Nys Common Core Mathematics Curriculum Grade 4 Lesson 4.5 Answers

Related Pages
Common Core Math in the Classroom: Teaching Resources and Worksheets
Math Worksheets

Common Core
Kindergarten	1st Grade	2nd Grade
3rd Grade	4th Grade	5th Grade
6th Grade	7th Grade	8th Grade
Number & Quantity	Algebra	Functions
Geometry	Statistics & Probability	NYS Common Core

What is the Common Core Standards? The Common Core State Standards Initiative is a U.S. education initiative that seeks to bring diverse state curricula into alignment with each other by following the principles of standards-based education reform. The initiative is sponsored by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO).

The Mathematics Standards include Standards for Mathematical Practice and Standards for Mathematical Content.

Mathematical Practice

The eight principles of mathematical practice are:

Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.

Mathematical Content

Mathematical content is organized in a number of domains.

Domains	Grades
Counting and Cardinality	Kindergarten
Operations and Algebraic Thinking	Kindergarten, Grades 1 - 5
Number and Operations in Base 10	Kindergarten, Grades 1 - 5
Number and Operations & Fractions	Grades 3 - 5
Measurement and Data	Kindergarten, Grades 1 - 5
Geometry	Kindergarten, Grades 1 - 8
The Number System	Grades 6 - 8
Expressions and Equations	Grades 6 - 8
Statistics and Probability	Grades 6 - 8
Ratios & Proportional Relationships	Grades 6 - 7
Functions	Grade 8

Common Core Standards By Grades

Lessons, Worksheets and Games that are suitable for the Common Core Math sorted by Grades. We have Common Core Math Lessons, Common Core Math Worksheets, Common Core Math Games and Common Core Math Lesson Plans.

Common Core for Kindergarten: Counting & Cardinality
Know number names and the count sequence.
Count to tell the number of objects.
Compare numbers.
Operations & Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
Number & Operations in Base Ten
Work with numbers 11-19 to gain foundations for place value.
Measurement and Data
Describe and compare measurable attributes.
Classify objects and count the number of objects in each category.
Geometry
Identify and describe shapes.
Analyze, compare, create, and compose shapes.
Common Core for Grade 1: Operations & Algebraic Thinking
Represent & solve problems involving addition & subtraction.
Understand & apply properties of operations and the relationship between addition and subtraction.
Add and subtract within 20.
Work with addition and subtraction equations.
Number & Operations in Base Ten
Extend the counting sequence.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measurement and Data
Measure lengths indirectly and by iterating length units.
Tell and write time.
Represent and interpret data.
Geometry
Reason with shapes and their attributes.
Common Core for Grade 2: Operations & Algebraic Thinking
Represent and solve problems involving addition and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain foundations for multiplication.
Number & Operations in Base Ten
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measurement and Data
Measure & estimate lengths in standard units.
Relate addition and subtraction to length.
Work with time and money.
Represent and interpret data.
Geometry
Reason with shapes and their attributes.
Common Core for Grade 3: Operations & Algebraic Thinking
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number & Operations & Fractions
Develop understanding of fractions as numbers.
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Geometry
Reason with shapes and their attributes.
Common Core for Grade 4: Operations & Algebraic Thinking
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number & Operations & Fractions
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Represent and interpret data.
Geometric measurement: understand concepts of angle and measure angles.
Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Common Core for Grade 5: Operations & Algebraic Thinking
Write and interpret numerical expressions.
Analyze patterns and relationships.
Number & Operations in Base Ten
Understand the place value system.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number & Operations &Fractions
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
Convert like measurement units within a given measurement system.
Represent and interpret data.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
Classify two-dimensional figures into categories based on their properties.
Common Core for Grade 6: Ratios & Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Multiply and divide multi-digit numbers and find common factors and multiples.
Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions & Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.
Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics & Probability
Develop understanding of statistical variability.
Summarize and describe distributions.
Common Core for Grade 7: Ratios & Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions & Equations
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry
Draw, construct and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics & Probability
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.

