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Math Standards Document
Fourth Grade
Final Draft
Hawaii School Districts
Prepared by Marzano and Associates
1
Grade 4 Summary
Strand
Numbers and Operations
Numbers and Operations
Numbers and Operations
Numbers and Operations
Numbers and Operations
Measurement
Measurement
Measurement
Geometry and Spatial
Sense
Geometry and Spatial
Sense
Geometry and Spatial
Sense
Geometry and Spatial
Sense
Geometry and Spatial
Sense
Patterns, Functions, and
Algebra
Patterns, Functions, and
Algebra
Patterns, Functions, and
Algebra
Patterns, Functions, and
Algebra
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Total
Standard
1
2
2
3
3
4
4
4
5
Topic
Number of
Elements
3
1
2
4
1
3
1
1
4
6
Numbers and Number Systems
Operations
Operation Properties
Computational Fluency
Estimation
Measurement Attributes and Units
Measurement Tools and Techniques
Measurement Formulas
Geometric Shapes and Their
Properties and Relationships
Transformation
6
Symmetry
1
7
Visualization and Spatial Reasoning
1
8
Coordinate Geometry
1
9
Patterns
1
9
Function
1
10
2
10
Numeric and Algebraic
Representations
Rates of Change
11
Data Collection and Representation
2
12
Data Interpretation
2
13
Predictions and Inferences
1
14
Probability
1
1
1
35
2
Topic: Numbers and Number Systems
Strand: Numbers and Operations
Standard 1: NUMBER SENSE: Understand numbers, ways of representing
numbers, relationships among numbers, and number systems.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.1.1) represents numbers from ten-thousandths to millions in a variety of
ways
 (4.1.2) compares factors, multiples, prime numbers, and composite numbers
up to 100
 (4.1.3) uses equivalent forms of commonly used fractions and decimals in
solving problems
Level 3.5
Level 3.0
While involved in tasks related to numbers and number systems the student
will:
 (4.1.1) identify place value from ten-thousandths to millions (e.g., identify
the value of a digit in a number. i.e., identify the value of each of the 7s in the
number 7,370,892,871)
 (4.1.2) identify and list factors, multiples, prime numbers, and composite
numbers (e.g., list all the factors of a number and identify that number as
prime or composite; list the first ten multiples of a given number)
 (4.1.3) identify equivalent forms of commonly used fractions and decimals
(e.g., identify the equivalent fraction for a common decimal and vice versa.
i.e., ½ = .50)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.1.1) recognizes or recalls specific terminology such as:
o place value
o factors
o multiples
o prime numbers
o composite numbers
o fractions
o decimals
 (4.1.2) performs basic processes such as:
o showing examples of numbers from ten-thousandths to millions
o listing factors, multiples, prime numbers, and composite numbers
under 144
o (4.1.3) recognizing or recalling examples of equivalent forms of
commonly used fractions and decimals
o listing commonly used fractions and decimals
o listing equivalent fractions for commonly used decimals
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
3
Level 0.0
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
4
Level 4.0
 (4.1.1) Ask student to write numbers from ten thousandths to millions in standard
form, expanded form and written form.
 Ask students to represents place value in drawings to illustrate the number.
 (4.1.2) Ask students to compare and order factor pairs, multiples of a number,
give equivalent names for numbers, shows factors of a composite number, list
prime numbers up to 100. (e.g. EDM Assessment 3.12)
 (4.1.3) Ask students to write two equivalent fractions and an equivalent decimal.
(e.g. EDM Assessment 7.13)
Level 3.0
 (4.1.1) Ask students to identify the value of a digit in a number (i.e., identify the
value of each of the 7s in the number 7,370,892,871).
 (4.1.2) Ask students to list all the factors of a number and identify that number as
prime or composite; list the first ten multiples of a given number.
 (4.1.3) Ask students to identify the equivalent fraction for a common decimal and
vice versa (i.e., ¾ = .75, ½ = .50, ¼ = .25, 4/4 = 1).
Level 2.0
 (4.1.1) Ask students to match the following terms with their definitions:
hundredths –ten-thousandths, millions, prime, composite, fractions, decimal.
 (4.1.2) Ask students to choose the appropriate value of a digit in a 6-digit number
using a place value chart.
 (4.1.3) Ask students to choose the set of factors for a number.
 Ask students to choose a set of prime numbers.
 Ask students to choose a set of composite numbers.
 Ask students to list 3 multiples of a number.
 Ask students to match equivalent fractions with decimals and vice versa.
5
Topic: Operations
Strand: Numbers and Operations
Standard 2: OPERATION SENSE: Understand the meaning of operations and how
they relate to each other.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.2.1) compares situations using addition and subtraction of fractions and/or
decimals
Level 3.5
Level 3.0
While involved in tasks related to operations the student will:
 (4.2.1) describe situations involving addition and subtraction of fractions and
decimals (e.g., create a situation that involves the addition (or subtraction) of
a fraction (and/or decimal)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.2.1) recognizes or recalls specific terminology such as:
o decimal point
o denominator
o numerator
o improper fraction
o equivalent fraction
o sums
o difference
 (4.2.1) performs basic processes such as:
o adding fractions and decimals
o subtracting fractions and decimals
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
6
Level 4.0
 (4.2.1) Ask students to compare situations using addition and subtraction of
fractions. Ask students to state the answers in decimals (e.g., Queen Arlene
decides to keep ½ of her land and have her three children divide the other 1/2.
She wants her oldest daughter to get more land than her sisters. Think of a way to
use fractions to divide the land. Explain your answer. Then state the fractions as
decimals). (e.g. EDM Assessment 7.13)
Level 3.0
 (4.2.1) Ask students to describe a situation that uses addition and subtraction of
fractions and decimals (e.g., Help Mrs. Wong create 3 teams that will be evenly
matched. Use their times from their last race to predict how fast they will run in
the relay race. Write the names of four students you think should be on each team.
Estimate how long it will take each team to complete the race. Explain how you
made your teams). (e.g. EDM Assessment 4.11)
 (4.2.1) Ask students to order decimals through thousandths from the least to the
greatest.
