Mathematics Grade 5

Chester Township Public Schools
Mathematics Curriculum

Mathematics - Grade 5

Mathematics

The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research on teaching and learning, and professional guidelines.

The Foundations of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Knowledge and Comprehension levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Foundations of Learning curriculum focuses on basic skills. Objectives primarily involve the identification, recognition, comprehension, or understanding of various math topics.

The Applications of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Application and Analysis levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Applications of Learning curriculum focuses on intermediate skills. The objectives primarily involve the application, examination, or analysis of various math topics.

The Higher Order Learning (1999) curriculum offers Grade 4 through Grade 12 objectives for the Synthesis and Evaluation levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Higher Order Learning curriculum focuses on advanced skills. The objectives primarily involve the synthesis and evaluation of various math topics.

The purpose of New Jersey's statewide assessment program is to measure what students at benchmark grade levels know and are able to do. The Mathematics Content Clusters that are covered in the tests unavoidably contain some overlapping content, since mathematical topics are not disconnected but are part of an interconnected whole.

The New Jersey Curriculum Content Standards for Mathematics is focused on achieving one crucial goal:

"To enable ALL of New Jersey's children to move into the twenty-first century with the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives."

The environment in the mathematics classroom should reflect the following two standards:

"1. All students' mathematical learning will embody the concepts that engagement in mathematics is essential, and that the decision-making, risk-taking, cooperative work, perseverance, self-assessment, and self-confidence are frequently keys to success."

"2. All students will be evaluated using a diversity of assessment tools and strategies, to provide multiple indicators of the quality of every student's mathematical learning and of overall program effectiveness."

The New Jersey Standards for Mathematics are as follows:

*"All students will develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences."

*"All students will communicate mathematically through written, oral, symbolic, and visual forms of expression."

*"All students will connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the roles that mathematics and mathematical modeling play in other disciplines and in life."

*"All students will develop reasoning ability and will become self-reliant, independent mathematical thinkers."

*"All students will regularly and routinely use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking, understanding, and power."

*"All students will develop number sense and an ability to represent numbers in a variety of forms and use numbers in diverse situations."

*"All students will develop spatial sense and an ability to use geometric properties and relationships to solve problems in mathematics and everyday life."

*"All students will understand, select, and apply various methods of performing numerical operations."

*"All students will develop an understanding of and will use measurement to describe and analyze phenomena."

*"All students will use a variety of estimation strategies and recognize situations in which estimation is appropriate."

*"All students will develop an understanding of patterns, relationships, and functions and will use them to represent and explain real-world phenomena."

*"All students will develop an understanding of statistics and probability and will use them to describe sets of data, model situations, and support appropriate inferences and arguments."

*"All students will develop an understanding of algebraic concepts and processes and will use them to represent and analyze relationships among variable quantities and to solve problems."

*"All students will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations."

*"All students will develop an understanding of conceptual building blocks of calculus and will use them to model and analyze natural phenomena."

*"All students will demonstrate high levels of mathematical thought through experiences which extend beyond traditional computation, algebra, and geometry."

In this area students concentrate on making mathematical connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects which require them to apply number systems, operations, and forms in real-world contexts.

Grade 5

The Foundations of Learning curriculum provides objectives for fifth grade students.

The Applications of Learning curriculum provides objectives for fifth grade students.

The Higher Order Learning curriculum provides objectives for fifth grade students.

In this course students explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities involving whole numbers, decimals, fractions, number sentences, measurement, estimation, making sense of real-world data (collecting, discussing, and making conclusions about data), conceptualizing and converting numbers in various forms, and justifying mathematics solutions by articulating the reasons behind the solutions. Course work includes using manipulatives to represent algebraic concepts. The course emphasizes the need for students to make mathematical connections and to use mathematics principles to communicate, reason, and solve problems. The Terra Nova Complete Battery assesses students in fifth grade (Level 15).

Algebraic Concepts

The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.

