8.1 NUMERATION/NUMBER SENSE

8.1.1 Students will recognize natural numbers, whole numbers, integers, and rational numbers.

5-M-8.1.1a Read, write, and compare whole numbers through the billions.
5-M-8.1.1b Read, write, and compare decimals through the thousandths.
6-M-8.1.1a Read, write, and compare decimals to the hundred-thousandths place.
6-M-8.1.1b Read, write, and compare integers through the billions place.
6-M-8.1.1c Identify positive and negative numbers using a number line
7-M-8.1.1a Round real numbers to any given place.
7-M-8.1.1b Read, write, and compare rational numbers.
7-M-8.1.1c Identify and define repeating and terminating decimals.
8-M-8.1.1 Read, write, and compare rational and irrational numbers.

8.1.2 Students will determine equivalencies among fractions, decimals, and percents.

5-M-8.1.2a Use a calculator to convert decimals to percents
5-M-8.1.2b Find least common multiple for numbers
5-M-8.1.2c Find common factors and greatest common factors
5-M-8.1.2d Find equivalent fractions(simple)
6-M-8.1.2a Compare and order fractions.
6-M-8.1.2b Write equivalent fractions, decimals, and percents.
6-M-8.1.2c Write fractions as decimals and decimals as fractions.
7-M-8.1.2 Find equivalencies between fractions, decimals and percents.
8-M-8.1.2a Sequence positive and negative rational numbers.
8-M-8.1.2b Solve problems with appropriate equivalencies(percents, decimals, fractions).

8.1.3 Students will write and use numbers in expanded exponential form and scientific notation.

5-M-8.1.3 Express a whole number in words and standard notation.
6-M-8.1.3 Express whole numbers in words, scientific, and standard notation.
7-M-8.1.3.a Write numbers in expanded form using exponential notation.
7-M-8.1.3.b Express small and large numbers using scientific notation.
8-M-8.1.3.a Interpret and use positive and negative exponents correctly.

8.1.4 Students will identify and display numbers including prime and composite, factors and multiples, divisibility, powers, and properties.

5-M-8.1.4a Define and identify prime and composite numbers upto 20.
5-M-8.1.4b Use the divisibility rules for 2, 5,10.
5-M-8.1.4c Compute squares of whole numbers 1 through 10.
5-M-8.1.4d Find the least common multiple for a number.
5-M-8.1.4e Find factors, common factors, and greatest common factors.
6-M-8.1.4a Identify prime and composite numbers up to 50.
6-M-8.1.4b Use divisibility rules for 3 and 6.
6-M-8.1.4c Identify the difference between factors and multiples.
6-M-8.1.4d Apply scientific and exponential notations.
7-M-8.1.4.a. Apply properties and identities to solving one step equations.
7-M-8.1.4.b Use divisibility rules for 4 and 9 in addition to others.
7-M-8.1.4.c Recognize prime and composite numbers less than100.
8-M-8.1.4.a. Apply properties and identities to solving one and two step equations.
8-M-8.1.4.b Use divisibility rules to simplify rational numbers.


8.2 COMPUTATION/ESTIMATION

8.2.1 Students will add, subtract, multiply, and divide decimals and proper, improper, and mixed fractions with uncommon and common denominators both with and without the use of technology.

5-M-8.2.1a Add and subtract fractions with common denominators.
5-M-8.2.1b Add and subtract fractions with uncommon denominators with concrete aids.
5-M-8.2.1c Add and subtract decimal numbers with place value to the thousandths.
6-M-8.2.1a Reduce fractions to lowest terms.
6-M-8.2.1b Add, subtract, multiply, and divide fractions and mixed numbers.
6-M-8.2.1c Multiply and divide decimals by decimals.
6-M-8.2.1d Convert improper (top-heavy) fractions to mixed numbers.
7-M-8.2.1a Apply order of operations to solve problems involving fractions and mixed numbers (with and without the use of technology).
7-M-8.2.1b Apply order of operations to solve problems involving decimals (with and without the use of technology).
8-M-8.2.1a Apply order of operations to solve problems involving real numbers (with and without the use of technology).

