Algebra Foundational Competencies Class
Units
Unit 1
Number Sense
Unit 2
Conceptual Understanding of Operations
Unit 3
Conceptual Understanding of Fractions
Unit 4
Conceptual Understanding of Decimals
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Read and Write Numbers
Compare Numbers
Place Value
Basic Integer Concepts
Add and Subtract Whole Numbers
Multiply and Divide Whole Numbers
Properties of Operations
Basic Fraction Concepts
Comparing Fractions
Add and Subtract Fractions
Multiply and Divide Fractions
Basic Decimal Concepts
Relate Fractions, Decimals, and Percents
Add and Subtract Decimals
Multiply and Divide Decimals
Algebra Foundational Competencies Class
Grading
Concepts
Read and
Write
Numbers
Compare
Numbers
Place Value
Level 2
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Basic Integer
Concepts
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Count to 100 by 1’s
Skip Count
Counting when not starting at 1
Cardinality (understanding along with counting)
Understand comparing groups (1 digit numbers)
Compare 2 written numerals (1 digit numbers)
Use symbols or written words in comparison >, <, =
(1 digit numbers)
Use whole numbers to denote powers of 10 in
exponential form
Use place value understanding to round whole
numbers to highest place value (2-3 digit numbers)
Add and subtract by multiples of 10
Multiply and divide by multiples of 10
Identify place values for a given whole number up
through millions
Use positive and negative numbers to represent
quantities in real-world context explaining the
meaning of zero in each situation
Recognize opposite signs of numbers as indicating
locations on opposite sides of 0 on the number line
Find and position rational numbers, including
integers, on a number line
Interpret statements of inequality as statements
about the relative position of two numbers on a
number line diagram
Level 3
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Write numbers in standard and written Form
Read Numbers
Compose and decompose numbers
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Understand comparing groups (2 and 3 digit numbers)
Order a set of written numbers (2 and 3 digit numbers
Use Symbols and written words in comparisons >, <, = (2
and 3 digit numbers)
Recognize the relationship between exponents and
standard form
Use place value understanding to round whole numbers to
any place (2 and 3 digit numbers)
Add and subtract by multiples of powers of 10
Multiply and divide by multiples of powers of 10
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Write, interpret, and explain statements of order for
rational numbers in real-world contexts
Interpret absolute value as magnitude for a positive or
negative quaintly in a real-world situation
Distinguish comparisons of absolute value from
statements about order
Algebra Foundational Competencies Class
Grading
Concepts
Add and
Subtract
Whole
Numbers
Level 2
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Multiply and
Divide Whole
Numbers
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Properties of
Operations
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Add and subtract multi-digit numbers using
place value strategies
Add and subtract using fluency strategies
(counting on, making 10, etc)
Add and subtract using properties of operations
(communitive and associative properties)
Relate multiplication and division problems
Multiply multi-digit numbers using a variety of
strategies
Divide multi-digit numbers using a variety of
strategies
Identify properties of mathematical operations
Level 3
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Fluently add and subtract multi-digit numbers using
the stand algorithm
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Fluently divide multi-digit numbers using the
standard algorithm
Fluently multiply and divide multi-digit numbers using
the standard algorithm
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Perform operations using properties (commutative,
associative, and distributive properties)
Algebra Foundational Competencies Class
Grading Concepts
Level 2
Level 3
Basic Fraction
Concepts
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Understand what a fraction is an the relationship
to division (numerator / denominator)
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Comparing Fractions
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Explain how two factions are equivalent
Convert between improper fractions and mixed
numbers
Compare fractions and mixed numbers by
reasoning about their size
Compare factions and mixed numbers with the
same denominator or the same numerator
Add and subtract fractions and mixed numbers
with unlike denominators (including cases where
the student must borrow/ regroup)
Add and subtract fractions and mixed numbers
with like denominators (including cases where the
student must borrow / regroup)
Divide fractions by fractions
Divide by unit fractions
Multiply fractions
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Add and Subtract
Fractions
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Multiply and Divide
Fractions
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Understand and represent a fraction as a
number on a number line and through
other models such as bar and pie
Compare fractions and mixed numbers
with different numerators and different
denominators
Solve word problems that involve adding
fractions and mixed numbers
Solve word problems that involve
subtracting fractions and mixed numbers
Solve word problems that require
multiplying fractions and mixed numbers
Solve word problems that require
dividing fractions and mixed numbers
Algebra Foundational Competencies Class
Grading Concepts
Basic Decimal Concepts
Level 2
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Read and write decimal numbers (including
money)
Identify decimal place value through ten
thousandths
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Relate Fractions,
Decimals, and Percent
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Relate around benchmark fractions, decimals and
percents (halves, fourths, tenths, hundredths)
Add and Subtract
Decimals
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Add and subtract decimals including money
(regroup or borrow)
Multiply and Divide
Decimals
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Multiply and divide decimals including money
using the standard algorithms
Identify proper placement of the decimal point in a
multiplication and division problem
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Level 3
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Represent decimals using number lines
and 100 square grids
Compare decimals
Round decimals using place value (ie
money)
Convert between fractions and decimals
Convert between fractions and percents
Convert between decimals and percents
Solve real world problems that require
adding and subtracting decimals
including money (regroup and borrow)
Solve real work problems that require
multiplying and dividing decimals
including money