Ask students to add and subtract decimals through thousandths. (eg. EDM
Assessment 4.11)
Level 2.0
 (4.2.1) Ask students to match the terminology with examples of the definitions.
decimal point, denominator, numerator, improper fraction, equivalent fraction,
sums, difference.
 Ask students to read and write decimals through thousandths.
 Ask students to choose the appropriate solution to addition of fractions and
decimals situations.
 Ask students to choose the appropriate solution to subtraction of fractions and
decimals. (e.g. EDM Assessment 7.13, 5.12)
7
Topic: Operation Properties
Strand: Numbers and Operations
Standard 2: OPERATION SENSE: Understand the meaning of operations and how
they relate to each other.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.2.2) applies two or more operation properties to solve problems
Level 3.5
Level 3.0
While involved in tasks related to operation properties the student will:
 (4.2.2) use associative, commutative, and distributive properties as they apply
to operations involving whole numbers (e.g., manipulate number sentences
using the distributive property, associative property, and commutative
property to make it easier to perform calculations with whole numbers. i.e.,
notice that 27 x 8 can be represented as [20 + 7} x 8 which equals [20 x 8] +
[7 x 8])
 (4.2.3) demonstrate the properties of zero and one as they relate to addition,
subtraction, multiplication, and division (e.g., use the properties of zero and
one to make quick mental calculations in his or her head then state the
answer)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.2.2, 4.2.3) recognizes or recalls specific terminology such as:
o associative, commutative, and distributive properties and
properties of zero and one
o whole numbers
o mental calculations
o operation symbols
 (4.2.2, 4.2.3) performs basic processes such as:
o recognizing or recalling examples of associative, commutative,
and distributive properties of operations
o recognizing or recalling examples of the properties of zero and
one
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
8
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.2.2) Ask student to apply two or more operation properties to solve problems.
(e.g. EDM Assessment 3.12)
o Kato was playing a game of “Name that Number”. He had the following
five number cards and target number: 3,2,8,6,5, target = 12 His teacher,
Ms. Ayers asked everyone to record their thinking. Here is what Kato
wrote:
5+ (6+8) / 2-3 = 12
6*2+ (8-5) – 3 = 12
3*2+ (8+5) - 6 = 12
1. Ms. Ayers saw that Kato had made mistakes in writing two of his
number sentences. Circle the mistakes in writing two of his sentences.
2. Explain in words how Kato can correct each number sentence.
3. Describe two more ways to reach the target number of 12. You do not
have to use all 5 numbers.
Level 3.0
 (4.2.2) Ask students to use associative, commutative, and distributive properties
as they apply to operations involving whole numbers.
 Ask students to manipulate number sentences using the distributive property,
associative property, and commutative property to make it easier to perform
calculations with whole numbers (i.e., notice that 27 x 8 can be represented as [20
+ 7} x 8 which equals [20 x 8] + [7 x 8]).
 (4.2.3) Ask students to demonstrate the properties of zero and one as they relate
to addition, subtraction, multiplication, and division
 Ask students to use the properties of zero and one to make quick mental
calculations in his or her head then state the answer.
Level 2.0
 (4.2.2, 4.2.3) Ask students to match definitions with the following vocabulary
words: associative, commutative, and distributive properties and properties of
zero and one, whole numbers, mental calculations, operation symbols.
 (4.2.2, 4.2.3) Ask students to perform basic processes such as: solve associative,
commutative, and distributive properties of operations: recognize examples of
properties of zero and one. (EDM Assessment 3.12)
9
Topic: Computational Fluency
Strand: Numbers and Operations
Standard 3: COMPUTATION STRATEGIES: Use computational tools and
strategies fluently and, when appropriate, use estimation.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.3.1) solves open sentences using multiplication and division facts up to 12 x
12
 (4.3.2) explains the strategies used to solve number sentences
 (4.3.3) compares fractions with like and unlike denominators
 (4.3.4) solves problems using addition and subtraction of more than two
numbers with decimals to three places
Level 3.5
Level 3.0
While engaged in tasks regarding computational fluency the student will:
 (4.3.1) recall all multiplication facts and the corresponding division facts up to
12 x 12 (e.g., write out the fact family for a multiplication sentence. i.e., 8 x 12
= 96; 12 x 8 = 96; 96/8 =12; 96/12 = 8)
 (4.3.2) select and use appropriate strategies and/or tools (mental math,
calculators, paper/pencil, standard algorithms) for computing whole numbers
(e.g., choose the method he or she wants to use to compute whole numbers and
explain whether the chosen method was the most appropriate method, or if
another method would have been more appropriate to use)
 (4.3.3) use more than one strategy to add and subtract fractions with like and
unlike denominators (e.g., show how to add (or subtract) fractions using one
strategy (fraction strips) then show how to add (or subtract) another set of
fractions using a different strategy, tiles, blocks, numberline)
 (4.3.4) add and subtract decimals to three places (e.g., add (or subtract)
decimals using appropriate strategy, and use number sense to accurately
place the decimal point in the answer)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.3.1,2,3,4) recognizes or recalls specific terminology such as:
o multiplication facts
o division facts
o mental math
o calculators, paper/pencil
o standard algorithms
o commonly used fractions and decimals
o fraction strips
o tiles, blocks, numberline
o unit fraction
o whole unit
 (4.3.1,2,3,4) performs basic processes such as:
o describing multiplication as adding groups and division takes
apart multiplication
o demonstrating mental math, using calculators, and standard
algorithms
o adding fractions with common denominators; subtracting fractions
with common denominators
o showing place value of decimals to thousandths
10
o adding and subtracting decimals to thousandths
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
11
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.3.1) Ask students to solve open sentences using multiplication and division
facts up to 12 x 12 and decimals with 3 places.
 Ask students to fill in the missing numbers for multiplication and division facts.
“What’s my rule?” (EDM Assessment 5.12, 6.11)
 (4.3.2) Ask students to explain the strategies used to solve number sentences.