8.2.2 Students will identify the appropriate operation and do the correct calculations when solving word problems.

5-M-8.2.2 Identify key words in story problems to determine the correct operation for making correct calculations.
6-M-8.2.2 Identify key words when solving word problems to decide correct operation.
7-M-8.2.2 Identify key vocabulary and connect to operations in problem-solving situations to help acquire a solution.
8-M-8.2.2 Identify key vocabulary and connect to operations in problem solving situations to help acquire a solution.

8.2.3 Students will solve problems involving whole numbers, integers, and rational numbers (fractions, decimals, ratios, proportions, and percents) both with and without the use of technology.

5-M-8.2.3a Solve problems involving multiplication and division of 4 digit by a 2 digit
5-M-8.2.3b Solve problems involving division of whole numbers by 1 digit divisors.
5-M-8.2.3c Solve problems involving addition and subtraction of decimals with place value to hundredths.
5-M-8.2.3d Solve problems involving addition and subtraction of fractions with common denominators.
5-M-8.2.3e Solve problems involving addition and subtraction of fractions with unlike denominators using concrete materials.
5-M-8.2.3f Solve problems involving addition of mixed numbers with common denominators.
6-M-8.2.3a Multiply a 5 digit number by a 3 digit number.
6-M-8.2.3b Divide whole numbers by 2 digit divisors.
6-M-8.2.3c Solve problems involving addition and subtraction of fractions and mixed numbers.
6-M-8.2.3d Solve problems involving multiplication and division of fractions.
6-M-8.2.3e Solve problems involving addition and subtraction of integers (positive and negative numbers).
7-M-8.2.3a Solve problems involving rational numbers.
7-M-8.2.3b Create one-step equations to aid in finding solutions.
8-M-8.2.3a Solve problems involving rational and irrational numbers.
8-M-8.2.3b Create multi-step equations to aid in finding solutions.
8-M-8.2.3c Utilize proportions when solving problems.

8.2.4 Students will apply the order of operations to solve problems with and without the use of technology.

5-M-8.2.4 Solve problems using left to right order of operations.
6-M-8.2.4 Solve problems using correct order of operations.
7-M-8.2.4 Solve problems using order of operations involving rational numbers, including grouping symbols and powers.
8-M-8.2.4 Solve problems using order of operations involving real numbers, including grouping symbols and powers.

8.2.5 Students will apply strategies of estimation when solving problems with and without the use of technology.

5-M-8.2.5a Estimate to determine the reasonableness of answers.
5-M-8.2.5b Round decimals to the nearest tenth.
5-M-8.2.5c Use rounding and compatible numbers to estimate and determine accuracy of answers in computation.
6-M-8.2.5a Use estimation to determine the reasonableness of answers.
6-M-8.2.5b Round to the nearest thousandth.
6-M-8.2.5c Perform mental math computations with accuracy.
7-M-8.2.5a Use rounding to estimate and determine the accuracy of operations.
7-M-8.2.5b Perform mental math using compatible numbers with accuracy.
7-M-8.2.5c Use a calculator to estimate square roots and decimals for fractions that are non-terminating/non-repeating.
8-M-8.2.5a Perform mental math using compatible numbers with accuracy.
8-M-8.2.5b Estimate square roots of whole numbers to the nearest whole number without the use of a calculator.


8.3 MEASUREMENT

8.3.1 Students will select measurement tools and measure quantities for temperature, time, money, distance, angles, area, perimeter, volume, capactiy, and weight/mass in standard and metric units at the designated level of precision.

5-M-8.3.1a Measure and calculate perimeter in standard and metric measurement.
5-M-8.3.1b Select the appropriate tool and units for temperature, time, money, weight and linear measurements.
5-M-8.3.1c Measure to the nearest 1/8 inch.
6-M-8.3.1a Measure length and width and use that information to figure area and perimeter.
6-M-8.3.1b Measure acute, obtuse, right, and reflex angles to the nearest degree.
7-M-8.3.1a Measure and calculate area, perimeter, and volume in standard and metric units.
7-M-8.3.1b Utilize appropriate tools and units of measure to find a specified measurement.
8-M-8.3.1a Measure and calculate volume and capacity in standard and metric units.