Number Sense: Manipulatives
The learner will be able to use manipulatives to demonstrate the following algebraic concepts: sets, elements of sets (a different shaped or colored manipulative can be used to represent a set of manipulatives), equal sets, variables representing unequal values (specific manipulatives can be used to equal five of another kind of manipulative), the symbolic nature of algebra, patterns in algebra, the connection between manipulatives and the written expressions they represent, and the concept of rules which govern how expressions can be manipulated. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Number Sense		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Problem Solving: Real-World Scenarios
The learner will be able to demonstrate an understanding of algebraic concepts by solving real-world scenario problems, and evaluate the nature and elements of problems, find solutions to given problems, and justify the solutions in writing, orally, or by using manipulatives. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Problem Solving		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Solution Methods: Addition/Subtraction
The learner will be able to describe procedures such as the following for addition and subtraction of whole numbers: mental arithmetic, estimation, computation, and using a calculator. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Solution Methods		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Missing Factor
The learner will be able to solve a multiplication problem to find a missing factor. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Missing Information	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Properties: Missing Number
The learner will be able to identify the missing number in an equation. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Missing Information	Knowledge	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Order of Operations: Determine
The learner will be able to determine the correct order of calculations when more than one operation is to be performed. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Order of Operations	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Equations: Whole Numbers
The learner will be able to identify the whole numbers that correspond to given whole number equations. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Equations	Knowledge	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiple Step Problems: Estimate
The learner will be able to estimate solutions to multiple step problems using whole, fraction, and decimal numbers. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Multiple-step Problems	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiple Step Story Problems
The learner will be able to solve multiple step word problems using whole numbers and decimals. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Multiple-step Problems	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Create a Story Problem
The learner will be able to use a given equation to develop a story problem. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Write/Create Story Problems	Synthesis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiple Step Problems: Writing
The learner will be able to compose both problems and story problems requiring multiple operations. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Write/Create Story Problems	Synthesis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Inequalities: Concept
The learner will be able to understand the concepts of inequalities. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Inequalities	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Inverse Operations: Checking
The learner will be able to check the correctness of an answer by using the inverse operation. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Inverse Operations	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Verify: Represent Results
The learner will be able to use manipulatives, pictures, and discussion to determine the reasonableness of results from sums, differences, products, and quotients involving fractions, mixed numbers, and decimals. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Verify	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiplication/Division: Methods
The learner will be able to describe procedures such as the following for multiplication and division of whole numbers: mental arithmetic, estimation, computation, and using a calculator. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Solution Methods	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Solution Methods: Describing
The learner will be able to describe estimating, computing, and mental math procedures for fractions, decimals, and mixed numbers. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Solution Methods	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Data Interpretation

The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving.

This unit includes presenting data in graphical forms and interpreting data given in graphical forms.

Evaluating: Graphical Forms
The learner will be able to evaluate a given graph to determine if the information is reasonable, if the graph format is the most effective one for the type of information presented, and to find possible inconsistencies in the information contained in the graph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Analyzing/Evaluating Graphical Forms		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Bar Graphs: Identify/Compare
The learner will be able to identify or compare amounts in a bar graph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Bar Graphs	Knowledge	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Bar Graphs: Interpret
The learner will be able to make interpretations of bar graphs (horizontal/vertical formats) to find patterns in data. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Bar Graphs	Analysis	Introduce	Applications of Learning, January 1999, Grade 5

Bar Graphs: Addition/Subtraction
The learner will be able to add or subtract information presented in the form of a bar graph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Bar Graphs	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Pictographs
The learner will be able to identify, compare, and add or subtract amounts read from pictographs. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Pictographs	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Pictographs: Analyze
The learner will be able to analyze data on a pictograph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Pictographs	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Line Graphs: Read
The learner will be able to read a line graph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Line Graphs	Application	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Table: Analyze
The learner will be able to analyze information presented in tables. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Tables/Charts	Analysis	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Table: Compute
The learner will be able to identify values from the graph, compare values from the graph, determine the value of multiple entries, and perform the necessary calculations to find the missing parts of a table. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Tables/Charts	Analysis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Graphs: Write Story Problems
The learner will be able to write a story problem based on information presented in a graph. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Graphing	Synthesis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Graphs: Create a Chart
The learner will be able to use given data to create a chart. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Tables/Charts	Synthesis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Graphs: Create
The learner will be able to make graphs, plots, and tables. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Graphing	Synthesis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Graphs: Applications
The learner will be able to determine the correct use of graphs, plots, and tables. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Graphing	Evaluation	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Decimals

The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. The Decimals Unit includes comparison, computing, money, estimation, problem solving and reasoning.

