Standard Description Videos Exercises

2 VIDEOS
2 EXERCISES

###### Counting and Cardinality
 K.CC.1 Count to 100 by ones and by tens.
 K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
 K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
 K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
 K.CC.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
 K.CC.4.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
 K.CC.4.c Understand that each successive number name refers to a quantity that is one larger.
 K.CC.5 Count to tell the number of objects.
 K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1
 K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.
###### Geometry
 K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
 K.G.2 Correctly name shapes regardless of their orientations or overall size.
 K.G.3 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
 K.G.4 Analyze, compare, create, and compose shapes.
 K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
 K.G.6 Analyze, compare, create, and compose shapes.
###### Measurement and Data
 K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
 K.MD.2 Describe and compare measurable attributes.
 K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3
###### Number and Operations in Base Ten
 K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
###### Operations and Algebraic Thinking
 K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
 K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
 K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
 K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
 K.OA.5 Fluently add and subtract within 5.

10 VIDEOS
3 EXERCISES

###### Geometry
 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4
 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
###### Measurement and Data
 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.
 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
###### Number and Operations in Base Ten
 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
 1.NBT.2.a Understand place value.
 1.NBT.2.b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
 1.NBT.2.c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
 1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
###### Operations and Algebraic Thinking
 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2
 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
 1.OA.3 Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
 1.OA.4 Understand and apply properties of operations and the relationship between addition and subtraction.
 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
 1.OA.6 Add and subtract within 20.
 1.OA.7 Work with addition and subtraction equations.
 1.OA.8 Work with addition and subtraction equations.

10 VIDEOS
13 EXERCISES

###### Geometry
 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
###### Measurement and Data
 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
 2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems4 using information presented in a bar graph.
 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.
 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
 2.MD.8 Work with time and money.
 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
###### Number and Operations in Base Ten
 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
 2.NBT.1.a Understand place value.
 2.NBT.1.b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
 2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.
 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
 2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
 2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
 2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
 2.NBT.8 Use place value understanding and properties of operations to add and subtract.
 2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.3
###### Operations and Algebraic Thinking
 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
 2.OA.2 Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.
 2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

49 VIDEOS
32 EXERCISES

###### Geometry
 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
###### Measurement and Data
 3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7
 3.MD.3 Represent and interpret data.
 3.MD.4 Represent and interpret data.
 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
 3.MD.5.a Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
 3.MD.5.b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
 3.MD.7 Relate area to the operations of multiplication and addition.
 3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
 3.MD.7b Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
 3.MD.7c Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
 3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
###### Number and Operations in Base Ten
 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
 3.NBT.3 Use place value understanding and properties of operations to perform multi-digit arithmetic.
###### Number and Operations--Fractions
 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 3.NF.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
 3.NF.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 3.NF.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
 3.NF.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
 3.NF.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
 3.NF.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
###### Operations and Algebraic Thinking
 3.OA.1 Represent and solve problems involving multiplication and division.
 3.OA.2 Represent and solve problems involving multiplication and division.
 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
 3.OA.4 Represent and solve problems involving multiplication and division.
 3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Associative Law of Multiplication Associative property for multiplication Basic Multiplication Commutative Law of Multiplication Example: 2-digit time 2-digit Example: Expressing division in multiple ways Example: Ways to represent multiplication Lattice Multiplication ...and 3 more ...
 3.OA.6 Understand properties of multiplication and the relationship between multiplication and division.
 3.OA.7 Multiply and divide within 100. Dividing Whole Numbers and Applications 2 Dividing Whole Numbers and Applications 3 Division 1 Division 2 Example: 2-digit time 2-digit Example: Expressing division in multiple ways Example: Ways to represent multiplication Lattice Multiplication ...and 4 more ...
 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3
 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

