3rd grade math curriculum map 2011 2012-1

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

Quarter 1
Unit Name and Description: Number Sense, Addition & Subtraction/ Trading Stickers, Combining Coins

Unit 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 value?
everyday problems using a variety of methods.
How can numbers be represented?
There are relationships between numbers.
What is the difference between comparing and ordering whole
The location of a digit determines its place value. numbers?

AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number through six Ones
Numbers; Models digits by constructing models and using numbers. Tens
Hundreds
S1C1PO1 Whole Numbers; [Model] whole numbers through six digits using and One Thousand
Multiple Representations connecting multiple representations. Ten Thousands
Hundred
[Analyze] whole numbers through six digits using and Thousands
connecting multiple representations. Standard Form
Expanded Form
S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying the Word Form
concept of place value. Ordinal Numbers
Equal To
Order whole numbers through six digits by applying the Less Than
concept of place value. Greater than

* = POs previously introduced Bold = Priority PO 1
Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

S1C1PO3 Money; Coins; Bills Count money using coins and bills to $100.00. Not Equal to
Represent money using coins and bills to $100.00. Order
Value
Place Sum
Addend Addition
S1C2PO1 Whole Numbers Add whole number to four digits. Difference
Subtraction
Subtract whole numbers to four digits. Commutative
property
Zero property
Associative
S1C2PO2 Word Problems; Create word problems based on addition, subtraction, property
Addition; Subtraction; multiplication, and division.
Regroup
Multiplication; Division Estimate Round
Solve word problems based on addition, subtraction, Front end
multiplication, and division. estimation
S3C3PO2 Symbol; Unknown Quantities Use a symbol to represent an unknown quantity in a given Friendly/
context. Compatible
numbers
Clustering
S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using Relevant
and multiplication facts addition multiplication facts. information
Missing
Create one-step equations that can be solved using information
addition multiplication facts. Extraneous
information


Quarter 1
Unit Name and Description: Data Analysis/ Surveys and Line Plots

Unit 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?
S2C1PO2 Frequency tables; Formulate and answer questions by interpreting and Frequency tables
Single bar graphs; analyzing displays of data, including frequency tables, Single bar graphs
Single line graphs single bar graphs, or single line graphs. Single line graphs
Data
S2C1PO1 Frequency tables; Collect, record, organize, and display data using Record
Single bar graphs;  frequency tables Arrays
Single line graphs  single bar graphs Charts
 single line graphs. Systematic Lists
Counting


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

S2C4PO1 Color Color complex maps using the least number of
Mapping colors and justify the coloring.


Quarter 1 (Thru the beginning of Quarter 2)
Unit Name and Description: Multiplication & Division/ Collection and Travel Stories
Unit 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?
AZ Essential Key Summative
Standard Learning Vocabulary Assessment
Knowledge Skills
S1C2PO3 Multiplication; 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
Factors
S1C2PO2 Word Problems; Addition; Create word problems based on addition, subtraction, Product
Subtraction; multiplication and division. Multiply
Multiplication; Multiples
Division Solve word problems based on addition, Divisibility
subtraction, multiplication and division. Inverse operations
S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts Operations
Fluency through 10. Identity property
Zero property
S1C2PO5 Multiplication and Division; Apply the concept of multiplication and division as inverse Commutative
Inverse operations operations to solve problems. property
Arrays
Interpret the concept of multiplication and division as Charts
inverse operations to solve problems.


S1C2PO6 Whole Numbers; [Compare] the effect of operations (multiplication and division) Systematic lists
Multiplication; Division on the size of whole numbers. Numerical
Whole Numbers Operations sequence
S1C2PO7 Commutative, Zero and Apply commutative, identity and zero properties to
Identity Properties; Division multiplication.

Apply the identity property to division.
S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting problems
Possibilities; Arrays; Charts; using arrays, charts, and systematic lists.
Systematic lists;
Conclusions 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.



