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Standard 1.0 Knowledge of Algebra, Patterns, AND Functions – Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.
|Grade 3 |Grade 4 |Grade 5 |Grade 6 |Grade 7 |Grade 8 |
|A. Patterns and Functions |A. Patterns and Functions |A. Patterns and Functions |A. Patterns and Functions |A. Patterns and Functions |A. Patterns and Functions |
| | | | | | |
|1. Identify, describe, extend, and create |1. Identify, describe, extend, and create |1. Identify, describe, extend, and create |1. Identify, describe, extend, and create |1. Identify, describe, extend, and create |1. Identify, describe, extend, and create |
|numeric patterns and functions |numeric patterns and functions |numeric patterns and functions |numeric patterns and functions |linear patterns and functions |patterns, functions and sequences |
|Represent and analyze numeric patterns |a) Represent and analyze numeric patterns |a) Interpret and write a rule for a |Identify and describe sequences represented|Complete a function table with a given |Determine the recursive relationship of |
|using skip counting |using skip counting |one-operation (+,-, x, ÷ with no |by a physical model or in a function table |two-operation rule |arithmetic sequences represented in words, |
|Assessment limit: Use 2, 5, 10, or 100 |Assessment limit: Use patterns of |remainders) function table |Interpret and write a rule for a |Assessment limit: Use the operations (+, -,|in a table or in a graph |
|starting with any whole number (0 – 1000) |3,4,6,7,8, or 9 starting with any whole |Assessment limit: Use whole numbers or |one-operation (+, -, x, ÷) function table |x), numbers no more than 20 in the rule and|Assessment limit: Provide the nth term no |
|Represent and analyze numeric patterns |number (0 – 100) |decimals with no more than 2 decimal places|Assessment limit: Use whole numbers or |whole numbers (0 – 500) |more than 10 terms beyond the last given |
|using skip counting |b) Create a one-operation (+ or -) |(0 – 1000) |decimals with no more than two decimal |Identify and extend a geometric sequence |term using common differences no more than |
|Assessment limit: Use 3 or 4 starting with |function table to solve a real world |b) Create a one-operation (x, ÷ with no |places (0 – 10,000) |Describe how a change in one variable in a |10 with integers (-100 to 5000) |
|0, 1, 2, 3, or 4 (0 – 30) |problem |remainders) function table to solve a real |Complete a function table with a given |linear function affects the other variable |Determine the recursive relationship of |
|Represent and analyze numeric patterns |c) Complete a function table using a |world problem |two-operation rule |in a table of values |geometric sequences represented in words, |
|using skip counting backward |one-operation (+,-, x, ÷ with no |c) Complete a one-operation function |Assessment limit: Use the operations of (+,| |in a table, or in a graph |
|Assessment limit: Use 10 or 100 starting |remainders) rule |table |-, x), numbers no more than 10 in the rule,| |Assessment limit: Provide the nth term no |
|with any whole number (0 – 1000) |Assessment limit: Use whole numbers (0 – |Assessment limit: Use whole numbers with +,|and whole numbers (0 – 50) | |more than 5 terms beyond the last given |
|Complete a function table using a given |50) |-, x, ÷ (with no remainders)or use | | |term using the recursive relationship of |
|addition or subtraction rule |d) Describe the relationship that |decimals with no more than two decimal | | |geometric sequences with whole numbers and |
| |generates a one-operation rule |places with + , - (0 – 200) | | |a common ratio of no more than 5:1 (0 – |
| | |d) Apply a given two operation rule for a | | |10,000) |
| | |pattern | | |Determine whether relationships are linear |
| | |Assessment limit: Use two operations (+, -,| | |or nonlinear when represented in words, in |
|2. Identify, describe, extend, and create | |x) and whole numbers (0 – 100) | | |a table, symbolically, or in a graph |
|non-numeric growing or repeating patterns | | | | |Assessment limit: Use a graph to determine |
|Represent and analyze growing patterns | | | | |if a relationship is linear or nonlinear |
|using symbols, shapes, designs, or pictures|2. Identify, describe, extend, analyze, | | | |Determine whether relationships are linear |
|Assessment limit: Start at the beginning, |and create a non-numeric growing or | | | |or nonlinear when represented symbolically |
|show at least 3 levels but no more than 5 |repeating pattern | | | | |
|levels, and ask for the next level |a) Generate a rule for the next level of | | | | |
|Represent and analyze repeating patterns |the growing pattern | | | | |
|using symbols, shapes, designs, or pictures|Assessment limit: Use at least 3 levels but| | | | |
| |no more than 5 levels | | | | |
|Assessment limit: Use no more than 4 |b) Generate a rule for a repeating pattern| | | | |
|objects in the core of the pattern |Assessment limit: Use no more than 4 | | | | |
| |objects in the core of the pattern | | | | |
| |Create a non-numeric growing or repeating | | | | |
| |pattern | | | | |
Standard 1.0 Knowledge of Algebra, Patterns, AND Functions – Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.