66 VIDEOS
45 EXERCISES

###### Geometry
 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
###### Measurement and Data
 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12,), (2, 24), (3, 36), ...
 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Adding and subtracting real numbers Adding and subtracting real numbers application Adding Fractions with Like Denominators Adding Mixed Numbers Adding Mixed Numbers Word Problem Adding real numbers with different signs Application of addition of real numbers Performing arithmetic calculations on units of volume ...and 5 more ...
 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
 4.MD.5.a Geometric measurement: understand concepts of angle and measure angles.
 4.MD.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
###### Number and Operations in Base Ten
 4.NBT.1 Generalize place value understanding for multi-digit whole numbers.
 4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.
 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
###### Number and Operations--Fractions
 4.NF.1 Extend understanding of fraction equivalence and ordering.
 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols, >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
 4.NF.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
 4.NF.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
 4.NF.3.c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
 4.NF.3.d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
 4.NF.4.a Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
 4.NF.4.b Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
 4.NF.4.c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
###### Operations and Algebraic Thinking
 4.OA.1 Use the four operations with whole numbers to solve problems.
 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1
 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimate strategies including rounding. Dividing Whole Numbers and Applications 2 Dividing Whole Numbers and Applications 6 Division 2 Example: Two digit multiplication More long division and remainder examples Multiplying Whole Numbers and Applications 5 Rounding to Estimate Differences Rounding to Estimate Sums ...and 4 more ...
 4.OA.4 Gain familiarity with factors and multiples.
 4.OA.5 Generate and analyze patterns.

64 VIDEOS
31 EXERCISES

###### Geometry
 5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
 5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
 5.G.3 Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
 5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
###### Measurement and Data
 5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Adding different units for weight Adding different units of length Application problems involving units of weight Conversion between metric units Converting Gallons to quarts pints and cups Converting pounds to ounces Converting units of length Converting within the metric system ...and 3 more ...
 5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
 5.MD.3.a Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
 5.MD.3.b A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
 5.MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
 5.MD.5.b Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition
 5.MD.5.c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
###### Number and Operations in Base Ten
 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
 5.NBT.3 Read, write, and compare decimals to thousandths.
 5.NBT.3.a Understand the place value system.
 5.NBT.3.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
 5.NBT.4 Use place value understanding to round decimals to any place.
 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Adding Decimals Dividing Decimals Dividing Decimals 2.1 Dividing real numbers with different signs Example: Multiplying numbers with different signs Multiplication 8: Multiplying decimals (Old video) Multiplying Decimals Multiplying Decimals 3 ...and 3 more ...
###### Number and Operations--Fractions
 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Adding and subtracting fractions Adding fractions examples Adding fractions with different signs Adding Fractions with Unlike Denominators Adding Mixed Numbers with Unlike Denominators Adding Mixed Numbers Word Problem Subtracting Mixed Numbers Subtracting Mixed Numbers 2 ...and 2 more ...
 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
 5.NF.3 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 5.NF.4.a Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 5.NF.4.b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 5.NF.5 Interpret multiplication as scaling (resizing), by:
 5.NF.5.a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 5.NF.5.b Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
 5.NF.7.a Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 5.NF.7.b Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 5.NF.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
###### Operations and Algebraic Thinking
 5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
 5.OA.2 Write and interpret numerical expressions.
 5.OA.3 Analyze patterns and relationships.

207 VIDEOS
70 EXERCISES

###### Expressions and Equations
 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. Dividing Monomials Dividing polynomials 1 Dividing polynomials with remainders Evaluating exponential expressions Evaluating exponential expressions 2 Exponent Properties 1 Exponent Properties 2 Exponent Properties 3 ...and 16 more ...
 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. Dividing real numbers with different signs Equation Special Cases Evaluating an expression with multiple variables Evaluating exponential expressions 2 Ex 2: Distributive property to simplify Example 1: Variables on both sides Examples of evaluating variable expressions Multiplying real number application ...and 5 more ...
 6.EE.2.a Apply and extend previous understandings of arithmetic to algebraic expressions
 6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
 6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Applying Radical Equations 2 Direct Variation Application Dividing Monomials Dividing polynomials 1 Dividing polynomials with remainders Dividing real numbers with different signs Evaluating an expression with multiple variables Evaluating exponential expressions 2 ...and 43 more ...
 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
 6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Algebra: Solving Inequalities Equation Special Cases Equations of Sequence Patterns Example 1: Solving systems by substitution Example 2: Solving systems by substitution Example 4: Solving a word problem with substitution Graphing Inequalities Graphing Inequalities 2 ...and 3 more ...
 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Averages Challenge example: Sum of integers Equations of Sequence Patterns Example 4: Solving a word problem with substitution Example: Dimensions of a garden Example: evaluate a formula using substitution Example: evaluating an expression Example: Solving for a variable ...and 6 more ...
 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Absolute Inequalities 2 Absolute Value Inequalities Absolute value inequalities example 3 Algebra: Solving Inequalities Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 ...and 14 more ...
 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
###### Geometry
 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
###### Ratios and Proportional Relationships
 6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems
 6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems
 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
 6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
 6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
 6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Adding different units for weight Application problems involving units of weight Comparing Celsius and Farenheit temperature scales Conversion between metric units Converting Fahrenheit to Celsius Converting Gallons to quarts pints and cups Converting pounds to ounces Converting units of length ...and 4 more ...
###### Statistics and Probability
 6.SP.1 Develop understanding of statistical variability
 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
 6.SP.5 Summarize numerical data sets in relation to their context, such as by:
 6.SP.5.a Reporting the number of observations.
 6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 6.SP.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Average or Central Tendency: Arithmetic Mean, Median, and Mode Central Limit Theorem ck12.org Exercise: Standard Normal Distribution and the Empirical Rule ck12.org Normal Distribution Problems: Empirical Rule ck12.org Normal Distribution Problems: Qualitative sense of normal distributions ck12.org Normal Distribution Problems: z-score ck12.org: More Empirical Rule and Z-score practice Law of Large Numbers ...and 8 more ...
 6.SP.5.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
###### The Number System
 6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions
 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Adding Decimals Dividing decimal Dividing Decimals Dividing Decimals 2.1 Dividing real numbers with different signs Dividing Whole Numbers and Applications 2 Dividing Whole Numbers and Applications 3 Dividing Whole Numbers and Applications 4 ...and 11 more ...
 6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples
 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the mean of 0 in each situation.
 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
 6.NS.6.a Apply and extend previous understandings of numbers to the system of rational numbers
 6.NS.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
 6.NS.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Absolute Value Inequalities Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 Inequalities on a number line Integers and Rational Numbers Locate integers on a number line ...and 11 more ...
 6.NS.7 Understand ordering and absolute value of rational numbers.
 6.NS.7.a Apply and extend previous understandings of numbers to the system of rational numbers Absolute Inequalities 2 Absolute Value and Number Lines Absolute Value Inequalities Absolute value inequalities example 3 Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 ...and 7 more ...
 6.NS.7.b Apply and extend previous understandings of numbers to the system of rational numbers
 6.NS.7.c Apply and extend previous understandings of numbers to the system of rational numbers Absolute Inequalities 2 Absolute Value 1 Absolute Value and Number Lines Absolute Value Equation Example 2 Absolute Value Equations Absolute Value Equations 1 Absolute Value Inequalities Absolute value inequalities example 3 ...and 3 more ...
 6.NS.7.d Apply and extend previous understandings of numbers to the system of rational numbers
 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