Quarter 2
Unit Name and Description: Measurement
Unit Cluster 4a

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 capacity using US Customary units. Length
Skills; US Customary Weight
units Capacity
US Customary
S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or units
Computation; Whole numbers computation with whole numbers. Equal groups
Multiplication
Array
Factors
Product
Commutative


S4C4PO3 Conversions; Length; Weight; Convert units of length, weight, and capacity Property
Capacity  inches or feet to yards, Multiply
 ounces to pounds, and Elapsed time
 cups to pints, pints to quarts, quarts to gallons. Hours Minutes
Half hours
S4C4PO4 Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Quarter Hour
figure; Model model. Cup Foot Pint
Miles Pound
S4C4PO5 Perimeter; 2-dimensional Measure perimeter of 2-dimensional figures.
Ruler
figures
Weight scale
Calculate perimeter of 2-dimensional figures.
Measuring cup
S2C1PO2* Frequency tables; Single bar Formulate and answer questions by interpreting and Inch
graphs; Single line graphs analyzing displays of data, including frequency tables, Half inch
single bar graphs, or single line graphs. Yard Quart
Gallon Ounce
S2C1PO1* Frequency tables; Single bar Collect, record, organize, and display data using Area Perimeter
graphs; Single line graphs • Frequency tables
• Single bar graphs
• Single line graphs


Quarter 2
Unit Name and Description: Geometry/ Perimeter, Angles, and Area

Unit Cluster 4b

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 three- 2-dimensional
Figures dimensional figures. 3-dimensional
Similar Figures
S1C2PO6* Whole Numbers; Operations; [Compare] the effect of operations (multiplication and Sequence
Effect; Multiplication; Division division) on the size of whole numbers. Sphere
Cube
Cone
S4C1PO1 Sequences of 2-Dimensional [Create] sequences of 2-dimensional figures created by Cylinder
Figures; Number of sides; increasing the number of sides, changing size or Pyramid
Size; Orientation changing orientation. Rectangular
prism
S4C4PO5* Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures. Translations
Reflections
Calculate perimeter of 2-dimensional figures. Rotation
Line of symmetry
Symmetrical
S4C1PO2 Similar Figures [Compare] similar figures (This is a Supplemental PO to be taught with
Area Perimeter
this unit..)
Array
Square unit(s)


S4C2PO2 Symmetry; 2-dimensional figure Identify all lines of symmetry in a 2-dimensional figure.

Justify all lines of symmetry in a 2-dimensional figure.
(This is a Supplemental PO to be taught with this unit..)

S2C4PO2 Vertex-Edge Graphs; Investigate properties of vertex-edge graphs
Circuits; Weights;  circuits in a graph
Vertices  weights on edges
 shortest path between two vertices.
(This is a Supplemental PO to be taught with this unit..)

S2C4PO3 Vertex-Edge Graphs; Problems Solve problems using vertex-edge graphs.
[Create] problems using vertex-edge graphs. (This is a
Supplemental PO to be taught with this unit..)



Quarter 2
Unit Name and Description: Multiplication and Division/ Equal Groups

Unit Cluster 5

Multiplication and division is the grouping and ungrouping of How are multiplication and division alike?
objects 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 Division; Demonstrate the concept of multiplication and division Quantities
Concept; Models using multiple models. Chart
Table Graph
S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Pattern Function
Addition; Subtraction; multiplication, and division. Add Addition
Multiplication; Division Subtract
S1C1PO4* Sets of Whole Numbers Solve wordnumbers into setson addition,the sort.
Sort whole problems based and justify subtraction, Subtraction
Equivalent
Unknown
quantity
S3C1PO2* Numerical Sequence Rule Explain the rule for a given numerical sequence. Solve
Combinations
Verify that the rule for a given numerical sequence works.


S3C2PO2 2 Whole Number
Quarter Translate between the different representations of whole
Relationships; number relationships, including symbolic, numerical, verbal or
Unit Name Representations
and Description: Patterns, pictorial. and Change/ Stories, Tables and Graphs
Functions
S4C4PO4* Area of Arrays; Rectangular Determine the area of a rectangular figure using an array
figure; Model
Unit Cluster 6 model.
Possibilities; using arrays, charts, and systematic lists.
Patterns occur everywhere in nature.
Arrays; Charts; Systematic Why are finding patterns important? Where might you find patterns?
S1C2PO5* lists; Conclusions;Division; and aw conclusions from these representations. as inverse
Patterns canMultiplication and
Dr
be recognized, generalized, Apply the concept of multiplication and division
extended with How can two or more numbers be related?
Inverse operations operations to solve problems.
words and symbols.
How do patterns help you think mathematically?
S1C2PO6*are symbols that take the place ofntompare] or concept of operations (multiplication and
Variables Whole Numbers; Operations; [C
I erpret the effect of multiplication and division as
numbers the ranges
of
Effect; Multiplication; Division division) on the size of whole numbers.
numbers. Functions can show the relationship between two sets of
S3C3PO1* Equivalent Forms of Whole Record equivalent forms of whole number through six digits
numbers. Numbers; Models by constructing models and using numbers.
AZ Essential Learning Summative
Key Vocabulary
Standard One-Step Equations;
S3C3PO3* Knowledge Solve simple one-step equations that can be solved using
Skills Assessment
S3C2PO1 Addition and between
Relationship addition multiplication facts.between two quantities, given
Recognize a relationship Quantities
multiplication facts
two quantities; Chart; by a chart, table or graph, in which the quantities change Chart
S4C4PO2* Table; Graph; Applyte one-step using words,measure length, weight and
Crea measurement skills that pictures or expressions.
proportionally, equations to can be solved using Table Graph
Length, Pictures;
Words; Weight and capacity using US Customary units. (This is a Supplemental PO to Pattern Function
Capacity; be taught with this unit..)
Expressions Describe a relationship between two quantities, given by Add Addition
Measurement Skills; a chart, table or graph, in which the quantities change Subtract
US Customary units proportionally, using words, pictures, or expressions. Subtraction
S4C4PO3* Conversions; Length; Convert units of length, weight, and capacity Equivalent
S1C2PO1” Weight; Capacity
Whole Numbers Add wholefeet to yards, digits.
inches or number to four Unknown quantity
 ounces to pounds, and Equations
Subtract pints, pints to quarts, quarts to gallons
cups to whole numbers to four digits. Equals
(This is a Supplemental PO to be taught with this unit..) Rule



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

Extend missing terms in a numerical sequence.

Create missing terms in a numerical sequence.

Find missing terms in a numerical sequence.

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

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


Quarter 3
Unit Name and Description: Fractions and Decimals/ Finding Fair Shares
Unit Cluster 7

Fractions represent equal parts or equal-sized portions of a whole 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, parts of a
sharing; Parts of a whole, or parts of a set.
whole; Parts of a set
S1C1PO6 Benchmark Fractions Compare and order benchmark fractions.

S1C1PO1* Whole Numbers; Multiple [Model] whole numbers through six digits using and
Representations connecting multiple representations.

[Analyze] whole numbers through six digits using and
connecting multiple representations.
S1C1PO2* Place value; Whole numbers Compare whole numbers through six digits by applying the
concept of place value.

Order whole numbers through six digits by applying the
concept of place value.


S1C1PO3* Money; Coins; Bills Count money using coins and bills to 100.00.

Represent money using coins and bills to 100.00.

S1C2PO1* Whole Numbers Add whole number to four digits.

Subtract whole numbers to four digits.

S1C2PO2* Word Problems; Create word problems based on addition, subtraction,
Addition; Subtraction; multiplication, and division.
Multiplication; Division
Solve word problems based on addition, subtraction,
multiplication, and division.
S1C3PO1* Estimation; Situation; Make estimates appropriate to a given situation or
Computation; computation with whole numbers.
Whole numbers

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.


Quarter 3
Unit Name and Description: Addition and Subtraction and the Number System 3/ How Many Hundreds? How Many
Miles?
Unit Cluster 8

Numbers can be represented in many ways and are used to solve How can two or more numbers be related?
everyday problems using a variety of methods.
How do patterns help you think mathematically?
There are relationships between numbers.
Why is it important to learn place value? How can numbers be
The location of a digit determines its place value. represented?

What is the difference between comparing and ordering whole
numbers?

