Fourth Grade Math Curriculum Map

4th Grade Math Curriculum Map
Isaac School District No. 5

Quarter: 1
Unit Name and Description: Multiplication and Division

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

There are multiple strategies to multiply and divide whole numbers. How are multiplication and division related?

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

When might you use division?

What is the value of learning multiplication

and divison?

AZ Essential Learning Key Summative
Standard Knowledge Skills Vocabulary Assessment
S1C2PO3 Multiplication and division Demonstrate fluency of multiplication facts through Multiplication
fluency facts through 12 12.
Division
Demonstrate fluency of division facts through 12. Factor
Multiple
Product
Quotient
S1C2PO2 Multiplication strategies Use multiple strategies to multiply whole numbers Divisor
• Two-digit by two-digit and Dividend
Array
• Multi-digit by one-digit
Digit

* = 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

S1C2PO4 Division strategies; whole [Develop] multiple strategies to divide whole numbers. Whole number
numbers
Commutative
S1C2PO5 Associative and distributive Apply associative property to solve multiplication Property
properties; multiplication and problems. Associative
division problems
Property
Apply distributive property to solve multiplication and Distributive
division problems. Property
S1C1PO2 Factors and multiples; whole Compose and decompose whole numbers using factors.
numbers Parenthesis
Addition
Compose and decompose whole numbers using factors. Subtraction
S1C3PO1 Benchmarks; points of Use benchmarks as meaningful points of comparison for
comparison; whole numbers; Strategy
whole numbers, decimals and fractions.
decimals; fractions Justify
S1C1PO5 Simple ratios; problems Use simple rations to describe problems in context. Compose
Decompose
Similar
Ratios



Quarter: 1
Unit Name and Description: Data Analysis

Cluster: 2

Data can be collected and organized in a variety of ways. How can you collect, organize, and display data?

Graphs are used to communicate information. How do you interpret the data you have collected?

Charts, tables, and graphs helps us make valid inferences, decisions, When would you collect data?
and arguments.
How does the type of data influence the choice of graph?

What methods can you use to analyze data?

What conclusions can you draw about the data?

S2C1PO1 Data; double bar graphs; Collect, record, organize, and display data using Data
single line graphs; circle double bar graphs, single line graphs, or circle Single line graph
graphs graphs.
Double bar graph
S2C1PO2 Questions; displays of data; Formulate and answer questions by interpreting and Circle graph
double bar graphs; single analyzing displays of data, including double bar graphs,
Median
line graphs; circle graphs. single line graphs or circle graphs.
Mode
Range


S2C1PO3 Median; mode; range; Compare two sets of data. Analyze
distribution data set Record
S4C4PO1 Elapsed time to the minute [Interpret] elapsed time to the minute Interpret
S1C3PO1 Benchmarks; points of Organize
Use benchmarks as meaningful points of comparison for
comparison; whole numbers; whole numbers, decimals, and fractions. Collect
decimals; fractions Display
Minute
Hour
Elapsed time
Benchmark
Comparison
Greater than
Less than



Quarter: 1
Unit Name and Description: Probability and discrete math

Cluster: 3

Probability can be applied to everyday events. Why do we organize possible outcomes?

There are a variety of ways to represent possible outcomes of an What conclusions can you draw from outcomes, results or graphs?
event.

Probability and discrete math can be used to draw conclusions about
possible outcomes and conflict situations.

S2C2PO1 Theoretical probability; all Describe elements of theoretical probability by Probability
possible outcomes; given listing or drawing all possible outcomes of a given Possible outcome
event; outcome; word and event and predicting the outcome using word and
Number
number benchmarks number benchmarks.
Benchmark
Justify
S2C3PO2 Possibilities Justify that all possibilities have been enumerated
Duplication
without duplication.
Possibilities
Enumerated



Quarter: 1
Unit Name and Description: Patterns

Cluster: 4

Patterns occur everywhere in nature. Where might you see a pattern?

A rule can be used to describe a pattern. How might you determine/test the rule of a pattern?

How do you identify a pattern?

S3C1PO1 Numerical sequences; Recognize, describe, create, extend, and find Numerical
missing sequence; whole missing terms in a numerical sequence involving Sequence
numbers; four basic whole numbers using all four basic operations.
Missing
operations
Sequence
Four basic
operations:
-addition
subtraction
-multiplication
-division
S3C1PO2 Numerical sequences; given Explain the rule for a given numerical sequence, Rule
rule; predictions [Test] that the rule works. Whole number
Use the rule to make predictions. Prediction/predict



Quarter: 1
Unit Name and Description: Algebra

Cluster: 5

Algebraic expressions can be used to represent and analyze What is this question asking?
mathematical situations.
How can I represent the information in this problem in a different way?

