Algebraic Ideas

• Interpret and compare integers in familiar situations using positive and negative numbers.
• Recognize and use exponents and power notation.
• Use a calculator to find approximate solutions to exponential equations.
• Represent a function with a table or values on a graph.
• Graph ordered pairs on a coordinate grid, using all four quadrants.
• Graph transformation of figures (translation, reflection, and rotation).
• Represent numbers in factor, exponent, and standard form.
• Compare numbers using exponents and <, >, and =.
• Define and identify equations and variables, write variable expressions given word phrases, and write word phrases given expressions.
• Solve equations with one variable, substituting the given value for the variable.
• Solve equations with 1 variable, using addition and subtraction, including concept of inverse operations.
• Solve word problems using equations with 1 variable, using addition and subtraction.
• Solve equations with 1 variable, using multiplication and division, including inverse operations.
• Solve word problems using equations with 1 variable, using multiplication and division.
• Use order of operations to simplify an expression.
• Solve equations with 1 variable, using all operations, and order of operations as needed.
• Solve equations with 1 variable, using all operations, when data is presented in tables and written form.
• Identify integers and compare and order integers, using a number line or other models.
• Add integers, using number lines.
• Solve 1- or 2-step word problems using addition of integers.
• Subtract integers, using number sentences.
• Solve 1- or 2-step word problems using subtraction of integers.

Fractions, Decimals, Percents, and Ratios

• Identify place value with decimals to thousandths.
• Estimate products using decimals.
• Solve problems using multiplication of decimals up to thousandths.
• Solve problems using division of decimals to thousandths.
• Solve multistep word problems using decimals.
• Find fractional part of whole numbers mentally (unit fractions).
• Solve problems using multiplication and division of fractions.
• Identify ratios from models and solve problems using ratios.
• Estimate ratios.
• Understand proportions and solve problems using proportions.
• Understand concept of percent.
• Convert fractions, decimals, and percents.
• Find percent that one number is of another number using proportion.
• Estimate percents.
• Rename decimals up to and including thousandths as fractions and mixed numbers.
• Rename fractions as a decimal, using equivalent fractions or by dividing denominator into numerator.
• Solve multistep consumer application word problems involving fractions and decimals.
• Find equivalent fractions, using n as a variable ( 1/2 = n/12).
• Compare and order fractions and mixed numbers with unlike denominators, using equivalent fractions. Round fractions and mixed numbers to the nearest half and nearest whole number.
• Estimate sums and differences of fractions and mixed numbers, using rounding and front-end estimation.
• Add fractions with like denominators up to and including 3 addends and subtract up to and including 3 fractions with like denominators. Answers in simplest form.
• Add up to and including 3 fractions with unlike denominators, using least common denominator and subtract 2 fractions with unlike denominators, using least common denominator. Answers in simplest form.
• Add and subtract fractions with unlike denominators, simplifying the answer.
• Add mixed numbers with like and unlike denominators up to and including 3 addends. Answers in simplest form.
• Subtract mixed numbers with unlike denominators. Answers in simplest form.
• Add and subtract mixed numbers with unlike denominators, simplifying the answer.
• Multiply fractions with any denominators using cross cancellation . Answers in simplest form.
• Identify reciprocals and find a variable, using reciprocals.
• Divide whole numbers by fractions, using models (fraction bars, circles, etc.).
• Divide fractions with like and unlike denominators, using reciprocals.
• Divide fractions and whole numbers, using reciprocals.
• Divide mixed numbers by fractions and mixed numbers by mixed numbers. Answers in simplest form.
• Convert fractions with denominators not a multiple of 10 to a percent.
• Solve multistep consumer application word problems, using percents.
• Identify equal ratios, using cross products.
• Identify rates and unit rates.
• Solve proportion problems, using cross products.
• Use proportions and scale drawings to calculate actual size.