This unit includes comparing decimals, performing operations with decimals, converting decimals to other number forms, using manipulatives to demonstrate decimals, and solving problems with decimals in real-world contexts.

Problem Solving: Application
The learner will be able to use manipulatives and calculators to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the required operation, setting up a number sentence, and solving the problem. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Problem Solving		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Connecting: Forms
The learner will be able to connect concepts relating decimals, whole numbers, fractions, and percents by demonstrating how these number forms are used to communicate place value, ordinality, and money amounts, and to evaluate the reasonableness of a given problem and solution. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Connecting		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Number Sense: Using Decimals
The learner will be able to articulate the reasoning behind placing the decimal point in the appropriate position when evaluating number sentences involving operations on decimals. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Number Sense		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Addition Story Problems
The learner will be able to analyze and solve decimal story problems which depict real-world scenarios by determining that addition is required, by regrouping numbers, and by adding decimals up to the hundredths position. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Add Decimals	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Subtraction Story Problems
The learner will be able to solve subtraction story problems depicting real-world money and other decimal scenarios by determining that subtraction is required, by regrouping, and by subtracting the appropriate decimal numbers (numbers are less than 100). (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Subtract Decimals	Analysis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Add/Subtract Decimals: Solution Methods
The learner will be able to use manipulatives, mental math, and calculators to find sums and differences of decimals. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Add/Subtract Decimals	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiply Decimal and Whole Numbers
The learner will be able to multiply a decimal number by a 1 digit whole number (regrouping when necessary). (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Multiply Decimals	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiply 2 Decimal Numbers
The learner will be able to multiply 2 decimal numbers. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Multiply Decimals	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiplication Story Problems
The learner will be able to solve real-world story problems by determining that multiplication is required, by regrouping the numbers, and by multiplying the appropriate decimals up to the hundredths position. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Multiply Decimals	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Decimals: Represent
The learner will be able to represent decimal numbers using pictures, diagrams, or manipulatives. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Decimals	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money: Estimating Large Amounts
The learner will be able to use prior knowledge to make reasonable estimations for possible prices of large items (cars, houses, etc.). (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Money	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Divide Decimal by Whole Number
The learner will be able to divide a decimal number by a whole number. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Divide Decimals	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Division Story Problems
The learner will be able to solve story problems by dividing decimals up to the hundredths position. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Divide Decimals	Application	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Compare Decimals: Up to 0.01
The learner will be able to compare decimal numbers up to the hundredths position using the order symbols (<, >, =). (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Compare Decimals	Analysis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Fractions

The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving.

This unit includes comparing fractions, performing computations with fractions, converting fractions to other number forms, using manipulatives to demonstrate fractions, and solving problems with fractions in real-world contexts.

Connecting: Using Fractions
The learner will be able to make connections between the functions of numerators and the functions of denominators by exploring fractions (i.e., drawing conclusions about fractions a/b, b/c, c/b, a/c, b/a, and c/a, when a > b > c). (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Connecting		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Number Sense: Forms/Applications
The learner will be able to relate fractions to concrete objects, to real-world events, to other number forms (whole numbers, decimals, percents), and incorporate the language of fractions to describe proportions in daily events and across the curriculum. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Number Sense		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Adding: Mixed Fractions
The learner will be able to add mixed fractions. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Add Fractions	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Addition Story Problems
The learner will be able to add two fractions, either mixed fractions or with different denominators, in the context of a story problem. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Add Fractions	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Subtraction Story Problems
The learner will be able to solve story problems involving subtracting two fractions with the same or different denominators. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Subtract Fractions	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Subtracting Mixed Fractions
The learner will be able to subtract two mixed fractions. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Subtract Fractions	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiply 2 Fractions
The learner will be able to multiply 2 fractions. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Multiply Fractions	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Multiplication Story Problems
The learner will be able to multiply two fractions, a fraction and a whole number, or a mixed fraction and a whole number in the context of a story problem. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Multiply Fractions	Knowledge	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Fractions: Multiple Step Problems
The learner will be able to solve multiple step problems involving fractions. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Fractions	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Compare Fractions: Equivalent/Mixed
The learner will be able to compare 2 equivalent fractions and equivalent and mixed fractions. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Compare Fractions	Analysis	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Geometry

The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.