155 VIDEOS
35 EXERCISES

###### Expressions and Equations
 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
 7.EE.2 Use properties of operations to generate equivalent expressions
 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making \$25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or \$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Absolute Value Inequalities Bunch of examples Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 Example: Dimensions of a garden Example: evaluate a formula using substitution ...and 18 more ...
 7.EE.4.a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Converting within the metric system Example 4: Solving a word problem with substitution Example: Dimensions of a garden Example: Solving for a variable Extraneous Solutions to Rational Equations Multiplying and Dividing Monomials 1 Multiplying and Dividing Monomials 2 Multiplying and Dividing Monomials 3 ...and 7 more ...
 7.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions. Absolute Value Inequalities Algebra: Solving Inequalities Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 Graphing linear inequalities in two variables 2 Inequalities ...and 6 more ...
###### Geometry
 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
 7.G.6 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.
###### Ratios and Proportional Relationships
 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
 7.RP.2 Recognize and represent proportional relationships between quantities.
 7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 7.RP.2.c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
 7.RP.2.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Advanced ratio problems Alternate Solution to Ratio Problem (HD Version) Another Percent Word Problem Growing by a percentage Introduction to interest Mixture problems 1 Mixture problems 2 Mixture problems 3 ...and 5 more ...
###### Statistics and Probability
 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Central Limit Theorem Confidence Interval Example Law of Large Numbers Margin of Error 1 Margin of Error 2 Sample mean versus population mean. Sampling Distribution of the Sample Mean Sampling Distribution of the Sample Mean 2 ...and 3 more ...
 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Central Limit Theorem ck12.org Normal Distribution Problems: Qualitative sense of normal distributions ck12.org Normal Distribution Problems: z-score ck12.org: More Empirical Rule and Z-score practice Clarification of Confidence Interval of Difference of Means Confidence Interval Example Confidence Interval of Difference of Means Introduction to the Normal Distribution ...and 7 more ...
 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Example: Bag of unfair coins Example: Picking a yellow marble Example: Probability of rolling doubles Example: Probability through counting outcomes Probability (part 2) Probability (part 3) Probability (part 4) Probability (part 5) ...and 2 more ...
 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Example: Bag of unfair coins Example: Picking a non-blue marble Example: Rolling even three times Example: Picking a yellow marble Example: Probability of rolling doubles Example: Probability through counting outcomes Probability (part 2) Probability (part 3) ...and 4 more ...
 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Example: Bag of unfair coins Example: Different ways to pick officers Example: Combinatorics and probability Example: Picking a yellow marble Example: Probability of rolling doubles Example: Probability through counting outcomes Probability (part 2) Probability (part 3) ...and 4 more ...
 7.SP.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
 7.SP.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Example: Bag of unfair coins Example: Picking a non-blue marble Example: Picking a yellow marble Example: Probability of rolling doubles Example: Probability through counting outcomes Probability (part 2) Probability (part 3) Probability (part 4) ...and 4 more ...
 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
 7.SP.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
 7.SP.8.b Investigate chance processes and develop, use, and evaluate probability models
 7.SP.8.c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
###### The Number System
 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
 7.NS.1.a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
 7.NS.1.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
 7.NS.1.c Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Absolute Value Equations Absolute Value Equations 2 Absolute Value Inequalities Adding and subtracting real numbers Adding and subtracting real numbers application Adding real numbers with different signs Adding/Subtracting negative numbers Application of addition of real numbers ...and 3 more ...
 7.NS.1.d Apply properties of operations as strategies to add and subtract rational numbers.
 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Dividing fractions Dividing real numbers with different signs Division of Rational Numbers Example: Multiplying numbers with different signs Fractional Exponent Expressions 1 Fractional Exponent Expressions 2 Fractional Exponent Expressions 3 Multiplication of Rational Numbers ...and 2 more ...
 7.NS.2.a Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
 7.NS.2.b Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers.
 7.NS.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.1

150 VIDEOS
39 EXERCISES

###### Expressions and Equations
 8.EE.1 Work with radicals and integer exponents Dividing Monomials Evaluating exponential expressions Evaluating exponential expressions 2 Exponent Properties 1 Exponent Properties 2 Exponent Properties 3 Exponent Properties 4 Exponent Properties 5 ...and 13 more ...
 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that _2 is irrational.
 8.EE.3 Work with radicals and integer exponents
 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Algebra: Equation of a line Algebra: Slope Algebra: Slope 2 Algebra: Slope 3 Algebra: Slope and Y-intercept intuition Equation of a line 1 Equation of a line 3 Graphical Slope of a Line ...and 6 more ...
 8.EE.7 Solve linear equations in one variable.
 8.EE.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
 8.EE.8 Analyze and solve pairs of simultaneous linear equations.
 8.EE.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Addition Elimination Method 3 Addition Elimination Method 4 Consistent and Inconsistent Systems Example 1: Graphically Solving Systems Example 2: Graphically Solving Systems Example 3: Graphically Solving Systems Example 3: Solving systems by substitution Graphical Systems Application Problem ...and 6 more ...
 8.EE.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Addition Elimination Method 1 Addition Elimination Method 2 Addition Elimination Method 3 Addition Elimination Method 4 Consistent and Inconsistent Systems Converting to slope-intercept form Example 1: Graphically Solving Systems Example 1: Solving systems by elimination ...and 15 more ...
 8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Converting to slope-intercept form Example 1: Graphically Solving Systems Example 1: Solving systems by elimination Example 2: Graphically Solving Systems Example 2: Solving systems by elimination Example 2: Solving systems by substitution Example 3: Graphically Solving Systems Example 3: Solving systems by elimination ...and 4 more ...
###### Functions
 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Converting to slope-intercept form Equation of a line 1 Equation of a line 2 Equation of a line 3 Ex: Constructing a function Exploring linear relationships Graphing a line in slope intercept form Graphing linear inequalities in two variables 2 ...and 5 more ...
 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Application problem with graph Converting to slope-intercept form Direct Variation 1 Equation of a line 1 Exploring linear relationships Exploring nonlinear relationships Functional Relationships 1 Graphical Slope of a Line ...and 7 more ...
###### Geometry
 8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
 8.G.1.a Lines are taken to lines, and line segments to line segments of the same length.
 8.G.1.b Angles are taken to angles of the same measure.
 8.G.1.c Parallel lines are taken to parallel lines.
 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
###### Statistics and Probability
 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5cm in mature plant height.
 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
###### The Number System
 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
 8.NS.2 Use rational approximations of irrational numbers to compare the size v`of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., _2). For example, by truncating the decimal expansion of _2, show that _2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

