GUSD Essential Standards:
Algebra Readiness
(Mathematics Framework for California Public Schools)
Topic 1: Whole Numbers
Number Sense 1.3 (grade3) Place Value
Identify digits in numbers
What is a digit's place value?
What digit is in this place?
Place value chart
English to number
Locate/plot a number on number line(include rounding)
Order numbers (least to greatest, greatest to least, and compare )
Number Sense 1.5 Expanded form
273=200+70+3
273=2x102 + 7x101 + 3x100 (powers of 10)
Powers of 10 on place value chart
Topic 2: Operations on Whole Numbers
Multiple representations of a number (complete fluency)
Basic math facts
Non-standard bases (ie: base 5)
Standard algorithm for +, -
Standard algorithm for x, /
Associative and commutative properties
Distributive property
Ten frames
Doubles plus one
Topic 2A:
Prime factorization
List of factors
LCM
GCF
Topic 3: Rational Numbers and Operations
Concept of whole and its parts (not mastery testable, writing prompt?)
Fraction
Equivalence (mixed, improper, simplifying, prime factors)
Order/compare/plot on a number line
Meaning of one
Multiply, divide, positive and negative, like and unlike denominators, prime factors, simplified forms
Fractions-conversions-decimals
Identify terminating/non terminating (repeating) decimals and notations
Decimals: meaning of decimal point : "and"
Identify digits in numbers (decimals)
Include negative exponents for expanded notations
Repeat whole numbers
Place value and expanded form
Operations (+, -, x, /)
Ratio- proportion- percent
Equivalency
Order/compare/plot on number line
Simple percent problems
Applications (% increase/decrease, sales, discounts, tips, commissions, unit rate,)
Topic 4: Negative numbers
Compare/order/plot on number line (include negative fractions)
Integer Operations
Opposites, absolute value
Definition of positive/negative exponents on whole numbers (NS 2.1, gr. 7)
Multiply/divide with exponents on whole numbers (AF 2.1, gr. 7)
Topic 5: Symbolic Notation
Order of operations including grouping symbols
Verbal models to math symbols, expressions and equations
Writing expressions
Write and solve one step equations
Evaluate expressions
Solve Simple linear equations
Graph and interpret results
Topic 6: Equations and Functions
Function rule: prescription Y=2x+5, when given an x, we obtain f(x) and data table
Write an equation of a verbal model
Equality property of addition and multiplication (Lombard-Fulton materials)
Simplify numerical expression by applying properties and justification
Solve 2 step equations
Solve multi-step equations
Topic 7: The Coordinate Plane
Plotting ordered pairs on the coordinate plane
Introduce plane as 4 quadrants and 2 axes
Plot a set of instructions such as a line or polygon
Graph lines from data tables
Concept: a graph is a collection of ordered pairs satisfying a defined condition
Length of lines
Topic 8: Graphing Proportional Relationships
Pythagorean Theorem (ie: integer values 3-4-5)
Ratio and proportion
AF 3.3 and 3.4 (7th)
MG 1.3 (7th)
Geometric context for ratio and proportion; similar right triangles on a graph
Complete fluency in graph and interpreting relationships for y=mx, direct variation
drawing and reading graphs of lines passing through the origin, the geometric context for ratio and proportion, similar right triangles on a graph, the concept of the slope of a line,
Complete fluency in graphing and interpreting relationships of the form y=mx
Algebra Standards:
Standard 2:
Students understand and use such operations as taking the
opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents.
Standard 4:
Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5)+4(x-2)=12.
Standard 5:
Students solve multistep problems, including word problems,
including word problems, involving linear equations and linear inequalities
in one variable and provide justification for each step.
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