Perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
· Add, subtract, multiply and divide with decimals (and verify the reasonableness of the results).
· Demonstrate proficiency with division, including division with positive decimals and long division with multi-digit divisors.
· Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less).
6th Grade
Competencies
Proficiencies
6th grade general math
1) Apply and extend previous undertandings of numbers to the system of rational numbers.
2) Understand ratio concepts.
3) Compute independently.
4) Analyze two and three-dimensional shapes.
5) Reason about and solve one-variable
equations and inequalities.
6) Develop understanding of counting principles and probable outcomes.
1a)Understand a rational number as a point on a number line. 1b)Understand ordering and absolute value of rational numbers.
1c)Solve real world problems. 2a) Solve unit rate problems including those involving unit pricing and constant speed. 2b) Find a percent of a quantity as it relates to hundedths. 2c) Convert within the measurement systems. 3a) Fluently divide multi-digit numbers. 3b) Fluently multiply and divide fractions and decimals 3c) Demonstrate an undertanding of integer operations. 4a) Identify, classify and distinguish different types of triangles, quadrilaterals, other polygons, and three-dimensional figures. 4b) Find the area of triangles and polygons . 4c) Find the volume of rectangular prisms. 5a) Understand solving an equation or inequality as a process of answering a question. 5b) Use variables to represent numbers and write expressions to solve a problem. 5c) Analyze two quantities using graphs and tables. 6a) Answer questions involving chance and possible combinations in a given situation. 6b) Analyze patterns, trends, or distributions using measures of central tendencies.
7th Grade
Competency
Proficiencies
Apply and extend previous understandings of numbers to add, subtract, multiply, and divide rational numbers.
-Add, Subtract, Multiply, and Divide: § Decimals § Fractions § Integers -Apply the order of operations when evaluating numeric expressions -Apply properties of numbers and operations
Analyze proportional relationships and use them to solve real-world and mathematical problems.
-Solve multi-step problems involving rate, average, speed, distance, time -Solve multistep ratio and percent problems. -Identify slope and y-intercept of a line
-Solve problems involving scale drawings of similar geometric figures
Solve real-life and mathematical using numerical and algebraic expressions and equations.
-Apply the order of operations when evaluating algebraic expressions -Simplify numerical and algebraic expressions by applying properties of rational numbers -Write expression , equations and inqualities using variables and appropriate operations -Understand inverse properties and use to solve one-step equations -Solve two-step equations
Apply geometric relationships of one-, two-, and three-dimensional figures to solve problems.
-Apply properties of angle relationships to solve problems -Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms -Apply the concept of congruency to solve problems on a coordinate plane, involving translations, rotations, and reflections
Interpret, and use data to solve problems
- Analyze patterns, trends, or distributions in data in a variety of contexts by solving problems using measures of central tendency -Organize and appropriately display data
8th Grade
Competency
Proficiencies
Evaluate problems with real numbers.
-Define, compare, and order rational and irrational numbers. -Evaluate and simplify algebraic and numeric expressions using the order of operations.
Solve linear equations in one and two variables, and apply this to real world situations.
-Use and explain the mulit-step process of solving linear equations.
-Translate written expressions into algebraic expressions.
-Graph linear equations, using a table of values, intercepts, and slope intercept form.
-Solve systems of equations graphically.
Analyze functions through a variety of methods.
-Find and interpret the slope fo the graph of a linear function.
Find and interpret patterns that define functions or other relations.
-Identify and evaluate functions using standard and non-standard notation.
Solve problems involving transformations, two- and three-dimensional figures.
-Explain properties of transformations.
-Explain and apply properties of angles created by parallel lines and a transversal, similar figures, and triangles.
-Explain and apply the Pythagorean Theorem.
-Analyze and solve geometric problems using the appropriate formula and units.
Analyze and communicate the pattern of association in bivariate data.
-Construct and interpret scatterplots.
-Find the line-of-best-fit for a scatterplot and write its equation.
-Find and explain clustering, outliers, and correlations.
Competency
· Add, subtract, multiply and divide with decimals (and verify the reasonableness of the results).
· Demonstrate proficiency with division, including division with positive decimals and long division with multi-digit divisors.
· Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less).
Competencies
Proficiencies
general math
- 1) Apply and extend previous undertandings of numbers to the system of rational numbers.
- 2) Understand ratio concepts.
- 3) Compute independently.
- 4) Analyze two and three-dimensional shapes.
5) Reason about and solve one-variableequations and inequalities.
1b)Understand ordering and absolute value of rational numbers.
1c)Solve real world problems.
2a) Solve unit rate problems including those involving unit pricing and
constant speed.
2b) Find a percent of a quantity as it relates to hundedths.
2c) Convert within the measurement systems.
3a) Fluently divide multi-digit numbers.
3b) Fluently multiply and divide fractions and decimals
3c) Demonstrate an undertanding of integer operations.
4a) Identify, classify and distinguish different types of triangles, quadrilaterals, other polygons, and three-dimensional figures.
4b) Find the area of triangles and polygons .
4c) Find the volume of rectangular prisms.
5a) Understand solving an equation or inequality as a process of answering a question.
5b) Use variables to represent numbers and write expressions to solve a problem.
5c) Analyze two quantities using graphs and tables.
6a) Answer questions involving chance and possible combinations in a given situation.
6b) Analyze patterns, trends, or distributions using measures of central tendencies.
Competency
Proficiencies
§ Decimals
§ Fractions
§ Integers
-Apply the order of operations when evaluating numeric expressions
-Apply properties of numbers and operations
-Solve multistep ratio and percent problems.
-Identify slope and y-intercept of a line
-Solve problems involving scale drawings of similar geometric figures
-Simplify numerical and algebraic expressions by applying properties of rational numbers
-Write expression , equations and inqualities using variables and appropriate operations
-Understand inverse properties and use to solve one-step equations
-Solve two-step equations
-Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
-Apply the concept of congruency to solve problems on a coordinate plane, involving translations, rotations, and reflections
solving problems using measures of central tendency
-Organize and appropriately display data
-Evaluate and simplify algebraic and numeric expressions using the order of operations.
-Translate written expressions into algebraic expressions.
-Graph linear equations, using a table of values, intercepts, and slope intercept form.
-Solve systems of equations graphically.
Find and interpret patterns that define functions or other relations.
-Identify and evaluate functions using standard and non-standard notation.
-Explain and apply properties of angles created by parallel lines and a transversal, similar figures, and triangles.
-Explain and apply the Pythagorean Theorem.
-Analyze and solve geometric problems using the appropriate formula and units.
-Find the line-of-best-fit for a scatterplot and write its equation.
-Find and explain clustering, outliers, and correlations.