K-6 Indiana Academic Standards for Mathematics
Kindergarten    Grade 1    Grade 2    Grade 3    Grade 4    Grade 5    Grade 6

Kindergarten    [Back to TOP]
Number Sense
K.1.1 Match sets of objects one-to-one.
K.1.2 Compare sets of up to ten objects and identify whether one set is equal to, more than, or less than another.
K.1.3 Know that larger numbers describe sets with more objects in them than sets described by smaller numbers.
K.1.4 Divide sets of ten or fewer objects into equal groups.
K.1.5 Divide shapes into equal parts.
K.1.6 Count, recognize, represent, name, and order a number of objects (up to 10).
K.1.7 Find the number that is one more than or one less than any whole number up to 10.
K.1.8 Use correctly the words one/many, none/some/all, more/less, and most/least.
K.1.9 Record and organize information using objects and pictures.
Computation
K.2.1 Model addition by joining sets of objects (for any two sets with fewer than 10 objects when joined).
K.2.2 Model subtraction by removing objects from sets (for numbers less than 10).
K.2.3 Describe addition and subtraction situations (for numbers less than 10).
Algebra and Functions
K.3.1 Identify, sort, and classify objects by size, number, and other attributes. Identify objects that do not belong to a particular group.
K.3.2 Identify, copy, and make simple patterns with numbers and shapes.
Geometry
K.4.1 Identify and describe common geometric objects: circle, triangle, square, rectangle, and cube.
K.4.2 Compare and sort common objects by position, shape, size, roundness, and number of vertices.
K.4.3 Identify and use the terms: inside, outside, between, above, and below.
Measurement
K.5.1 Make direct comparisons of the length, capacity, weight, and temperature of objects and recognize which object is shorter, longer, taller, lighter, heavier, warmer, cooler or holds more.
K.5.2 Understand concepts of time: morning, afternoon, evening, today, yesterday, tomorrow, week, month, and year. Understand that clocks and calendars are tools that measure time.
Problem Solving
K.6.1 Choose the approach, materials, and strategies to use in solving problems.
K.6.2 Use tools such as objects or drawings to model problems.
K.6.3 Explain the reasoning used with concrete objects and pictures.
K.6.4 Make precise calculations and check the validity of the results in the context of the problem.
   
  Grade 1    [Back to TOP]
  Number Sense
1.1.1 Count, read, and write whole numbers up to 100.
1.1.2 Count and group objects in ones and tens.
1.1.3 Identify the number of tens and ones in numbers less than 100.
1.1.4 Name the number that is one more than or one less than any number up to 100.
1.1.5 Compare whole numbers up to 10 and arrange them in numerical order.
1.1.6 Match the number names first, second, third, etc. with an ordered set of up to 10 items.
1.1.7 Recognize when a shape is divided into congruent (matching) parts.
1.1.8 For a shape divided into 8 or fewer congruent (matching) parts, describe a shaded portion as "__ out of ___" parts and write the fraction.
1.1.9 For a set of 8 or fewer objects, describe a subset as “__ out of __ parts” and write the fraction.
1.1.10  Represent, compare, and interpret data using pictures and picture graphs.
Computation
1.2.1 Show the meaning of addition (putting together, increasing) using objects.
1.2.2 Show the meaning of subtraction (taking away, comparing, finding the difference) using objects.
1.2.3 Show equivalent forms of the same number (up to 20) using objects, diagrams, and numbers.
1.2.4 Demonstrate mastery of the addition facts (for totals up to 20) and the corresponding subtraction facts.
1.2.5 Understand the meaning of the symbols +, −, and =.
1.2.6 Understand the role of zero in addition and subtraction.
1.2.7 Understand and use the inverse relationship between addition and subtraction facts (such as 4+2=6, 6-2=4, etc) to solve simple problems.
Algebra and Functions
1.3.1 Write and solve number sentences from problem situations involving addition and subtraction.
1.3.2 Create word problems that match given number sentences involving addition and subtraction.
1.3.3 Recognize and use the relationship between addition and subtraction.
1.3.4 Create and extend number patterns using addition.
Geometry
1.4.1 Identify, describe, compare, sort, and draw triangles, rectangles, squares, and circles.
1.4.2 Identify triangles, rectangles, squares, and circles as the faces of three-dimensional objects.
1.4.3 Classify and sort familiar plane and solid objects by position, shape, size, roundness, and other attributes. Explain the rule you need.
