Proxima Centauri, the closest star to our
own, is still 39,900,000,000,000 km
away. Write this on the board.
Explain to the students that this
number is so large that we need to
reduce it. We use scientific notation
to do this. Explain how to move the
decimal and write the number
Give the students a list of numbers to
the power of ten. Practice ordering
them. E.g. 2X10^2 is larger than
2x10^3)
Estimation and Computation
307.03.a
307.03.b
307.03.c
307.02.f
Learning
Continuum
Return to Top
For Learning:
Have students take turn coming to
the board to “teach” the other
students how to do a problem.
Whole
Numbers
Math
Benchmark
Teacher
Observable
Learning
Continuum
For Learning:
Decimals
Math
Benchmark
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Teacher
Observable
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
RIT 201-210 (Money)
RIT 211-220 (Money)
Divide a 3 or 4 digit number by a one
or two digit number. Check by
multiplication.
Use manipulatives to show division
the why of division
Estimate the answer mentally and
then do the work.
Demonstrate using real life items,
how to estimate the price of a group
of items.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
307.03.a
307.03.b
307.03.c
307.02.b
Fractions
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Listed in the
RIT range
Percents
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Integers
Math
Benchmark
Teacher
Observable
Learning
Continuum
Squares
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a set of fractions and mixed
numbers the student will round to the
nearest whole number.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
For Learning:
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Use estimation to predict you
answers before you solve:
Adding fractions with like
denominators
Adding mixed numbers with
regrouping
Use manipulatives to explain the
why’s
Of Learning:
RIT 201-210
RIT 221-230
For Learning:
Given a worksheet with thermometers
showing different temperatures,
students will write positive and
negative numbers to tell the
temperature.
Of Learning:
RIT 211-220
RIT 221-230
For Learning:
Have the students draw a picture or
representation that explains the
relationship between multiplying a
number by itself and squaring a
number.
Of Learning:
RIT 221-230
Teacher uses a number line to define
integers as positive and negative
numbers. Students read a
thermometer using positive and
negative numbers.
Practice dividing a number by itself.
Explain that a shorter way of writing
this is to square the number
Use Manipulatives to show the
relation of the two.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment
and Sample Quizzes
Mathematical Reasoning and Problem Solving
308.02.a
308.02.b
308.02.c
Reasoning
and Problem
Solving
Learning
Continuum
Math
Benchmark
Teacher
Observable
For Learning:
Students will be given a 1 – 100
number chart and working in
cooperative learning groups, students
will use the number chart to solve
problems involving multiples,
inequalities, properties of numbers,
even, odd, sums, and products.
(Equals, Lawrence Hall of Science, c.
1989, p. 16 - 21)
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
308.01.a
308.01.b
308.01.c
Using
Problem
Solving
Skills
Math
Benchmark
Teacher
Observable
For Learning:
Student write word problems for two
of the problem solving strategies
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources

Return to Top
After reviewing problem solving
strategies, Set the student up in
groups. Give each group a different
word problem. Have each group
decide which strategy will work best
for their type of problem. Once done
the groups will come to the board and
defend their choice.
Figure out the perimeter and area of
the classroom. How much carpet
would you need to re-carpet the
class.
Place test scores on the board and
have the students figure the mean for
the class
Students use information from the
calendar and logical reasoning to
solve problems about dates in the
future.
Ask students:
If there are 7 days in a week and
today is Tuesday the 8th what will be
the date in three weeks on Friday.
Problem
solvercreative
publications
Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
308.03.a
308.03.b
308.03.c
Applying
Technology
And Models to
find Solutions
308.04.a
308.04.b
308.04.c
Communicate
results using
appropriate
terminology
and methods
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a set of numbers in a short
time frame, students will find the
answer by moving the decimal point
to the right or left.
Given a series of “story” problems,
students will explain what problem
solving strategy that they used to
arrive at their answer.
Math
Benchmark
Teacher
Observable
For Learning:
Given an array of data, such as
students’ favorite sports, they will
make a bar graph, pie graph, or line
graph.
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Teacher will demonstrate how to use
a calculator to explore the pattern
when multiplying by multiples of 10.
Students will see the relationship and
learn how to move the decimal point
when using multiples of 10.
Using individual white boards, each
student will solve problems presented
by the teacher. Problems will include
different strategies: 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, Write an
equation, or Logical Deduction
Students will use a Venn diagram to
show number of brothers and sisters
in each student’s family.
Teacher will show how to construct a
bar graph on the students’ favorite ice
cream flavors.
Students will trace and cut out premeasured strips of paper to make
discoveries about triangles. Data is
entered in a table and the information
is used to evaluate the triangles.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Concepts and Principles of Measurement
309.01.a
309.01.b
309.01.d
Length,
Weight,
Volume
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample
Sequence
Sample Assessment
and Sample Quizzes
Minimum
Hours
Allotted
Sample Teaching
Strategy
Return to Top
For Learning:
Given a ruler, the students will
measure the height of their desk from
the floor and express it in inches and
centimeters.
Given a worksheet with problems
involving weight of objects, using
pounds and ounces, students will
write the answers. Additional
problems include adding pounds and
ounces and correctly carrying the
ounces to pounds.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
©State of Idaho 2003
Length: Teacher will demonstrate to
the class how to read a ruler,
yardstick, and meter stick. Teacher
will show how to make comparisons
between units (for example a
centimeter is about a half-inch, a yard
is equivalent to a meter, a mile is
equivalent to a kilometer). Students
will measure the length of their
textbook, work in groups to measure
the length of the room using yards
and meters.
Weight: Teacher discusses with the
students that 1 pound = 16 ounces
and 2,000 pounds = 1 ton. Teachers
discusses when it is appropriate to
use ounces (like in baking), pounds to
weigh themselves, and tons to weigh
an automobile. Students will
complete worksheets using this
information.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Area and
Volume
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given a ruler, students will measure
the area of their desktop and express
the answer in square inches and
square centimeters.
Given a problem on the board with
the dimensions of a container that is
8” high X 6” wide X 7” deep, students
will compute the volume and express
the answer in cubic inches.
309.01.f
Time,
Temperature
Learning
Continuum
Math
Benchmark
Teacher
Observable
For Learning:
Time: Given a clock with a time set
by the teacher, teacher will ask
students to add and subtract time.
Students will write answers on paper.
Temperature: Teacher will put a
drawing of a thermometer on the
board and use increments of 1, 2, or
5. Teacher colors in the fluid and
students read the temperature and
write the answers on paper.
Of Learning:
RIT 201-210
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Area: Teacher uses carpeting a room
to show how to use area. Teacher
presents the formula for area: length
X width. Teacher explains that
answers are in square units. Teacher
gives students the measurements
and students compute the area of a
rectangle.
Volume: Teacher gives the formula
for volume: length X width X height.
Teacher explains that volume is
expressed in cubic units. Teacher
gives example of using volume to fill
a fish tank with water or to fill a
swimming pool with water. Teacher
presents a problem with a tank and
students compute the volume.
Temperature: Using a classroom set
of thermometers, teacher has
students go outside and find the
warmest and coldest spot in the area
around the school building. Teacher
observes students and asks them to
tell the reading. Teacher also
discusses the way thermometers may
use different increments of
measurement.
Time: Teacher uses a model of a
clock to set a clock time and then
present problems to students
involving addition and subtraction of
time. For example: It’s 8:30 now,
what time will it be in two hours.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
309.01.e
Converting
Units of
Measurement
309.02.a
Apply
Dimensional
Analysis
Math
Benchmark
Teacher
Observable
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given the height of the room in feet
and inches, students will convert the
measurement to inches.
For Learning:
Students solve the following problem:
A student reads for 30 minutes a
night for 4 nights a week. Students
need 8 hours for an extra recess.
How many nights will it take a student
to earn a free recess?
Of Learning:
RIT 201-210 (Angle Measurement)
RIT 211-220 (Angle Measurement)
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Teacher explains the relationship
between inches, feet, yard, and miles
and their metric equivalents. Teacher
poses problems to the class such as:
78” of material is how many feet and
inches; if we have 2.5 meters of
yarn, how many centimeters does
that equal? Teacher poses more
problems to students using real life
situations, such as size of the room,
students compute the problems and
express answers in multiple forms.
Given real life situations and objects,
students will choose an appropriate
type of measurement and compute
the answer. For example: A student
reads 30 minutes a night for 4 nights
a week. How many hours will the
student read in a month?
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
309.01.c
Perimeter,
area of
rectangle,
square,
triangle
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
For Learning:
Teacher draws rectangular and
triangular shapes on the board with
measurements provided. Students
compute the perimeter and area and
write answers on paper.
Perimeter: Teacher explains that
perimeter is the distance around an
object. Teacher may present the
formula for perimeter of a square:
perimeter = side squared and
rectangle: perimeter = 2L + 2W.
Students will measure perimeter of
objects around the school, such as
the pad for the basketball court.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Algebra, Functions, and Mathematical Models
310.01.a
313.01.a
313.01.b
313.02.a
Patterns,
Sequences,
Functions
Learning
Continuum
Math
Benchmark
Teacher
Observable
For Learning:
Given the sequence 2, 5, 11, ___, 47,
___, students will fill in the blanks.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Sample Teaching
Strategy
Area: (rectangle and square, see
above). Area of a triangle: Teacher
presents the formula: area = ½ base
X height. Teacher makes sure that
students understand that you find the
area of the triangle and divide by 2.
Teacher draws triangles on the board
and students compute the area and
express the area in square units.
Return to Top
Teacher presents sequences of
numbers, such as 6, 12, ___, 24, ___.
Students identify the pattern and
complete the sequence or fill in the
blanks. Students create sequences
for their peers to solve.
Can also use pattern blocks, skittles,
pencils and pens, etc. To create a
pattern.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
310.01.c
310.02.a
310.02.b
310.03.a
307.02.e
Solving
Equations
and
Inequalities,
Simplifying
Expressions, Order
of
Operations
310.01.a
310.01.b
Properties
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Given the problem: 5(8 – 3) + 62 =
___ students will solve the problem.
Given a problem such as:
5 * 3 + X = 2 * 20
Students will write the answer to the
problem.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Learning
Continuum
Math
Benchmark
Teacher
Observable
For Learning:
Students will be given a variety of
equations, and they will solve for X
using the inverse operation.
Given a variety of example problems,
students will label the problem for the
property that is shown: commutative,
associative, distributive, and zero
property.
Of Learning:
RIT 201-210
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Order of operations: Teacher
presents the saying: “please excuse
my dear Aunt Sally” which stands for
parentheses, exponents, multiply,
divide, add, and subtract. Teacher
explains that you work from left to
right. Students complete sample
problems.
Solving for X: Teacher presents a
problem such as: 10 * 2 + X = 12 * 2
and demonstrates how to solve for X.
Algebraic expressions involving
addition: Teacher demonstrates how
to solve addition problems with a
variable, and to think of a related
subtraction equation. Teacher
demonstrates how to solve a
subtraction problem with a variable
and to think of a related addition
problem. Students solve problems
from the math book.
Properties of integers: Commutative,
associative, distributive, and zero
property. Teacher provides
examples and explanations.
Students complete problems.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment
and Sample Quizzes
Concepts and Principles of Geometry
311.01.a
311.01.e
Shapes and
Figures, 2- &
3dimensional
311.01.c
Congruency
and
Similarity
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Math
Benchmark
Teacher
Observable
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources

Return to Top
For Learning:
Using a worksheet, students will
identify and label solid and plane
figures.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
For Learning:
Given a worksheet with pairs of lines,
angles, and shapes, the student will
label congruent and not congruent
pairs.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Solid objects: Students will make a
model for rectangular prisms,
triangular pyramids, square pyramids,
cones, and cylinders. Using the
models, the teacher explains the
concepts of edges, faces, vertices
(corners), and surface area.
Identifying polygons including
quadrilaterals (square, rectangle,
parallelograms, rhombus, trapezoid),
pentagon, octagon, triangles
(scalene, right, isosceles, equilateral).
Students will find polygon shapes
around the room. Teacher explains
and discusses each shape and gives
more examples.
Students find examples of shapes at
home and brings them in
Congruent: Teacher explains that
congruent means a line, an angle, or
a shape that is exactly the same size.
Students identify congruent and not
congruent shapes, lines, or angles.
Have the students cut lines form
string. Move the lines around the
page to see that they are the same.
Geometer’s
Sketchpad
http://www.ke
ypress.com/s
ketchpad/pro
duct_info.htm
l
Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
311.01.c
Symmetry
and
Transformations
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Learning
Continuum
Math
Benchmark
Teacher
Observable
311.01.b
311.01.d
311.01.f
Learning
Continuum
Geometric
Properties
and
Terminology
Math
Benchmark
Teacher
Observable
311.02.a
Coordinate
Learning
Continuum
Math
Benchmark
Teacher
Observable
Sample Assessment
and Sample Quizzes
For Learning:
Teacher will fold paper in front of the
class and ask if there is symmetry or
more than one line of symmetry.
Students will write the answers for
each example.
Given a shape or image, students will
create a symmetric image and then
transform the image
Of Learning:
RIT 201-210
RIT 211-220
For Learning:
Students will draw and label a point,
line, line segment, ray, parallel lines,
perpendicular lines, and intersecting
lines.
Teacher will draw three angles on the
board and students will identify the
type of angle.
Of Learning:
RIT 201-210
RIT 211-220
RIT 221-230
For Learning:
Given a piece of graph paper with the
X and Y-axis, students will use
coordinates (ordered pairs) to draw a
figure.
Of Learning:
RIT 201-210 (Graphing)
RIT 211-220 (Graphing)
RIT 221-230 (Graphing)
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Sample
Resources
Students use paper to fold plane
figures. If it can be folded in half and
both halves match, then the figure
has symmetry. Examples are given
showing more than one line of
symmetry.
Use mirror to project symmetric
shapes and angles on a page
Interactive
manipulatives
http://www.m
atti.usu.edu/nl
vm/nav/index.
html
Students define Transformation as a
rotation of a shape or image
Practice transformations using mires
Using the board the teacher will
demonstrate and explain point, line,
line segment, ray, parallel lines,
perpendicular lines, and intersecting
lines.
Angles: Using a protractor, the
teacher will show right angles, acute,
and obtuse angles.
Students will practice making angles
Students learn appropriate symbols
for line, point, line segment, ray,
parallel lines, etc.
Teacher introduces the concept of X
and Y-axis and ordered pairs using
graph paper. Teacher explains that
the X-axis is horizontal and the Y-axis
is vertical. Teacher explains that the
first number in an ordered pair is X
coordinate and the second number is
the Y coordinate. Teacher explains
negative numbers on the X and Yaxis.

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment
and Sample Quizzes
Data Analysis, Probability, and Statistics
312.02.a
312.01.a
312.01.b
312.01.c
Data
Analysis
312.04.a
312.04.b
312.05.a
312.05.b
Probability
& Prediction
Combinations and
Permutations
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Math
Benchmark
Teacher
Observable
Learning
Continuum
Math
Benchmark
Teacher
Observable
Minimum
Hours
Allotted
Sample Teaching
Strategy
Return to Top
For Learning:
Given a table of data, such as
number of students in after school
activities, students will construct a bar
graph, a line graph, and a circle
graph for the same information.
For Learning:
Given a problem with socks.
Sock drawer contains 1 pair of blue
socks, 2 pairs of red socks, 3 pair of
brown socks, and 6 pair of white
socks. What is the probability of
pulling a pair of white socks out of
drawer without looking at the pair you
draw.
Of Learning:
RIT 201-210
RIT 221-230
For Learning:
Given a list of numbers students will
list all of the ways they can be put
together
Of Learning:
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Teacher presents and explains how
to use a various types of graphs
made from data given in the text or
collected by the students.
Students practice making graphs for
different situations, i.e. Bar graph for
favorite ice cream flavors
Teacher uses a graph to show the
favorite flavors of ice cream. Using
probability, students predict the
probability that someone will choose
one of the favorites.
Using a spinner or coin, explain the
chances of getting a 2. Give each
student or pair of students a coin or
spinner and have them test it.
Give each student a bag with 4 green
skittles, 2 red skittles, and three
yellow skittles. Tell them they need
to draw out two and write down what
they get. Return to the bag and
repeat until all combinations have
been drawn. Discuss that this is an
arrangement and then do two to three
problems as a class.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
State
Standard
and
Benchmark
312.03.a
312.03.b
Statistics
Local
Curriculum
Learning
Continuum
and other
Performance
Objectives
Sample Assessment
and Sample Quizzes
This is not
listed on the 5th
grade RIT but
is on the one
above and
below
For Learning:
Given a set of sample test scores the
student will find the mean, median,
and mode.
Learning
Continuum
Math
Benchmark
Teacher
Observable
Of Learning:
RIT 201-210
RIT 221-230
Sample
Sequence
©State of Idaho 2003
Minimum
Hours
Allotted
Sample Teaching
Strategy
Teacher will introduce mean, median,
and mode using classroom test
scores. Explain the mean, or
average, is the sum of the scores
divided by the number of scores. The
mean should be rounded to the
nearest tenth. The mode is the score
that occurs the most often. The
median is the middle number when
the items are arranged in order. The
range is the difference between the
greatest and least numbers.
Sample
Resources

