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Chester Township Public Schools |
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Mathematics Curriculum |
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Mathematics - Grade 5 |
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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 |
Activities |
| Number Sense |
|
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Problem Solving |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Solution Methods |
|
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Missing Information |
Application |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Missing Information |
Knowledge |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Order of Operations |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Equations |
Knowledge |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Multiple-step Problems |
Comprehension |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Multiple-step Problems |
Application |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| 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. |
Classroom
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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 |
Activities |
| 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. |
Classroom
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Inequalities: Concept
The learner will be able to
understand the concepts of inequalities. (NJCCCS 4.1, 4.2).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Inequalities |
Comprehension |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Inverse Operations |
Comprehension |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Verify |
Comprehension |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Solution Methods |
Comprehension |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Solution Methods |
Comprehension |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Analyzing/Evaluating Graphical Forms |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Bar Graphs |
Knowledge |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Bar Graphs |
Analysis |
Introduce |
Applications of Learning, January 1999, Grade 5 |
Classroom
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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 |
Activities |
| Bar Graphs |
Comprehension |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Pictographs |
Analysis |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Pictographs |
Analysis |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Line Graphs |
Application |
Master |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Tables/Charts |
Analysis |
Master |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Tables/Charts |
Analysis |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Graphing |
Synthesis |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Tables/Charts |
Synthesis |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Graphing |
Synthesis |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Graphing |
Evaluation |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Problem Solving |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Connecting |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Number Sense |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Add Decimals |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Subtract Decimals |
Analysis |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Add/Subtract Decimals |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Multiply Decimals |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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Multiply 2 Decimal Numbers
The learner will be able to
multiply 2 decimal numbers. (NJCCCS 4.1, 4.2).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Multiply Decimals |
Comprehension |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Multiply Decimals |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Decimals |
Comprehension |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Money |
Comprehension |
Reinforce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Divide Decimals |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Divide Decimals |
Application |
Master |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Compare Decimals |
Analysis |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Connecting |
|
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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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 |
Activities |
| Number Sense |
|
Master |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
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Adding: Mixed Fractions
The learner will be able to
add mixed fractions. (NJCCCS 4.1).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Add Fractions |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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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 |
Activities |
| Add Fractions |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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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 |
Activities |
| Subtract Fractions |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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Subtracting Mixed Fractions
The learner will be able to
subtract two mixed fractions. (NJCCCS 4.1).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Subtract Fractions |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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Multiply 2 Fractions
The learner will be able to
multiply 2 fractions. (NJCCCS 4.1).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Multiply Fractions |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
|
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 |
Activities |
| Multiply Fractions |
Knowledge |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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Fractions: Multiple Step Problems
The learner will be able to
solve multiple step problems involving fractions. (NJCCCS 4.1).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Fractions |
Application |
Introduce |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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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 |
Activities |
| Compare Fractions |
Analysis |
Master |
National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Fifth Grade. |
Classroom
|
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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 |
Activities |
| Spatial Thinking |
|
Introduce |
| |