1.4.4 Identify objects as two- or three-dimensional.
1.4.5 Give and follow directions for finding a place or object.
1.4.6 Arrange and describe objects in space by position and direction: near, far, under, over, up, down, behind, in front of, next to, to the left or right of.
1.4.7 Identify geometric shapes and structures in the environment and specify their location.
Measurement
1.5.1 Measure the length of objects by repeating a non-standard unit or a standard unit.
1.5.2 Use different units to measure the length of the same object and predict whether the measure will be greater or smaller when a different unit is used.
1.5.3 Recognize the need for a fixed unit of length.
1.5.4 Measure and estimate the length of an object to the nearest inch and centimeter.
1.5.5 Compare and order objects according to area, capacity, weight, and temperature, using direct comparison or a nonstandard unit.
1.5.6 Tell time to the nearest half-hour and relate time to events (before/after, shorter/longer).
1.5.7 Identify and give the values of pennies, nickels, and dimes.
Problem Solving
1.6.1 Choose the approach, materials, and strategies to use in solving problems.
1.6.2 Use tools such as objects or drawings to model problems.
1.6.3 Explain the reasoning used and justify the procedures selected in solving a problem.
1.6.4 Make precise calculations and check the validity of the results in the context of the problem.
1.6.5 Understand and use connections between two problems.
 
Grade 2    [Back to TOP]
Number Sense
2.1.1 Count by ones, twos, fives, and tens to 100.
2.1.2 Identify the pattern of numbers in each group of ten, from tens through nineties.
2.1.3 Identify numbers up to 100 in various combinations of tens and ones.
2.1.4 Name the number that is ten more or ten less than any number 10 through 90.
2.1.5 Compare whole numbers up to 100 and arrange them in numerical order.
2.1.6 Match the number names (first, second, third, etc.) with an ordered set of up to 100 items
2.1.7 Identify odd and even numbers up to 100.
2.1.8 Recognize fractions as parts of a whole or parts of a group (up to 12 parts).
2.1.9 Recognize, name, and compare the unit fractions: 1/2 , 1/3 , 1/4 , 1/5 , 1/6 , 1/8 , 1/10, and 1/12 .
2.1.10 Know that, when all fractional parts are included, the result is equal to the whole and to one.
2.1.11 Collect and record numerical data in systematic ways.
2.1.12 Represent, compare, and interpret data using tables, tally charts, and bar graphs.
Computation
2.2.1 Model addition of numbers less than 100 with objects and pictures.
2.2.2 Add two whole numbers less than 100 with and without regrouping.
2.2.3 Subtract two whole numbers less than 100 without regrouping.
2.2.4 Understand and use the inverse relationship between addition and subtraction.
2.2.5 Use estimation to decide whether answers are reasonable in addition problems.
2.2.6 Use mental arithmetic to add or subtract 0, 1, 2, 3, 4, 5, or 10 with numbers less than 100.
Algebra and Functions
2.3.1 Relate problem situations to number sentences involving addition and subtraction.
2.3.2 Use the commutative and associative rules for addition to simplify mental calculations and to check results.
2.3.3 Recognize and extend a linear pattern by its rules.
2.3.4 Create, describe, and extend number patterns using addition and subtraction.
Geometry
2.4.1 Construct squares, rectangles, triangles, cubes, and rectangular prisms with appropriate materials.
2.4.2 Describe, classify, and sort plane and solid geometric shapes (triangle, square, rectangle, cube, rectangular prism) according to the number and shape of faces and the number ofs sides, edges, and/or vertices.
 
2.4.3 Investigate and predict the result of putting together and taking apart two-dimensional and three-dimensional shapes.
2.4.4 Identify congruent two-dimensional shapes in any position.
2.4.5 Recognize geometric shapes and structures in the environment and specify their locations.
Measurement
2.5.1 Measure and estimate length to the nearest inch, foot, yard, centimeter, and meter.
2.5.2 Describe the relationships among inch, foot, and yard. Describe the relationship between centimeter and meter.
2.5.3 Decide which unit of length is most appropriate in a given situation.
2.5.4 Estimate area and use a given object to measure the area of other objects.
2.5.5 Estimate and measure capacity using cups and pints.
2.5.6 Estimate weight and use a given object to measure the weight of other objects.
2.5.7 Recognize the need for a fixed unit of weight.
2.5.8 Estimate temperature. Read a thermometer in Celsius and Fahrenheit.
2.5.9 Tell time to the nearest quarter hour, be able to tell five-minute intervals, and know the difference between a.m. and p.m.
