4th grade math curriculum map 2011 2012-1

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

Quarter: 1
Unit Name and Description: Multiplication and Division

Unit Cluster: 1
Big Ideas/Enduring Understandings Essential Question(s)
How are multiplication and division related?
There are multiple strategies to multiply and divide whole
numbers. When might you use multiplication?

There is a relationship between multiplication and division. 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
Whole number
S1C2PO4 Division strategies; whole [Develop] multiple strategies to divide whole numbers. Commutative
numbers

* = 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

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
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

Unit Cluster: 2

How can you collect, organize, and display data?
Data can be collected and organized in a variety of ways.
How do you interpret the data you have collected?
Graphs are used to communicate information.
When would you collect data?
Charts, tables, and graphs helps us make valid inferences, decisions,
and arguments. How does the type of data influence the choice of graph?

What conclusions can you draw about the data?

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


S2C1PO3 Median; mode; range; Compare two sets of data. (This is a Supplemental PO to be taught with this Minute
distribution data set unit..)
Hour
Elapsed time
S4C4PO1 Elapsed time to the [Interpret] elapsed time to the minute (This is a Supplemental PO to be Benchmark
minute taught with this unit..)
Comparison
S1C3PO1 Benchmarks; points of Use benchmarks as meaningful points of comparison for whole Greater than
comparison; whole numbers, decimals, and fractions. Less than
numbers; decimals;
fractions



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

Unit 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

Unit 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:
S3C1PO2 Numerical sequences; given Explain the rule for a given numerical sequence, -addition
rule; predictions [Test] that the rule works. subtraction
Use the rule to make predictions. -multiplication
-division
Rule
Whole number
Prediction/predict



Quarter: 1
Unit Name and Description: Algebra

Unit 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
Unit Cluster: 1

Where might you see a pattern?
Patterns occur everywhere in nature.
How might you determine/test the rule of a pattern?
A rule can be used to describe a pattern.
How do you identify a pattern?

S3C1PO1* Numerical sequences; Recognize, describe, create, extend and find missing Numerical
Missing sequence; terms in numerical sequence involving whole numbers
Sequence
Whole Numbers; Four using all four basic operations.
basic operations Missing
Sequence
S3C1PO2* Numerical sequences; Four basic
Explain the rule for a given numerical sequence.
Given rule; Predictions operations:
[Test] that the rule works. Use the rule to make predictions.
-addition
subtraction
-multiplication
S3C3PO2* One-step equations; Create one step equations that can be solved using addition, -division
Addition, subtraction, subtraction, multiplication, and division of whole numbers. Rule
multiplication, and division
Solve one step equations that can be solved using addition, Whole number
of whole numbers
subtraction, multiplication, and division of whole numbers. Prediction/predict
Missing terms



Quarter: 2
Unit Name and Description: Fractions

Unit Cluster: 2

What strategy could I use to solve this problem?
Problem solving can be approached and represented through many
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?

When might ¼ be larger than ½?
The size of a fractional part is dependent on the whole.
When are fractions used?

S1C1PO3 Fractions; Parts; Set; [Model] fractions as fair sharing, parts of a whole, Fraction
Locations; Number line parts of a set, and locations on a real number line. Numerator
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
Unit Cluster: 3
There are appropriate units of measurement to use in different
situations. Why do we have a system of measurement?

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
Measurement involves assigning a number to characteristic of an measure on an object or situation?
object or situation.
What strategies can be used to convert within the same
measurement system?
AZ Essential Learning Summative
Key Vocabulary
Standard Knowledge Skills Assessment
S4C4PO2 Measurement skills; Apply measurement skills to measure length, Measurement System
Length; Mass; mass and capacity using metric units. Length; Mass
Capacity; Metric units
Capacity; Meter
Centimeter; Millimeter;
Kilometer; Ton; Ounce;
Liter; Milliliter; Metric
Inch; Feet; Yard
S4C4PO3 Measurement system: Solve problems involving conversion within the Mile; Gallon; Quart
Conversions; Problems same measurement system.
Pint; Cup



Quarter: 2
Unit Name and Description: Geometry

Unit Cluster: 4

Why is it important to have an understanding of the attributes of two-
Geometric figures can be described and grouped by their dimensional figures?
attributes.
What is the relationship between geometric attributes?
Mathematical information is used to justify reasoning.
There is a 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 (This is a Supplemental PO to Ray
and perpendicularity be taught with this unit..) 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
Congruent
S4C1PO6 Right, acute, obtuse, and Draw right, acute, obtuse, and straight angles and Right triangle
straight angles; Geometric identify these angles in other geometric figures. Acute triangle
figures Obtuse triangle
Isosceles triangle
Scalene triangle
Equilateral
triangle



Quarter: 2
Unit Name and Description: Perimeter and Area

Unit Cluster: 5

How are perimeter and area related?
There are appropriate situation to use perimeter and area.
How can you describe the relationship between the perimeter and area
There are similarities and differences between 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. (This is a Supplemental PO to
be taught with this unit..) Rectangle
Attribute
Length
S4C4PO5 Perimeter, Area, Attribute [Model] the change in perimeter or area when one
(length or width), Rectangle Width
attribute (length or width) of a rectangle changes.