Idaho State Expanded Curriculum Guide Math 5th Grade
©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.
PROFICIENT: Meets Standards
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.
Idaho State Expanded Curriculum Guide Math 5th Grade
BASIC: Below Standards
©State of Idaho 2003
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.
Idaho State Expanded Curriculum Guide Math 5th Grade
©State of Idaho 2003
State Standards—5th Grade Math
Return to Top
306.
MATHEMATICS STANDARDS – GRADE 5, SECTIONS 307 THROUGH 313.
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.
307.
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:
01. Understand and
use numbers.
Content Knowledge and Skills:
a.
Return to Number Sense—
Whole Numbers
Read, write, order, and compare
whole numbers through billions,
commonly used fractions, and
decimals through thousandths.
Samples of Applications:
i.
ii.
iii.
iv.
Return to Place Value
b.
Return to Ordering,
Equalities, and Inequalities
Demonstrate and apply the
knowledge of whole numbers,
decimal place value, and patterns of
periods (thousandths to billions).
Explore the relationship between
equivalent fractions.
Return to Number Sense-Decimals
c.
Return to Factorization/
Divisibility
d.
Explore the relationship between
decimals and simple fractions through
thousandths.
e.
Return to Number Sense-Decimals
Return to Ordering,
Equalities, and Inequalities
Return to Fractions, Ratio,
Proportion
i.
Read, write, and compare large
numbers.
Identify a digit’s value in whole
numbers and decimals.
Read, write, and compare decimal
numbers.
Write a number with a 4 in the
thousandth place and a 3 in the
thousandth place.
Use numbers, words, and pictures
to explain how a tenth and a
hundredth are related.
i.
Use numbers, words, and pictures
to explain how 0.50 and 1/2 are
related.
Show a sense of magnitudes and
relative magnitudes of whole
numbers, decimals, and simple
fractions.
i.
Order a list of decimals
Order a list of simple fractions,
for instance, 1/4, 1/3, 1/2, or 2/3,
1/2, 3/4.
Explore and apply number theory
concepts (prime, composite,
multiples, factors).
i.
ii.
Return to Number Sense-Decimals
Return to Factorization/
Divisibility
f.
ii.
What are the multiples of 12 and
the factors of 12?
Use composite numbers to
discover the divisibility rules for
2 and 5.
Idaho State Expanded Curriculum Guide Math 5th Grade
02.
Perform
computations
accurately.
a.
Multiply and divide whole numbers.
ii.
Use basic arithmetic facts to solve
more complex problems.
Identify and use mathematical
properties (zero property,
associative, distributive,
communicative, and identity
property), for instance, 4 x 12 =
(4 x 10) + (4 x 2).
Add 1/4 + 1/4.
Subtract 3/4 - 1/4.
i.
Add 2.34 + 51.602.
i.
Complete 100 division facts with
single-digit factors in 3 minutes.
Solve basic expressions that have
parenthesis, for instance, 4 + (2 x
3).
i.
ii.
Return to Factorization/
Divisibility
Return to Estimation—
Fractions
Return to Number Sense—
Whole Numbers
b.
c.
d.
Return to Solving Equations
e.
Return to Est/Comp—Whole
Numbers
f.
g.
03.
Estimate and judge
reasonableness of
results.
a.
©State of Idaho 2003
Add and subtract fractions with like
denominators and simplify as
necessary.
Add and subtract decimals through
thousandths.
i.
Instantly recall basic multiplication
and division facts up to 10s.
Evaluate numerical expressions that
include parentheses.
i.
Select and use an appropriate method
of computation from mental math,
paper and pencil, calculator, or a
combination of the three.
Use appropriate vocabulary.
Use estimation to predict computation
results.
i.
ii.
Estimate all computation to
determine if reasonable.
Round to estimate reasonable
solutions (11.436 - 6.1 = □).
Return to Estimation—
Whole Numbers
Return to Estimation—
Fractions
b.
Recognize when estimation is
appropriate and understand the
usefulness of an estimate as distinct
from an exact answer.
i.
Is $20 enough money to buy 2
CD’s? Do you need an exact sum
or an estimate?
c.
Determine whether a given estimate
is an overestimate or underestimate.
i.
Is your estimate greater or less
than the actual answer? Explain.
Return to Estimation—
Whole Numbers
Return to Estimation—
Fractions
Return to Estimation—
Whole Numbers
Return to Estimation—
Fractions
Idaho State Expanded Curriculum Guide Math 5th Grade
d.
308.
©State of Idaho 2003
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.
Use a variety of strategies to compute
problems drawn from real-world
situations.
Return to Using Problem
Solving Skills
b.
Return to Using Problem
Solving Skills
c.
Use reasoning
skills to recognize
problems and
express them
mathematically.
i.
ii.
Return to Using Problem
Solving Skills
02.
Samples of Applications:
Solve problems using the 4-step
process of problem solving (explore,
plan, solve, examine).
Make predictions and decisions based
on information.
Use a variety of methods, such as
words, numbers, symbols, charts,
graphs, tables, diagrams, and models,
to explain mathematical reasoning
and concepts.
i.
b.
Apply solutions and strategies to new
problem situations.
i.
c.
Formulate conjectures and discuss
why they must be or seem to be true.
i.
a.
ii.
There were 31 wheels and 12
seats in a bike shop. The bike
shop sold bicycles and tricycles.
How many bicycles and how
many tricycles were in the bike
shop?
Plan a party for the 5th grade.
Estimate how many packages of
