Grade 5 Math Learning Standards
G
Grraaddee 55 M
Maatthheem
maattiiccss CCuurrrriiccuulluum
mO
Ovveerrvviieew
w
The fifth grade math program builds on and extends the concepts begun in the earlier grades. Students entering fifth grade are fluent and
automatic with basic number facts for all operations. They are able to compute accurately in multiplication for up to three digit multiplicands by two
digit multipliers and divide up to three digit dividends by one digit divisors, with and without remainders. Students also compute with fractions and
decimals, and develop an understanding of the relationship between fractions and decimals. During the geometry units, students become skilled in
measuring angles and build upon previously presented geometric concepts such as
classifying triangles and angles, identifying geometric solids, defining congruency,
measuring circumference/radius, and creating tessellations. Students collect,
organize, analyze, and present data using a variety of graphing structures including
bar graphs, line graphs, circle graphs, line plots, stem and leaf plots, and tree
diagrams. They analyze data and determine the significance of median, mean, mode,
maximum, minimum, and range for a data set. Students explore the probability of an
event occurring using experimental results and become familiar with predicting
outcomes. Students continue to apply many problem solving strategies and are
asked to communicate their mathematical reasoning and solutions orally and in
writing using the appropriate symbols and vocabulary.
Maximizing the development of every student and strengthening connections
between mathematics in school and the world at large are primary goals of the fifth
grade math program.
Strand: Number Sense
Understanding
Students will understand that
Mathematical terminology and
symbols are used in precise
ways.
Essential Questions
• Why is it important to use precise
mathematical vocabulary and
symbols?
• How does mathematical terminology
relate to common English words?
• How does the use of different symbols
or terminology change the meaning or
result of our work?
Knowledge
Students will know the/that
• Powers of 10.
• Know the following types of numbers:
squares, prime and composite.
• Meaning of the term multiple & factors.
• Divisibility rules for 2, 3, 5, 10.
• Connection between addition &
subtraction and multiplication & division.
• Meaning of the terms proper fraction,
improper fraction and mixed numbers.
28
Skills
Students will be able to
• Use powers of 10 to facilitate mental math.
• Identify squares, prime and composite
numbers.
• Recognize when one number is a multiple of
another number.
• Find the greatest common factor and least
common multiple of 2 whole numbers.
Grade 5 Math Learning Standards
Understanding
Students will understand that
All numbers have a distinct
position on the real number line.
There are equivalent forms for
any real number.
The results of an operation
depend on the types of numbers
involved.
Essential Questions
Knowledge
Students will know the/that
• What is the relationship between the
position of a number on the number
line and the value of the number?
• What are the different structures for a
number line?
• What is the significance of each of the
elements of the number line?
• How can we use a number line to solve
problems?
• When is one form of a number more
useful than another form?
• How are the different forms of numbers
connected?
• How does identifying the types of
numbers in an operation help in
determining the reasonableness of the
result?
Skills
Students will be able to
• Find and position fractions, mixed numbers
and decimals on a number line and in an
ordered list.
• Simplify fractions.
• Find the factors of composite numbers.
•
•
•
•
•
•
•
•
Estimation is a logical, useful
tool.
• How can estimation be used to
determine the reasonableness of an
answer?
• When is estimation the best strategy?
• How does rounding impact a result?
•
29
Apply the divisibility rules for 2, 3, 5, 10.
Divide with 2 digit divisors.
Divide with decimals in the dividend.
Identify commonly used fractions and their
decimal and percent equivalents.
Demonstrate understanding of multiplication
and division of decimals using diagrams and
manipulatives.
Select appropriate operations to complete
problems involving operations with fractions,
mixed numbers, decimals, and percents.
Find sums, differences, and products with
fractions.
Find sums, differences, products and quotients
with decimals.
Estimate sums, differences, products and
quotients.
Grade 5 Math Learning Standards
Strand: Algebra (Patterns & Functions)
Understanding
Essential Questions
Students will understand that
Many patterns exist in
• What are number patterns and why are
mathematics.
they useful?
• How can we find number or picture
patterns?
• Where do patterns exist in the physical
world?
Knowledge
Students will know the/that
Skills
Students will be able to
• Identify, describe and extend whole number
sequences.
• Represent patterns with manipulatives.
Equations are fundamental tools
for modeling situations.
• How do we use equations to model
situations?
• How do we express solutions?
• Concept of a variable as the missing
number in a number sentence
(equation).
• Find the ‘missing number’ in a number
sentence (equation).
Relations and functions are used
to describe physical relationships
in the real world.
• How do we represent functions through
graphic representations?
• Meaning of ordered pairs in quadrant
one of the Cartesian coordinate plane.
• Identify the coordinates of the ordered pairs
that name points in quadrant one of the
Cartesian coordinate plane.
• Analyze and represent real situations with
concrete models, tables, graphs and rules in
words and symbols.
Knowledge
Students will know the/that
• Stem and leaf plots and circle graphs
can be used to represent data.
Skills
Students will be able to
• Construct stem and leaf plots and circle
graphs using data.
• Make predictions and draw conclusions from a
set of data.
• Rank, compare and interpret data using
percents.
• Identify the maximum, minimum, median,
mode and mean for a data set.
Strand: Data, Statistics and Probability
Understanding
Essential Questions
Students will understand that
There are a variety of ways to
• How can we use data to interpret
represent, model, and analyze
events in the physical world and in our
data and to predict future events.
society?
30
Grade 5 Math Learning Standards
Strand: Geometry and Measurement
Understanding
Essential Questions
Students will understand that
Mathematical terminology and
• Why is it important to use precise
symbols for geometry and
mathematical vocabulary and
measurement are used in
symbols?
precise ways.
• How does mathematical terminology
relate to common English words?
Different types of measurements
are required depending on the
situation or objects involved.
• How do we use different types of
measurements?
Perimeter and area are distinct
concepts that require different
units of measure and appropriate
labels.
Different transformations can be
applied to plane figures.
• How do we appropriately label
perimeter and area?
• What are the connections between
perimeter and area?
• What are the effects of transformations
on plane figures?
Knowledge
Students will know the/that
• Polygons: pentagons, hexagons and
octagons.
• Properties of a parallelogram.
• Types of angles: acute, obtuse and right.
• Types of triangles (equilateral, isosceles,
scalene).
• Meaning of perpendicular lines.
• 3-dimensional shapes: spheres and
cubes.
• Meaning of radius and diameter of a
circle.
• Angle sum of a triangle.
• Uses of linear, square and cubic
measures.
• Meaning of circumference as the
perimeter of a circle.
• Meaning of surface area.
• Meaning of rotational symmetry.
31
Skills
Students will be able to
• Identify pentagons, hexagons and octagons.
• Identify and construct the radius and diameter
of a circle.
• Find the distance between 2 points on
horizontal number lines.
• Measure and draw angles with a protractor.
• Estimate the measure of angles in simple
polygons.
• Determine congruence through measurement.
• Describe how to find and also calculate area of
squares, rectangles, triangles, and
parallelograms.
• Find the surface area of a cube.
• Perform and record simple transformations.
• Draw reflected images.
• Illustrate and record examples/patterns that
represent rotational symmetry.
• Determine congruence through
transformations.