Common Core for Grade 8: The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
Work with radicals and integer exponents.
Understand the connections between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.
Statistics and Probability
Investigate patterns of association in bivariate data.
High School: Number & Quantity: The Real Number System
Extend the properties of exponents to rational exponents
Classify numbers as rational or irrational
Quantities
Reason quantitatively and use units to solve problems
The Complex Number System
Perform arithmetic operations with complex numbers
Represent complex numbers and their operations on the complex plane
Use complex numbers in polynomial identities and equations
Vector and Matrix Quantities
Represent and model with vector quantities.
Perform operations on vectors.
Perform operations on matrices and use matrices in applications.
High School Algebra: Seeing Structure in Expressions
Interpret the structure of expressions
Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational Functions
Perform arithmetic operations on polynomials
Understand the relationship between zeros and factors of polynomials
Use polynomial identities to solve problems
Rewrite rational functions
Creating Equations
Create equations that describe numbers or relationships
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
Solve equations and inequalities in one variable
Solve systems of equations
Represent and solve equations and inequalities graphically.
High School: Functions: Interpreting Functions
Understand the concept of a function and use function notation
Interpret functions that arise in applications in terms of the context
Analyze functions using different representations
Building Functions
Build a function that models a relationship between two quantities
Build new functions from existing functions
Linear, Quadratic, and Exponential Models
Construct and compare linear and exponential models and solve problems
Interpret expressions for functions in terms of the situation they model
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
Model periodic phenomena with trigonometric functions
Prove and apply trigonometric identities.
High School: Geometry: Congruence
Experiment with transformations in the plane
Understand congruence in terms of rigid motions
Prove geometric theorems
Make geometric constructions
Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
Prove theorems involving similarity
Define trigonometric ratios and solve problems involving right triangles
Apply trigonometry to general triangles
Circles
Understand and apply theorems about circles
Find arc lengths and areas of sectors of circles
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems
Visualize relationships between two-dimensional and three-dimensional objects
Modeling with Geometry
Apply geometric concepts in modeling situations.
High School: Statistics and Probability: Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
Summarize, represent, and interpret data on two categorical and quantitative variables
Interpret linear models
Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying
statistical experiments
Make inferences and justify conclusions from sample surveys, experiments and observational studies
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data
Use the rules of probability to compute probabilities of compound events in a uniform probability model
Using Probability to Make Decisions
Calculate expected values and use them to solve problems
Use probability to evaluate outcomes of decisions

Common Core Standards By Domains

Click on the following links to find lessons suitable for the Common Core Math sorted by domains.

Counting & Cardinality: Kindergarten
Know number names and the count sequence.
Count to tell the number of objects.
Compare numbers.
Operations & Algebraic Thinking: Kindergarten
Understand addition, and understand subtraction.
Grade 1
Represent and solve problems involving addition and subtraction.
Understand and apply properties of operations and the relationship between addition and subtraction.
Add and subtract within 20.
Work with addition and subtraction equations.
Grade 2
Represent and solve problems involving addition and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain foundations for multiplication.
Grade 3
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Grade 4
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
Grade 5
Write and interpret numerical expressions.
Analyze patterns and relationships

Number & Operations in Base Ten: Kindergarten
Work with numbers 11-19 to gain foundations for place value.
Grade 1
Extend the counting sequence.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Grade 2
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Grade 3
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4
Generalize place value understanding for multi-digit whole numbers.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 5
Understand the place value system.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations and Fractions: Grade 3
Develop understanding of fractions as numbers.
Grade 4
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions.
Understand decimal notation for fractions, and compare decimal fractions.
Grade 5
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division.
Measurement and Data: Kindergarten
Describe and compare measurable attributes.
Classify objects and count the number of objects in each category.
Grade 1
Measure lengths indirectly and by iterating length units.
Tell and write time.
Represent and interpret data.
Grade 2
Measure and estimate lengths in standard units.
Relate addition and subtraction to length.
Work with time and money.
Represent and interpret data.
Grade 3
Solve problems involving measurement and estimation.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Geometric measurement: recognize perimeter.
Grade 4
Solve problems involving measurement and conversion of measurements.
Represent and interpret data.
Geometric measurement: understand concepts of angle and measure angles.
Grade 5
Convert like measurement units within a given measurement system.
Represent and interpret data.
Geometric measurement: understand concepts of volume.
Ratios and Proportional Relationships: Grade 6
Understand ratio concepts and use ratio reasoning to solve problems.
Grade 7
Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System: Grade 6
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Compute fluently with multi-digit numbers and find common factors and multiples.
Apply and extend previous understandings of numbers to the system of rational numbers.
Grade 7
Apply and extend previous understandings of operations with fractions.
Grade 8
Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations: Grade 6
Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.
Represent and analyze quantitative relationships between dependent and independent variables.
Grade 7
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Grade 8
Expressions and Equations Work with radicals and integer exponents.
Understand the connections between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions: Grade 8
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
Geometry: Kindergarten
Identify and describe shapes.
Analyze, compare, create, and compose shapes.
Grade 1
Reason with shapes and their attributes.
Grade 2
Reason with shapes and their attributes.
Grade 3
Reason with shapes and their attributes.
Grade 4
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Grade 5
Graph points on the coordinate plane to solve real-world and mathematical problems.
Classify two-dimensional figures into categories based on their properties.
Grade 6
Solve real-world and mathematical problems involving area, surface area, and volume.
Grade 7
Draw construct, and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Grade 8
Understand congruence and similarity using physical models, transparencies, or geometry software.
Understand and apply the Pythagorean Theorem.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability: Grade 6
Develop understanding of statistical variability.
Summarize and describe distributions.
Grade 7
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
Grade 8
Investigate patterns of association in bivariate data.

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