Third Grade Math Curriculum Map

3rd Grade Math Curriculum Map
Isaac School District No. 5

Quarter 1
Unit Name and Description: Number Sense, Addition & Subtraction

Cluster 1
Big Ideas/Enduring Understandings Essential Question(s)

Numbers can be represented in many ways and are used to solve Why is it important to learn place
everyday problems using a variety of methods.
value? How can numbers be
There are relationships between numbers.
represented?
The location of a digit determines its place value.
What is the difference between comparing and ordering whole
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number Ones
Numbers; Models through six digits by constructing models and Tens
using numbers. Hundreds
S1C1PO1 Whole Numbers; Multiple [Model] whole numbers through six digits using and One Thousand
Representations connecting multiple representations. Ten Thousands
Hundred
[Analyze] whole numbers through six digits using Thousands
and connecting multiple representations. Standard Form
S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying Expanded Form
the Word Form
concept of place value. Ordinal
Numbers Equal
Order whole numbers through six digits by To
S1C1PO3 Money; Coins; Bills Count money using coins and bills to Less Than
Greater
$100.00. Represent money using coins Than Not
Equal To

* = POs previously introduced Bold = Priority PO 1
Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 8-4-2011


S1C2PO1 Whole Numbers Add whole number to four digits. Order
Value
Subtract whole numbers to four digits. Place
Sum
Addend
S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Addition
Addition; Subtraction; multiplication, Difference
Multiplication; Division and division. Subtractio
S3C3PO2 Symbol; Unknown Quantities Use a symbol to represent an unknown quantity in a given n
context. Commutativ
e property
S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using Zero property
and addition multiplication facts. Associativ
multiplication facts e property
S5C2PO2 Relevant, Missing and Identify relevant information related to the solution to a Regroup
Extraneous problem. Estimate
Information Round
Identify missing information related to the solution Front end
to a problem. estimatio
n
Identify extraneous information related to the solution Friendly/
to a problem. Compatibl
e numbers
S5C2PO6 Mathematical Information; Summarize mathematical information. Clustering
Reasoning; Conclusions Relevant
Explain reasoning of mathematical informatio
n Missing
information. Draw conclusions of informatio
n
mathematical information. Extraneou
s
informatio
n
Draw conclusion


Quarter 1
Unit Name and Description: Data Analysis

Cluster 2

Data can be collected, organized and analyzed to help us How can we collect, organize, and display data?
make valid inferences, decisions, and arguments in real
world situations. What types of data would you collect, organize and

display? What conclusions can you make from data?
AZ Standard Essential Learning Key Summative
Knowledge Skills Vocabulary Assessment
S2C1PO2 Frequency tables; Formulate and answer questions by interpreting Frequency
Single bar graphs; and analyzing displays of data, including tables Single
Single line graphs frequency tables, single bar graphs, or single bar graphs
line graphs. Single line
S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is graphs Data
Question; reasonable. Record
Mathematically Correct Arrays
Charts
Analyze and evaluate whether a solution is Systematic
mathematically correct. lists Counting
Analyze and evaluate whether a solution
answers the question.
S2C1PO1 Frequency tables; Single Collect, record, organize, and display data using
bar graphs; Single line frequency tables
graphs single bar graphs
single line graphs.


S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting
Possibilities; Arrays; problems
Charts; Systematic lists; using arrays, charts, and systematic lists.
Conclusions;
Representations Draw conclusions from these representations.
S2C3PO2 Multiplication principle Solve a variety of problems based on the
of counting multiplication principle of counting.

S5C2PO6* Mathematical information; Summarize mathematical information
Reasoning; Conclusions
Draw conclusions of mathematical

information. Defend conclusion of


Quarter 2
Unit Name and Description: Multiplication & Division

Cluster 3

Multiplication and division is the grouping and ungrouping of objects How are multiplication and division alike?
using patterns to solve everyday real world problems.
What happens to the value of a number when you multiply it?
There is an inverse relationship between multiplication and division.
How might you use multiplication or division to solve problems in
the real world?
S1C2PO3 Multiplication and Demonstrate the concept of multiplication and Multiplication
Division; Concept; division using multiple models. Division
Models Equal groups
S1C1PO4* Sets of Whole Numbers Sort whole numbers into sets and justify the sort. Multiplication
Array
S1C2PO2 Word Problems; Addition; Create word problems based on addition, subtraction, Factors
Subtraction; multiplication and division. Product
Multiplication; Division Multiply
Solve word problems based on addition, Multiples
subtraction, multiplication and division. Divisibility
S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts Inverse
Fluency through 10. operations
Operation
s