S3C3PO2 One step equations; addition, Create one-step equations that can be solved using Equation
subtraction, multiplication, addition, subtraction, multiplication, and division of Addition
and division of whole whole numbers.
Subtraction
numbers.
Multiplication
Solve one step equations that can be solved using
Division
addition, subtraction, multiplication, and division of
whole numbers. Whole numbers
Factor
Product
Divisor
Dividend
Quotient



Quarter: 2

Cluster: 1



How do you identify a pattern?

S3C1PO1* Numerical sequences; Recognize, describe, create, extend and find Numerical
Missing sequence; Whole missing terms in numerical sequence involving
Sequence
Numbers; Four basic whole numbers using all four basic operations.
operations Missing
Sequence
S3C1PO2* Numerical sequences; Given Four basic
Explain the rule for a given numerical sequence.
rule; Predictions operations:
[Test] that the rule works.
-addition
Use the rule to make predictions.
subtraction
-multiplication


S3C3PO2* One-step equations; Addition, Create one step equations that can be solved using -division
subtraction, multiplication, and addition, subtraction, multiplication, and division of whole Rule
division of whole numbers numbers.
Whole number
Solve one step equations that can be solved using
Prediction/predict
addition, subtraction, multiplication, and division of whole
numbers. Missing terms



Quarter: 2
Unit Name and Description: Fractions

Cluster: 2

Problem solving can be approached and represented through many What strategy could I use to solve this problem?
different methods.
What makes me think that the answer is correct?
Fractions, decimals, and percents represent parts of a whole.
Could I represent the information in this problem in a different way?
The size of a fractional part is dependent on the whole.
When might ¼ be larger than ½?

When are fractions used?

S1C1PO3 Fractions; Parts; Set; [Model] fractions as fair sharing, parts of a whole, Fraction
Locations; parts of a set, and locations on a real number line. Numerator
Number line Denominator
Fair sharing
Whole
Whole numbers; Fractions, [Construct] whole numbers, fractions, decimals, and Part
S1C1PO1 Decimals; Percents; Multiple percents using and connecting multiple representations.
Set
Representations
Number line
Decimal


S1C3PO1* Benchmarks; Points of Use benchmarks as meaningful points of comparison for Percent
comparison; Whole numbers; whole numbers, decimals and fractions. Tenths
Decimals; Fractions Hundredths
S1C2PO1 Decimals; Fractions; Money to Add and subtract decimals through hundredths including
$1000.00; Denominators money to $1000.00 Estimate
Sum
Add and subtract fractions with like denominators. Difference
Analyze
S1C1PO4 Decimals to hundredths Compare and order decimals to hundredths.
Appropriate
Comparison
S1C3PO2 Estimates; Given situation or [Analyze] estimates appropriate to a given situation or Greater than
computation; Whole numbers computation with whole numbers. Less than
Equal
[Analyze] estimates appropriate to a given situation or
computation with fractions.



Quarter: 2
Unit Name and Description: Measurement

Cluster: 3

There are appropriate units of measurement to use in different Why do we have a system of measurement?
situations.
How do you determine which tool(s) to use when measuring?
There are variety of tools that can be used to measure.
What are some examples of different characteristics you can measure
Measurement involves assigning a number to characteristic of an on an object or situation?
object or situation.
What strategies can be used to convert within the same measurement
system?



S4C4PO2 Measurement skills; Length; Apply measurement skills to measure length, mass Measurement
Mass; Capacity; Metric and capacity using metric units. System
units
Length
Mass
Capacity
Meter
Centimeter
Millimeter
Kilometer
Ton
Ounce
Liter
Milliliter
Metric
Inch
Feet
Yard
Mile
Gallon
Quart
S4C4PO3 Measurement system: Solve problems involving conversion within the same Pint
Conversions; Problems measurement system. Cup
Customary
Conversion



Quarter: 2
Unit Name and Description: Geometry

Cluster: 4

Geometric figures can be described and grouped by their attributes. Why is it important to have an understanding of the attributes of two-
dimensional figures?
Mathematical information is used to justify reasoning.
There is a relationship between geometric attributes. What is the relationship between geometric attributes?