plates you will need if plates
come in packages of ten.
Identify when a problem has too
much or too little information.
Check for reasonable answers.
I. Explain how to use the array model
of multiplication to solve this
problem, for instance, 27 x 42.
ii.Explain how you know that 0.5 and
0.50 are equivalent.
Return to Reasoning and
Problem Solving
Return to Reasoning and
Problem Solving
Return to Reasoning and
Problem Solving
Determine how many cubes will
be needed to fill a box that is 3
centimeters wide, 2-centimeters
long, and 2 centimeters high.
Formulate a conjecture about
multiplying with multiples of ten
and explain why it is true, for
instance, 20 x 30 = 600.
Idaho State Expanded Curriculum Guide Math 5th Grade
03.
Apply appropriate
technology and
models to find
solutions to
problems.
©State of Idaho 2003
a.
Understand the purpose and
capabilities of appropriate technology
use as a tool to solve problems.
i.
Use a calculator to explore the
pattern when multiplying with
multiples of ten, for instance, 400
x 20 = 8,000.
b.
Use computer applications to display
and manipulate data.
i.
c.
Select appropriate models to represent
mathematical ideas.
i.
Use computer applications to
create a bar graph representing
student collected data.
Make a model to show 2/3 is
equal to 4/6.
Make a model of 4 x 25 in
different ways.
Use a bar graph to show favorite
flavors of ice cream in the class.
Return to Applying
Technology
Return to Applying
Technology
Return to Applying
Technology
04.
Communicate
results using
appropriate
terminology and
methods.
ii.
a.
Use a variety of methods, such as
words, numbers, symbols, charts,
graphs, tables, diagrams, and models,
to communicate mathematical
information.
b.
Use appropriate vocabulary to
communicate mathematical
information.
Use appropriate notation.
i.
Return to Communicate
Results
Return to Communicate
Results
Return to Communicate
Results
309.
c.
i.
Convert a one-step story problem
to a number equation using
appropriate notations, terms, and
labels.
CONCEPTS AND PRINCIPLES OF MEASUREMENT.
Rationale: The step in scientific investigation is understanding the measurable attributes of objects.
Standard – The student will:
01.
Understand and
use U.S.
customary and
metric
measurements.
Return to Length, Weight,
Volume
Return to Perimeter, Area of
Rectangle, Square
a.
Content Knowledge and Skills:
Select and use appropriate units and
tools to make formal measurements in
both systems.
i.
ii.
Samples of Applications:
Measure the length of your desk.
Draw a 6-centimeter line and a 6inch line.
Idaho State Expanded Curriculum Guide Math 5th Grade
Return to Length, Weight,
Volume
b.
Apply estimation of measurement to
real-world and content problems
using actual measuring devices.
Return to Perimeter, Area of
Rectangle, Square
c.
Explore the differences and
relationships between perimeter and
area in both systems.
i.
ii.
Return to Length, Weight,
Volume
d.
Return to Converting Units
of Measurement
Return to Time/Temperature
Apply dimensional
analysis.
Form 2 different rectangles, each
with a perimeter of 50
centimeters.
Form 2 different rectangles, each
with an area of 100 centimeters.
Solve problems involving length,
perimeter, area, weight, mass, and
temperature.
i.
e.
Convert unit of measurement within
each system.
i.
Each 5th grader in the classroom
needs 1 foot of string for an art
project. How many yards of string
does the class need?
f.
Apply understanding of relationships
to solve real-world problems related
to time.
Use appropriate vocabulary.
i.
If a student started reading at
10:55 a.m. and finished at 12:15
p.m., how much time has passed?
Understand units and their
relationship to one another and to
real-world applications.
i.
Each student reads 15 minutes a
night. How many hours did each
student read in a week?
g.
02.
©State of Idaho 2003
a.
ii.
Find the perimeter of your desk.
Look around the room and find an
obtuse, right and acute angle.
Return to Apply Dimensional
Analysis
310.
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.
Return to Patterns,
Sequences, Functions
Return to Properties
Content Knowledge and Skills:
a.
Explore the meaning and use of
variables in simple expressions and
equations.
Samples of Applications:
i.
ii.
What is the value of n + 3 if n =
2?
What is the value of n if n + 3 =
11?
Idaho State Expanded Curriculum Guide Math 5th Grade
©State of Idaho 2003
b.
Translate simple word statements and
story problems into algebraic
equations.
i.
Write an equation to match a
story problem.
Return to Solving Equations
c.
Use symbols (<, >, =) to express
relationships.
i.
Evaluate algebraic
expressions.
a.
Explore and use the following
properties as they relate to addition
and multiplication: commutative,
associative, identity, zero, and
inverse.
b.
Investigate the order of operations
(parentheses only).
Solve missing addends and missing
factor problems using inverse
operations.
Use the correct symbol to make
this number sentence true: 24 + 6
 18 + 9.
i.
Give an example or
demonstrate the
following properties:
zero, identity,
commutative,
associative,
distributive, and
inverse.
Compare (2 + 3) x 4 and 2 + (3 x
4).
3 x n = 9.
5 + n = 16.
Give the family of facts for (6, 4,
10) and (6, 4, 24).
Return to Properties
02.
Return to Solving Equations
Return to Solving Equations
03.
Solve algebraic
equations and
inequalities.
a.
i.
i.
ii.
iii.
Return to Solving Equations