S1C2PO5 Multiplication and Division; Apply the concept of multiplication and division as inverse Identity property
Inverse operations operations to solve problems. Zero property

Interpret the concept of multiplication and division as Commutative
inverse operations to solve problems. property
Arrays
S1C2PO6* Whole Numbers; Operations; [Compare] the effect of operations (multiplication and Charts
Effect; Multiplication; Division division) Systematic
Whole Numbers Operations; on the size of whole numbers. lists
S1C2PO7 Commutative, Zero and Identity Apply commutative, identity and zero properties to Numerical
Properties; Division multiplication. sequence

Apply the identity property to division.
S2C3PO1 Counting Problems; Possibilities; Represent all possibilities for a variety of counting
Arrays; Charts; Systematic problems
lists; Conclusions; using arrays, charts, and systematic lists.
Representations
Draw conclusions from these representations.
S3C1PO2 Numerical Sequence Rule Explain the rule for a given numerical sequence.

Verify that the rule for a given numerical sequence works.

S5C2PO3* Strategies; Problems Select and use one or more strategies to efficiently solve
the
problem.

Justify the strategy (ies) used to efficiently solve the
S5C2PO6* Mathematical Information; Summarize mathematical information.
Explain reasoning of mathematical

information. [Defend] conclusions of


S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable.
Question;
Mathematically Correct Analyze and evaluate whether a solution is
mathematically correct.




Quarter 2
Unit Name and Description: Geometry

Cluster 3

Our environment is made up of 2 dimensional & 3 dimensional figures. Why is it important to understand 2 and 3-dimensional figures?

The attributes of 2 dimensional & 3 dimensional figures can help us How do you describe a 2- or 3-dimensional figure using its attributes?
describe the environment and solve real-life problems.

S4C1PO4 Two and three-dimensional Describe and compare attributes of two- and Attributes
Figures three- dimensional figures. 2-dimensional
3-
S1C2PO6 Whole Numbers; Operations; [Compare] the effect of operations (multiplication and dimensional
Effect; Multiplication; Division division) on the size of whole numbers. Similar
Figures
S4C1PO1 Sequences of 2-Dimensional [Create] sequences of 2-dimensional figures created by Sequence
Figures; Number of sides; increasing the number of sides, changing size or Sphere
Size; Orientation changing orientation. Cube
Cone
S4C2PO2 Symmetry; 2-dimensional figure Identify all lines of symmetry in a 2-dimensional figure. Cylinder
Pyramid
Justify all lines of symmetry in a 2-dimensional figure. Rectangular
prism
Translations
Reflections
Rotation



S4C4PO4 Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Line of symmetry
figure; Model model. Symmetrical
Area
Perimete
r Array
Square unit(s)

S4C4PO5 Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures.

Calculate perimeter of 2-dimensional figures.
S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve
the
problem.


S5C2PO7 Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable.
Question;




Quarter 2
Unit Name and Description: Measurement

Cluster 4

Measurement is assigning a numerical unit to an attribute of a real What are some examples of when you might need to determine the
world object. correct unit of measurement?

There are appropriate units of measurement to use in different What are some different ways of measuring an object?
situations.
Why would we measure the area or perimeter of 2-dimensional objects?

When would you need to find the area or perimeter of 2-dimensional

objects? What might be some tools you can use to measure objects?
S4C4PO2 Length, Weight and Apply measurement skills to measure length, weight Measure
Capacity; Measurement and Length
Skills; US Customary units capacity using US Customary units. Weight
S1C3PO1* Estimation; Situation; Make estimates appropriate to a given situation or Capacity
Computation; Whole numbers computation with whole numbers. US
Customary
S4C4PO3 Conversions; Length; Weight; Convert units of length, weight, and capacity units
Capacity inches or feet to yards, Equal groups
ounces to pounds, and Multiplication
cups to pints, pints to quarts, quarts to gallons. Array
Factors
Product
Commutativ
e



