HADDON TOWNSHIP MATHEMATICS
GRADE FIVE
The fifth grade mathematics curriculum provides developmentally appropriate mathematics
experiences that reflect New Jersey Core Curriculum Content Standards for Mathematics. As
fifth grade students experience mathematics through the Everyday Math program, they develop
skills in numeration and order, measures and measurement, geometry and spatial sense, and patterns,
functions, and sequences rules. They will also begin to explore data and chance, and
gain experience with concrete problems that arise in the daily life of children.
ESSENTIAL LEARNINGS: All fifth grade
mathematics students will demonstrate an
understanding of the following NJ Core Curriculum
Content Strands...
CHARACTERISTICS OF EFFECTIVE
LEARNERS: All fifth grade students will
demonstrate growth in the development of the
following characteristics of effective learners:
Number and Numerical Operations (NJ 4.1)
• Develop number sense and perform
standard numerical operations and
estimations on all types of numbers in a
variety of ways
Trustworthiness, demonstrated by the ability to…
• Be honest in words and actions
• Keep promises
• Stand up for beliefs and do what is right
• Be a good friend
Geometry and Measurement (NJ 4.2)
• Develop spatial sense and the ability to use
geometric properties, relationships, and
measurements to model, describe and
analyze phenomena
Respect, demonstrated by the ability to…
• Treat others the way you would want to be
treated
• Be polite and courteous
• Treat others well even if they look, act, or
believe differently than you do
Patterns and Algebra (NJ 4.3)
• Represent and analyze relationships
among variable quantities and solve
problems involving patterns, functions, and
algebraic concepts and processes
Data Analysis, Probability, and Discrete
Mathematics (NJ 4.4)
• Develop an understanding of the concepts
and techniques of data analysis, probability,
and discrete mathematics, and will use
them to model situations, solve problems,
and analyze and draw appropriate
inferences from data
Mathematical Processes (NJ 4.5)
• Use mathematical processes of problem
solving, communication, connections,
reasoning, representations, and technology
to solve problems and communicate
mathematical ideas
New Jersey Core Curriculum Content
Standards are indicated in parentheses
Responsibility, demonstrated by the ability to…
• Do what you are supposed to do
• Think about how your actions will affect
others
• Always try to do your best
Fairness, demonstrated by the ability to…
• Play by the rules
• Take turns and share
• Try to see the other person’s side
• Speak up if you know something is unfair
Caring, demonstrated by the ability to…
• Be kind with your words and actions
• Help others
• Think about other people’s feelings and
needs
• Be thankful for what others do for you
Citizenship, demonstrated by the ability to…
• Cooperate with others
• Obey rules and laws
• Do your best to make your school and
neighborhood better
• Help protect the Earth
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Everyday Mathematics
Fifth Grade End of Unit Skills for Assessment
Unit 1: Number Theory
- identify place value in large numbers
- build arrays and identify factors that describe arrays
- identify factor pairs
- identify prime numbers
- factor numbers in the form of arrays
- use exponential notation to write square numbers
- solve and compare multiplication facts
- find factors of a number
- write numbers that are dictated
- identify numbers divisible by 2, 3, 5, 6, 9, 10
- write whole numbers and identify the value of digits
Unit 2: Estimation and Computation
- solve extended facts problems mentally
- solve multi-digit addition problems
- solve multi-digit subtraction problems
- write open number sentences to model given situations
- compare decimals
- explain the connection of probability to fractions, decimals, and percents
- add and subtract whole numbers
- make magnitude estimates for multiplication problems
- use lattice multiplication to solve multiplication problems
- compare large numbers
- identify the ten-thousands and hundred-thousands digits
- identify the tenths and tens digits
- add and subtract whole numbers and decimals
- convert between U.S. customary units of length
- identify multiplication errors
- describe given numerical probabilities using words or phrases
Unit 3: Geometry Explorations and the American Tour
- read and write whole numbers
- add and subtract whole numbers and decimals
- use the relationship between circles and polygons to identify angle measures
- use full-circle and half- circle protractors to measure
- solve extended multiplication facts mentally
- compare decimals
- draw, estimate, and measure angles
- use the sum of angles in triangles to find the sums of angles in other polygons
- make magnitude estimates for division problems
- round numbers to the nearest ten, whole number, and tenth
- circle and underline digits in indicated places
- solve multiplication problems
- measure angles
- identify types of angles
- identify place value in numbers to billions
- draw types of triangles
- identify types of triangles and compare properties
- compare the properties of polygons
Unit 4: Division
- use multiplication and division facts to solve division problems with 1-digit-divisors
- use the partial-quotients algorithm to solve division problems
- identify place value in decimals
9/2008
-
write a number story
make magnitude estimates for division problems
interpret the remainder in division problems
find the value of an algebraic expression
use map scale to estimate distance
use friendly-number strategy to divide
use the partial-quotients algorithm
make magnitude estimates to place a decimal point
solve number sentences for given variables
write number sentences that model number stories
Unit 5: Fractions, Decimals, and Percents
- find the fraction of a collection of objects