 “Walking away with a Million Dollars” (EDM Assessment 5.12)
Ask students to imagine that they have inherited one million dollars. The bank has
only $700,000 in $100 bills. The bank gives them the rest of the money in $20
bills and in $10 bills. Their suitcases will bold as much as 1 carton of paper. Will
one million dollars fit in their suitcase? Ask students to show all of their work and
explain their answer. (Information needed to solve the problem: You can cover a
sheet of paper with about six $100.00 bills. There are 500 sheets in one ream of
paper. There are 10 reams in one carton.)


(4.3.3) Ask students to compare fractions with like and unlike denominators.
(EDM Assessment 7.13, 8.9)
(4.3.4) Ask students to solve problems using addition and subtraction of more than
two numbers with decimals to three places.
Level 3.0
 (4.3.1) Ask students to recall all multiplication facts and the corresponding
division facts.
 Ask students to write out the fact family for a multiplication sentence (i.e., 8 x 12
= 96; 12 x 8 = 96; 96/8 =12; 96/12 = 8 up to 12 x 12).
 (4.3.2) Ask students to select and use appropriate strategies and/or tools (mental
math, calculators, paper/pencil, standard algorithms) for computing whole
numbers. Ask students to choose the method he or she wants to use to compute
whole numbers and explain whether the chosen method was the most appropriate
method, or if another method would have been more appropriate to use.
 (4.3.3) Ask students to use more than one strategy to add and subtract fractions
with like and unlike denominators.
 Ask students to show how to add (or subtract) fractions using one strategy
(fraction strips) then show how to add (or subtract) another set of fractions using a
different strategy, tiles, blocks, numberline.
 (4.3.4) Ask students to add and subtract decimals to three places. Ask students to
add (or subtract) decimals using appropriate strategy, and use number sense to
accurately place the decimal point in the answer. (EDM Assessment 5.12)
Level 2.0
 (4.3.1,2,3,4) Ask students to recognize or recall specific terminology such as:
multiplication facts, division facts, mental math, calculators, paper/pencil, standard
algorithms, commonly used fractions and decimals, fraction strips, tiles, blocks,
numberline, unit fraction, whole unit.
 (4.3.1,2,3,4) Ask students to perform basic processes such as:
Fill in the missing number of the fact triangle. (EDM 3.12)
12
Demonstrate mental math, use calculators, and standard algorithms.
Add fractions with common denominators; (EDM 7.13, 8.9))
Subtract fractions with common denominators. (EDM 7.13, 8.9)
Complete the place value chart of decimals to thousandths.
(EDM 4.11)
Add and subtract decimals to thousandths. (EDM 4.11)
13
Topic: Estimation
Strand: Numbers and Operations:
Standard 3: COMPUTATION STRATEGIES: Use computational tools and
strategies fluently and, when appropriate, use estimation.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 4.3.5 demonstrates the reasonableness of numerical solutions in word
problems
Level 3.5
Level 3.0
While engaged in tasks involving estimation the student will:
 (4.3.5) determine the reasonableness of numerical solutions (e.g., for the
problem, “How many buses should be reserved if each bus fits 48 students,
and there are 570 students attending the field trip?” the student responds that
12 buses are needed, even though the answer to 570/48 = 11.875)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.3.5) recognizes or recalls specific terminology such as:
o estimate
o benchmark or landmark numbers
o rounding
 (4.3.5) performs basic processes such as:
o estimating the result
o using benchmark numbers
o rounding off answers to nearest tens, hundreds, thousands,
millions, tenths, hundredths, thousandths
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
14
Level 4.0
 (4.3.5) Ask students to demonstrate the reasonableness of numerical solutions in
word problems by using benchmark numbers.
o It was reported that on New Year’s Day in 1907, Theodore Roosevelt
shook hands with 8,513 people. If the average person could shake hands
properly with 10 people per minute, does shaking hands with 8,513 people
seem reasonable? Estimate the total number of people and how many
hands it takes to shake in one hour. Then multiply to find out how many
handshakes could be made in a 10 hour work day. Use an equation to help
explain your answer. Write a sentence to explain your answer. (EDM
12.7)
Level 3.0
 (4.3.5) Ask students to determine the reasonableness of numerical solutions by
estimating the answer and using the landmark numbers to help find the answer.
o Joey goes to Doreen’s Delicious Doughnuts to buy doughnuts for the class
party. What is the least amount of money he will have to pay for 30
doughnuts? How many dozen donuts does Joey have to buy? Use a
drawing to show your answer. Write a sentence to explain your answer.
(EDM 12.7)
Level 2.0
 Ask students to match definitions to terminology such as: estimate, benchmark or
landmark numbers and rounding.
 Ask students to choose the estimated the result, use benchmark numbers, round
off numbers to nearest tens, hundreds, thousands, millions, tenths, hundredths,
thousandths.
15
Topic: Measurement Attributes and Units
Strand: Measurement
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.4.1) demonstrates use of standard measurements to find length, perimeter,
area and volume
 (4.4.2) converts customary and metric units of length using appropriate tools
to show perimeter, area and volume
 (4.4.3) compares the measure of angles according to their categories; right
angle, acute angles, obtuse angles, and straight angles
Level 3.5
Level 3.0
While involved in tasks regarding measurement attributes and units the
student will:
 (4.4.1) use standard measurements correctly (e.g., when given an experiment,
the student will measure area, perimeter, volume and capacity as applies to
the task)
 (4.4.2) select and apply appropriate customary and metric units and tools to
measure length, perimeter, area and volume for the degree of accuracy needed
(e.g., select a unit of measurement for a specific task and explain why that unit
was chosen over another unit)
 (4.4.3) classify right angles, acute angles, obtuse angles, and straight angles
(e.g., sort pictures of given angles into four categories: acute, obtuse, right, or
straight)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.4.1) recognizes or recalls specific terminology such as:
o customary and metric units
o length
o perimeter
o area
o volume
o capacity
o straight angles
o right angles
o acute angles
o obtuse angles
o reflex angles
 (4.4.2) performs basic processes such as:
o using appropriate standard units for measuring perimeter, area and
volume
o using customary and metric units and tools to measure length
o (4.4.3) recognizing or recalling examples of attributes of right
angles, acute angles, obtuse angles, and straight angles; measure
angles
o using a protractor and a compass
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
16
Level 0.5
Level 0.0
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
17
Level 4.0
 (4.4.1) Ask students to demonstrate use of standard measurement to find length,
perimeter, area and volume.