311.
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.
Identify, compare, and analyze
attributes of two- and threedimensional shapes and develop
vocabulary to describe the attributes.
Return to Shapes & Figures
Samples of Applications:
i.
ii.
iii.
Return to Geometric
Properties and Terminology
b.
Explore the fundamental concepts,
properties, and relationships among
points, lines, rays, angles, and shapes.
i.
ii.
Find examples of these figures
and objects in the real world:
sphere/circle,
rectangle/rectangular prism,
triangle/triangular pyramid.
Draw a trapezoid, parallelogram,
and regular polygons.
Explain the classification system
of quadrilaterals.
Construct and label an acute
angle, right angle, and an obtuse
angle.
Construct and label a line, line
segment, and ray.
Idaho State Expanded Curriculum Guide Math 5th Grade
Return to Congruency and
Similarity
c.
Explore congruence, similarities, and
symmetry of shapes.
Return to Symmetry and
Transformations
i.
ii.
Return to Geometric
Properties and Terminology
d.
Return to Shapes & Figures
e.
Determine perimeters of polygons
and area of rectangles/squares in realworld situations.
Predict and describe the results of
sliding, flipping, and turning twodimensional shapes.
i.
i.
ii.
iii.
Return to Geometric
Properties and Terminology
f.
Use appropriate vocabulary.
Apply graphing in
two dimensions.
a.
Identify and plot points on a
coordinate plane.
02.
i.
ii.
Return to Coordinate
312.
©State of Idaho 2003
Find lines of symmetry by
drawing or folding a variety of
shapes.
Divide a square into 4 congruent
parts in more than 1 way.
Find the perimeter of a variety of
closed shapes.
Create a design by rotating a
square around a fixed point.
Identify shapes that will
tessellate.
Create a design by reflecting your
name.
Play Battleship!
Plot a set of points on a
coordinate plane to form a
picture.
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
Content Knowledge and Skills:
Samples of Applications:
will:
01. Understand data
a.
Read and interpret tables, charts, and i. Find a graph in the social studies
analysis.
graphs.
textbook and interpret it.
Return to Data Analysis
b.
Return to Data Analysis
c.
Explain and justify conclusions drawn
from tables, charts, and graphs.
Understand and use vocabulary.
Return to Data Analysis
02.
Collect, organize,
and display data.
Return to Data Analysis
03. Apply simple
statistical
measurements.
Return to Statistics
a.
Collect, organize, and display data
with appropriate notation in tables,
charts, and graphs.
i.
Collect and display
data from a class on their favorite
sports.
a.
Find measures of central tendency mean, median, and mode - with
simple sets of data.
i.
Given a set of data, identify the
mean, median, and mode.
Line up from shortest to tallest
and find the “median”, or, if even
number of students, find two
students to “represent the
median.”
ii.
Idaho State Expanded Curriculum Guide Math 5th Grade
Return to Statistics
04.
Understand basic
concepts of
probability.
b.
Determine the range of a set of data.
i.
a.
Predict, perform, and record results of
simple probability experiments.
i.
b.
Understand and use the language of
probability.
i.
a.
Make predictions based on simple
experimental probabilities.
i.
b.
Understand and use appropriate
vocabulary.
©State of Idaho 2003
Using the lengths of pencils in the
classroom, determine the range.
Using 1 dice, roll the dice thirty
times and record the results.
Return to Probability and
Prediction
Return to Probability and
Prediction
05.
Make predictions
or decisions based
on data.
Use outcome, probable, certain,
likely, unlikely, and impossible when
conducting a probability experiment.
Knowing the probability of a given
outcome such as rolling dice, predict
the likelihood of a future event.
Return to Probability and
Prediction
Return to Probability and
Prediction
313.
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.
Samples of Applications:
Content Knowledge and Skills:
a.
Extend patterns and identify a rule
(function) that generates the pattern
using whole numbers and decimals.
i.
ii.
Return to Patterns,
Sequences, Functions
Return to Patterns,
Sequences, Functions
Return to Applying
Technology and Models
b.
c.
d.
02.
Apply functions to
a variety of
problems.
Return to Patterns,
Sequences, Functions
a.
Discover, describe, and extend
patterns by using manipulatives and
pictorial representations.
Use mathematical models to show
change in real context.
Understand and use appropriate
vocabulary.
Use patterns to represent and solve
simple problems.
Given a numerical pattern extend it
and identify the rule in as many ways
as possible.
Create a numerical pattern.
i.Using toothpicks, create a geometric
pattern that can be continued.
i.Create a graph showing how a candle’s
height changes over time after being lit.
i.
Would you rather have 15-minutes
recess each day for the next 2 weeks
or would you rather have 1 minute the
1st day, 2 minutes the 2nd day, 4
minutes the 3rd day, and so on,
through the 2 weeks. Explain your
thinking using words, numbers, and
pictures.
Idaho State Expanded Curriculum Guide Math 5th Grade
©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
Idaho State Expanded Curriculum Guide Math 5th Grade
©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
Idaho State Expanded Curriculum Guide Math 5th Grade
©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