This unit includes exploring geometric concepts from multiple perspectives.

Spatial Thinking: Properties
The learner will be able to show an awareness of the spatial properties of figures by investigating how to cover a flat surface by using one or more geometric figures, by identifying and drawing similar figures, and by drawing solids made with cubes on triangle dot paper. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Spatial Thinking		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Angles: Exploring
The learner will be able to explore various types of angles, their relationship to each other. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Angle Relationships		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Shapes: Features
The learner will be able to discover distinguishing features of triangles, quadrilaterals, and circles. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Two-Dimensional Shapes	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Figures: Attributes/Explain
The learner will be able to describe which attributes of a figure are being considered when the figure is used for classification. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Figures: Attributes	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Triangles: Similar
The learner will be able to identify similar triangles. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Triangles	Knowledge	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Circle: Relating Diameter/Circumference
The learner will be able to determine how diameter and circumference are related. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Circles	Synthesis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Similarity: Describe
The learner will be able to describe similar figures as not differing in shape but only in size or proportion. (NJCCCS 4.2, 4.4, 4.6).

Strand	Bloom's	Scope	Source
Similarity	Knowledge	Introduce	Foundations of Learning, January 1999, Grade 5

Measurement

The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. The Measurement Unit includes concepts of length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns and problem solving.

This unit includes experimenting with formal, informal, customary, and metric units of measurement, and distinguishing between situations which call for exact measurement and those which call for estimation.

Problem Solving: Length/Perimeter
The learner will be able to solve real-world scenario problems (involving perimeter or length), use manipulatives to isolate the nature of the problem, articulate how a given measurement situation can be solved, and select appropriate measurement tools for a given situation (without being told the specific unit of measurement which should be used). (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Problem Solving		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Communicating: Measurement Concepts
The learner will be able to articulate how measurement terms relate to real-world objects, proportions, and amounts, justify why a particular form of measurement should be used, and distinguish between situations which call for estimation and those which call for exact measurement. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Communicating Measurement Concepts		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Length: Standard Ruler
The learner will be able to measure an object using a standard ruler. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Length	Comprehension	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Time: Elapsed
The learner will be able to calculate the amount of time which has elapsed between two given times. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Time	Comprehension	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money Problems: Separate/Result Unknown
The learner will be able to identify the amount of money left after spending. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money Problems: Join/Change Unknown
The learner will be able to identify the amount needed to make an amount equal to a given amount. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money: Finding Change
The learner will be able to identify the change from a purchase. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money: Add/Subtract Word Problems
The learner will be able to determine that addition or subtraction is needed to solve word problems involving money (including converting cents to dollars). (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money: Purchasing Items
The learner will be able to identify the number of items that could be purchased for a specific amount. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Money: Multiplication Story Problem
The learner will be able to use multiplication to solve a problem presented in a real world scenario using money notation. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Money	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Temperature: Problem Solving
The learner will be able to solve temperature problems. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Temperature	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Perimeter: Compare
The learner will be able to understand and compare the perimeters of rectangular figures. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Perimeter	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Area: Appropriate Units
The learner will be able to determine the appropriate units in which to measure an object's area in both the metric and standard systems. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Area	Analysis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Perimeter/Area: Discovering Formulas
The learner will be able to use constructed physical models to discover formulas for perimeter and area. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Perimeter/Area/Volume	Synthesis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Volume: Discovering Formulas
The learner will be able to discover formulas for volume using physical models. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Volume	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Volume: Measure
The learner will be able to measure the volume of figures. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Volume	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Measurement Solution: Length/Area/Volume
The learner will be able to determine whether a word problem requires a solution of length, area, or volume. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Measurement: Application	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.

Area of a Rectangle: Calculate
The learner will be able to calculate the area of a rectangle given its measurements. (NJCCCS 4.9).

Strand	Bloom's	Scope	Source
Area of a Rectangle	Comprehension	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade.