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Hempfield School District Curriculum: Unit Template
Course Title: Pre-Algebra Grade 8
Unit Title: Numbers and Operations
Names of Teachers who Developed Unit: Ringler
Dates Developed: May – July 2010
Approximate Dates when Taught During School Year: August –September
Approximate Number of Periods: 13 Class Periods
Summary: In this unit students will begin to build the foundational number sense necessary for
the remainder of the course. They will investigate number patterns and properties as well as
discuss rounding answers appropriately. Students will learn how to do integer, fraction, and
decimal operations with and without calculators and apply these skills to simplify expressions
using order of operations. These expressions can be numeric or algebraic if given values to
substitute for the variables.
Print Materials Needed:
Resources:
McDougal Littell’s Pre-Algebra Textbook (sections 1.1 – 1.7, 2.1, 2.7, 5.2 – 5.5)
McDougal Littell’s Middle School Math Course 3 Textbook (sections 1.2 – 1.4,
2.1 – 2.6, 4.3, 5.1 – 5.7)
Internet Resource Links: classzone.com
Essential Questions (Include PA Standards, Anchors & Eligible Content)
Big Ideas:
 The set of real numbers has infinite subsets including the sets of whole numbers, integers,
rational, and irrational numbers.
 There are some mathematical relationships that are always true and these relationships
are used as the rules of arithmetic and algebra and are useful for writing equivalent forms
of expressions and solving equations and inequalities.
Essential Questions:
 How can numbers and operations be used to represent and solve problems?
 When are integers appropriate to represent problems?
Assessment Anchors:
 M8.A.1 Demonstrate an understanding of numbers, ways of representing numbers,
relationships among numbers and number systems
 M8.A.2 Understand the meaning of operations, use operations and understand how they
relate to each other
 M8.A.3 Compute accurately and fluently and make reasonable estimates
 M8.D.1 Demonstrate an understanding of patterns, relations and functions
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Hempfield School District Curriculum: Unit Template
Eligible Content:
 M8.A.1.1.2 Find the square or cube of a whole number (single digit)
 M8.A.2.1.1 Simplify numeric expressions involving integers, using the order of
operations. (May include grouping symbols. No combining negatives with exponents or
compound exponents)
 M8.A.3.1.1 Identify, use and/or explain when it is appropriate to round up or round
down.
 M8.A.3.1.2 Identify, apply and/or explain when an exact answer is needed or when
estimation is appropriate
 M8.A.3.3.1 Add, subtract, multiply and/or divide integers, fractions, and/or decimals with
and without a calculator (straight computation or word problems)
 M8.D.1.1.1 Continue a numeric or algebraic pattern (pattern must show 3 repetitions –
may include up to 2 operations, squares and square roots)
Know
Vocabulary:
exponent, power, base,
order of operations,
numerical expression,
variable, variable
expression, evaluate,
substitute, integer,
negative integer, positive
integer, absolute value,
opposite, sum, difference,
product, quotient,
numerator, denominator,
common denominator,
least common
denominator, equivalent
fractions, reciprocal,
commutative property,
associative property,
identity property
Facts:
order of operations,
addition rules, subtraction
rule, multiplication and
division rules
Understand
Do
Students will understand: The students will be able to:
 Numbers and
 Complete a number pattern
operations can be
 Read and write exponents in
used to represent
equivalent forms (exponent
and solve real
form and multiplication of
world problems
factors)
 There are some
 Simplify numeric expressions
mathematical
using order of operations
relationships that
 Simplify algebraic expressions
are always true and
by substituting values for all
these relationships
variables and then using order
are used as the rules
of operations
of arithmetic and
 Write expressions by
algebra
translating sentences
 What type of
 Write expressions from word
answer is
problems
appropriate for a
 Use rounding rules to
given problem and
approximate answers
if their answer
 Locate points on a number
makes sense
line
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Compare and order numbers
Find opposites and absolute
values of numbers
Add, subtract, multiply, and
divide integers without a
calculator
Add, subtract, multiply, and
divide fractions and decimals
with and without a calculator
Identify what property is
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Hempfield School District Curriculum: Unit Template
being shown (commutative,
associative, identity)
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Determine if the answer they
obtain is a valid solution to the
problem at hand
Determine what type of
answer is appropriate or
inappropriate for a given
problem (rounding up or
down, estimation or exact)
Stage 2: Assessment Evidence
Assessments/Performance Tasks
Rubric Titles
Benchmark(s) for Course: Unit’s key Assessments
Self-Assessments
Other Evidence, Summarized
Stage 3: Learning Activities
Differentiation:
Readiness
Profile: Learning Styles /
Multiple Intelligences
Interest
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Hempfield School District Curriculum: Unit Template
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Accommodations for ELLs:
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