S4C4PO4* Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Property
figure; Model model. Multiply
Elapsed
time Hours
Minutes
S4C4PO5* Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures. Half hours
Quarter Hour
Calculate perimeter of 2-dimensional figures. Cup
S2C1PO2 Frequency tables; Single bar Formulate and answer questions by interpreting and Foot
graphs; Single line graphs analyzing displays of data, including frequency tables, Pint
single bar graphs, or single line graphs. Miles
Poun
d
S2C1PO1 Frequency tables; Single bar Collect, record, organize, and display data using Ruler
graphs; Single line graphs • Frequency tables Weight scale
• Single bar graphs Measuring cup
• Single line graphs Inch
Half inch
S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently solve Yard
the Quart
problem. Gallon
Ounce
Justify the strategy (ies) used to efficiently solve the Area
S5C2PO6* Mathematical Information; Summarize mathematical information. Perimete
Reasoning; Conclusions r Array
Explain reasoning of mathematical Square unit(s)
2-Dimensional


S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable.
Question;



Quarter 2
Unit Name and Description: Patterns, Algebra, & Functions

Cluster 5

Patterns occur everywhere in nature. Why are finding patterns

Patterns can be recognized, generalized, and extended with important? Where might you find
words and symbols.
patterns?
Variables are symbols that take the place of numbers or ranges of
How can two or more numbers be related?
numbers. Functions can show the relationship between two sets of
How do patterns help you think mathematically?
numbers.
AZ Essential Learning Summative
Key Vocabulary
Standard Knowledge Skills Assessment
S3C2PO1 Relationship between two Recognize a relationship between two quantities, Quantities
quantities; Chart; Table; given by a chart, table or graph, in which the Chart
Graph; quantities change Table
Words; Pictures; Expressions proportionally, using words, pictures or expressions. Graph
Pattern
Describe a relationship between two quantities, Function
given by a chart, table or graph, in which the Add
quantities change proportionally, using words, Addition
S1C2PO2* Word Problems; pictures, or expressions.
Create word problems based on addition, subtraction, Subtract
Addition; Subtraction; multiplication, Subtractio
Multiplication; Division and division. n
Equivalent
Unknown quantity



S1C1PO4 Sets of Whole Numbers Sort whole numbers into sets and justify the sort. Solve
Combinations

S3C1PO2 Numerical Sequence Rule Explain the rule for a given numerical sequence.

Verify that the rule for a given numerical sequence works.

S3C2PO2 Whole Number Relationships; Translate
Representations

S5C2PO1 Problem Situations; Analyze a problem situation to determine the question(s)
Questions to be
answered.

S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently solve
the problem.

problem.
S5C2PO5 Problem Situations; Numbers; Represent a problem situation using any combinations of
Pictures; Physical objects; words, numbers, pictures, physical objects or symbols.
Symbols


S5C2PO6* Mathematical Summarize mathematical information.
Information; Reasoning;
Conclusions Explain reasoning of mathematical



Quarter 3
Unit Name and Description: Fractions

Cluster 6

Fractions represent equal parts or equal-sized portions of a whole or When might you use fractions?
set.
How are parts of a whole

represented? How are parts of a

set represented?

What does it mean to be close to a whole?
S1C1PO5 Benchmark Fractions; Fair Express benchmark fractions as fair sharing, Fractions
sharing; Parts of a whole; parts of a whole, or parts of a set. Numerator
Parts of a set Denominator
S1C1PO6 Benchmark Fractions Compare benchmark fractions.

Order benchmark fractions.

S5C2PO4 Problem Solving; Strategies Determine whether a problem to be solved is
similar to
previously solved problems.

Identify possible strategies for solving the problem.



S5C2PO5* Problem Situations; Numbers; Represent a problem situation using any combinations of
Pictures; Physical objects; words, numbers, pictures, physical objects or symbols.
Symbols




Quarter 3
Unit Name and Description: Number Sense, Addition & Subtraction

Cluster 7

Numbers can be represented in many ways and are used to solve Why is it important to learn place
everyday problems using a variety of methods.
value? How can numbers be
There are relationships between numbers.
represented?
The location of a digit determines its place value.
What is the difference between comparing and ordering whole
S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number Ones
Numbers; Models through six digits by constructing models and Tens
using numbers. Hundreds
S1C1PO1 Whole Numbers; Multiple [Model] whole numbers through six digits using and One Thousand
Representations connecting multiple representations. Ten Thousands
Hundred
[Analyze] whole numbers through six digits using Thousands
and connecting multiple representations. Standard Form
S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying Expanded Form
the Word Form
concept of place value. Ordinal
Numbers Equal
Order whole numbers through six digits by To
S1C1PO3 Money; Coins; Bills Count money using coins and bills to Less Than
Greater
$100.00. Represent money using coins Than Not
Equal To