transformation, hypotenuse, edge,
isosceles, scalene triangle, similar
trapezoids, alternate interior
angles, sum of angles in triangle
intersection,
quadrilaterals, octagon,
parallelogram,
pyramid, isosceles,
right angle, diameter,
right angle, geometric,
perpendicular, plane
 for triangle, angle
symbol
RIT 211-220

o
RIT 241-250

o
symmetrical halves,
diameter, radius, angle
bisector, tangent,
corresponding parts of
congruent triangles,
Pythagorean theorem,
corresponding angles,
complementary angles,
construction
sign for parallel lines
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

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
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
postulate (261-270)
HL (271-280)
Idaho State Expanded Curriculum Guide Math 5th Grade
©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)
Idaho State Expanded Curriculum Guide Math 5th Grade
©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)
Idaho State Expanded Curriculum Guide Math 5th Grade
©State of Idaho 2003
New Vocabulary () and Symbols ()
ISAT “Sub-Goal”
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

decimals, fractions,
what shape, hour,
minutes, gallons,
average, probability,
graph, squares
o %
RIT 251-260
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

mortality, odometer,
magic square, deducted,
less than twice, addends,
less than sum, rectangle,
diameter, radius, label
(units), area, perimeter
o I = prt
RIT 261-300
Idaho State Expanded Curriculum Guide Math 5th Grade
©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
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
RIT 201-210
©State of Idaho 2003
RIT 211-220
RIT 221-230
Algebra
Solving
Equations,
Simplifying
Expressions,
Order of
Operations

Return to Guide




Evaluate an expression involving
more than one operation (order of
operations)
Use the basic properties of
multiplication to write an algebraic
expression that is equivalent to a
given algebraic expression
Solve equations involving more
than one operation
Multiply and divide polynomials
Solve equations involving rational
numbers (addition and subtraction)




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







Patterns,
Sequences,
Functions

Use of a function “machine” to
determine input and output

Use logic to solve a problem
involving a function table


Return to Guide


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)
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
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Properties

Return to Guide


RIT 201-210
Use strategies to develop
computational fluency with
multiplication: zero property,
property of one, arrays, doubles,
nine patterns
Use the basic properties of addition
to write an algebraic expression
equivalent to a given algebraic
expression
Understand the properties of
integers: commutative, associative,
identity, zero property of
multiplication, distributive property
of multiplication over addition, and
inverse property of addition

©State of Idaho 2003
RIT 211-220
Understand the properties of
integers: commutative, associative,
identity, zero property of
multiplication, distributive property
of multiplication over addition, and
inverse property of addition
RIT 221-230
Data Analysis, Probability, and Statistics
Combinations
and
Permutations
Return to Guide
Data Analysis

Return to Guide

Solve problems using information
from a picture graph (symbol may
represent more than one)
Interpret data given in percent form
on a circle graph and broken line
graph

Solve problems involving
arrangements

Read and interpret information from 
a graph
Interpret Venn Diagrams
Make predictions from a graph



Use a tree diagram to determine the
number of possible outcomes of an
event
Interpret data given in horizontal
and vertical bar graphs to solve
problems
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Probability and
Prediction


Return to Guide

Statistics

Return to Guide
RIT 201-210
Compute simple probability
outcomes
Determine the probability of an
outcome (multiple events)
Use the counting principle to
determine probability
Solve practical problems involving
the mean (average) of a set of
numbers

©State of Idaho 2003
RIT 211-220
Investigate experimental probability 
of an event using a coin or spinner

RIT 221-230
Investigate experimental probability
of an event using a coin or spinner
Predict outcomes using probability

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

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
Estimation and Computation
Decimals

Return to Guide





Add decimals to hundredths place
using both horizontal and vertical
format
Subtract decimals to hundredths
place
Compute and count change greater
than $20.00
Subtract decimals through hundredthousandths with a calculator
Compute and count change up to
and including $10.00 (addition and
subtraction only)
Solve written word problems
involving the addition or
subtraction of monetary amounts




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




Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Fractions

Return to Guide




RIT 201-210
Add mixed numbers with like
denominators with regrouping
Subtract mixed numbers with like
denominators with regrouping
Subtract mixed numbers with unlike
denominators with regrouping
Multiply a fraction by a fraction;
answer in lowest terms
Multiply mixed numbers





©State of Idaho 2003
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

Add integers with like signs
Add integers with unlike signs
Add several integers
Multiply integers with unlike signs
Divide integers with unlike signs

Find a percent of a number

Return to Guide
Squares
Return to Guide


Calculate the square of any number
less than 100
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
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)
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Whole Numbers

Return to Guide






RIT 201-210
Understand the concept of division
using pictorial representation
Use front-end estimation strategy
for multiplication and division
Divide a 2-digit number by a 2-digit
number with a remainder
Subtract multi-digit numbers
without using a calculator
Multiply by multiples of 10 and 100
with an emphasis on mental math
Divide a 3-digit number by a
multiple of 10
Divide a 3-digit number by a 2-digit
number (no zeros)




©State of Idaho 2003
RIT 211-220
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



RIT 221-230
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
Geometry
Congruency and 
Similarity
Return to Guide
Coordinate
Return to Guide
Identify congruent figures, angles
and line segments



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)
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Geometric
Properties and
Terminology
Return to Guide





RIT 201-210
Identify points, lines, line segments,
rays, planes, and angles
Identify the diameter of a circle
Identify intersecting, parallel, and
perpendicular lines
Calculate the surface area of a
rectangular prism
Identify angles according to their
measure: right, obtuse, and acute





©State of Idaho 2003
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






Shapes and
Figures, 2- and
3-Dimensional

Return to Guide



Symmetry and
Transformations
Return to Guide

Identify faces, edges, and corners
(vertices) on solid figures
Identify polygons: triangle,
quadrilateral, pentagon, and octagon
Identify quadrilaterals: square,
rectangle, and parallelogram
Identify, name, and analyze solid
figures: cube, cylinder, triangular
pyramid and square pyramid (faces,
edges, and vertices)