Quarter: 2
Unit Name and Description: Coordinate Geometry

Unit Cluster: 6

How might you determine the ordered pairs needed to plot a geometric
A coordinate plane can be used to display two-dimensional geometric figure?
figures.
Why is there a systematic method to plotting points a coordinate
There is a systematic method to plot points on a coordinate plane plane?

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



Quarter: 3
Unit Name and Description: Algebra

Unit 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 How can I represent the information in this problem in a different
ways. way?

S3C3PO2* One-step equations; Addition, Create and solve one step equations that can be Equation
subtraction, multiplication, solved using addition, subtraction, multiplication,
Addition
and division of whole and division of whole numbers.
numbers Subtraction
Multiplication
S1C2PO2* Multiplication Strategies Division
Use multiple strategies to multiply whole numbers
Whole numbers
• Two-digit by two-digit and
Factor
• Multi-digit by one-digit
Multiple


S1C2PO4* Division Strategies; whole [Develop] multiple strategies to divide whole numbers. Product
numbers
Divisor
S1C2PO6 Order of operations; whole Apply order of operations with whole numbers. (This is a Dividend
numbers Supplemental PO to be taught with this unit..)
Quotient
Array
S1C3PO2* Estimates; given situation of [Analyze] estimates appropriate to a given situation or
computation; whole numbers computation with fractions. Commutative
Property
S3C3PO1 Symbol; Unknown quantity; Use a symbol to represent an unknown quantity in a Associative
Simple algebraic expression; simple algebraic expression involving all operations. (This Property
Operations is a Supplemental PO to be taught with this unit..)
Distributive
Property
Parenthesis
Order of
operations
Analyze
Estimate
Algebraic
Expression
Symbol
Unknown
quantity



Quarter: 3

Unit Cluster: 2

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?

Changing the value of one quantity corresponds to a change in the When might one quantity change as the result of another quantity
value of another quantity. changing?

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



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

Unit Cluster: 3

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

Why do we organize possible outcomes?
There is a variety of ways to represent possible outcomes of an
event.
What conclusions can you draw from outcomes, results or
graphs?
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
Tree diagram
S2C4PO1 Connection; map and vertex Examine the connection between map coloring and
Map coloring
coloring vertex coloring. (This is a Supplemental PO to be taught with this
unit..) Vertex coloring
Vertex edge-
graph


S2C4PO2 Vertex-edge graphs; Construct vertex-edge graphs to represent concrete Path
concrete situations; paths; situations. Circuit
circuits Conflict
[Model] paths and circuits. (This is a Supplemental PO to be taught Possibilities
with this unit..)
Properties
S2C4PO3 Conflict problems; vertex edge Solve conflict problems by constructing and coloring Representing
graphs vertex edge graphs. (This is a Supplemental PO to be taught with this
unit..)
Drawing
Conclusions

S2C3PO1* Tree diagrams; problems in Construct tree diagrams to solve problems in
context; possibilities, context by:
properties, conclusions • Representing all possibilities for a variety of
counting problems,
• Explaining how its properties relate to the
problem,
• Representing the same counting problems in
multiple ways and
• Drawing conclusions.



Quarter: 3
Unit Name and Description: Data Analysis

Unit Cluster: 4

How can you collect, organize, and display data?
Data can be collected and organized in a variety of ways.
How do you interpret the data you have collected?
Graphs are used to communicate information.
When would you collect data?
Charts, tables, and graphs help us make valid inferences, decisions,
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?
Essential Learning
AZ Key Summative

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* graph
Questions; displays of data; Formulate and answer questions by interpreting and
double bar graphs; single line analyzing displays of data, including double bar graphs, Single line
graphs; circle graphs. single line graphs or 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

Unit Cluster: 5

Geometric figures can be described and grouped by their Why is it important to have an understanding of the attributes of 2-
dimensional figures?
attributes.
What is the relationship between geometric attributes?
Mathematical information is used to justify reasoning.
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 given Geometric
objects in a collection geometric description. description
Geometric figure
S4C1PO7 3-Dimensional figures; net(s) Recognize the relationship between a 3-dimensional 3-Dimensional
figure and its corresponding net(s).
Net



Process Objectives: MUST BE Integrated throughout Clusters


Essential Learning
AZ Summative
Key Vocabulary
Standard Assessment
Knowledge Skills
S5C1PO1
Analytical skills Analyze common algorithms for computing
with whole numbers using the associative,
commutative and distributive properties.
S5C2PO1
Analytical skills; Analyze a problem situation to determine the
question(s) to be answered
Questions
S5C2PO2 Information;Relevant; Identify relevant, missing and extraneous
Extraneous information related to the solution of a
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.
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.


4th grade math curriculum map 2011 2012-1

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4th grade math curriculum map 2011 2012-1