Grade 7 Math Learning Standards
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7th Grade Accelerated Course (Please read all the information relative to accelerated course expectations in the above list.)
Topics in the 7th grade accelerated class include: exploring patterns in numbers and geometry; understanding and working with integers and
variables; simplifying expressions; understanding the properties of equality and solving equations; number theory; and geometry. The accelerated
class will not review skills and concepts that students are expected to have mastered in prior years.
Student assignments and assessments include numerous critical thinking and challenge problems. They are expected to work diligently in
and outside of class. They are expected to do every problem on all of their
assignments trying even the most difficult according to information they had in
class or by using their text.
7th Grade Standard Course
Students in both the standard and accelerated courses will use the
text Prealgebra. In addition, all students will learn how to solve equations
through the “Hands On Equations” method. This method introduces students
to solving equations using manipulatives; this process is followed by pictorial
representations and finally through typical symbolic notations. “Hands On
Equations” is very effective in enabling students to visualize and understand
this process which, on the surface, can appear very mechanical. It is a
concrete method that will help students be more successful when they are
exposed to Algebra I in the eighth grade.
Students in the standard classes will study rates, ratios, percents, and proportions; probability and simulations; operations with signed
numbers, generalizations about numbers, and number theory; triangles, polygons and circles. All activities will require students to carefully consider,
practice, write about and apply all of the concepts. They will be expected to learn and to use appropriate mathematical language. Practice with
arithmetic skills is provided within the context of topics that students are studying. However, we encourage parents to work with their children on
number facts, fractions, decimals and percents since these are areas that students should have mastered by the end of the sixth grade. It is
particularly helpful if parents point out the use and importance of mathematics to their children in their everyday lives.
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Grade 7 Math Learning Standards
Strand: Number Sense
Understanding
Students will understand that
Mathematical terminology and symbols
are used in precise ways.
All numbers have a distinct position on
the real number line.
There are equivalent forms for any real
number.
Essential Questions
• Why is it important to use precise
mathematical vocabulary & symbols?
• How does mathematical terminology
relate to common English words?
• How do we distinguish between the
meaning of mathematical terminology
and similar English words?
• How does the use of different
symbols or terminology change the
meaning or result of our work?
• 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?
Knowledge
Students will know the/that
• Vocabulary related to numbers and their
operations.
• Symbols related to mathematical terms
and operations.
• Meaning of perfect squares and perfect
cubes; square roots.
Skills
Students will be able to
• Use proper symbols and vocabulary to
communicate their mathematical ideas.
• Translate between the language of
English and the language of
mathematics.
• Use fraction bar as a division symbol.
• Use parentheses in multiplication
problems.
• Place value of the digits in any number.
• Types of numbers that can be
represented on a number line.
• Compare and order all real numbers.
• Locate, label and read numbers on the
real number line.
• Use absolute value to identify
distances on the number line.
• Construct a number line with any type
of real number.
• Determine place value of any digit in a
number.
• Use prime factorization to find greatest
common factor/least common multiple.
• Apply divisibility rules for 4, 6, 8, 9, 12*.
• Convert numbers from one form to
another (fractions, decimals, percents).
• Follow the order of operations properly
including other grouping symbols.
• Find roots of perfect square numbers
and perfect cube numbers.
• Make logical predictions about the
result of an operation.
• Write the numbers in an operation
based on the verbal statement in a
problem or based on a diagram.
• Make reasonable estimates based on
data in a problem.
• Round numbers.
The results of an operation depend on
the types of numbers involved.
• How does identifying the types of
numbers involved in an operation
assist in determining the
reasonableness of the result?
• Vocabulary related to all operations including exponentiation.
• Symbols related to all operations
(including the ‘fraction bar’ as a division
symbol).
Estimation is a logical, useful tool.
• How can estimation be used to
determine the reasonableness of an
answer?
• How does rounding impact a result?
• Difference between rounding and
estimation.
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Grade 7 Math Learning Standards
Understanding
Students will understand that
Ratios and proportions describe
relationships between quantities.
Essential Questions
• In what situations are
ratio/proportions most useful?
Strand: Algebra (Patterns & Functions)
Understanding
Essential Questions
Students will understand that
Patterns of numbers correspond to
• How can we write algebraic
algebraic expressions that can be used
expressions to model patterns of
in problem solving.
numbers?
• How are algebraic expressions
applied to solving problems?
Knowledge
Students will know the/that
• Vocabulary related to ratios and
proportions.
• Different forms of a ratio.
• Connections among ratios, rates and
proportions.
Skills
Students will be able to
• Determine if 2 ratios can form a
proportion.
• Determine the scale factor based on a
diagram or information in a given
situation.
• Set up a proportion based on
information in a given situation.
• Solve proportions. Use proportions to
convert units of measure.
Knowledge
Students will know the/that
• Distributive property.
• Meaning of like terms.
• Expressions can be represented in
numerous ways.
Skills
Students will be able to
• Write algebraic expressions that model
a given pattern.
• Write a pattern that matches an
algebraic expression.
• Use a pattern to predict subsequent
values.
• Simplify expressions by combining like
terms and using the distributive
property.
• Evaluate expressions by substituting
numerical values.
• Record the process of solving an
equation pictorially and algebraically.
• Use properties of equality to isolate the
variable.
• Solve equations requiring several steps.
• Check the solution of an equation.
• Identify the coordinates of an ordered
pair that names a point on the
Cartesian coordinate plane.
• Analyze and represent real situations
and mathematical relations with
concrete models, tables, graphs and
rules in words and symbols.
Equations are fundamental tools for
modeling situations.
• How do we use equations to model
situations?
• How do we write solutions?
• Concept of a variable as the missing
number in an equation.
• Concept of maintaining a balance while
solving an 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 and a
Cartesian coordinate plane.
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Grade 7 Math Learning Standards
Strand: Geometry and Measurement
Understanding
Students will understand that
Mathematical terminology and symbols
for geometry and measurement are
used in precise ways.
Different types of measurements are
required depending on the situation or
objects involved.
Essential Questions
• Why is it important to use precise
mathematical vocabulary and
symbols?
• How does mathematical terminology
relate to common English words?
• How do we use different types of
measurements?
Knowledge
Students will know the/that
• Regular polygons.
• Concave & convex polygons.
• Symbols for congruent, perpendicular,
parallel.
• Reflex angles.
• Uses of linear, square and cubic
measures.
Perimeter and area are distinct
concepts that require different units of
measure and appropriate labels.
• How do we appropriately label
perimeter and area?
• What are the connections between
perimeter and area?
• Meaning of circumference as the
perimeter of a circle.
Different transformations can be
applied to plane figures.
• What are the effects of
transformations on plane figures?
• Meaning of rotational symmetry.
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 data
events in the physical world and in
and to predict future events.
our society?
Knowledge
Students will know the/that
• Stem and leaf plots and circle graphs
can be used to represent data.
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Skills
Students will be able to
• Identify regular polygons.
• Concave & convex polygons.
• Introduce symbol markings on a
diagram.
• Draw angles with specific measures
using a protractor.
• Convert simple units of measure such
as feet to yards or ounces to pound.
• Describe how to find & also calculate
area of circles & typical plane figures.
• Find any missing part in a standard
formula using algebraic processes for
solving an equation (e.g. the length of
the rectangle when given the width and
area.)
• Perform/record simple transformations.
Skills
Students will be able to
• Construct stem and leaf plots and
circle graphs using data.
• Conduct an experiment that produces
data and compute a ratio to represent
the probability.