 Ask students to draw three line segments to show the nearest millimeter, centimeter
and decimeter.
 Ask students to draw three line segments to show the nearest 1/16th of an inch, 1/4th
of an inch, and ½ of an inch.
 Ask students to draw a rectangle with an area of 12 square centimeters and a
perimeter of 16 centimeters. (EDM 8.9)
 (4.4.2) Ask students to convert customary and metric units of length using appropriate
tools to show perimeter, area and volume.
 Ask student to solve problems converting customary units of length.
o Mrs. Lopez wants to tile her kitchen floor. The room is 10 feet wide and 12
feet long. How many 1-square-foot tiles does she need to cover the floor? If
she chooses 6 inch tiles, how many 6 inch tiles will she need? (EDM 8.9)
o Imagine that it rained 42 inches in a classroom 27 feet long and 24 feet wide.
About how many cubic feet of water would be in the classroom?
 (4.4.3) Ask students to compare the measure of angles according to their categories;
right angle, acute angles, obtuse angles, and straight angles.
o Tonya used her half-circle protractor and measured the angle at 50 degrees.,
Alexi used his protractor and measured the angle at 130 degrees, Jose used his
full-circled protractor and measured 310 degrees. Measure the angle to find
out who you agree with? Why? (EDM 6.11)
Level 3.0
 (4.4.1) Ask students to use standard measurements correctly (e.g., when given an
experiment, the student will measure area, perimeter, volume and capacity as applies
to the task).
 (4.4.2) Ask students to select and apply appropriate customary and metric units and
tools to measure length, perimeter, area and volume for the degree of accuracy
needed (e.g., select a unit of measurement for a specific task and explain why that
unit was chosen over another unit).
 Ask students to use a map scale to find the number of miles from one city to another.
(EDM 3.12)
 Ask students to measure a line segment to the nearest ½ centimeter.
 Ask students to measure a line segment to the nearest ½ inch. (EDM 2.10)
 Ask students to find the area of each polygon using square centimeters. (EDM 8.9)
 Ask students to measure a rectangle to find area in square centimeters and a perimeter
in centimeters. (EDM 8.9)
 Ask students to measure and record measurements of each angle on a rectangle and a
triangle. (EDM 6.11)
 (4.4.3) Ask students to classify right angles, acute angles, obtuse angles, and straight
angles (e.g., sort pictures of given angles into four categories: acute, obtuse, right, or
straight).
 Ask students to measure angles and name the category of each angle.
Level 2.0
18



(4.4.1) Ask students to match terminology with definitions. Customary and metric
units, length, perimeter, area, volume, capacity, straight angles, right angles, acute
angles, obtuse angles, reflex angles.
(4.4.2) Ask students to use appropriate standard units for measuring the perimeter,
area and volume of items in the classroom; ask students to use customary and metric
units and tools to measure length.
(4.4.3) Ask students to match attributes of right angles, acute angles, obtuse angles,
and straight angles; measurements of angles using a protractor and a compass.
Topic: Measurement Tools and Techniques
19
Strand: Measurement
Standard 4: FLUENCY WITH MEASUREMENT: Understand attributes, units,
and systems of units in measurement and develop and use techniques, tools, and
formulas for measuring.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.4.4) demonstrates more than one way to measure surface area and
volume of a rectangular prism using customary and metric units
Level 3.5
Level 3.0
While involved in tasks regarding measurement tools and techniques the
student will:
 (4.4.4) estimate and measure surface area and volume using U.S. customary
units and metric units (e.g., cover each side of a box with inch or centimeter
grid paper and determine the area of each face; fill the box with inch or
centimeter cubes to determine the volume of the box)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.4.4) recognizes or recalls specific terminology such as:
o surface area
o volume
o customary units
o metric units
 (4.4.4) performs basic processes such as:
o measuring in U.S. customary units and metric units
o estimating total surface area and volume of a shape
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
20
Level 4.0
 (4.4.4) Ask students to demonstrate more than one way to measure surface area
and volume of a rectangular prism using customary and metric units.
Level 3.0
 (4.4.4) Ask students to cover each side of a box with inch or centimeter grid paper
and determine the area of each face.
Ask students to find the volume of each stack of centimeter cubes. (EDM 7.11)
Level 2.0
 (4.4.4) Ask students to match specific terminology with definitions; surface area,
volume, customary units, metric units.
 (4.4.4) Ask students to measure in U.S. customary units and metric units.
 Ask students to estimate total surface area and volume of a shape.
21
Topic: Measurement Formulas
Strand: Measurement
Standard 4: FLUENCY WITH MEASUREMENT: Understand attributes, units,
and systems of units in measurement and develop and use techniques, tools, and
formulas for measuring.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.4.5) demonstrates steps used to calculate the unknown measurement in
the area and the perimeter of a square or rectangle
Level 3.5
Level 3.0
While engaged in tasks involving measurement formulas the student will:
 (4.4.5) use known measurements to calculate desired measurements of squares
and rectangles (e.g., apply a formula to determine the area and perimeter of a
square (or rectangle) when its side lengths are given; determine the area of a
square when its perimeter is given; determine the possible perimeters of a
rectangle when the area is given)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.4.5) recognizes or recalls specific terminology such as:
o formula of area
o formula of perimeter
 (4.4.5) performs basic processes such as:
o choosing appropriate formulas for area; choosing appropriate
formulas for perimeter
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
22
Level 4.0
 (4.4.5) Ask students to demonstrate steps used to calculate the unknown
measurement in the area and the perimeter of a square or rectangle.

Level 3.0
 (4.4.5) Ask students to apply a formula to determine the area and perimeter of a
square (or rectangle) when its side lengths are given.
 Ask students to determine the area of a square when its perimeter is given
 Ask students to determine the possible perimeters of a rectangle when the area is
given.

Level 2.0
 (4.4.5) Ask students to match specific terminology to definitions; formula of area,
formula of perimeter.
 (4.4.5) Ask students to choose appropriate formulas for area.
 Ask students to choose appropiate formulas for perimeter.