8.3.2 Students will convert units within measurement systems using standard and metric, given conversion factors.

7-M-8.3.2a Make conversions within metric or standard units for length, mass, and capacity.
7-M-8.3.2b Make conversions between metric or standard units for length, mass, and capacity.
8-M-8.3.2 Use rates and ratios to convert various units of length, mass, and capacity.


8.4 GEOMETRY/SPATIAL CONCEPTS

8.4.1 Students will identify, describe, compare, and classify two- and three-dimensional geometric figures such as plane figures like polygons, and circles; solid figures like prisms, pyramids, cones, spheres, and cylinders; and line segments, rays, angles, parallel and perpendicular lines.

5-M-8.4.1a Identify and describe geometric figures such as plane figures like polygons and circles, lines, line segments, rays, angles, parallel and perpendicular lines.
5-M-8.4.1b Identify acute, obtuse, and right angles.
6-M-8.4.1a Identify and describe lines, line segments, rays and angles.
6-M-8.4.1b Explore relationships among angles and find missing angles formed by parallel lines and a transversal.
6-M-8.4.1c Find missing angles of a parallelogram.
7-M-8.4.1a Classify various polygons by number of sides and vertices.
7-M-8.4.1b Describe lines, line segments, rays, and angles using mathematical vocabulary and symbols.
8-M-8.4.1a Classify various polygons by number of diagonals.
8-M-8.4.1b. Name the vertices, faces, and edges of a solid figure.
8-M-8.4.1c Recognize and apply properties of various angles.

8.4.2 Students will use geometric properties, the Pythagorean theorem, and the relationships of congruence, similarity, and symmetry.

6-M-8.4.2a Define congruence.
6-M-8.4.2b Use tools to construct congruent copies.
7-M-8.4.2 Use congruence to describe relationships between polygons and angles.
8-M-8.4.2a Use similarity to describe relationships between polygons and angles.
8-M-8.4.2b Recognize symmetry of various figures.
8-M-8.4.2c Apply the Pythagorean theorem to situations involving right triangles.

8.4.3 Students will use formulas to solve problems involving perimeter and area of a square, rectangle, parallelogram, trapezoid, and triangle as well as the area and circumference of circles.

5-M-8.4.3a Compute perimeter formula for squares and rectangles.
5-M-8.4.3b Identify radius and diameter of circle.
6-M-8.4.3a Calculate perimeter and area of squares, rectangles, and triangles using a formula.
6-M-8.4.3b Calculate circumference of circles.
7-M-8.4.3a Find the perimeter of all polygons.
7-M-8.4.3b Determine the area of triangles and special quadrilaterals.
7-M-8.4.3c Use formulas to calculate the circumference and area of circles.
8-M-8.4.3a Apply formulas to solve problems involving perimeter and area of regular and irregular plane figures.
8-M-8.4.3b Apply formulas to solve problems involving the circumference and area of circles.

8.4.4 Students will solve problems given formulas for volume and surface area of rectangular prisms, cylinders, and cones.

7-M-8.4.4a Find the surface area of rectangular prisms.
7-M-8.4.4b Apply the formula for the surface area of rectangular prisms to situations.
8-M-8.4.4 Find surface area and volume of solid figures.


8.4.5 Students will apply transformations to two- and three-dimensional geometric figures.

8-M-8.4.5.a Apply transformations to plane figures.
8-M-8.4.5.b Recognize the relationships between transformations and the concepts of similarity and congruence.

8.4.6 Students will use geometric terms and representations to describe the physical world.

5-M-8.4.6a Use squares and rectangles to describe the physical world.
5-M-8.4.6b Use geometric representations to solve problems.
6-M-8.4.6 Solve problems using perimeter and area in everyday life situations.
7-M-8.4.6 Use geometric terminology to describe the physical world.
8-M-8.4.6 Use geometric representations to solve world problems.