S1C2PO1 Whole Numbers Add whole number to four digits. Order
Value
Subtract whole numbers to four digits. Place
Sum
Addend
S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Addition
Addition; Subtraction; multiplication, Difference
Multiplication; Division and division. Subtractio
S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using n
and addition multiplication facts. Commutativ
multiplication facts e property
S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or Zero property
Computation; computation with whole numbers. Associativ
Whole numbers e property
Regroup
Estimate
Round
S5C2PO2 Relevant, Missing and Identify relevant information related to the solution to a Front end
Extraneous problem. estimatio
Information n
Identify missing information related to the solution Friendly/
to a problem. Compatibl
e numbers
Identify extraneous information related to the solution Clustering
to a problem. Relevant
informatio
S5C2PO6 Mathematical Information; Summarize mathematical information. n Missing
Reasoning; Conclusions informatio
Explain reasoning of mathematical n
Extraneou
information. Draw conclusions of s
informatio
mathematical information. n



S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting
Possibilities; Arrays; problems
Charts; Systematic lists; using arrays, charts, and systematic lists.
Conclusions;
Representations Draw conclusions from these representations.
S2C3PO2 Multiplication principle Solve a variety of problems based on the
of counting multiplication principle of counting.

S1C2PO3 Multiplication and Demonstrate the concept of multiplication and
Division; Concept; division using multiple models.
Models

S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts
Fluency through 10.

S2C3PO1 Counting Problems; Represent all possibilities for a variety of counting
Possibilities; problems
Arrays; Charts; using arrays, charts, and systematic lists.
Systematic lists;
Conclusions; Draw conclusions from these representations.
S4C4PO1 Elapsed Time; Months; [Assess] elapsed time
Calendar; across months using a calendar
Hours; Half hours; Clock by hours and half hours using a clock.

S5C2PO6* Mathematical information; Summarize mathematical information
Draw conclusions of mathematical

information. Defend conclusion of


Quarter 3
Unit Name and Description: Geometry

Cluster 8

Our environment is made up of 2 dimensional & 3 dimensional figures. Why is it important to understand 2 and 3-dimensional figures?

The attributes of 2 dimensional & 3 dimensional figures can help us How do you describe a 2- or 3-dimensional figure using its attributes?
describe the environment and solve real-life problems.

S4C1PO4 Two and three-dimensional Describe and compare attributes of two- and Attributes
Figures three- dimensional figures. 2-dimensional
3-
S4C1PO2 Similar Figures [Compare] similar figures. dimensional
Similar
Figures
S4C1PO3 3-Dimensional Figures; Identify and describe 3-dimensional figures including their Sequence
Relationship; Real world relationship to real world objects: sphere, cube, cone, Sphere
objects; Sphere; Cube; Cone; cylinder, pyramids, and rectangular prisms. Cube
Cylinder; Cone
S4C2PO1 Translation; Reflection; Rotation; Identify a translation and model its effect on a 2- Cylinder
Model dimensional Pyramid
figure. Rectangular
prism
Identify a reflection and model its effect on a 2- Translations
S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve Reflections
the Rotation
problem.



S5C2PO6* Mathematical Information; Summarize mathematical information. Line of symmetry
Reasoning; Conclusions Explain reasoning of mathematical information. Symmetrical
[Defend] conclusions of mathematical information. Area
Perimete
r Array
Square unit(s)

S5C2PO7 Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable.
Question;




Quarter 3
Unit Name and Description: Patterns, Algebra, & Functions

Cluster 9

Patterns occur everywhere in nature. Why are finding patterns

Patterns can be recognized, generalized, and extended with important? Where might you find
words and symbols.
patterns?
Variables are symbols that take the place of numbers or ranges of
How can two or more numbers be related?
numbers. Functions can show the relationship between two sets of
How do patterns help you think mathematically?
numbers.
Key Vocabulary
S3C2PO1 Relationship between two Recognize a relationship between two quantities, Quantities
quantities; Chart; Table; given by a chart, table or graph, in which the Chart
Graph; quantities change Table
Words; Pictures; Expressions proportionally, using words, pictures or expressions. Graph
Pattern
Describe a relationship between two quantities, Function
given by a chart, table or graph, in which the Add
quantities change proportionally, using words, Addition
*S1C2PO1 Whole Numbers pictures, or expressions. digits.
Add whole number to four Subtract
Subtractio
Subtract whole numbers to four digits. n
Equivalent
Unknown quantity



S3C1PO1 Numerical Sequence; Missing Recognize missing terms in a numerical sequence. Equation
terms Equals
Describe missing terms in a numerical Rule

sequence. Extend missing terms in a

numerical sequence. Create missing terms

in a numerical sequence. Find missing

S3C3PO2 Symbol; Unknown Quantities Use a symbol to represent an unknown quantity in a given
context.