Geometry

• Find area of right triangle in customary or metric units given the formula.
• Measure angles in degrees using a protractor.
• Find perimeter of equilateral triangle and regular pentagons, hexagons, and octagons given the length of one side.
• Recognize and define equilateral triangles, hexagons, octagons, parallelograms, kites, and rhombuses. Identify what is meant by the volume of three-dimensional shapes, using words, pictures, and/or models.
• State that volume is measured in cubic units indicated by superscript 3.
• Find volume of cube in customary or metric units given the formula.
• Find volume of rectangular solid in customary or metric units given the formula.
• Identify complimentary and supplementary angles.
• Identify the exterior and adjacent interior angles of a triangle and recognize that the sum of the exterior and adjacent interior angles = 180 degrees.
• Find missing angles given necessary information about triangle.
• Recognize the use of a compass and straight edge to identify congruent line segments and congruent angles.
• Compare the features of cone, cube, cylinder, rectangular and triangular prism, rectangular and triangular pyramid, and sphere.
• Identify intersecting, perpendicular, and parallel lines, and label using correct symbols.
• Compare properties of obtuse, right, acute, scalene, and isosceles triangles.
• Identify and label similar and congruent figures, using symbols and identify and label corresponding sides and angles of those figures.
• Recognize the use of a compass and straight edge to identify construction of regular polygons.
• Identify translations (slides), rotations (turns), and reflections (flips) of figures.

Measurement

• Find area using formula: A=LxW--customary and metric.
• Find volume using formula: V=LxWxH--customary and metric.
• Choose appropriate unit of measure for length, area, volume-customary and metric.
• Identify relationships among units of length-customary: inches, feet, yards.
• Use table of equivalents to convert among units of length-customary.
• Solve multistep word problems-customary: inches, feet, and yards.
• Solve multistep word problems-metric: kilometers.
• Identify relationships between customary units of liquid capacity.
• Use table of equivalents to convert between customary units of liquid capacity.
• Read units of measurement of liquid capacity-customary.
• Solve multistep word problems using liquid capacity-customary.
• Use table of equivalents to convert between metric units of liquid capacity.
• Solve multistep word problems using liquid capacity-metric, incl. kiloliters.
• Demonstrate how to make change up to $5.
• Identify relationship between ounces, pounds, and tons.
• Use a table of equivalents to convert between units of mass/weight-customary.
• Solve multistep word problems using mass/weight-customary.
• Use a table of equivalents to convert between units of mass/weight-metric.
• Solve multistep word problems using grams and kilograms.
• Identify formula to find perimeter of object or polygon-customary.
• Estimate perimeter of object or polygon-customary.
• Solve multistep word problems using perimeter-customary.
• Solve multistep word problems using perimeter-metric
• Understand relationship between units of time and convert among them.
• Solve multistep word problems using conversion of time.
• Solve multistep word problems involving elapsed time.
• Solve multistep word problems using Celsius and Fahrenheit scales.
• Estimate the area of irregular figures using a grid (round to nearest tenth of a unit).
• Find the area of circle to nearest tenth using the formula.
• Find the area of compound figures.
• Find the area of triangles and parallelograms using a formula.
• Read customary ruler to the nearest 1/2, 1/4, 1/8, 1/16 inch.
• Add, subtract, or multiply customary units of length then simplify and rename.
• Convert measure of length within the metric system using decimals.
• Compare metric units of length using decimals (>,<, =).
• Add, subtract, or multiply metric units of length, using decimals) then simplify and rename.
• Convert customary measure of liquid capacity, including fluid ounces, teaspoons, and tablespoons.
• Add, subtract, or multiply customary units of liquid capacity then simplify and rename.
• Convert measure of liquid capacity within the metric system using decimals.
• Compare metric units of liquid capacity using decimals.
• Add, subtract, or multiply metric units of liquid capacity then simplify and rename.
• Add, subtract, or multiply customary units of weight then simplify and rename.
• Convert measure of weight within the metric system using decimals, including metric tonnes.
• Compare metric measures of weight using decimals.
• Add, subtract, or multiply metric units of weight then simplify and rename.
• Find the diameter of a circle given the length of a radius and find the radius given the length of the diameter.
• Identify and calculate the circumference of a circle to the nearest tenth using formula.
• Add and subtract units of time.

Statistics and Probability

• Make circle graphs from data collected, using approximate fractional parts.
• Identify information and solve word problems in complex picture graphs in which each symbol represents many objects and fractions of symbols are used.
• Predict outcomes of probability problems before computing them.
• Use fractions to state probabilities of occurrence of given events.
• Use information from circle graphs to solve related word problems.
• Interpret misleading graphs and tables.
• Use formula to determine probability of simple events.
• Count outcomes, using combinations with models, diagrams, and organized lists.
• Count outcomes, using permutations with models, diagrams, and organized lists.
• Understand and solve problems using experimental and actual probability.
• Understand and solve problems using dependent and independent events.
• Interpret surveys using population, sample, and a representative sample.