Identify mirror-images





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)
Identify types of transformations
(rotation)


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
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
RIT 201-210
©State of Idaho 2003
RIT 211-220
RIT 221-230
Measurement
Area, Perimeter, 
Circumference

Return to Guide

Length, Weight,
Volume


Return to Guide


Time,
Temperature
Return to Guide

Find the perimeter of a square or
rectangle using the formula
Solve practical word problems
involving perimeter and area of a
square, rectangle or triangle
Calculate the area of a triangle
Find the volume of a figure using
cubic units
Perform conversions between units
of mass in the metric system; also
as necessary in addition or
subtraction problems
Select appropriate unit of measure
for length and area
Find the volume of rectangular
solids using the formula
Compute basic operations with
units of time (include basic concept
of time zones)



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




Compute word problems with time
and calendars
Measure length with metric
measures (centimeter)
Measure length with customary
measures (inch)
Select the appropriate unit of
measure for length, area, and
volume
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
RIT 201-210
©State of Idaho 2003
RIT 211-220
RIT 221-230
Number Sense
Decimals

Return to Guide



Write a decimal for a shaded region
(hundredths)
Write a terminating decimal as a
fraction or mixed number
Round decimals to nearest whole
number, tenth, hundredth, or
thousandth
Multiply a decimal by multiples of
10, 100, or 1000






Exponents and
Scientific
Notation

Write whole number in exponential
form and compute the power of a
number



Return to Guide
Factorization /
Divisibility


Return to Guide

Apply rules of divisibility
Identify the greatest common factor
of two whole numbers each of
which is less than 100
List the prime and composite
numbers less than 50 in a word
problem



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



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)

Identify and use powers of 10

Identify the least common
denominator for 3 or more
fractions: list the multiples or prime
factorization
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Fractions, Ratio, 
and Proportions

Return to Guide

RIT 201-210
Change a fractional numeral to its
simplest form (lowest terms)
Write the missing number in two
equivalent ratios
Use a number line to identify a
fractional point




©State of Idaho 2003
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






Integers

Order integers on a number line

Return to Guide
Ordering

Return to Guide




Percents
Return to Guide



Order numbers from least to
greatest and greatest to least
Compare and order numbers
through the billions
Order decimals and fractions to the
hundred thousandths
Identify the greater or lesser of 2
integers
Ordering integers that include
fractions and wholes
Ordering exponential values
Write a decimal or fraction as a
percent or vice versa



Identify the greater or lesser of 2
integers
Order integers on a number line

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


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
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
Place Value

Return to Guide


Whole Numbers

Return to Guide

RIT 201-210
Understand and identify the place
value and value of each digit in
numerals through the billions
Write the word name for a decimal
and vice versa
Write numerals in expanded form
through the hundred billions
Round to the nearest millions and
billions
Write the Roman numeral
equivalent of Arabic numbers 12000 and vice versa

©State of Idaho 2003
RIT 211-220
Understand and identify the place
value and value of each digit in
numerals through the billions

RIT 221-230
Match word names to numerals to
the hundred thousands in decimals
Idaho State Expanded Curriculum Guide Math 5th Grade
ISAT “Sub-Goal”
RIT 201-210
©State of Idaho 2003
RIT 211-220
RIT 221-230
Mathematical Reasoning and Problem Solving
Mathematical

Reasoning and
Problem Solving

Return to Guide







Translate verbal statements into
equations (all four operations;
several operations)
Estimate the answers to word
problems
Solve written word problems
involving the addition or
subtraction of monetary amounts
Solve word problems involving
customary and metric measurement
Solve word problems involving
distance, rate and time
Use logic to solve problems
Solve word problems using
proportional reasoning
Solve geometry problems by
making a drawing or diagram
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,
Write an equation, or Logical
Deduction






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





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
Idaho State Expanded Curriculum Guide Math 5th Grade
Sample Test Items
Return to Top
RIT 201-210: Algebraic Concepts
Return
Return
Return
RIT 211-220: Algebraic Concepts
Return
Return
RIT 221-230: Algebraic Concepts
Return
Return
RIT 201-210: Computation
Return
Return
Return
Return
RIT 211-220: Computation
Return
Return
Return
Return
RIT 221-230: Computation
Return
Return
Return
Return
Return
©State of Idaho 2003
Idaho State Expanded Curriculum Guide Math 5th Grade
RIT 201-210: Geometry
Return
Return
Return
Return
RIT 211-220: Geometry
Return
Return
Return
Return
RIT 221-230: Geometry
Return
Return
Return
RIT 201-210: Measurement
Return
Return
Return
Return
RIT 211-220: Measurement
Return
Return
Return
RIT 221-230: Measurement
Return
Return
Return
Return
©State of Idaho 2003
Idaho State Expanded Curriculum Guide Math 5th Grade
©State of Idaho 2003
RIT 201-210: Number Sense and Numeration
Return
Return
Return
Return
Return
Return
Return
RIT 211-220: Number Sense and Numeration
Return
Return
Return
Return
Return
Return
RIT 221-230: Number Sense and Numeration
Return
Return
Return
Return
RIT 201-210: Problem Solving
Return
RIT 211-220: Problem Solving
Return
Return
Return
Return
Return
Idaho State Expanded Curriculum Guide Math 5th Grade
RIT 221-230: Problem Solving
Return
RIT 201-210: Statistics, Probability, & Graphing
Return
Return
Return
RIT 211-220: Statistics, Probability, & Graphing
Return
RIT 221-230: Statistics, Probability, & Graphing
Return
Return
Return
Return
©State of Idaho 2003