2.5.10 Know relationships of time: seconds in a minute, minutes in an hour, hours in a day, days
2.5.11 Find the duration of intervals of time in hours.
2.5.12 Find the value of a collection of pennies, nickels, dimes, quarters, half-dollars, and dollars.
Problem Solving
2.6.1 Choose the approach, materials, and strategies to use in solving problems.
2.6.2 Use tools such as objects or drawings to model problems.
2.6.3 Explain the reasoning used and justify the procedures selected in solving a problem.
2.6.4 Make precise calculations and check the validity of the results in the context of the problem.
2.6.5 Understand and use connections between two problems.
 
Grade 3    [Back to TOP]
Number Sense
3.1.1 Count, read, and write whole numbers up to 1,000.
3.1.2 Identify and interpret place value in whole numbers up to 1,000.
3.1.3 Use words, models, and expanded form to represent numbers up to 1,000.
3.1.4 Identify any number up to 1,000 in various combinations of hundreds, tens, and ones.
3.1.5 Compare whole numbers up to 1,000 and arrange them in numerical order.
3.1.6 Round numbers less than 1,000 to the nearest ten and the nearest hundred.
3.1.7 Identify odd and even numbers up to 1,000 and describe their characteristics.
3.1.8 Show equivalent fractions using equal parts.
3.1.9 Identify and use correct names for numerators and denominators.
3.1.10 Given a pair of fractions, decide which is larger or smaller by using objects or pictures.
3.1.11 Given a set of objects or a picture, name and write a decimal to represent tenths and hundredths.
3.1.12 Given a decimal for tenths, show it as a fraction using a place-value model.
3.1.13 Interpret data displayed in a circle graph and answer questions about the situation.
3.1.14 Identify whether everyday events are certain, likely, unlikely, or impossible.
3.1.15 Record the possible outcomes for a simple probability experiment.
Computation
3.2.1 Add and subtract whole numbers up to 1,000 with or without regrouping, using relevant properties of the number system.
3.2.2 Represent the concept of multiplication as repeated addition.
3.2.3 Represent the concept of division as repeated subtraction, equal sharing, and forming equal groups.
3.2.4 Know and use the inverse relationship between multiplication and division facts,
3.2.5 Show mastery of multiplication facts for 2, 5, and 10.
3.2.6 Add and subtract simple fractions with the same denominator.
3.2.7 Use estimation to decide whether answers are reasonable in addition and subtraction problems.
3.2.8 Use mental arithmetic to add or subtract with numbers less than 100.
Algebra and Functions
3.3.1 Represent relationships of quantities in the form of a numeric expression or equation.
3.3.2 Solve problems involving numeric equations.
3.3.3 Choose appropriate symbols for operations and relations to make a number sentence true.
3.3.4 Understand and use the commutative and associative rules of multiplication.
3.3.5 Create, describe, and extend number patterns using multiplication.
3.3.6 Solve simple problems involving a functional relationship between two quantities.
3.3.7 Plot and label whole numbers on a number line up to 10.
Geometry
3.4.1 Identify quadrilaterals as four-sided shapes.
3.4.2 Identify right angles in shapes and objects and decide whether other angles are greater or less than a right angle.
3.4.3 Identify, describe, and classify: cube, sphere, prism, pyramid, cone, cylinder.
3.4.4 Identify common solid objects that are the parts needed to make a more complex solid object.
3.4.5 Draw a shape that is congruent to another shape.
3.4.6 Use the terms point, line, and line segment in describing two-dimensional shapes.
3.4.7 Draw line segments and lines.
3.4.8 Identify and draw lines of symmetry in geometric shapes (by hand or using technology).
3.4.9 Sketch the mirror image reflections of shapes.
3.4.10 Recognize geometric shapes and their properties in the environment and specify their locations.
Measurement
3.5.1 Measure line segments to the nearest half-inch.
3.5.2 Add units of length that may require regrouping of inches to feet or centimeters to meters.
3.5.3 Find the perimeter of a polygon.
3.5.4 Estimate or find the area of shapes by covering them with squares.
3.5.5 Estimate or find the volume of objects by counting the number of cubes that would fill them.
3.5.6 Estimate and measure capacity using quarts, gallons, and liters.
3.5.7 Estimate and measure weight using pounds and kilograms.
3.5.8 Compare temperatures in Celsius and Fahrenheit.
3.5.9 Tell time to the nearest minute and find how much time has elapsed.
3.5.10 Find the value of any collection of coins and bills. Write amounts less than a dollar using the ¢ symbol and write larger amounts in decimal notation using the $ symbol.