- find the value of a region based on a defined unit fraction
- explain the relationship between the numerator and denominator of a fraction
- find equivalent fractions
- convert between fractions and decimals
- compare fractions
- compare features of bar and circle graphs
- estimate and find the measure of circle-graph sectors
- use fractions to draw circle-graph sectors
- estimate answers to +, -, *, and ÷ problems
- write equivalent mixed numbers or whole numbers
- convert between fractions and mixed numbers
- add fractions using fraction sticks
- order fractions
Unit 6: Using Data: Addition and Subtraction of Fractions
- display data on a line plot and identify the data landmarks
- measure lengths to the nearest centimeter and ¼ inch
- explain the advantage of displaying data in stem-and-leaf plots
- interpret data displayed in line plots
- describe how to find the percent of a number
- name fraction-decimal equivalents
- rename fractions as decimals and percents
- add and subtract fractions
- add and subtract fractions with unlike denominators
- explain how to use fraction strips to find common denominators
- indicate whether a number is divisible by a given number
- round numbers up or down to the indicated place value
- find and use data landmarks
- add and subtract fractions with like denominators
- add and subtract fractions with unlike denominators
- find a common denominator
- understand how sample size affects results
Unit 7: Exponents and Negative Numbers
- identify and correct mistakes in writing numbers using exponential notation
- use powers of 10 to write equivalent names for numbers
- understand place value to convert numbers written in scientific notation to standard notation
- write expressions containing parentheses to represent a number story
- compare decimals
- add and subtract fractions with like and unlike denominators
- use order of operations to solve problems
- model problems with positive and negative counters
- compare decimals and understand scientific notation
- identify and extend number patterns
- convert fractions to whole numbers or mixed numbers in simplest form
- use >, <, or = to compare numbers
9/2008
-
identify powers of 10 for given numbers
order and compare positive and negative numbers
add and subtract positive and negative numbers
identify number sentences and tell whether they are true or false
understand and apply order of operations to evaluate expressions and solve number stories
Unit 8: Fractions and Ratios
- compare fractions
- add mixed numbers
- add and subtract mixed numbers
- order fractions
- use a number-line model to solve fraction multiplication problems
- use an area model to solve fraction multiplication problems
- convert fractions to decimals and percents
- multiply mixed numbers
- convert between fractions, decimals, and percents
- use unit fractions and unit percents to solve problems
- add fractions
- use a common denominator algorithm to divide fractions
- indicate if given fractions and mixed numbers are equivalent or not
- find a common denominator for given pairs of fractions
- use an algorithm to subtract mixed numbers with like denominators
- convert between fractions and whole or mixed numbers
Unit 9: Coordinates, Area, Volume, and Capacity
- translate numbers written in scientific notation to standard notation and number-and-word notation
- plot ordered number pairs
- plot points on a coordinate grid
- calculate area
- draw line segments and explain that congruent line segments have the same length
- write formulas for finding the area of triangles and parallelograms
- solve fraction of problems
- find common denominators and write fractions in simplest form
- match polygons with their properties
- distinguish between volume and capacity
- indicate if statements about area and volume are true or false
- identify and plot ordered pairs on a one- and four-quadrant coordinate grid
- understand the concept of area of a figure
- identify the base and height of triangles and parallelograms
- understand the concept of volume of a figure
- use formulas to find the volume of figures
Unit 10: Using Data; Algebra Concepts and Skills
- extend basic division facts
- solve equations using a pan-balance model
- write algebraic expressions that model situations
- use table data to plot points on a graph
- solve addition and subtraction open sentences containing negative and positive numbers
- read and interpret graphs
- interpret line graphs
- describe area and perimeter
- replace variables in number sentences and solve problems
- indicate if circumference would be used to solve given problems
- interpret mystery line plots and graphs
- distinguish between circumference and area of a circle
Unit 11: Volume
- identify the properties of geometric solids
9/2008
- compare prisms, pyramids, cylinders, and cones
- explain what is similar and what is different between finding the volume of cylinders and finding the
volume of prisms
- calculate a fraction of a whole
- compare fractions
- write number sentences using the order of operations
- find the area of circles, triangles, and rectangles
- know the properties of geometric solids
- use formulas to find the area of polygons and circles
Unit 12: Probability, Ratios, and Rates
- factor numbers and identify the prime factorizations
- express probability using fractions and basic probability terms
- convert between fractions, decimals, and percents
- solve ratio problems
- estimate and solve multidigit multiplication problems
- express ratios in a variety of ways
- round numbers
- plot points in all four quadrants of a coordinate grid
- indicate if the first number given is a factor of the second or not
- name all the factors of a number
- find the greatest common factor or two numbers
- find the least common multiple of two numbers
- solve ratio and rate number stories
9/2008