S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using
and addition multiplication facts.
multiplication facts
Create one-step equations that can be solved using
addition multiplication facts.

*S5C2PO1 Problem situations; Questions Analyze a problem situation to determine the question(s)
to be
answered.



*S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve
the
problem.

*S5C2PO5 Problem Situations; Numbers; Represent a problem situation using any
Pictures; Physical objects; combinations of
Symbols words, numbers, pictures, physical objects or symbols.
*S5C2PO6 Mathematical Information; Summarize mathematical information.

information. [Defend] reasoning of

*S5C2PO7 Solutions; Reasonable; Question; Analyze and evaluate whether a solution is reasonable.
Mathematically Correct
Analyze and evaluate whether a solution is




Quarter 3
Unit Name and Description: Discrete Mathematics

Cluster 10

Vertex-edge graphs are used to model and solve problems What conclusions can you make from vertex-edge
involving paths, networks, and relationships.
graphs? Why do we use vertex-edge graphs?
Vertex-edge graphs can represent a real-world maps that helps us
find routes and paths. Why is it important to find all the possible combinations of a given
set of items?
Systematic lists, charts, and arrays help us keep track of finding all
possible combinations of a given set of items.
Key Vocabulary
S2C4PO2 Vertex-Edge Graphs; Investigate properties of vertex-edge graphs Vertex-edge
Circuits; Weights; Vertices circuits in a graph graphs
weights on edges Circuits
shortest path between two vertices. Weight
s Paths
S2C3PO1* Counting Problems; Possibilities; Represent all possibilities for a variety of counting Vertice
Arrays; Charts; Systematic problems s
lists; Conclusions; using arrays, charts, and systematic lists. Arrays
Representations Charts
Draw conclusions from these representations. Systematic
S2C4PO1 Color Mapping Color complex maps using the least number of lists Relevant
colors and justify the coloring. Extraneous
Conjectures
Data



S2C4PO3 Vertex-Edge Graphs; Problems Solve problems using vertex-edge graphs. Experiment
Coloring maps
[Create] problems using vertex-edge graphs. Edge
S5C2PO1* Problem situations; Questions Analyze a problem situation to determine the Vertex
question(s) to
be answered.
S5C2PO2* Relevant, Missing and Extraneous Identify relevant information related to the solution to a
Information problem.

Identify missing information related to the solution
to a problem.

Identify extraneous information related to the solution
to a problem.

S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently
solve the
problem.

Justify the strategy (ies) used to efficiently
solve the problem.
S5C2PO4* Problem Solving; Strategies Determine whether a problem to be solved is
similar to
previously solved problems.

Identify possible strategies for solving the problem.
Reasoning;
Conclusions Explain reasoning of mathematical

information. [Defend] reasoning of



S5C2PO8 Conjectures; Data; Explorations; Make conjectures based on data (or information)
Experiments collected
from explorations and experiments.

Test conjectures based on data (or information)
collected from explorations and experiments.

[Evaluate] conjectures based on data (or information)
collected from exploration and experiments.



Quarter 4
Unit Name and Description: Multiplication and Division

Cluster 11

There are multiple strategies to multiply and divide whole How are multiplication and division

numbers. There is a relationship between multiplication and related? When might you use

division. multiplication?

When might you use division?

What is the value of learning multiplication and division?
M4S1C2PO3 Multiplication and Division Demonstrate fluency of multiplication facts through Multiplication
Fluency facts through 12 12. Division
Factor
Demonstrate fluency of division facts through 12. Multiple
Product
M4S1C2PO2 Multiple Strategies of [Develop] multiple strategies to multiply whole numbers Quotient
Multiplication two-digit by two-digit and Divisor
multi-digit by one-digit. Dividend
Array
M4S1C2PO4 Multiple Strategies of Division [Develop] multiple strategies to divide whole numbers. Digit
Whole number
Estimate
Fraction



M4S1C3PO2 Estimates; Given situation; [Develop] estimates appropriate to a given situation or Numerator
Computation with whole computation with whole numbers and fractions. Denominator
numbers and fractions
M4S5C2PO5 Problem situation; Combination Represent a problem situation using any combination of
of words, numbers, pictures, physical objects, or symbols.
words, numbers, pictures,


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