540 VIDEOS
116 EXERCISES

###### Arithmetic with Polynomials and Rational Expressions
 9-12.A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Adding and Subtracting Polynomials 1 Adding and Subtracting Polynomials 2 Adding and Subtracting Polynomials 3 Adding Polynomials Addition and Subtraction of Polynomials Dividing Monomials Dividing multivariable polynomial with monomial Dividing polynomials 1 ...and 21 more ...
 9-12.A-APR.2 Understand the relationship between zeros and factors of polynomial
 9-12.A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
 9-12.A-APR.4 Use polynomial identities to solve problems
 9-12.A-APR.5 Use polynomial identities to solve problems
 9-12.A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
 9-12.A-APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Adding and Subtracting Rational Expressions 1 Adding and Subtracting Rational Expressions 2 Adding and Subtracting Rational Expressions 3 Adding Rational Expressions Example 1 Adding Rational Expressions Example 2 Adding Rational Expressions Example 3 Applying Rational Equations 1 Applying Rational Equations 2 ...and 11 more ...
###### Building Functions
 9-12.F-BF.1 Write a function that describes a relationship between two quantities._
 9-12.F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
 9-12.F-BF.1.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
 9-12.F-BF.1.c Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
 9-12.F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms._
 9-12.F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
 9-12.F-BF.4 Find inverse functions.
 9-12.F-BF.4.a Build new functions from existing functions
 9-12.F-BF.4.b Verify by composition that one function is the inverse of another.
 9-12.F-BF.4.c Read values of an inverse function from a graph or a table, given that the function has an inverse.
 9-12.F-BF.4.d Produce an invertible function from a non-invertible function by restricting the domain.
 9-12.F-BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
###### Circles
 9-12.G-C.1 Prove that all circles are similar.
 9-12.G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
 9-12.G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
 9-12.G-C.4 Construct a tangent line from a point outside a given circle to the circle.
 9-12.G-C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
###### Conditional Probability & the Rules of Probability
 9-12.S-CP.1 Understand independence and conditional probability and use them to interpret data
 9-12.S-CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
 9-12.S-CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
 9-12.S-CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
 9-12.S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
 9-12.S-CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model
 9-12.S-CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model
 9-12.S-CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
 9-12.S-CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems. Birthday Probability Problem Combinations Conditional Probability and Combinations Example: Lottery probability Example: 9 card hands Example: Ways to arrange colors Example: Ways to pick officers Permutations ...and 2 more ...
###### Congruence
 9-12.G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
 9-12.G-CO.10 Prove geometric theorems
 9-12.G-CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
 9-12.G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
 9-12.G-CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
 9-12.G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
 9-12.G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
 9-12.G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
 9-12.G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
 9-12.G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
 9-12.G-CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 9-12.G-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
 9-12.G-CO.9 Prove geometric theorems
###### Creating Equations*
 9-12.A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Absolute Value Inequalities Another percent example Applying Rational Equations 1 Applying Rational Equations 2 Applying Rational Equations 3 Bunch of examples Compound Inequalities Compound Inequalities 2 ...and 21 more ...
 9-12.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Epsilon Delta Limit Definition 2 Graphs of Linear Equations Introduction to Limits Introduction to limits Limit Examples (part 1) Mixture problems 1 Mixture problems 2 Mixture problems 3 ...and 4 more ...
 9-12.A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Absolute Value Inequalities Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 Epsilon Delta Limit Definition 2 Limit Examples (part 1) Multi-Step Inequalities ...and 8 more ...
 9-12.A-CED.4 Create equations that describe numbers or relationship
###### Expressing Geometric Properties with Equations
 9-12.G-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
 9-12.G-GPE.2 Derive the equation of a parabola given a focus and directrix.
 9-12.G-GPE.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
 9-12.G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, _3) lies on the circle centered at the origin and containing the point (0, 2).
 9-12.G-GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
 9-12.G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
 9-12.G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula._
###### Geometric Measurement and Dimension
 9-12.G-GMD.1 Explain volume formulas and use them to solve problems
 9-12.G-GMD.2 Explain volume formulas and use them to solve problems
 9-12.G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems._
 9-12.G-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
###### Interpreting Categorical and Quantitative Data
 9-12.S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
 9-12.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
 9-12.S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
 9-12.S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Central Limit Theorem ck12.org Exercise: Standard Normal Distribution and the Empirical Rule ck12.org Normal Distribution Problems: Empirical Rule ck12.org Normal Distribution Problems: Qualitative sense of normal distributions ck12.org Normal Distribution Problems: z-score ck12.org: More Empirical Rule and Z-score practice Confidence Interval Example Introduction to the Normal Distribution ...and 7 more ...
 9-12.S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
 9-12.S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
 9-12.S-ID.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
 9-12.S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals.
 9-12.S-ID.6.c Fit a linear function for a scatter plot that suggests a linear association.
 9-12.S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
 9-12.S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
 9-12.S-ID.9 Distinguish between correlation and causation.
###### Interpreting Functions
 9-12.F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
 9-12.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
 9-12.F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n _ 1.
 9-12.F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity._ Calculus: Maximum and minimum values on an interval Equation of a line 1 Functional Relationships 1 Functions (Part III) Graphing a line in slope intercept form Limit Examples (part 2) Parametric Equations 1 Testing if a relationship is a function ...and 3 more ...
 9-12.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function._
 9-12.F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph._
 9-12.F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases._ Another example graphing with derivatives Functional Relationships 1 Graphing a line in slope intercept form Graphing using derivatives Graphing with Calculus Introduction to definite integrals Introduction to Limits More Limits ...and 2 more ...
 9-12.F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima. Applying Quadratic Functions 1 Applying Quadratic Functions 3 Calculus: Maximum and minimum values on an interval Converting to slope-intercept form Example: Graphing a quadratic Example: Parabola vertex and axis of symmetry Function example problems Graphical Systems Application Problem ...and 12 more ...
 9-12.F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
 9-12.F-IF.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
 9-12.F-IF.7.d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
 9-12.F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
 9-12.F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
 9-12.F-IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
 9-12.F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y = (1.2)^t/10, and classify them as representing exponential growth or decay.
 9-12.F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
###### Linear, Quadratic, and Exponential Models
 9-12.F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
 9-12.F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
 9-12.F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 9-12.F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 9-12.F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
 9-12.F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
 9-12.F-LE.4 For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
 9-12.F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
###### Making Inferences and Justifying Conclusions
 9-12.S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Central Limit Theorem Confidence Interval Example Law of Large Numbers Margin of Error 1 Margin of Error 2 Sample mean versus population mean. Sampling Distribution of the Sample Mean Sampling Distribution of the Sample Mean 2 ...and 4 more ...
 9-12.S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
 9-12.S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
 9-12.S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
 9-12.S-IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. ANOVA 1 - Calculating SST (Total Sum of Squares) ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi ANOVA 3 -Hypothesis Test with F-Statistic Chi-Square Distribution Introduction Comparing Population Proportions 1 Comparing Population Proportions 2 Confidence Interval of Difference of Means Contingency Table Chi-Square Test ...and 4 more ...
 9-12.S-IC.6 Evaluate reports based on data.
###### Modeling with Geometry
 9-12.G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)._
 9-12.G-MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot)._
 9-12.G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)._
###### Quantities
 9-12.N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
 9-12.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.
 9-12.N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
###### Reasoning with Equations and Inequalities
 9-12.A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
 9-12.A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
 9-12.A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions._
 9-12.A-REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Graphical System of Inequalities Graphing Inequalities Graphing Inequalities 2 Graphing linear inequalities in two variables 2 Graphing Systems of Inequalities Graphing systems of inequalities Graphing systems of inequalities 2 Graphing systems of inequalities 3 ...and 3 more ...
 9-12.A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Applying Radical Equations 1 Applying Radical Equations 2 Applying Radical Equations 3 Extraneous Solutions to Radical Equations More Involved Radical Equation Example Radical Equation Examples Simplifying Radical Expressions 2 Simplifying Radical Expressions 3 ...and 11 more ...
 9-12.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Challenge example: Sum of integers Compound Inequalities Compound Inequalities Compound Inequalities 2 Compound Inequalities 3 Compound Inequalities 4 Ex 1: Distributive property to simplify Ex 3: Distributive property to simplify ...and 21 more ...
 9-12.A-REI.4 Solve quadratic equations in one variable. Applying Quadratic Functions 1 Applying Quadratic Functions 2 Applying Quadratic Functions 3 Evaluating a polynomial at a given value Example 1: Solving a quadratic equation by factoring Example 1: Using the quadratic formula Example 2: Solving a quadratic equation by factoring Example 2: Using the quadratic formula ...and 13 more ...
 9-12.A-REI.4.a Solve equations and inequalities in one variable
 9-12.A-REI.4.b Solve equations and inequalities in one variable Completing the square (old school) Discriminant of Quadratic Equations Example 1: Completing the square Example 1: Solving a quadratic equation by factoring Example 2: Completing the square Example 2: Solving a quadratic equation by factoring Example 3: Completing the square Example 3: Solving a quadratic equation by factoring ...and 13 more ...
 9-12.A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
 9-12.A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Addition Elimination Method 1 Addition Elimination Method 2 Addition Elimination Method 3 Addition Elimination Method 4 Domain of a Rational Expression 1 Example 1: Graphically Solving Systems Example 1: Solving systems by elimination Example 2: Graphically Solving Systems ...and 24 more ...
 9-12.A-REI.7 Solve systems of equations
 9-12.A-REI.8 Represent a system of linear equations as a single matrix equation in a vector variable.
 9-12.A-REI.9 Solve systems of equations
###### Seeing Structure in Expressions
 9-12.A-SSE.1 Interpret expressions that represent a quantity in terms of its context._
 9-12.A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients. Algebraic Expression Least Common Multiple Difference of Cubes Factoring Example 1: Factoring by grouping Example 1: Factoring difference of squares Example 1: Factoring quadratic expressions Example 2: Factoring by grouping Example 3: Factoring by grouping Example 4: Factoring by grouping ...and 12 more ...
 9-12.A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P. Algebraic Expression Least Common Multiple Chain Rule Examples Difference of Cubes Factoring Example 1: Factoring by grouping Example 1: Factoring difference of squares Example 1: Factoring quadratic expressions Example 1: Factoring trinomials with a common factor Example: Factoring perfect square trinomials ...and 3 more ...
 9-12.A-SSE.2 Interpret the structure of expressions Adding and Subtracting Rational Expressions Chain Rule Examples Complicated Rational Expressions Deductive Reasoning 2 Difference of Cubes Factoring Dividing and Simplifying Rational Expressions Example 1: Factoring by grouping Example 1: Factoring difference of squares ...and 28 more ...
 9-12.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression._ Adding and Subtracting Rational Expressions Complicated Rational Expressions Difference of Cubes Factoring Example 1: Factoring by grouping Example 1: Factoring difference of squares Example 1: Factoring quadratic expressions Example 1: Factoring trinomials with a common factor Example: Factoring perfect square trinomials ...and 4 more ...
 9-12.A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
 9-12.A-SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 9-12.A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^1/12)^12t _ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
 9-12.A-SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments._
###### Similarity, Right Triangles, and Trigonometry
 9-12.G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
