Mathematics

8^th GRADE CORE

OUTCOMES

Develop number and number relationships with integers, rational and irrational numbers

Use computation and estimation strategies with rational numbers and integers

Demonstrate an understanding of simple Algebraic Concepts

Use Elementary Statistics and Probability to analyze Data

Explore Geometry and measurement in two and three dimensions

Mathematics

GRADE 8

CORE

Develop number and number relationships with integers, rational and irrational numbers

Initial Understanding

Rename equivalent fractions and mixed numbers as equivalent decimals and vice versa.

Rename fractions and decimals as equivalent percents & vice versa or state rules for given pattern

Write equivalent fractions and determine whether fractions are equivalent.

Find percent of a number

Order and Compare whole numbers, fractions and decimals, integers and irrational numbers

Describe the absolute value of a numbers

Describe magnitude of fractions, mixed numbers and decimals

Round whole numbers, fractions and decimals in context

Developing an Interpretation

Write factors and multiples of a number

Decide whether a number is prime or composite.

Write the prime factorization of a number.

Find greatest common factor of a number

Find the least common multiple of numbers.

Identify alternative forms of expressing numbers using scientific notation .

Locate points on lines, scales, integers, rational, and irrational numbers.

Use computation and estimation strategies with rational numbers and integers

Initial Understanding

Write and interpret, numbers using exponential notation

Multiply and divide numbers using exponential notation

Add integers. Subtract integers, multiply integers and find integer quotients.

Add and subtract rational numbers with like unlike denominators.

Multiply and divide rational numbers expressed as a fractions and a mixed #

Find the quotient of two numbers expressed with negative exponents.

Developing an Interpretation

Estimate whole number sums and differences by using rounding and front-end estimation.

Use strategies, to solve problems with numbers and variables

Developing an Interpretation

Use Make a Table, Look for a Pattern, to solve problems.

Making Connections

Solve problems involving: 0.1/0.01 more/less.

Solve word problems involving numbers

Solve non-routine problems using the strategies choose the operation of Guess, Check, Revise.

Solve problems using the strategy Draw a Diagram.

Solve problems, using metric units.

Solve problems, using the strategy make an Organized List.

Solve problems using Logical

Solve word problems by writing and solving equations

Estimate decimal sums, differences, products and quotients, by rounding.

Estimate a reasonable answer to a problem

Critical Stance

Estimate to make and defend a decision.

Develop Algebraic Concepts

Initial Understanding

Evaluate numerical and algebraic expressions.

Use order of operations to evaluate expressions.

Write a rule that represents the relationship between two numbers

Translate a verbal phrase to a numerical or algebraic expression.

Use the basic properties of addition to write algebraic expression equivalent to another expression

Use the basic properties of multiplication to write and algebraic expression equivalent to another

expression.

Use the Associative and Distributive properties to simplify expressions.

Solve equations for a replacement set.

Solve equations using the multiplicative inverse.

Use mental math or Guess, Check, Revise to solve equation

Use addition and subtraction to solve equation

Use multiplication and division to solve equations

Evaluate formulas

Use addition subtraction, multiplication and division to solve equations with integers

Translate verbal statements into equations

Write and interpret, variables using exponential notation

Multiply and divide variables using exponential notation

Graph an ordered pair on the coordinate plane.

Use divisibility rule

Developing an Interpretation

Describe the relationship between two variables in words

Describe the relationship between two variables graphically.

Translate verbal statements into equations.

Identify or extend patterns involving numbers and attributes

Making Connections

Solve equations involving more than one operation

Solve word problems by writing and solving equations

Graph simple linear equations using slope intercept

Write formula for given pattern

Use Elementary Statistics and Probability to analyze Data

Initial Understanding

Identify correct information: graphs, tables, charts.

Create graphs from data: tables and charts.

Developing an Interpretation

Draw and justify reasonable conclusions from graphs, tables, charts.

Make frequency tables for sets of data to find range and mode

Solve problems involving means and medians of sets of data.

Construct and interpret stem-and -leaf diagrams.

Recognize positive and negative correlations in scatter plots.

Analyze scatter plots.

Making Connections

Find the probability of simple events and mutually exclusive events.