3.5.11 Use play or real money to decide whether there is enough money to make a purchase.
3.5.12 Carry out simple unit conversions within a measurement system (e.g., centimeters to meters, hours to minutes).
Problem Solving
3.6.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
3.6.2 Decide when and how to break a problem into simpler parts.
3.6.3 Apply strategies and results from simpler problems to solve more complex problems.
3.6.4 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
3.6.5 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
3.6.6 Know and use strategies for estimating results of whole-number addition and subtraction.
3.6.7 Make precise calculations and check the validity of the results in the context of the problem.
3.6.8 Decide whether a solution is reasonable in the context of the original situation.
3.6.9 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
 
Grade 4     [Back to TOP]
Number Sense
4.1.1 Read and write whole numbers up to 1,000,000.
4.1.2 Identify and write whole numbers up to 1,000,000, given a place-value model.
4.1.3 Round whole numbers up to 10,000 to the nearest ten, hundred, and thousand.
4.1.4 Order and compare whole numbers using symbols for “less than” (<), “equal to” (=), and “greater than” (>).
4.1.5 Rename and rewrite whole numbers as fractions.
4.1.6 Name and write mixed numbers, using objects or pictures.
4.1.7 Name and write mixed numbers as improper fractions, using objects or pictures.
4.1.8 Write tenths and hundredths in decimal and fraction notations. Know the fraction and decimal equivalents for halves and fourths (
4.1.9 Round two-place decimals to tenths or to the nearest whole number.
Computation
4.2.1 Understand and use standard algorithms for addition and subtraction.
4.2.2 Represent as multiplication any situation involving repeated addition.
4.2.3 Represent as division any situation involving the sharing of objects or the number of groups of shared objects.
4.2.4 Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts.
4.2.5 Use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system.
4.2.6 Use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system. 
4.2.7 Understand the special properties of 0 and 1 in multiplication and division.
4.2.8 Add and subtract simple fractions with different denominators, using objects or pictures.
4.2.9 Add and subtract decimals (to hundredths), using objects or pictures.
4.2.10 Use a standard algorithm to add and subtract decimals (to hundredths).
4.2.11 Know and use strategies for estimating results of any whole-number computations.
4.2.12 Use mental arithmetic to add or subtract numbers rounded to hundreds or thousands.
Algebra and Functions
4.3.1 Use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities (i.e., demonstrate an understanding of and the use of the concept of a variable).  
4.3.2 Use and interpret formulas to answer questions about quantities and their relationships.
4.3.3 Understand that multiplication and division are performed before addition and subtraction in expressions without parentheses.
4.3.4 Understand that an equation such as y = 3x + 5 is a rule for finding a second number when a first number is given.
4.3.5 Continue number patterns using multiplication and division.
4.3.6 Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems. 
4.3.7 Relate problem situations to number sentences involving multiplication and division.
4.3.8 Plot and label whole numbers on a number line up to 100. Estimate positions on the number line.
Geometry
4.4.1  Identify, describe, and draw rays, right angles, acute angles, obtuse angles, and straight angles using appropriate mathematical tools and technology.
4.4.2 Identify, describe, and draw parallel, perpendicular, and oblique lines using appropriate mathematical tools and technology.
4.4.3 Identify, describe, and draw parallelograms, rhombuses, and trapezoids, using appropriate mathematical tools and technology.
4.4.4 Identify congruent quadrilaterals and give reasons for congruence using sides, angles, parallels, and perpendiculars.
4.4.5 Identify and draw lines of symmetry in polygons.
4.4.6 Construct cubes and prisms and describe their attributes.
Measurement
4.5.1 Measure length to the nearest quarter-inch, eighth-inch, and millimeter.
4.5.2 Subtract units of length that may require renaming of feet to inches or meters to centimeters.
4.5.3 Know and use formulas for finding the perimeters of rectangles and squares.
4.5.4 Know and use formulas for finding the areas of rectangles and squares.
4.5.5 Estimate and calculate the area of rectangular shapes using appropriate units, such as square centimeter (cm2), square meter (m2), square inch (in2), or square yard (yd2).  
4.5.6 Understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.
4.5.7 Find areas of shapes by dividing them into basic shapes such as rectangles.
4.5.8 Use volume and capacity as different ways of measuring the space inside a shape.
4.5.9 Add time intervals involving hours and minutes.
4.5.10 Determine the amount of change from a purchase.
Data Analysis & Probability
4.6.1 Represent data on a number line and in tables, including frequency tables.
4.6.2 Interpret data graphs to answer questions about a situation.
4.6.3 Summarize and display the results of probability experiments in a clear and organized way.
Problem Solving
4.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 
4.7.2 Decide when and how to break a problem into simpler parts.
4.7.3 Apply strategies and results from simpler problems to solve more complex problems.
4.7.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, tools, and models to solve problems, justify arguments, and make conjectures.
4.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
4.7.6 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 
4.7.7 Know and use appropriate methods for estimating results of whole-number computations.
4.7.8 Make precise calculations and check the validity of the results in the context of the problem.
4.7.9 Decide whether a solution is reasonable in the context of the original situation.
4.7.10 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
 
Grade 5      [Back to TOP]
Number Sense
5.1.1 Convert between numbers in words and numbers in figures, for numbers up to millions and decimals to thousandths.
5.1.2 Round whole numbers and decimals to any place value.
5.1.3 Arrange in numerical order and compare whole numbers or decimals to two decimal places by using the symbols for less than (<), equals (=), and greater than (>).
5.1.4 Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
5.1.5 Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.
5.1.6 Describe and identify prime and composite numbers.
5.1.7 Identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive decimals.
Computation
5.2.1 Solve problems involving multiplication and division of any whole numbers.
5.2.2 Add and subtract fractions (including mixed numbers) with different denominators.
5.2.3 Use models to show an understanding of multiplication and division of fractions.
5.2.4 Multiply and divide fractions to solve problems.
5.2.5 Add and subtract decimals and verify the reasonableness of the results.
5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems.
5.2.7 Use mental arithmetic to add or subtract simple decimals.
Algebra and Functions
5.3.1 Use a variable to represent an unknown number.
5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution.
5.3.3 Use the distributive property in numerical equations and expressions.
5.3.4 Identify and graph ordered pairs of positive numbers.
5.3.5 Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.
5.3.6 Understand that the length of a horizontal line segment on a coordinate plane equals the difference between the x-coordinates and that the length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.
5.3.7 Use information taken from a graph or equation to answer questions about a problem situation.
Geometry
5.4.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, triangles, and circles by using appropriate tools (e.g., ruler, compass, protractor, appropriate technology, media tools).
5.4.2 Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangular.
5.4.3 Identify congruent triangles and justify your decisions by referring to sides and angles.
5.4.4 Identify, describe, draw, and classify polygons, such as pentagons and hexagons.
5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.
5.4.6 Identify shapes that have reflectional and rotational symmetry.
5.4.7 Understand that 90°, 180°, 270°, and 360° are associated with quarter, half, three-quarters, and full turns, respectively.
5.4.8 Construct prisms and pyramids using appropriate materials.
5.4.9 Given a picture of a three-dimensional object, build the object with blocks.
Measurement
5.5.1 Understand and apply the formulas for the area of a triangle, parallelogram, and trapezoid.
5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.5.3 Use formulas for the areas of rectangles and triangles to find the area of complex shapes by dividing them into basic shapes.
5.5.4 Find the surface area and volume of rectangular solids using appropriate units.
5.5.5 Understand and use the smaller and larger units for measuring weight (ounce, gram, and ton) and their relationship to pounds and kilograms.
5.5.6 Compare temperatures in Celsius and Fahrenheit, knowing that the freezing point of water is 0°C and 32°F and that the boiling point is 100°C and 212°F.
5.5.7 Add and subtract with money in decimal notation.
Data Analysis & Probability
5.6.1 Explain which types of displays are appropriate for various sets of data.
5.6.2 Find the mean, median, mode, and range of a set of data and describe what each does and does not tell about the data set.
5.6.3 Understand that probability can take any value between 0 and 1, events that are not going to occur have probability 0, events certain to occur have probability 1, and more likely events have a higher probability than less likely events.
5.6.4 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4, 3/4).
Problem Solving
5.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
5.7.2 Decide when and how to break a problem into simpler parts.
5.7.3 Apply strategies and results from simpler problems to solve more complex problems.
5.7.4 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
5.7.5 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
5.7.6 Know and apply appropriate methods for estimating results of rational-number computations.
5.7.7 Make precise calculations and check the validity of the results in the context of the problem.
5.7.8 Decide whether a solution is reasonable in the context of the original situation.
5.7.9 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
 
Grade 6    [Back to TOP]
Number Sense
6.1.1 Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in “owing”).
6.1.2 Interpret the absolute value of a number as the distance from zero on a number line, and find the absolute value of real numbers.