23
Topic: Geometric Shapes and Their Properties and Relationships
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.5.1) compares examples of triangles and quadrilaterals from life
experiences to classify two-dimensional shapes
 (4.5.2) shows or describes examples from life experiences of lines in a
plane (parallel, perpendicular, intersecting)
 (4.5.3) describes examples of points, lines, line segments, and rays found
in real life situations
 (4.5.4) creates shapes in a two-dimensional figure. Identify the shapes that
make up a solid three-dimensional figure.
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (4.5.1) classify different types of triangles and quadrilaterals according to their
properties and identify the properties that define the classifications (e.g.,
identify and justify the class to which a two-dimensional shape belongs. i.e.,
put a square and a rhombus in a category entitled “equilateral
quadrilateral”)
 (4.5.2) describe lines in the plane (parallel, perpendicular, intersecting) (e.g.,
describe and illustrate the difference between parallel, perpendicular, and
intersecting lines)
 (4.5.3) compare points, lines, line segments, and rays (e.g., explain the
similarities and differences among points, lines, line segments, and rays)
 (4.5.4) predict and confirm the results of putting together and taking apart twoand three- dimensional shapes (e.g., select a paper shape then draw the
subdivided figure that he or she thinks will be made if the shape is subdivided;
uses scissors to cut the shape into the shapes drawn)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.5.1,2,3,4) recognizes or recalls specific terminology such as:
o triangles
o circles
o quadrilaterals, polygons,
o two-dimension
o three-dimension
o plane
o parallel, perpendicular
o intersecting
o points, lines, line segments, and rays
 (4.5.1,2,3,4) performs basic processes such as:
o measuring length of sides and measurement of angles
o recognizing or recalling examples of parallel, perpendicular, and
intersecting lines
o illustrating points, lines, line segments, and rays
o recognizing or recalling combinations of smaller shapes within
simple 2-d and 3-d shapes
24
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
25
Level 4.0
 (4.5.1) Ask students to compare examples of triangles and quadrilaterals from life
experiences to classify two-dimensional shapes.
 (4.5.2) Ask students to show or describe examples from life experiences of lines
in a plane (parallel, perpendicular, intersecting)
 (4.5.3) Ask students to describe examples of points, lines, line segments, and rays
found in real life situations.
 (4.5.4) Ask students to create shapes in a two-dimensional figure and identify the
shapes that make up a solid three-dimensional figure.
Level 3.0
 (4.5.1) Ask students to identify and justify the class to which a two-dimensional
shape belongs (i.e., put a square and a rhombus in a category entitled “equilateral
quadrilateral”).
 (4.5.2) Ask students to describe and illustrate the difference between parallel,
perpendicular, and intersecting lines.
 (4.5.3) Ask students to explain the similarities and differences among points,
lines, line segments, and rays.
 (4.5.4) Ask students to select a paper shape then draw the subdivided figure that
he or she thinks will be made if the shape is subdivided; uses scissors to cut the
shape into the shapes drawn.
Level 2.0
 (4.5.1,2,3,4) Ask students to match specific terminology to definitions; triangles,
circles, quadrilaterals, polygons, two-dimension, three-dimension, plane,
parallel, perpendicular, intersecting, points, lines, line segments, and rays.
 (4.5.1,2,3,4) Ask students to measure length of sides and measurement of angles.
 Ask students to recognize or recall examples of parallel, perpendicular, and
intersecting lines.
 Ask students to illustrate points, lines, line segments, and rays.
 Ask students to recognize or recall combinations of smaller shapes within simple
2-d and 3-d shapes.
26
Topic: Transformation
Strand: Geometry and Spatial Sense
Standard 6: TRANSFORMATIONS AND SYMMETRY: Use transformations and
symmetry to analyze mathematical situations.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.6.1) creates a pattern using shapes to show flips, slides and turns
Level 3.5
Level 3.0
While engaged in tasks involving transformation the student will:
 (4.6.1) use flips, slides, and turns to determine if two figures are congruent
(e.g., copy a given figure from a worksheet, and through a series of flips,
slides, and/or turns, determine if the figure is congruent to a second given
figure that appears somewhere else on the same worksheet; the student then
describes the motions that proved that the two figures are congruent)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.6.1) recognizes or recalls specific terminology such as:
o flip, reflection, mirror image
o slide, translation
o turn, rotation
 (4.6.1) performs basic processes such as:
o showing a flip, slide, and turn using two congruent shapes
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
27
Level 4.0
 (4.6.1) Ask students to create a pattern using shapes to show flips, slides and
turns.
Level 3.0
 (4.6.1) Ask students to copy a given figure from a worksheet. Through a series of
flips, slides, and/or turns ask students to determine if the figure is congruent to a
second given figure that appears somewhere else on the same worksheet.
 Ask the students to describe the motions that proved that the two figures are
congruent.
Level 2.0
 (4.6.1) Ask students to match specific terminology to definitions; flip, reflection,
mirror image, slide, translation, turn, rotation.
 Ask students to show a flip, slide, and turn using two congruent shapes.
28
Topic: Symmetry
Strand: Geometry and Spatial Sense
Standard 6: TRANSFORMATIONS AND SYMMETRY: Use transformations and
symmetry to analyze mathematical situations.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.6.2) creates or illustrates the missing symmetrical side along the plane
of symmetry
Level 3.5
Level 3.0
While engaged in tasks involving symmetry the student will:
 (4.6.2) locate the plane of symmetry in three-dimensional objects (e.g., make a
three-dimensional clay model then “cuts” it along the plane of symmetry
using a string or dental floss)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.6.2) recognizes or recalls specific terminology such as:
o plane of symmetry
o 3-dimensional object
 (4.6.2) performs basic processes such as:
o recognizing or recalling accurate statements about symmetry
o recognizing or recalling examples of symmetrical twodimensional pictures; recognizing or recalling examples of a
three-dimensional objects
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
29
Level 4.0
 (4.6.2) Ask students to create or illustrate the missing symmetrical side along the
plane of symmetry.
Level 3.0
 (4.6.2) Ask students to make a three-dimensional clay model then “cuts” it along
the plane of symmetry using a string or dental floss.
Level 2.0
 (4.6.2) Ask students to match specific terminology to definitions; plane of
symmetry, 3-dimensional object.
 (4.6.2) Ask students to recognize or recall accurate statements about symmetry.
 Ask student to choose a symmetrical three-dimensional object and a symmetrical
two-dimensional picture.
30
Topic: Visualization and Spatial Reasoning
Strand: Geometry and Spatial Sense
Standard 7: VISUAL AND SPATIAL SENSE: Use visualization and spatial
reasoning to solve problems both within and outside of mathematics.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.7.1) measures and draws at least three two-dimensional nets to show the
base, side, top and front of a pyramid, prism, and cone
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving visual and spatial reasoning the student will:
 (4.7.1) predict the three-dimensional object that will result from folding a twodimensional net of the object and justify the prediction (e.g., predict the threedimensional figure that will result from folding a given two-dimensional net of
the figure and use characteristics of the net to justify the prediction)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.7.1) recognizes or recalls specific terminology such as:
o two-dimensional net
o base, sides, top, front
o pyramid, prism, cone, cube, cylinder
 (4.7.1) performs basic processes such as:
o recognizing or recalling examples of simple three-dimensional
objects (cube, rectangular prism, triangular prism, rectangular
pyramid, triangular pyramid, cone, cylinder) from a twodimensional net
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
31
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.7.1) Ask students to measure and draw at least three two-dimensional nets to
show the base, side, top and front of a pyramid, prism, and cone.
Level 3.0
 (4.7.1) Ask students to predict the three-dimensional figure that will result from
folding a given two-dimensional net of the figure.
Ask students to use characteristics of the net to justify the prediction.
Level 2.0
 (4.7.1) Ask students to match specific terminology to definitions; twodimensional net, base, sides, top, front, pyramid, prism, cone, cube, cylinder.
 (4.7.1) Ask students to choose the appropriate simple three-dimensional object
(cube, rectangular prism, triangular prism, rectangular pyramid, triangular
pyramid, cone, cylinder) from a two-dimensional net.
32
Topic: Coordinate Geometry
Strand: Geometry and Spatial Sense
Standard 8: REPRESENTATIONAL SYSTEMS: Select and use different
representational systems, including coordinate geometry.
Level 4.0
Level 3.0
Grade 4
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.8.1) accurately labels and plots missing ordered pairs on a coordinate
grid to create a picture representing shapes
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving coordinate geometry the student will:
 (4.8.1) use ordered pairs to plot points on a coordinate grid (e.g., plot points on
a coordinate grid using a list of ordered pairs)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.8.1) recognizes or recalls specific terminology such as:
o ordered pairs
o coordinate grid
o horizontal axis (x-axis)
o vertical axis (y-axis)
o origin
o first quadrant
 (4.8.1) performs basic processes such as:
o finding ordered pairs on a coordinate grid
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
33
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.8.1) Ask students to accurately label and plot missing ordered pairs on a
coordinate grid to create a picture representing shapes.
Level 3.0
 (4.8.1) Ask students to plot points on a coordinate grid using a list of ordered
pairs.
Level 2.0
 (4.8.1) Ask students to match specific terminology to definitions; ordered pairs,
coordinate grid, horizontal axis (x-axis), vertical axis (y-axis), origin, first
quadrant.
 (4.8.1) Ask students to choose the appropriate ordered pairs on a coordinate grid.
34
Topic: Patterns
Strand: Patterns, Functions, and Algebra
Standard 9: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand
various types of patterns and functional relationships.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.9.1) applies a rule for a growing and shrinking patterns and geometric
patterns to solve word problems
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving patterns the student will:
 (4.9.1) extend, create, and generalize growing and shrinking numeric and
geometric patterns (including multiplication patterns) (e.g., describe how the
patterns changes from one term to the next, state a general rule for the
pattern, and extend the pattern by giving the next three terms)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.9.1) recognizes or recalls specific terminology such as:
o growing pattern
o shrinking pattern
o geometric pattern
 (4.9.1) performs basic processes such as:
o completing growing patterns and shrinking patterns; solving basic
mathematical operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
35
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.9.1) Ask students to apply a rule for a growing and shrinking patterns and
geometric patterns to solve word problems.
Level 3.0
 (4.9.1) Ask students to describe how the patterns changes from one term to the
next.
 Ask students to state a general rule for the pattern.
 Ask students to extend the pattern by giving the next three terms.
Level 2.0
 (4.9.1) Ask students to match specific terminology to definitions: growing pattern,
shrinking pattern, geometric pattern.
 (4.9.1) Ask students to fill in the missing parts of the growing patterns and
shrinking patterns.
 Ask students to solve basic mathematical operations.
36
Topic: Function
Strand: Patterns, Functions, and Algebra
Standard 9: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand
various types of patterns and functional relationships.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.9.2) creates a problem that shows the relationship between quantities in
a variety of forms. Uses manipulatives, tables, pictures, or symbols.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving functions the student will:
 (4.9.2) represent the relationship between quantities in a variety of forms
(manipulatives, tables, pictures, symbols) (e.g., represent the relationship
between two quantities i.e. total number of cars and total number of wheels in
a variety of ways and describes how each representation helps someone to
understand the relationship between the two quantities)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.9.2) recognizes or recalls specific terminology such as:
o tables
o representations, pictures, symbols
o relationship between two quantities
 (4.9.2) performs basic processes such as:
o describing the relationship between quantities (basic groupings);
showing how quantities of groups increase or decrease
o describing the representations, pictures and/or symbols
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
37
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.9.2) Ask students to create a problem that shows the relationship between
quantities in a variety of forms. Ask students to use manipulatives, tables,
pictures, or symbols.
Level 3.0
 (4.9.2) Ask students to represent the relationship between quantities in a variety
of forms (manipulatives, tables, pictures, symbols).
 Ask students to explain the relationship between the two quantities.
Level 2.0
 (4.9.2) Ask students to match specific terminology to definitions; tables,
representations, pictures, symbols, relationship between two quantities
 (4.9.2) Ask students to describe the relationship between quantities (basic
groupings) and show how quantities of groups increase or decrease.
 Ask students to describe the representations, pictures and/or symbols.
38
Topic: Numeric and Algebraic Representations
Strand: Patterns, Functions, and Algebra
Standard 10: SYMBOLIC REPRESENTATION: Use symbolic forms to represent,
model, and analyze mathematical situations.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.10.1, 2) creates word problems using symbols to represent unknown
quantities in open sentences and determine the unknown quantities by
applying the commutative, associative, distributive properties
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving numeric and algebraic representations the
student will:
 (4.10.1) use symbols to represent unknown quantities in open sentences and
determine the unknown quantities (e.g., place a symbol (a box or a star) in a
numeric sentence in place of an unknown quantity and show how he or she
determined the unknown quantity)
 (4.10.2) represent the commutative, associative, and distributive properties
symbolically (e.g., show a representation of the associative property (or
associative or distributive) using shapes)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.10.1,2) recognizes or recalls specific terminology such as:
o unknown quantities
o open sentences
o numeric sentences
 (4.10.1,2) performs basic processes such as:
o recognizing or recalling accurate statements about variables;
writing an open sentence
o solving an open number sentence using commutative, associative,
or distributive properties
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
39
Level 4.0
 (4.10.1, 2) Ask students to create word problems using symbols to represent
unknown quantities in open sentences and determine the unknown quantities by
applying the commutative, associative, distributive properties.
Level 3.0
 (4.10.1) Ask students to use symbols to represent unknown quantities in open
sentences and determine the unknown quantities.
 Ask students to place a symbol (a box or a star) in a numeric sentence in place of
an unknown quantity and show how he or she determined the unknown quantity.
 (4.10.2) Ask students to represent the commutative, associative, and distributive
properties symbolically.
 Ask students to show a representation of the associative property or distributive
using shapes.
Level 2.0
 (4.10.1,2) Ask students to match specific terminology to definitions; unknown
quantities, open sentences, numeric sentences.
 (4.10.1,2) Provide students with statements about variables, ask students to identify
which are correct and which are incorrect.
 Ask students to write an open number sentence.
 Ask students to solve an open number sentence using the commutative, associative, or
distributive properties.
40
Topic: Rates of Change
Strand: Patterns, Functions, and Algebra
Standard 10: SYMBOLIC REPRESENTATION: Use symbolic forms to represent,
model, and analyze mathematical situations.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.10.3) creates a data table showing rate of change numerically. Graphs
the data and writes a hypothesis to explain the rate of change.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving rates of change the student will:
 (4.10.3) describe the rate of change numerically and verbally based on data
recorded in a table or graph (e.g., analyze a data table or graph, state the rate
of change using appropriate units and explain how he or she determined the
rate of change. i.e., analyze the data and states that the water from the leaky
faucet dripped 12 mL per minute)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.10.3) recognizes or recalls specific terminology such as:
o rate of change
o data table or graph
o appropriate units
 (4.10.3) performs basic processes such as:
o interpreting data on a table or graph; showing change in data
o recognizing or recalling examples of the rate of change in data
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
41
Level 4.0
 (4.10.3) Ask students to create a data table showing rate of change numerically.
Ask students to graph the data and write a hypothesis to explain the rate of
change.
Level 3.0
 (4.10.3) Ask students to analyze a data table or graph.
 Ask students to state the rate of change using appropriate units and explain how
he or she determined the rate of change (i.e., analyze the data and states that the
water from the leaky faucet dripped 12 mL per minute).
Level 2.0
 Ask students to match specific terminology to definitions; rate of change, data
table or graph, appropriate units.
 (4.10.3) Ask students to interpret data from a table or graph.
 Ask students to plot the change in data on a graph.
 Ask students to pick examples of the appropriate rate of change in data.
42
Topic: Data Collection and Representation
Strand: Data Analysis, Statistics, and Probability
Standard 11: FLUENCY WITH DATA: Pose questions and collect, organize, and represent
data to answer those questions.
Grade 4
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.11.1, 2) organizes data in a table and uses a bar graph to compare results
and validate questions. Uses cumulative frequency to show the sum of each
new line of entry on the table. All parts of the graph are appropriately labeled.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
Level 3.0
While involved in tasks regarding data collection and representation the
student will:
 (4.11.1) pose questions, collect data using observations and experiments, and
organize the data into tables or graphs (e.g., record outcomes from an
experiment (rolling two numbered cubes) and organize the data (the sum of
the two number cubes) in a table and a bar graph)
 (4.11.2) label the parts of a graph (axes, scale, legend, title) (e.g., select an
appropriately descriptive title for a graph, labels the axes with proper units,
and include a scale and legend when necessary)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.11.1,2) recognizes or recalls specific terminology such as:
o observations
o outcomes
o table, bar graph
o axes
o scale
o legend
o title
o cumulative frequency
 (4.11.1,2) performs basic processes such as:
o recognizing or recalling examples of different types of tables and
graphs; organizing data; asking good questions
o labeling the parts of a graph; legend, scale, title, axes
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
43
Level 4.0
 (4.11.1, 2) Ask students to organize data in a table.
 Ask students to use a bar graph to compare results and validate questions.
 Ask students to use cumulative frequency to show the sum of each new line of
entry on the table. All parts of the graph are appropriately labeled.
Level 3.0
 (4.11.1) Ask students to record outcomes from an experiment by rolling two
numbered cubes and organize the data (the sum of the two number cubes) in a
table and a bar graph.
 (4.11.2) Ask students to select an appropriately descriptive title for a graph, label
the axes with proper units, and include a scale and legend when necessary.
Level 2.0
 (4.11.1,2) Ask students to match specific terminology to definitions; observations,
outcomes, table, bar graph, axes, scale, legend, title, cumulative frequency.
 (4.11.1,2) Ask students to name different types of tables and graphs; organize
data; ask good questions.
 Ask students to label the parts of a graph; legend, scale, title, axes.
44
Topic: Data Interpretation
Strand: Data Analysis, Statistics, and Probability
Standard 12: STATISTICS: Interpret data using methods of exploratory data
analysis.
Level 4.0
Level 3.0
Grade 4
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.12.1, 2) collects and graphs two related data sets. Analyzes the similarities
and differences of data to propose possible trends. Explains the reasons for the
trends
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving data interpretation the student will:
 (4.12.1) describe data sets (height of 4th grade boys vs. height of 4th grade
girls) with an emphasis on how data are distributed (e.g., compare two sets of
data by analyzing the distribution of the data, and report similarities and
differences between them)
 (4.12.2) analyze sets of data in the graph (e.g., propose possible trends)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.12.1,2) recognizes or recalls specific terminology such as:
o compare
o analyze
o similarities
o differences
o trends
 (4.12.1,2) performs basic processes such as:
o describing similarities and differences in data
o recognizing or recalling examples of patterns in data on a graph
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
45
Level 4.0
 (4 .12.1,2) Ask students to collect and graph two related data sets. Analyze the
similarities and differences of data to propose possible trends. Explain the reasons
for the trends.
Level 3.0
 (4.12.1) Ask students to compare two sets of data by analyzing the distribution of
data. What is similar? What is different?
 (4.12.2) Ask students to describe a trend in the data.
Level 2.0
 (4.12.1, 2) Ask students to match terminology with definitions; compare, analyze,
similarities, differences, trends.
 (4.12.1, 2) Ask students to describe similarities and differences in data.
 Ask students to recognize or recall examples of patterns in data on a graph.
46
Topic: Predictions and Inferences
Strand: Data Analysis, Statistics, and Probability
Standard 13: DATA ANALYSIS: Develop and evaluate inferences, predictions, and
arguments that are based on data.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.13.1) collects data using a table. Uses landmarks to describe mean, median,
mode. Shows data in various ways. Makes a conclusion explaining data.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving predictions and inferences the student will:
 (4.13.1) state conclusions based on data (e.g., explain the conclusion that he or
she drew from a data set and support with information from a graphical
representation)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.13.1) recognizes or recalls specific terminology such as:
o mean, median, mode, maximum, minimum, range, set of data,
landmark numbers
 (4.13.1) performs basic processes such as:
o making conclusions based on data
o organizing and displaying graphical representations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
Sample Tasks for Levels 4.0, 3.0, & 2.0
47
Level 4.0
 (4.13.1) Ask students to collect data using a table, use landmarks to describe
mean, median, mode, show data on a line plot or tally chart and then on a bar
graph.
o Mr. Evans gave bags of jelly beans to students in his class. Each student
counted the jelly beans in the bag and wrote the number on the board.
Then the students found the landmarks for the class data. (EDM 2.10)
o Suppose there were 11 students participating in the experiment. List the
data the students could have reported using the landmarks: minimum 9,
maximum 18, mode 12, median 13.
o Ask students to explain how they found their answer and graph their data
in a line plot or tally chart and a bar graph.
Level 3.0
 (4.13.1) Ask students to state conclusions based on data.
 Ask students to make a bar graph from the table showing data of how many
wrapping paper rolls were sold to earn money for school. Ask students to explain
how to find the mean, median, mode and range of number of wrapping paper sold.
o What can you conclude about the amount of wrapping paper sold? (EDM
2.10, Assessment problem 14)
Level 2.0
 (4.13.1) Ask students to match terminology with specific examples of mean, median,
mode, maximum, minimum, range, set of data, landmark numbers. (EDM 2.10,
Written assessment problems 9-13), (Harcourt Brace 10.5)
 (4.13.1) Ask students to organize data and make conclusions.
 Ask students to make a bar graph of data to show the number of cookies eaten at a
class party. What is your conclusion about the number of cookies eaten at the party?
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0
1
2
3
4
5
6
7
8
Cookies eaten at a party
X = students
48
Topic: Probability
Strand: Data Analysis, Statistics, and Probability
Standard 14: PROBABILITY: Understand and apply basic notions of chance and
probability.
Grade 4
Level 4.0
Level 3.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 (4.14.1) conducts a simple probability experiment. Identifies possible
outcomes of the data and give a prediction about the chance of an event
occurring. States the outcomes in a fraction. Checks that the probability of
each outcome is equal or unequal.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and
applications with partial success.
While engaged in tasks involving probability the student will:
 (4.14.1) identify possible outcomes of simple experiments (coin toss, 4colored spinner) and test predictions (e.g., make a prediction about the chance
of an event occurring in a simple experiment and support the prediction with
valid data or theoretical probability)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 (4.14.1) recognizes or recalls specific terminology such as:
o expected results, outcomes, possible ways
o likely
o equally likely
o more likely
o unlikely
o impossible
o predicted and actual results
o frequency
 performs basic processes such as:
o choosing possible outcomes; making predictions; defining
likelihood
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
49
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 (4.14.1) Ask students to identify the possible outcomes for a set of data and to
give a prediction about the chance of an event occurring. Justify the probability
of each outcome is equal or unequal.
o Make a spinner with 4 parts. Color one part yellow and one part blue.
Then color 2 parts red. Predict the likely outcomes. Use the formula to
help state the outcomes in a fraction. Make a table of data to show the
results of 24 spins. (Harcourt Brace, 11.4)
Probability = Number of ways the event happens
Number of ways all events can happen
What did you predict would be the likely outcome?
Did the outcomes support your prediction? Use the factions to explain.
Why is the probability of spinning green impossible?
Level 3.0
 (4.14.1) Ask students to make a prediction about the chance of an event
happening. Give an explanation for their prediction.
o Roll two number cubes numbered 1-6. Find all possible ways that can
happen when finding sums of 2 through 12. Make a table to show all the
ways.
Write a statement to explain the data. (Harcourt Brace, 11.3)
Level 2.0
 (4.14.1) Ask students to match terminology with their definitions.
 Ask students to use a bag of marbles, 5 red, three blue, three yellow, one green, 0
white, what are the outcomes?
1. Which color is most likely to be pulled out or occurs most frequently?
2. Unlikely to pull?
3. Which one is impossible to pull?
 (4.14.1) Ask students to make a prediction based on the following information.
o On a spinner with six spaces, three red, two yellow, one blue and zero
green, what is the probability of spinning each color?
1. Which color is more likely to spin?
2. Which color is unlikely to be picked?
3. Which color is impossible to spin?
50