Distinguish between and calculate the probability of independent dependent events.

Use probability to decided if a game is fair

Explore Geometry and measurement in two and three

Initial Understanding

Classify polygons by name.

Measure of vertical and corresponding angles

Find the circumference, radius, or diameter of a circle.

Find the area of rectangles and parallelograms.

Find the area of triangles and trapezoids.

Find the area of circles.

Use the Pythagorean Theorem to find lengths of sides of a right triangle.

Determine volume of rectangular prisms

Developing an Interpretation

Estimate lengths, area, and angle measurement.

Critical Stance

In Mathematics justifying, proving or explaining a conjecture or answer is connected to the learning

Environment. Students are encouraged and expected to question one an others’ ideas and to explain and support

their own ideas in the face of others’ challenges. Each objective in mathematics can be framed to have students

defend support, explain or prove their answer. To understand what they learn, students must enact for themselves

verbs that permeate the mathematics curriculum: “examine”, “represent”, “transform”, “solve”, “apply”, “and

prove”.

Mathematics

OUTCOMES

Grade 8

Algebra 1 Part A (Full Year)

Demonstrate number sense strategies with rational numbers.

Develop number and number relationships with integers, absolute value, rational and irrational numbers.

Use properties of mathematics to understand Algebra

Evaluate variables using equations and inequalities

Interpret and analyze data using statistical techniques

Evaluate variables using simple probability

Use functions relationships to investigate problems

Use graphs to demonstrate a visual representation of Algebraic Concepts

Mathematics

Grade 8

Algebra 1 Part A (Full Year)

Demonstrate number sense strategies with rational numbers

Initial Understanding

Skip counting (3, 4, 5, 6, 7, 8, 9)

Doubles in addition and multiplication

Making a ten

Divisibility of whole numbers.

Factors and Prime numbers

Fractions for numbers between 1 and 0 and greater than 1

Picturing a fraction

Placing a fraction on a number line

Order, estimating, and comparing fractions

Using the multiplication of one to add, subtract, multiply and divide fractions

Develop number and number relationships with integers, absolute value, rational and irrational numbers

Developing an Interpretation

Represent problem situations as equations and solve.

Represent linear patterns with equations.

Represent linear equations with graphs.

Making Connections

Compare real numbers

Find equivalence among fractions, decimals and percents

Critical Stance

Make predictions by identify patterns in a number sequence

Predict line of best fit interpret data in scatter plot.

Use properties of mathematics to understand Algebra

Developing an Interpretation

Define property of zero.

Making Connections

Apply Commutative, Associative and Distributive properties to Algebraic Concepts

Use the Distributive property to simplify expressions.

Evaluate variables using equations and inequalities

Initial Understanding

Multiply and divide expressions that contain variables

Solve equations using addition and subtraction

Solve equations using multiplication and division.

Solve inequalities using addition and subtraction

Solve inequalities using multiplication and division.

Developing an Interpretation

Solve multi-step equation.

Solve Literal equations for a variable.

Solve multi-step inequalities

Solve compound inequalities.

Solve absolute value equations and inequalities

Making Connections

Use equations to solve real world multi-step problems.

Use the Distributive property to solve equations.

Use formulas to solve problems.

Use proportions to solve problems.

Interpret and analyze data using statistical techniques

Initial Understanding

Find mean, median, mode and range.

Developing an Interpretation

Interpret and analyze bar and circle graphs.

Represent and interpret stem-and-left plots, histograms and box, and whisker plots

Evaluate variables using simple probability

Making Connections

Find the experimental probability that and event will occur.

Use functions relationships to investigate problems

Describe the range and domain of a relation or function justify it designation

Use graphs to demonstrate a visual representation of Algebraic Concepts

Initial Understanding

Calculate the slope of a line.

Making Connections

Use the slope intercepts formula to graph a linear function

Use the standard and point -slope form to graph linear equations

Critical Stance

Prove lines a are parallel or perpendicular using slope

Critical Stance

In Mathematics justifying, proving or explaining a conjecture or answer is connected to the learning environment. Students are encouraged and expected to question one an others’ ideas and to explain and support their own ideas in the face of others’ challenges. Each objective in mathematics can be framed to have students defend support, explain or prove their answer. To understand what they learn, students must enact for themselves verbs that permeate the mathematics curriculum: “examine”, “represent”,”transform”, “solve”, “apply”, and “prove”.