6.1.3 Compare and represent on a number line positive and negative integers, fractions, decimals (to hundredths), and mixed numbers.
6.1.4 Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator.
6.1.5 Recognize decimal equivalents for commonly used fractions without the use of a calculator.
6.1.6 Use models to represent ratios.
6.1.7 Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
Computation
6.2.1 Add and subtract positive and negative integers.
6.2.2 Multiply and divide positive and negative integers.
6.2.3 Multiply and divide decimals.
6.2.4 Explain how to multiply and divide positive fractions and perform the calculations.
6.2.5 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
6.2.6 Interpret and use ratios to show the relative sizes of two quantities. Use the notations: a/b, a to b, a:b.
6.2.7 Understand proportions and use them to solve problems.
6.2.8 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
6.2.9 Use estimation to decide whether answers are reasonable in decimal problems.
6.2.10 Use mental arithmetic to add or subtract simple fractions and decimals.
Algebra and Functions
6.3.1 Write and solve one-step linear equations and inequalities in one variable and check the answers.
6.3.2 Write and use formulas with up to three variables to solve problems.
6.3.3 Interpret and evaluate mathematical expressions that use grouping symbols such as parentheses.
6.3.4 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.
6.3.5 Use variables in expressions describing geometric quantities.
6.3.6 Apply the correct order of operations and the properties of real numbers (e.g., identity, inverse, commutative, associative, and distributive properties) to evaluate numerical expressions. Justify each step in the process.
6.3.7 Identify and graph ordered pairs in the four quadrants of the coordinate plane.
6.3.8 Solve problems involving linear functions with integer values. Write the equation and graph the resulting ordered pairs of integers on a grid.
6.3.9 Investigate how a change in one variable relates to a change in a second variable.
Geometry
6.4.1 Identify and draw vertical, adjacent, complementary, and supplementary angles and describe these angle relationships.
6.4.2 Use the properties of complementary, supplementary, and vertical angles to solve problems involving an unknown angle. Justify solutions.
6.4.3 Draw quadrilaterals and triangles from given information about them.
6.4.4 Understand that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve problems.
6.4.5 Identify and draw two-dimensional shapes that are similar.
6.4.6 Draw the translation (slide) and reflection (flip) of shapes.
6.4.7 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.
Measurement
6.5.1 Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.
6.5.2 Understand and use larger units for measuring length by comparing miles to yards and kilometers to meters.
6.5.3 Understand and use larger units for measuring area by comparing acres and square miles to square yards and square kilometers to square meters.
6.5.4 Understand the concept of the constant π as the ratio of the circumference to the diameter of a circle. Develop and use the formulas for the circumference and area of a circle.
6.5.5 Know common estimates of π (3.14, 22/7) and use these values to estimate and calculate the circumference and the area of circles. Compare with actual measurements.
6.5.6 Understand the concept of significant figures and round answers to an appropriate number of significant figures.
6.5.7 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area of these objects.
6.5.8 Use strategies to find the surface area and volume of right prisms and cylinders using appropriate units.
6.5.9 Use a formula to convert temperatures between Celsius and Fahrenheit.
6.5.10 Add, subtract, multiply, and divide with money in decimal notation.
Data Analysis & Probability
6.6.1 Organize and display single-variable data in appropriate graphs and stem-and-leaf plots, and explain which types of graphs are appropriate for various data sets.
6.6.2 Make frequency tables for numerical data, grouping the data in different ways to investigate how different groupings describe the data. Understand and find relative and cumulative frequency for a data set. Use histograms of the data and of the relative frequency distribution, and a broken line graph for cumulative frequency, to interpret the data.
6.6.3 Compare the mean, median, and mode for a set of data and explain which measure is most appropriate in a given context.
6.6.4 Show all possible outcomes for compound events in an organized way and find the theoretical probability of each outcome.
6.6.5 Use data to estimate the probability of future events.
6.6.6 Understand and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable.
Problem Solving
6.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
6.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
6.7.3 Decide when and how to break a problem into simpler parts.
6.7.4 Apply strategies and results from simpler problems to solve more complex problems.
6.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
6.7.6 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
6.7.7 Select and apply appropriate methods for estimating results of rational-number computations.
6.7.8 Use graphing to estimate solutions and check the estimates with analytic approaches.
6.7.9 Make precise calculations and check the validity of the results in the context of the problem.
6.7.10 Decide whether a solution is reasonable in the context of the original situation.
6.7.11 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.