Number Concepts

• Add four numbers up to 6 digits.
• Estimate sum of numbers with 4, 5, or 6 digits.
• Solve word problems using no more than four 3-digit numbers.
• Read and write numbers to millions.
• Divide 5-digit dividend by 1-digit divisor without remainder.
• Solve multistep word problems: 3- or 4- digit dividends & 2-digit divisors.
• Find factors of a number < 200.
• Find greatest common factor of two numbers.
• Find least common multiple.
• Identify the greater/lesser number using the correct symbol up to millions.
• Solve word problems involving real-life situations: 3-digit by 2-digit numbers.
• Identify the properties of multiplication.
• Predict and calculate sums, differences, products, and quotients as odd or even.
• Choose most appropriate method of computation.
• Explore prime numbers to 100.
• Explore prime factorization.
• Recognize and state place value of each digit up to millions.
• Regroup numbers using place value up to 6 digits.
• Solve grade appropriate word problems using 4 basic operations.
• Mentally add whole numbers using the following strategies: commutative and associative properties, compensation.
• Add 7 digits with 2 addends with regrouping.
• Add decimal numbers up to and including 3 digits and 3 or 4 decimal places with up to and including 4 addends with and without regrouping.
• Identify terminating and repeating decimals and round repeating decimals.
• Mentally divide whole numbers that are multiples of 10, 100, and 1,000 by divisors that are multiples of 10, 100, and 1,000.
• Divide 5- and 6-digit dividends by a 2- or 3-digit divisors with a remainder.
• Divide 4- to 6-digit dividends by 2-digit divisors and up to and including 5-digit dividends by 3-digit divisors without a remainder, using a calculator.
• Mentally solve division problems using decimal number dividends with 1- and 2-digit whole numbers and decimals up to and including 4 place values by divisors of 10, 100, and 1,000.
• Divide decimal numbers up to and including hundred thousandths by 1- and 2-digit divisors.
• Solve division problems with 2-digit whole number divisors and decimal dividends to thousandths with zeros in dividend.
• Divide decimals by decimals (hundred-thousandths dividends by thousandths divisors).
• Estimate sums using rounding and front-end estimation up to and including 6 digits with up to and including 4 addends.
• Estimate decimal number sums using rounding and front-end estimation using a 1-digit whole number and up to and including 3 decimal places.
• Estimate whole number differences using 5- and 6-digit numbers.
• Estimate decimal number differences using rounding and front-end estimation using a 1-digit whole number and up to and including 3 decimal places.
• Estimate whole number products using front-end estimation and rounding.
• Estimate decimal products using decimals x decimals using front-end estimation and rounding.
• Estimate quotients with 1- or 2-digit divisors using compatible numbers.
• Estimate decimal quotients by rounding, using compatible numbers (whole number dividend by a decimal number divisor and a decimal number dividend by a whole number divisor).
• Compare (>, <, =) whole numbers to whole numbers (6 digits), decimals to decimals to thousandths place (0.291< 0.30), and decimal numbers (up to 2 whole numbers with decimal places up to thousandths, e.g. 26.12 > 26.125).
• Mentally multiply whole numbers using multiplication properties.
• Mentally multiply whole numbers by multiples of 100, 1,000 and 10,000.
• Solve multiplication problems using 4 digit x 3 digit (to include money) with and without regrouping.
• Mentally multiply decimal x decimal using patterns and properties of multiplication.
• Multiply decimals (up to and including hundred thousandths) or decimal numbers x whole numbers (up to and including 2-4 digits).
• Recognize and state place value to billions.
• Read and write whole numbers (hundred thousands to billions) using words, standard form, short word names, and expanded form.
• Recognize and state place value of decimals to ten-thousandths and hundred-thousandths.
• Read and write decimals to hundred-thousandths using words, standard form, short word names, and expanded form.
• Round whole numbers (millions and billions).
• Round decimals (hundredths and thousandths).
• Mentally subtract whole numbers using equal additions (4 digits minus 3 digits to include money).
• Subtract up to 6 digits minus 5 digits with up to 3 regroupings and include up to 3 zeros in the middle.
• Subtract decimal numbers using 1- and 2-digit whole numbers and up to and including 3 decimal places with and without regrouping.