1. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 1
Unit Name and Description: Multiplication and Division/ Number Puzzles and Multiple Towers
Unit Cluster: 1
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic methods are used to explore a variety of real world problem How might we use algebra to solve real life problems?
solving situations.
How are numbers related?
Numbers can be represented in many ways.
Operations have inverse relationships.
AZ Essential Learning
Standard Knowledge Skills
S1C1PO2 Prime; Composite; Factors; Differentiate between prime and composite
Multiplies; Whole Numbers numbers; differentiate between factors and
multiples for whole numbers.
Key Summative
Vocabulary Assessment
S1C2PO2 Multi-digit; Whole Numbers Multiply multi-digit whole numbers.
S1C2PO3 Division; Multi-digit whole Divide multi-digit whole numbers by whole number
numbers; Divisors; Remainders divisors with and without remainders.
S1C2PO4 Properties of Associative; Apply the Associative, Commutative, and Distributive multiplication,
Distributive; Computation properties to solve numerical problems.
division,
* = 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

2. 5th Grade Math Curriculum Map
Isaac School District No. 5
S2C3PO1 Relationships; Multiplication Analyze relationships to create representations and factors,
principle of counting make connections to the multiplication principle of
product
counting.
multiplication
S1C3PO1 Estimates; Whole Numbers; Make estimates appropriate to a given situation or combinations,
Fractions; Decimals; computation with whole numbers, fractions, and multiples,
Computation decimals. Prime and
composite
numbers,
representation,
less than, greater
than
dividend, divisor,
quotient,
* = POs previously introduced Bold = Priority PO 2
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

3. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 1
Unit Name and Description: 3-D Geometry and Measurement/ Prisms and Pyramids
Unit Cluster: 2
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic methods are used to explore a variety of real world problem How might we use algebra to solve real life problems?
solving situations.
How are numbers related?
Numbers can be represented in many ways.
Operations have inverse relationships.
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S3C1PO1 Numerical sequence; Recognize, describe, create, and analyze a volume,
Fractions; Decimals; numerical sequence involving fractions and rectangular
Addition; Simplest Form decimals using addition and subtraction. prism, Cubic
S1C3PO1* Estimates; Whole Numbers; Make estimates appropriate to a given situation or centimeter/meter
Fractions; Decimals; computation with whole numbers, fractions, and s, linear, length,
Computation decimals. width, height,
pyramids,
S1C2PO2* Multi-digit; Whole Numbers cylinders, cones,
Multiply multi-digit whole numbers.
S1C2PO3* Division; Multi-digit whole Divide multi-digit whole numbers by whole number
numbers; Divisors; Remainders divisors with and without remainders.
* = POs previously introduced Bold = Priority PO 3
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

4. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 1
Unit Name and Description: Addition, Subtraction, and Number System/ Thousands of Miles, Thousands of Seats
Unit Cluster: 3
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic methods are used to explore a variety of real world problem How might we use algebra to solve real life problems?
solving situations.
How are numbers related?
Numbers can be represented in many ways.
Operations have inverse relationships.
Essential Learning
AZ Key Summative
Standard Knowledge Skills Vocabulary Assessment
S3C3PO1 Two-step equation; inverse Create and solve two-step equations that can be closest estimate,
operations; whole numbers solved using inverse operations with whole
difference,
numbers.
million, billion,
trillion,
Subtracting in
parts, Adding up,
S1C3PO1* Estimates; Whole Numbers; Make estimates appropriate to a given situation or subtracting back,
Fractions; Decimals; computation with whole numbers, fractions, and distance,
Computation decimals. algorithm,
* = POs previously introduced Bold = Priority PO 4
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

5. 5th Grade Math Curriculum Map
Isaac School District No. 5
S1C2PO4 Properties of Associative; Apply the Associative, Commutative, and Distributive
Distributive; Computation properties to solve numerical problems.
S2C3PO1 Relationships; Multiplication Analyze relationships to create representations and
principle of counting make connections to the multiplication principle of
counting.
* = POs previously introduced Bold = Priority PO 5
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

6. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 2
Unit Name and Description: Fractions and Percents/ What’s that Portion?
Unit Cluster: 4
Big Ideas/Enduring Understandings Essential Question(s)
Equivalent relationships exist among numbers. How are numbers related to each other?
Numbers can be represented in many ways. What number forms are appropriate to use in a given situation?
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S1C1PO4 Positive Fractions; Compare and order positive fractions, decimals, and fractions,
Decimals; Percents percents. decimals,
percents,
S1C1PO1 Equivalency between Determine equivalence by converting between benchmark
equivalent,
Fractions; Decimals; fractions, decimals, and percents.
Percents comparing and
ordering,
S1C2PO1 Add; Subtract; Decimals; Add and subtract decimals though thousandths and
Thousandths; Fractions; fractions expressing solutions in simplest form.
Simplest form
S1C1PO5 Ratio; Unit Rates; Problem in Use ratios and unit rates to model, describe, and extend
context problems in context.
S3C1PO1* Numerical sequence; Recognize, describe, create, and analyze a numerical
Fractions; Decimals; sequence involving fractions and decimals using addition
Addition; Simplest Form and subtraction.
* = POs previously introduced Bold = Priority PO 6
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

7. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 2
Unit Name and Description: 2D Geometry and Measurement / Measuring Polygons
Unit Cluster: 5
Big Ideas/Enduring Understandings Essential Question(s)
Attributes of 2D and 3D figures can be used to solve real world How do 2D and 3D figures relate to the real world?
problems.
Why do we measure?
Various forms of measurement exist in life.
Why would we calculate area and perimeter?
Space can be calculated using area/perimeter.
How might we solve problems using area and perimeter?
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S4C4PO4 Properties of 2-dimensional Solve problems involving the area of 2-dimensional right angle, acute
figures; Parallelograms; figures by using the properties of parallelograms angle, obtuse
Triangles; Problems involving and triangles. angle,
area equilaterals,
scalene and
S4C1PO1 Attribute of 2-dimensional Draw and label 2-dimensional figures given specific isosceles
figures; Angle measure; Side attributes including angles measure and side length. triangles,
length quadrilaterals,
parallel,
S4C1PO2 Properties of triangles; Solve problems by understanding and applying the trapezoid,
Sum of interior angles=180° property that the sum of the interior angles of a triangle parallelograms,
is 180°
* = POs previously introduced Bold = Priority PO 7
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

8. 5th Grade Math Curriculum Map
Isaac School District No. 5
S4C4PO3 Angles Measure angles between 0 and 360 degrees. rectangle,
Degrees-0; 360 degrees rhombus, square,
supplementary,
S4C1PO4 Attributes of 2-dimensional Compare attributes of 2-dimensional figures with 3- convex, regular
figures; 3-dimensional figures; dimensional figures by drawing and constructing nets polygons,
Nets; Models and models. hexagon,
octagon,
pentagon,
S4C1PO3 Quadrilaterals properties Classify quadrilaterals by their properties. decagon,
heptagon, interior
angles, exterior
S4C4PO5 Area and perimeter; Regular Solve problems involving area and perimeter of regular angles,
polygons; Irregular Polygons; and irregular polygons using re-allotment of square dimensions,
Square Units units. perimeter, area,
similar,
S4C4PO2 Appropriate measure; State an appropriate measure and degree of accuracy in
Degree of accuracy context a given context.
* = POs previously introduced Bold = Priority PO 8
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

9. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 2
Unit Name and Description: Decimals, Fractions, and Percents/ Decimals on Grids and Number Lines
Unit Cluster: 6
Big Ideas/Enduring Understandings Essential Question(s)
Real world data can be represented through integers. In what situations would it be necessary to interpret integers?
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S1C1PO4* Positive Fractions; Compare and order positive fractions, decimals, and percents. fractions,
Decimals; Percents decimals,
S1C1PO1* Equivalency between Determine equivalence by converting between benchmark fractions, percents,
Fractions; Decimals; decimals, and percents. tenths,
Percents thousandths,
hundredths,
number line,
S1C3PO1* Estimates; Whole Make estimates appropriate to a given situation or computation with numerator,
Numbers; Fractions; whole numbers, fractions, and decimals. denominator,
Decimals; Computation repeating
decimal,
S1C2PO1* Add; Subtract; Add and subtract decimals though thousandths and fractions
Decimals; expressing solutions in simplest form.
Thousandths;
(There is no subtraction of decimals in this unit, please supplement.)
Fractions;
* = POs previously introduced Bold = Priority PO 9
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

10. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 3
Unit Name and Description: Multiplication and Division/ How Many People? How Many Teams?
Unit Cluster: 7
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic methods are used to explore a variety of real world problem How might we use algebra to solve real life problems?
solving situations.
How are numbers related?
Numbers can be represented in many ways.
Operations have inverse relationships.
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S1C2PO3* Division; Multi-digit whole Divide multi-digit whole numbers by whole number algorithm,
numbers; Divisors; divisors with and without remainders.
Remainders
S1C2PO4* Properties of Associative; Apply the Associative, Commutative, and Distributive
Distributive; Computation properties to solve numerical problems.
S1C2PO2* Multi-digit; Whole Numbers Multiply multi-digit whole numbers.
S1C3PO1* Estimates; Whole Numbers; Make estimates appropriate to a given situation or
Fractions; Decimals; computation with whole numbers, fractions, and
Computation decimals.
S2C3PO1* Relationships; Multiplication Analyze relationships to create representations and
principle of counting make connections to the multiplication principle of
counting.
* = POs previously introduced Bold = Priority PO 10
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

11. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 3
Unit Name and Description: Patterns, Functions, and Change/ Growth Patterns
Unit Cluster: 8 (Please refer to cluster 10 prior to teaching Unit Cluster 9)
Big Ideas/Enduring Understandings Essential Question(s)
Space can be calculated using area/perimeter. Why would we calculate area and perimeter?
Patterns can fluctuate over time. How might we solve problems using area/perimeter?
How might patterns fluctuate over time?
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S3C4PO1 Patterns of change; Describe patterns of change including constant rate and rate of change,
constant rate; Increasing increasing or decreasing rate. steepness,
rate; Decreasing rate steady rate, area,
S4C4PO5 Area and perimeter; Regular Solve problems involving area and perimeter of regular and perimeter,
polygons; Irregular irregular polygons using re-allotment of square units.
Polygons; Square Units
S2C1PO2 Displays of data; Multi-bar Formulate and answer questions by interpreting and
graph; Double line graph analyzing displays of data, including multi-bar graphs or
double line graphs.
S3C1PO1* Numerical sequence; Recognize, describe, create, and analyze a numerical
Fractions; Decimals; sequence involving fractions and decimals using addition
Addition; Simplest Form and subtraction.
* = POs previously introduced Bold = Priority PO 11
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

12. 5th Grade Math Curriculum Map
Isaac School District No. 5
S3C3PO1* Two-step equation; Create and solve two-step equations that can be solved
inverse operations; whole using inverse operations with whole numbers.
numbers
Quarter: 3 (Thru beginning of Quarter 4)
Unit Name and Description: How Long Can You Stand on One Foot? Data Analysis and Probability
Unit Cluster: 9
Big Ideas/Enduring Understandings Essential Question(s)
Probability is the likelihood of an event to occur. What is the difference between probability and a guess?
Probability can be represented in various forms. Why do we use more than one form to represent probability?
Mathematical methods can be used to maximize efficiency. Why is it important to take the most efficient path?
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
* = POs previously introduced Bold = Priority PO 12
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

13. 5th Grade Math Curriculum Map
Isaac School District No. 5
S2C2PO2 Probability; Data; Explore probability when performing experiments by probability,
Experiments; Multiple • Predicting the outcomes experiments,
repetitions
• Recording data
• Comparing outcomes of the experiment to predictions
• Comparing the results of multiple repetitions of the
experiment
S2C1PO3 Mean; Median; Mode; Produce mean, median, and range to analyze describe and
Range; Data describe the distribution of a given data set.
(This is a Supplemental PO to be taught with this unit..)
S2C1PO1 Display of data; Multi-bar Collect, record, organize, and display data using multi-bar graphs
graph; Double line graph and double line graphs.
S2C1PO2 Displays of data; Multi- Formulate and answer questions by interpreting and analyzing
bar graph; Double line displays of data, including multi-bar graphs or double line graphs.
graph
S2C2PO1 Theoretical Probability; Describe theoretical probability of events and represent the
Fraction; Decimal; probability as a fraction, decimal, or percent. (Additional supplementation is
Percent necessary)
* = POs previously introduced Bold = Priority PO 13
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

14. 5th Grade Math Curriculum Map
Isaac School District No. 5
Quarter: 3
Unit Name and Description: Additional Supplemental Teaching Days
Cluster: 10
Big Ideas/Enduring Understandings Essential Question(s)
AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S1C2PO5 Numerical Expressions; Order Simplify numerical expressions (including fractions (for your use)
of operations; Symbols; and decimals) using the order of operations with or
Whole Numbers without grouping symbols.
S1C1PO3 Integers; Number line Develop and interpret integers on a number line. (Additional
supplementation is necessary)
S1C1PO6 Numbers; Positive; Negative Express or interpret positive and negative numbers in
context. (Additional supplementation is necessary)
S2C3PO2 Multiplication principle of Solve a variety of counting problems and explain the
counting multiplication principle of counting.
* = POs previously introduced Bold = Priority PO 14
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

15. 5th Grade Math Curriculum Map
Isaac School District No. 5
S2C4PO1 Properties of Vertex edge Investigate properties of vertex edge graphs
graphs; Degree of vertex • Euler paths
Euler paths; Euler Circuits
• Euler Circuits
• Degree of a vertex
S2C4PO2 Euler paths; Euler circuits Solve problems related to Euler paths and circuits.
S4C4PO1 Elapsed Time Solve problems using elapsed time.
* = POs previously introduced Bold = Priority PO 15
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

16. 5th Grade Math Curriculum Map
Isaac School District No. 5
Process Objectives: MUST BE Integrated throughout Clusters
Big Ideas/Enduring Understandings Essential Question(s)
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
Extraneous problem.
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.
* = POs previously introduced Bold = Priority PO 16
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012

17. 5th Grade Math Curriculum Map
Isaac School District No. 5
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,
Reasoning explain, 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.
* = POs previously introduced Bold = Priority PO 17
Italics = POs taught at earlier grade level [ ] = Increased Skill Rigor Isaac School District
Underlining = Cognitive rigor 1/6/2012