How might you classify a group of geometric figures?

What makes me think that my reasoning is correct?
S4C1PO2 Geometric Description; Justify which objects in a collection match a given Geometric figures
Objects in a collection geometric description. Justify
Classify
Point
Line
S4C1PO1 Relationships between points, Draw and describe the relationships between points,
Line segment
line segments, rays and lines, line segments, rays and angles including
angles including parallelism parallelism and perpendicularity. Ray
and perpendicularity Angle
Parallel


S4C1PO5 Congruent figures; Given Recognize and draw congruent figures, and match them Perpendicular
collection in a given collection. Right angle
Acute angle
Obtuse angle
S4C1PO3 Triangles; Angles; Sides Describe and classify triangles by angles and sides.
Straight angle
S4C1PO6 Right, acute, obtuse, and Draw right, acute, obtuse, and straight angles and Congruent
straight angles; Geometric identify these angles in other geometric figures. Right triangle
figures Acute triangle
Obtuse triangle
Isosceles triangle
Scalene triangle
Equilateral
triangle



Quarter: 2
Unit Name and Description: Perimeter and Area

Cluster: 5

There are appropriate situation to use perimeter and area. How are perimeter and area related?

There are similarities and differences between perimeter and area. How can you describe the relationship between the perimeter and area
of given figure?

When might you use perimeter and area?

S4C4PO4 Perimeter of 2 dimensional Solve problems involving perimeter of 2- Perimeter
figures; Area of rectangles dimensional figures and area of rectangles. Area
Shape
S4C4PO4 Attributes (such as shape and [Model] which attributes (such as shape and area) 2-dimensional
area); 2-dimensional change and which do not change when 2-dimensional figures
figures figures are cut up or rearranged.
Rectangle
Attribute


S4C4PO5 Perimeter, Area, Attribute [Model] the change in perimeter or area when one Length
(length or width), Rectangle attribute (length or width) of a rectangle changes. Width



Quarter: 2
Unit Name and Description: Coordinate Geometry

Cluster: 6

A coordinate plane can be used to display two-dimensional geometric How might you determine the ordered pairs needed to plot a geometric
figures. figure?

There is a systematic method to plot points on a coordinate plane. Why is there a systematic method to plotting points a coordinate
plane?

S4C3PO3 Geometric figures with Construct geometric figures with vertices at points Geometric
vertices; Points on the on the coordinate plane. Figures
coordinate plane Coordinate plane
S4C3PO1 Ordered Pairs, First quadrant, Name points in the first quadrant of the coordinate plane Vertices
coordinate plane using ordered pairs. Quadrant
Locate points in the first quadrant of the coordinate Ordered pairs
plane using ordered pairs.
Line segments
Graph points in the first quadrant of the coordinate plane
Plot
using ordered pairs.
Y- axis
S4C3PO2 Line segments; First X- axis
Plot line segments in the first quadrant of the coordinate
quadrant; Coordinate plane; plane using a set of ordered pairs in a table.
Ordered pairs in a table.



Quarter: 3
Unit Name and Description: Algebra

Cluster: 1

Algebraic expressions can be used to represent and analyze What is this question asking?
mathematical situations.
Do you have enough information to solve this problem?
Unknown quantities can be represented by a symbol.
When might you use algebra?
Problem situations can be represented and solved in variety of
ways. How can I represent the information in this problem in a different
way?

S3C3PO2* One-step equations; Addition, Create one step equations that can be solved using Equation
subtraction, multiplication, addition, subtraction, multiplication, and division of
and division of whole whole numbers. Addition
numbers Subtraction
Solve one-step equations that can be solved using Multiplication
addition, subtraction, multiplication, and division of
whole numbers
Division
Whole numbers


S1C2PO2* Multiplication Strategies Use multiple strategies to multiply whole numbers Factor
• Two-digit by two-digit and Multiple
• Multi-digit by one-digit Product
Divisor
S1C2PO4* Division Strategies; whole [Develop] multiple strategies to divide whole numbers. Dividend
numbers Quotient
S1C2PO6 Order of operations; whole Apply order of operations with whole numbers. Array
numbers Commutative
Property
S1C3PO2* Estimates; given situation of [Analyze] estimates appropriate to a given situation or
computation; whole numbers computation with fractions. Associative
Property
S3C3PO1 Symbol; Unknown quantity; Use a symbol to represent an unknown quantity in a Distributive
Simple algebraic expression; simple algebraic expression involving all operations.
Property
Operations
Parenthesis
Order of
operations
Analyze
Estimate
Algebraic
Expression
Symbol
Unknown
quantity



Quarter: 3

Cluster: 2



Changing the value of one quantity corresponds to a change in the How do you identify a pattern?
value of another quantity.
When might one quantity change as the result of another quantity
changing?