S3C3PO1* Equivalent Forms of Whole Record equivalent forms of whole number Ones, tens,
Numbers; Models through six digits by construction models and hundreds, one
using numbers. thousand, ten
S1C1PO1” Whole Numbers; [Model] whole numbers through six digits using and thousands,
Multiple Representations connecting multiple representations. hundred
thousands,
S1C1PO2” Place value; Whole numbers [Analpare whole numbers through six digits using and the
Com yze] by applying standard form,
concept of place value. expanded form,
word form,
Order whole numbers through six digits by applying ordinal
the concept of place value.


S3C3PO3* One-Step Equations; Addition Solve simple one-step equations that can be solved using numbers, equal
and addition multiplication facts. to, less than ,
multiplication facts positive,
Create one-step equations that can be solved using negative,
addition multiplication facts. expressions,
estimate,
S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or
Computation; Whole numbers computation with whole numbers.

S1C2PO2* Word Problems; Addition; Create word problems based on addition, subtraction,
Subtraction; multiplication and division.
Multiplication; Division
Solve word problems based on addition,
subtraction, multiplication and division.


Quarter 3
Unit Name and Description: 3-D Geometry and Measurement/ Solids and Boxes
Unit Cluster 9

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-dimensional
S4C1PO2* Similar Figures [Compare] similar figures. Similar Figures
Sequence
Sphere
S4C1PO3 3-Dimensional Figures; Identify and describe 3-dimensional figures including their Cube Cone
Real world objects; Sphere; relationship to real world objects: sphere, cube, cone, Cylinder Pyramid
Cube; Cone; Cylinder; cylinder, pyramids, and rectangular prisms. Rectangular
Pyramids; Rectangular prism
Prisms Translations
Reflections
S4C2PO1 Translation; Reflection; Identify a translation and model its effect on a 2-dimensional Rotation
Rotation; Model figure. Line of symmetry
Symmetrical
Identify a reflection and model its effect on a 2-dimensional Area
figure.



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.
AZ Essential Learning Summative
Key Vocabulary
Standard Knowledge Skills Assessment
S2C4PO2* Vertex-Edge Graphs; Investigate properties of vertex-edge graphs Vertex-edge
Circuits; Weights;  circuits in a graph graphs
Vertices  weights on edges Circuits
 shortest path between two vertices. Weights Paths
Vertices Arrays
Charts
Possibilities; Arrays; Charts; using arrays, charts, and systematic lists.
Systematic lists
Systematic lists;
Relevant
Conclusions; Draw conclusions from these representations.
Extraneous
S2C4PO1* Color Mapping Color complex maps using the least number of colors and Conjectures Data
justify the coloring. Exploration
Experiment
Coloring maps
S2C4PO3* Vertex-Edge Graphs; Solve problems using vertex-edge graphs.
Problems
[Create] problems using vertex-edge graphs.



Process Objectives: MUST BE Integrated throughout Clusters


Essential Learning
Summative
AZ Standard Key Vocabulary
Assessment
Knowledge Skills
S5C2PO1
Analytical skills Analyze a problem situation to determine the
question(s) to be answered
Questions
S5C2PO2 Information; Identify relevant, missing and extraneous
Relevant; information related to the solution of a problem.
Extraneous

S5C2PO3 Mathematical Select and apply one or more strategies to
Strategies efficiently solve the problem and justify the
selection of the strategy.

S5C2PO4 Problem-Solving Determine whether a problem to be solved is
Strategies similar to previously solved problems, and
identify possible strategies for solving the
problem.


S5C2PO5 Representations; Represent a problem situation using any
Words; Numbers; combination of words, numbers, pictures,
Pictures; Physical physical objects, or symbols.
Objects; Symbols

S5C2PO6 Conclusions; Summarize mathematical information, explain,
Reasoning reasoning, and draw conclusions.

S5C2PO7 Problems Analyze and evaluate whether a solution is
reasonable, is mathematically correct, and
answers the questions being asked.

S5C2PO8 Data; Explorations; Make and test conjectures based on data
Experiments collected from explorations and experiments.


3rd grade math curriculum map 2011 2012-1

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3rd grade math curriculum map 2011 2012-1