8.5 DATA ANALYSIS, PROBABILITY, AND STATISTICAL CONCEPTS

8.5.1 Students will collect, construct, and interpret data displays and compute mean, median, and mode.

5-M-8.5.1a Collect and display data.
5-M-8.5.1b Read and interpret tables, charts, graphs(simple).
6-M-8.5.1 Collect, analyze, interpret, and display data on a variety of different graphs.
7-M-8.5.1 Collect, analyze, interpret, and display data from a variety of sources.
8-M-8.5.1 Collect, analyze, interpret, and display data from a variety of sources in a variety of ways.

8.5.2 Students will read and interpret tables, charts, and graphs to make comparisons and predictions.

5-M-8.5.2 Interpret tables, charts, and graphs to make comparisons.
6-M-8.5.2 Construct, read, and interpret charts and graphs to make comparisons and predictions.
7-M-8.5.2 Identify factors leading to the use of specific graphs used to display data.
8-M-8.5.2 Make inferences concerning information found in tables, charts, and graphs.

8.5.3 Students will conduct experiments or simulations to demonstrate theoretical probability and relative frequency.

5-M-8.5.3 Explore situations that demonstrate probability.
6-M-8.5.3 Chart outcomes of a probability activity and draw conclusions based on the data.
7-M-8.5.3 Perform experiments to compare relative frequency to theoretical probability.
8-M-8.5.3 Compare the probability of dependent and independent events.

8.5.4 Students will identify statistical methods and probability for making decisions.

5-M-8.5.4a Calculate range, mean, median, mode.
5-M-8.5.4b Write word problems using averages(mean).
5-M-8.5.4c Compute averages(mean) to the nearest whole number.
6-M-8.5.4 Calculate mean, median, mode, and range and apply it to real-life situations
7-M-8.5.4a Calculate the mean, median, mode and range for data.
7-M-8.5.4b Use appropriate displays for data.
8-M-8.5.4 Explain in writing and apply in problems the concepts of mean, median, mode, and range.


8.6 ALGEBRAIC CONCEPTS

8.6.1 Students will demonstrate knowledge and use of the one- and two-dimensional coordinate systems.

5-M-8.6.1a Graph given positive pairs of whole numbers on a grid.
5-M-8.6.1b Order positive and negative numbers on a number line.
6-M-8.6.1 Graph ordered pairs on four-quadrant grids.
7-M-8.6.1a Graph rational numbers on a number line.
7-M-8.6.1b Graph solutions to equations and inequalities using a number line.
8-M-8.6.1a Graph ordered pairs on a coordinate graph.
8-M-8.6.1b Graph solutions to equations and inequalities on a number line as well as a coordinate graph.
8-M-8.6.1c Generate a table of values for situations leading to equations in two variables.

8.6.2 Students will apply algebraic concepts and operations to solving linear equations and word problems.

5-M-8.6.2a Interpret algebraic problems with one variable.
5-M-8.6.2b Recognize and use different ways to denote addition and subtraction.
6-M-8.6.2a Write and evaluate algebraic expression.
6-M-8.6.2b Evaluate formulas by substituting numbers for each of the variables (perimeter and area).
7-M-8.6.2a Use order of operations to evaluate algebraic expressions after substituting.
7-M-8.6.2b Recognize and apply properties (commutative, associative, identity, inverse, distributive, and zero) involving rational numbers.
7-M-8.6.2c Solve one step equations involving rational numbers.
8-M-8.6.2a Solve linear equations and inequalities.
8-M-8.6.2b Recognize and apply properties (commutative, associative, identity, inverse, distributive, and zero) involving real numbers.
8-M-8.6.2c Solve one and two step equations involving rational numbers.
8-M-8.6.2d Perform monomial operations.

8.6.3 Students will describe and represent relations, using tables, graphs, and rules.

6-M-8.6.3 Solve problems using a spreadsheet.
7-M-8.6.3 Describe patterns algebraically.
8-M-8.6.3 Describe situations involving two unknowns algebraically.