Download Grade 5 Mathematics Content

Grade 5 Mathematics Content
Whole Numbers
Place Value through millions
Read, write, compare, order, round
numbers through millions
Addition, subtraction, multiplication,
division
Basic Facts
Addition with regrouping
Subtraction across zeroes
Division with and without remainders
Estimating of sums, differences, products,
and quotients
Order of Operations
Introduction to expanded notation
Rounding of whole numbers and decimals
Percent and Ratio
Express a ratio
Express ratio in different forms
Understand that percent means part of
means part of 100, and write percent as
fractions and decimals
Decimals
Place value
Order and compare
Rounding decimals
Estimating decimals
Addition, subtraction, multiplication and
division of decimals
Interpreting the remainder
Fraction Concepts and
Operations
Divisibility
Prime Factors
Least common multiple
Greatest common factor
Equivalent fractions and simplest form
Mixed numbers and fractions
Compare and Order fractions
Recognize proper and improper fractions
Convert Improper fractions to mixed
numbers, and mixed numbers to improper
fractions
Reduce to simplest form
Add and subtract fractions with like and
unlike denominators
Geometry
Lines, rays, angles
Congruence, similar figures, symmetry
Identify and classify polygons and triangles
by properties of their angles and sides
Know that the sum of the interior angles of
a triangle is 180 degrees
Know that the sum of the interior angle of a
quadrilateral is 180 degrees
Calculate the perimeter of regular and
irregular polygons
Identify pairs of congruent and similar
triangles
Identify and draw lines of symmetry of
basic geometric shapes
Identify the ratio of corresponding sides of
similar triangles
Identify and plot points in the first quadrant
Plot points to form basic geometric shapes
Calculate perimeter of basic geometric
shapes drawn on a coordinate plane
Quadrilaterals, triangles, and solid figures
Integers
Solid figures – face, edge, vertex
Measurement
Customary length
Customary metric
Changing linear units
Determine the tool and technique to
measure with an appropriate level of
precision: lengths and angles
Measure and draw angles using a
protractor
Calculate elapsed time in hours and
minutes
Determine personal references for
customary and metric units of length
Statistics and Probability
Collecting and organizing data
Mean of a group of numbers
Making a graph with a problem solving
strategy
Analyzing graphs such as bar, line, circle,
and pictograph
Graphing ordered pairs
Formulate conclusions and make
predictions from line graphs and
histograms
Algebra and Functions
Define and use appropriate terminology
when referring to constants, variables, and
algebraic expressions
Translate simple verbal expressions into
algebraic expressions
Substitute assigned values into variable
expressions and evaluate using order of
operations
Evaluate the perimeter formula for given
input values
Create and explain patterns and algebraic
relationships algebraically (e.g.: 2n
(doubling))
Problem solving (Strategies used
in all units)
Make a table, model, graph or organized
list
Estimate or find exact answers
Justify the reasonableness of estimates
Draw conclusions
Sequence information
Choose the correct operation(s)
Solve a simpler problem
Write an equation
Predict and test
Find a pattern
Draw a diagram
New York State Education Department Learning Standard for Mathematics
Students will understand the concepts of and become proficient with the skills of mathematics; communicate and reason
mathematically; become problem solvers by using appropriate tools and strategies through the integrated study of number sense and
operations, algebra, geometry, measurement, and statistics and probability.
Content Strands
Strand 1:
Number Sense
and Operations
Definition
Example
Students will understand numbers, multiple ways of representing numbers, 1. Verbally count by 1’s to 20.
relationships among numbers, and number systems; understand meanings 2. Solve proportions using equivalent fractions.
of operations and procedures, and how they relate to one another; compute
accurately and make reasonable estimates.
Strand 2:
Algebra
Students will represent and analyze algebraically a wide variety of
problem solving situations; perform algebraic procedures accurately;
recognize, use, and represent patterns, relations, and functions
algebraically.
1. Use a variety of manipulative materials to
create patterns using attributes of color, size,
or shape.
2. Solve simple one-step equations using basic
whole number facts.
Strand 3:
Geometry
Students will use visualization and spatial reasoning to analyze
characteristics and properties of geometric shapes; identify and justify
geometric relationships, formally and informally; apply transformations
and symmetry to analyze problem solving situations; apply coordinate
geometry to analyze problem solving situations.
1. Identify and appropriately name twodimensional shapes: circle, square,
rectangle, and triangle (both regular and
irregular).
2. Classify angles as acute, obtuse, right and
straight.
Strand 4:
Measurement
Students will determine what can be measured and how, using appropriate
methods and formulas; use units to give meaning to measurements;
understand that all measurement contains error and be able to determine
its significance; develop strategies for estimating measurements.
1. Compare the length of two objects by
representing each length with string or a
paper strip.
2. Identify radius, diameter, chords, and central
angles of a circle.
Strand 5:
Statistics
and Probability
Students will collect, organize, display, and analyze data; make
predictions that are based upon data analysis; understand and apply
concepts of probability.
1. Display data in bar graphs using concrete
objects with intervals of one.
2. Calculate the mean for a given set of data
and use it to describe a set of data.
S:\Ci\MS Word\Math\New Parent Handouts 2005\Gd.2. Parent Handout.doc
1. Example for Primary Instruction.
2. Example for Intermediate Instruction.