Mathematics

OUTCOMES

8^th Grade Algebra

Develop number and number relationships with integers, absolute value, rational and irrational numbers.

Use properties of mathematics to understand Algebra

Evaluate variables using equations and inequalities

Interpret and analyze data using statistical techniques

Investigate real world problems by using problem solving techniques

Evaluate variables using simple probability

Use functions relationships to investigate problems

Use graphs to demonstrate a visual representation of Algebraic Concepts

Exploring operations on polynomials

Mathematics

8^TH GRADE

ALGEBRA 1

Developing and understanding of number and variables relationships with integers, absolute value, rational and irrational numbers

Initial Understanding

Apply order of operations

Plot points on a coordinate plain

Simplify expressions with opposites and absolute value.

Multiply and divide positive and negative numbers

Define exponents and powers.

Simplify products of a monomial

Simplify quotients of a power.

Simplify powers of a fraction

Identify or estimate the value of a square root

Simplify square roots

Perform mathematical operations with radicals

Developing an Interpretation

Represent problem situations as equations and solve.

Represent linear patterns with equations.

Represent linear equations with graphs.

Solve expressions that contain zero and negative exponents

Making Connections

Compare real numbers

Find equivalence among fractions, decimals and percents

Find products of powers

Find powers of a power

Find the power of a product

Critical Stance

Justify why you use scientific notation to represent large and small numbers.

Make predictions by identify patterns in a number sequence

Use properties of mathematics to understand Algebra

Developing an Interpretation

Define property of zero.

Making Connections

Apply Commutative, Associative and Distributive properties to Algebraic Concepts

Use the Distributive property to simplify expressions.

Evaluate variables using equations and inequalities

Initial Understanding

Multiply and divide expressions that contain variables

Use addition and subtraction to Solve equations

Use multiplication and division to solve equations

Use addition and subtraction to Solve inequalities

Use multiplication and division to solve inequalities

Developing an Interpretation

Solve multi-step equation.

Solve Literal equations for a variable.

Solve multi-step inequalities

Solve compound inequalities.

Solve absolute value equations and inequalities

Solve equations containing radicals

Solve equations by using radicals

Solve quadratic equations by factoring

Making Connections

Use the Distributive property to solve equations.

Find solutions to systems of linear equations by the substitution method

Find solutions to systems of linear equations by the elimination method.

Use the quadratic formula to find the roots of a quadratic equation

Use the quadratic formula to find the zeros of a quadratic function.

Evaluate the discriminate to find how many real roots a function has

Investigate real world problems by using problem solving techniques

Making Connections

Use equations to solve real world multi-step problems

Use formulas to solve problems.

Use proportions to solve problems.

Critical Stance

Solve and justify Puzzles problems in two variables.

Interpret and analyze data using statistical techniques

Initial Understanding

Find mean, median, mode and range.

Developing an Interpretation

Interpret and analyze bar and circle graphs.

Represent and interpret stem-and-left plots, histograms and box, and whisker plots

Critical Stance

Predict line of best fit interpret data in scatter plot and.

Evaluate variables using simple probability

Making Connections

Find the experimental probability that and event will occur.

Use functions relationships to investigate problems

Initial Understanding

Describe the range and domain of a relation or function.

Critical Stance

Justify the designation of a function or relation

Use graphs to demonstrate a visual representation of Algebraic Concepts

Initial Understanding

Calculate the slope of a line.

Making Connections

Use the slope intercepts formula to graph a linear function

Use the standard and point -slope form to graph linear equations

Critical Stance

Prove lines a are parallel or perpendicular using slope

Exploring operations on polynomials

Developing an Interpretation

Find the product of a binomial by using the Distributive Property

Find the product of a binomial by using the Foil Method.

Making Connections

Factor a polynomial by finding and using the greatest common factor.

Factor a polynomial by finding and using a binomial factor

Factor finding perfect square trinomials.

Factor a polynomial by finding and using the difference of two squares.