 9-12.G-SRT.1.a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
 9-12.G-SRT.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
 9-12.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems.
 9-12.G-SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
 9-12.G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
 9-12.G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
 9-12.G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
 9-12.G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
 9-12.G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
 9-12.G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
 9-12.G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems._ 30-60-90 Triangles II 45-45-90 Triangles Basic Trigonometry Basic Trigonometry II Ferris Wheel Trig Problem Ferris Wheel Trig Problem (part 2) Graph of the sine function IIT JEE Trigonometric Constraints ...and 15 more ...
 9-12.G-SRT.9 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
###### The Complex Number System
 9-12.N-CN.1 Perform arithmetic operations with complex numbers
 9-12.N-CN.2 Perform arithmetic operations with complex numbers
 9-12.N-CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
 9-12.N-CN.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
 9-12.N-CN.5 Represent complex numbers and their operations on the complex plane
 9-12.N-CN.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
 9-12.N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. Applying Quadratic Functions 1 Applying Quadratic Functions 2 Applying Quadratic Functions 3 Evaluating a polynomial at a given value Example 1: Solving a quadratic equation by factoring Example 1: Using the quadratic formula Example 2: Solving a quadratic equation by factoring Example 2: Using the quadratic formula ...and 13 more ...
 9-12.N-CN.8 Use complex numbers in polynomial identities and equations
 9-12.N-CN.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
###### The Real Number System
 9-12.N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5^(1/3)3 to hold, so (5^1/3) must equal 5.
 9-12.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Adding and Subtracting Polynomials 1 Adding and Subtracting Polynomials 2 Adding and Subtracting Polynomials 3 Deductive Reasoning 2 Exponent Rules 1 Exponent Rules 2 Exponent Rules 3 Exponent Rules Part 1 ...and 19 more ...
 9-12.N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
###### Trigonometric Functions
 9-12.F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
 9-12.F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
 9-12.F-TF.3 Extend the domain of trigonometric functions using the unit circle
 9-12.F-TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
 9-12.F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline._
 9-12.F-TF.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
 9-12.F-TF.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context._
 9-12.F-TF.8 Prove the Pythagorean identity sin2(_) + cos^2(_) = 1 and use it to find sin(_), cos(_), or tan(_) given sin(_), cos(_), or tan(_) and the quadrant of the angle.
 9-12.F-TF.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
###### Using Probability to Make Decisions
 9-12.S-MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
 9-12.S-MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
 9-12.S-MD.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. Binomial Distribution 1 Binomial Distribution 2 Binomial Distribution 3 Binomial Distribution 4 Birthday Probability Problem Example: Getting two questions right on an exam Expected Value of Binomial Distribution Expected Value: E(X) ...and 4 more ...
 9-12.S-MD.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? ANOVA 1 - Calculating SST (Total Sum of Squares) Bernoulli Distribution Mean and Variance Formulas Binomial Distribution 1 Binomial Distribution 2 Binomial Distribution 3 Binomial Distribution 4 Chi-Square Distribution Introduction Expected Value of Binomial Distribution ...and 8 more ...
 9-12.S-MD.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
 9-12.S-MD.5.a Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant.
 9-12.S-MD.5.b Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.
 9-12.S-MD.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
 9-12.S-MD.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Conditional Probability and Combinations Confidence Interval of Difference of Means Hypothesis Testing and P-values Introduction to Random Variables One-Tailed and Two-Tailed Tests Poisson Process 1 Poisson Process 2 Probability (part 6) ...and 7 more ...
###### Using Probability to Make Decisions
 9-12.S.MD.1 #N/A
 9-12.S.MD.2 #N/A
 9-12.S.MD.3 #N/A
 9-12.S.MD.4 #N/A
 9-12.S.MD.5 #N/A
 9-12.S.MD.5.a #N/A
 9-12.S.MD.5.b #N/A
 9-12.S.MD.6 #N/A
 9-12.S.MD.7 #N/A
###### Vector and Matrix Quantities
 9-12.N-VM.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
 9-12.N-VM.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
 9-12.N-VM.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
 9-12.N-VM.12 Perform operations on matrices and use matrices in applications
 9-12.N-VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
 9-12.N-VM.3 Solve problems involving velocity and other quantities that can be represented by vectors.