S3C1PO1 Numerical sequences; Recognize, describe, create, extend and find Missing
* missing sequence; whole missing terms in a numerical sequence Sequence
numbers; four basic involving whole numbers using all four basic Rule
operations operations.
Whole number
Prediction
Numerical
Sequence



S3C1PO2 Numerical sequences; given Explain the rule for a given numerical sequence. Four basic
* rule; predictions operations:
[Test] that the rule works.
Use the rule to make predictions. -addition
-subtraction
-multiplication
-division



Quarter: 3
Unit Name and Description: Probability and discrete math

Cluster: 3

Probability can be applied to everyday events. When would you use a tree diagram/vertex edge graph?

There is a variety of ways to represent possible outcomes of an Why do we organize possible outcomes?
event.
What conclusions can you draw from outcomes, results or
Probability and discrete math can be used to draw conclusions graphs?
about possible outcomes and conflict situations.

S2C2PO1 Theoretical probability; all Describe elements of theoretical probability by Probability
* possible outcomes; given listing or drawing all possible outcomes of a Possible
event; outcome; word and given event and predicting the outcome using outcome
number benchmarks word and number benchmarks.



S2C3PO1 Tree diagrams; problems in Construct tree diagrams to solve problems in Number
* context; possibilities, context by: Benchmark
properties, conclusions • Representing all possibilities for a variety of Tree diagram
counting problems, Map coloring
• Explaining how its properties relate to the Vertex coloring
problem,
Vertex edge-
• Representing the same counting problems in graph
multiple ways and
Path
• Drawing conclusions. Circuit
S2C4PO1 Connection; map and vertex Examine the connection between map coloring and
Conflict
coloring vertex coloring.
S2C4PO2 Vertex-edge graphs; concrete Possibilities
Construct vertex-edge graphs to represent concrete
situations; paths; circuits situations. Properties
Representing
[Model] paths and circuits. Drawing
S2C4PO3 Conflict problems; vertex Solve conflict problems by constructing and coloring Conclusions
edge graphs vertex edge graphs.



Quarter: 3
Unit Name and Description: Data Analysis

Cluster: 4

Data can be collected and organized in a variety of ways. How can you collect, organize, and display data?

Graphs are used to communicate information. How do you interpret the data you have collected?

Charts, tables, and graphs helps us make valid inferences, decisions, When would you collect data?
and arguments.
How does the type of data influence the choice of graph?

What methods can you use to analyze data?

What conclusions can you draw about the data?

S2C1PO1 Data; double bar graphs; Collect, record, organize, and display data using Data
* single line graphs; circle double bar graphs, single line graphs, or circle Related data
graphs graphs.
Double bar
S2C1PO2 Questions; displays of data; Formulate and answer questions by interpreting and graph
* double bar graphs; single analyzing displays of data, including double bar graphs,
single line graphs or circle graphs. Single line
line graphs; circle graphs.
graph


S2C1PO4 Related Data Compare two sets of related data. Circle graph
Collect
S3C4PO1 Change in quantity over time; [Measure] the change in quantity over time and make Record
simple predictions simple predictions. Organize
Display
Interpret
Analyze
Quantity
Predictions



Quarter: 3
Unit Name and Description: Geometry

Cluster: 5

Geometric figures can be described and grouped by their Why is it important to have an understanding of the attributes of 2-
attributes. dimensional figures?

Mathematical information is used to justify reasoning. What is the relationship between geometric attributes?

How might you classify a group of geometric figures?
There is a relationship between geometric attributes.
What makes me think that my reasoning is correct?
Nets represent a 3-dimensional geometric figure.
What is the relationship between a 3-dimensional figure and its net?

Essential Learning
AZ Key Summative
S4C1PO2 Geometric description; Justify which objects in a collection match a Geometric
* objects in a collection given geometric description. Description
Geometric
S4C1PO7 3-Dimensional figures; net(s) Recognize the relationship between a 3- Figure
dimensional figure and its corresponding net(s). Justify
3-Dimensional
Net


Fourth Grade Math Curriculum Map

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Fourth Grade Math Curriculum Map