|Grade 3 |Grade 4 |Grade 5 |Grade 6 |Grade 7 |Grade 8 |
|B. Expressions, Equations, and |B. Expressions, Equations, and Inequalities|B. Expressions, Equations, and Inequalities |B. Expressions, Equations, and Inequalities|B. Expressions, Equations, and |B. Expressions, Equations, and |
|Inequalities | | | |Inequalities |Inequalities |
| |1. Write and identify expressions |1. Write and identify expressions | | | |
|1. Write and identify expressions |a) Represent numeric quantities using |a) Represent unknown quantities with one |1. Write and evaluate expressions |1. Write and evaluate expressions |1. Write, simplify, and evaluate |
|Represent numeric quantities using |operational symbols (+, - , x, ÷ with no |unknown and one operation |Write an algebraic expression to represent |Write an algebraic expression to represent |expressions |
|operational symbols (+, -, x, () |remainders) |(+, -, x, ÷ with no remainders) |unknown quantities |unknown quantities |Write an algebraic expression to represent|
|Assessment limit: Use operational symbols |Assessment limit: Use whole numbers (0 – |Assessment limit: Use whole numbers (0 – 100)|Assessment limit: Use one unknown and one |Assessment limit: Use one unknown and one |unknown quantities |
|(+ or -) and whole numbers (0 – 50) |100) |or money ($0 - $100) |operation (+, -) with whole numbers, |or two operations (+, -, x, ÷ with no |Assessment limit: Use one unknown and no |
| |b) Determine equivalent expressions |b) Determine the value of algebraic |fractions with denominators as factors of |remainders) with whole numbers, fractions |more than 3 operations and rational |
| |Assessment limit: Use whole numbers (0 – |expressions with one unknown and one-operation|24, or decimals with no more than two |with denominators as factors of 100, or |numbers (-1000 to 1000) |
| |100) |Assessment limit: Use +, - with whole numbers|decimal places (0 – 200) |decimals with no more than three decimal |Evaluate an algebraic expression |
| | |(0 – 1000) or (, ( (with no remainders) with |Evaluate an algebraic expression |places |Assessment limit: Use one or two unknowns |
| | |whole numbers (0 – 100) and the number for the|Assessment limit: Use one unknown and one |(0 – 500) |and up to three operations and rational |
| | |unknown is no more than 9 |operation (+, -) with whole numbers (0 – |Evaluate algebraic expressions |numbers |
| | |c) Use parenthesis to evaluate a numeric |200), fractions with denominators as factors|Assessment limit: Use one unknown and no |(-100 to 100) |
| | |expression |of 24 (0 – 50), or decimals with no more |more than two operations (+, -, x,|Evaluate numeric expressions using the |
| | | |than two decimal places (0 – 50) |÷ with no remainders) with whole numbers (0|order of operations |
| | | |Evaluate numeric expressions using the order|– 200), fractions with denominators as |Assessment limit: Use no more than 5 |
| | | |of operations |factors of 100 (0 – 100), or |operations including exponents of no more |
| | | |Assessment limit: Use no more than 4 |decimals with no more than three decimal |than 3 and 2 sets of parentheses, |
| | | |operations (+, -, x, ÷ with no remainders) |places (0 – 100) |brackets, a division bar, or absolute |
| | | |with or without 1 set of parentheses or a |Evaluate numeric expressions using the |value with rational numbers (-100 to 100) |
| | | |division bar and whole numbers (0 – 100) |order of operations |Simplify algebraic expressions by |
| | | |Represent algebraic expressions using |Assessment limit: Use no more than 4 |combining like terms |
| | | |physical models, manipulatives, and drawings|operations (+, -, x, ÷ with no remainders) |Assessment limit: Use no more than 3 |
| | | | |with or without up to 2 sets of |variables with integers (-50 to 50), or |
| | | | |parentheses, brackets, or a division bar, |proper fractions with denominators as |
| | | | |with whole numbers (0 – 200), fractions |factors of 20 (-20 to 20) |
| | | | |with denominators as factors of 100 (0 – |Describe a real-world situation |
| | | | |100), or decimals with no more than three |represented by an algebraic expression |
| | | | |decimal places (0 – 100) | |
| | | | |d) Simplify algebraic expressions |2. Identify, write, solve, and apply |
| | | |2. Identify, write, solve, and apply |represented as physical models by combining|equations and inequalities |
| | |2. Identify, write, solve, and apply |equations and inequalities |like terms |Write equations or inequalities to |
|2. Identify, write, solve, and apply |2. Identify, write, solve, and apply |equations and inequalities |Identify and write equations and | |represent relationships |
|equations and inequalities |equations and inequalities |a) Represent relationships using the |inequalities to represent relationships |2. Identify, write, solve, and apply |Assessment limit Use a variable, the |
|Represent relationships using appropriate |a) Represent relationships using relational|appropriate relational symbols (>, , , >, , ................
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