USING SYMBOLIC EQUATIONS TO SOLVE REAL WORLD PROBLEMS
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Algebra  K3, 46, 712 . Algebra K3 (printable PDF) Essential Skills: 1. Understand patterns, relations, and functions 2. Represent and analyze mathematical situations and structures using algebraic symbols 3. Use mathematical models to represent and understand quantitative relationships 4. Analyze change in various contexts 5. Use paper and pencil to demonstrate skills prior to using technology . Kindergarten Important to Know Using Concrete Materials • Represent a pattern using objects, drawings, rhythms, and body movements. • Verbally describe a pattern • Copy a given pattern • Continue a pattern • Recognize a pattern in the environment • Sort objects using the attributes: size, color, shape, or weight • Translate from one pattern representation to another . Grade 1 Important to Know Using Concrete Materials • Represent, copy, and continue patterns • Sort objects by multiple attributes • Identify and extend missing elements of repeating patterns and sequences of numbers. • Create real life problems and translate them to number sentences • Calculate missing addend problems using concrete materials • Describe change of quality using er and est words • Describe change of quantity . Grade 2 Important to Know • Identify and extend patterns of objects and symbols • Recognize patterns in numbers and number combinations • Use patterns to make generalizations and predictions by: 1. Determine the rules and identify missing numbers in a sequence of numbers with emphasis on addition and subtraction; 2. Determine the rules and identify missing numbers in a table of number pairs; 3. Identify missing elements in a pattern and justify their inclusion 4. Analyze both repeating and growing patterns using charts, tables, and skip counting • Find the value of the empty box in addition and subtraction • Model situations that involve addition and subtraction of whole numbers using objects, pictures and symbols . Grade 3 Important to Know • Can recognize multiplication patterns • Use patterns to make generalizations and predictions by: 1. Determining the rules and identifying missing numbers in a sequence of numbers; 2. Determining the rules identifying missing numbers in a table of number pairs for multiplication, division, addition and subtraction 3. Identify missing elements in numeric and geometric patterns • Can find the value of the empty box in multidigit addition and subtraction problems and basic multiplication problems • Write and explain orally thinking strategies for making computations with emphasis on addition, subtraction and multiplication • Create reallife problems and translate them to number sentences • Model problem situations with objects and use representations such as graphs, tables and equations to draw conclusions . . Algebra 46 (printable PDF) Essential Skills: 1. Understand patterns, relations, and functions 2. Represent and analyze mathematical situations and structures using algebraic symbols 3. Use mathematical models to represent and understand quantitative relationships 4. Analyze change in various contexts 5. Use paper and pencil to demonstrate skills prior to using technology . Grade 4 Important to Know • Recognize and extend a repetitive numeric pattern and communicate the rule • Understand the use of letters/box as a variable to represent 1 unknown • Communicate/explain strategies for solving computation problems with 1 variable • Graph ordered pairs of letters and numbers in all four quadrants on a coordinate plane. . Grade 5 Important to Know • Extend a progressive numeric pattern using one operation. • Graph ordered pairs and describe their relationship • Communicate/explain strategies for solving computation problems with one variable • Express/solve math equations using + and  with one variable. • Demonstrate how to solve a problem using order of operations. • Given a partially completed table of 2 columns, recognize the pattern in the table and complete it and explain the rule used in the table. . Grade 6 Important to Know • Graph ordered pairs and describe their relationship • Communicate/explain strategies for solving computation problems with one variable • Express/solve math equations using + and  with one variable. • Use parentheses to change results of a computation • Given a partially completed table of 2 columns, recognize the pattern in the table and complete it or extend the table and explain the rule used in the table. . . Algebra 712 (printable PDF) Essential Skills: 1. Understand patterns, relations and functions 2. Represent and analyze mathematical situations and structures using algebraic symbols 3. Use mathematical models to represent and understand quantitative relationships 4. Analyze change in various contexts 5. Use paper and pencil to demonstrate skills prior to using technology . Grade 7 Important to Know • Use parentheses accurately to group numbers for applying operations • Apply formulas to problem situations • Describe problems involving ratios, proportions, and percents with algebraic expressions • Solve linear equations with one variable using +, , x, / • Evaluate algebraic expressions • Interpret graphs of problem situations describing linear relationships • Construct graphs describing real world problems; and assign and label scales to axes • Construct tables to describe a linear problem situation • Write a linear equation to represent a real world problem • Symbolize, using variables, the relations between addition, subtraction, multiplication, and division . Grade 8 Important to Know • Use and relate tables, graphs, and equations to solve problems • Explain in words the meaning of the expression "solution of an equation" • Interpret problems described by linear inequalities in words and graphs • Find the distance between two points in the coordinate plane • Explore and interpret the concepts of slope and intercept as characteristics of linear functions • Factor mathematical expressions involving a common monomial factor • Relate ratios and proportions to equations • Solve linear equations using integers • Graph linear equations on a coordinate plane • Solve linear equations using +, , x, and / . Grade 9 Important to Know • Represent relations and linear and quadratic functions in various forms • Analyze functions of one variable by investigating rates of change, intercepts and zeros • Perform transformation such as arithmetically combining commonly used functions • Interpret representations of linear and quadratic functions • Identify the equivalent forms of expressions, equations, inequalities and relations • Write and solve equivalent forms of equations, inequalities and systems of equations • Use symbolic algebra to represent and explain mathematical relationships • Identify quantitative relationships in a situation and determine classes of functions that might model the relationship • Translate word problems into mathematical symbolic expressions • Judge the meaning usefulness, and reasonableness of solutions • Approximate and interpret rates of change from graphical and numerical data . Grade 10 Important to Know • Represent relations and linear and quadratic functions in various forms • Analyze functions of one variable by investigating rates of change, intercepts and zeros • Perform transformations such as arithmetically combining commonly used functions • Interpret representations of quadratic functions • Write and solve equivalent forms of equations, inequalities and systems of equations mentally, with paper and pencil, and using technology • Use symbolic algebra to represent and explain mathematical relationships • Judge the meaning, usefulness, and reasonableness of solutions • Identify quantitative relationships in a situation and determine classes of functions that might model the relationship • Translate, solve and test the reasonableness of word problems into mathematical symbolic expressions (linear quadratic approximate and interpret rates of change from graphical and numerical data . Grade 11 Important to Know • Generalize patterns using explicitly defined and recursively defined functions • Represent relations and logarithmic, exponential and trig functions in various forms • Analyze functions of one variable by investigating asymptotes and local and global behavior • Perform transformation such as arithmetically combining, composing and inverting commonly used functions • Compare the properties of classes of functions including exponential, polynomial, rational, logarithmic and periodic functions • Interpret representations of nonlinear functions • Use symbolic algebra to represent and explain mathematical relationships • Use a variety of symbolic representations, including recursive and parametric equations for functions and relations • Judge the meaning usefulness, and reasonableness of solutions . Grade 12 Important to Know • Generalize patterns using explicitly defined and recursively defined functions • Represent relations and logarithmic, exponential, and trig functions in various forms • Identify quantitative relationships in a situation and determine classes of functions that might model the relationship • Translate, solve and test the reasonableness of word problems into mathematical symbolic expressions (linear quadratic, nonlinear) • Approximate and interpret rates of change from graphical and numerical data  
