1.G.A | ||
---|---|---|
Grade 1 » Geometry » Reason with shapes and their attributes. |
1.G.A.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.^{1} Grade levels |
1.MD.A | ||
---|---|---|
Grade 1 » Measurement & Data » Measure lengths indirectly and by iterating length units. |
1.MD.A.1 | ||
---|---|---|
Order three objects by length; compare the lengths of two objects indirectly by using a third object. Grade levels |
1.MD.B | ||
---|---|---|
Grade 1 » Measurement & Data » Tell and write time. |
1.MD.B.3 | ||
---|---|---|
Tell and write time in hours and half-hours using analog and digital clocks. Grade levels |
1.MD.C | ||
---|---|---|
Grade 1 » Measurement & Data » Represent and interpret data. |
1.NBT.A | ||
---|---|---|
Grade 1 » Number & Operations in Base Ten » Extend the counting sequence. |
1.NBT.A.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. Grade levels |
1.NBT.B | ||
---|---|---|
Grade 1 » Number & Operations in Base Ten » Understand place value. |
1.NBT.B.2 | ||
---|---|---|
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: Grade levels |
1.NBT.B.2a | ||
---|---|---|
10 can be thought of as a bundle of ten ones — called a "ten." Grade levels |
1.NBT.B.2b | ||
---|---|---|
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Grade levels |
1.NBT.B.2c | ||
---|---|---|
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). Grade levels |
1.NBT.B.3 | ||
---|---|---|
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Grade levels |
1.NBT.C | ||
---|---|---|
Grade 1 » Number & Operations in Base Ten » Use place value understanding and properties of operations to add and subtract. |
1.NBT.C.5 | ||
---|---|---|
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Grade levels |
1.OA.A | ||
---|---|---|
Grade 1 » Operations & Algebraic Thinking » Represent and solve problems involving addition and subtraction. |
1.OA.B | ||
---|---|---|
Grade 1 » Operations & Algebraic Thinking » Understand and apply properties of operations and the relationship between addition and subtraction. |
1.OA.B.4 | ||
---|---|---|
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Grade levels |
1.OA.C | ||
---|---|---|
Grade 1 » Operations & Algebraic Thinking » Add and subtract within 20. |
1.OA.C.5 | ||
---|---|---|
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Grade levels |
1.OA.D | ||
---|---|---|
Grade 1 » Operations & Algebraic Thinking » Work with addition and subtraction equations. |
2.G.A | ||
---|---|---|
Grade 2 » Geometry » Reason with shapes and their attributes. |
2.G.A.2 | ||
---|---|---|
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Grade levels |
2.MD.A | ||
---|---|---|
Grade 2 » Measurement & Data » Measure and estimate lengths in standard units. |
2.MD.A.1 | ||
---|---|---|
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Grade levels |
2.MD.A.3 | ||
---|---|---|
Estimate lengths using units of inches, feet, centimeters, and meters. Grade levels |
2.MD.A.4 | ||
---|---|---|
Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Grade levels |
2.MD.B | ||
---|---|---|
Grade 2 » Measurement & Data » Relate addition and subtraction to length. |
2.MD.C | ||
---|---|---|
Grade 2 » Measurement & Data » Work with time and money. |
2.MD.C.7 | ||
---|---|---|
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Grade levels |
2.MD.D | ||
---|---|---|
Grade 2 » Measurement & Data » Represent and interpret data. |
2.NBT.A | ||
---|---|---|
Grade 2 » Number & Operations in Base Ten » Understand place value. |
2.NBT.A.1a | ||
---|---|---|
100 can be thought of as a bundle of ten tens — called a "hundred." Grade levels |
2.NBT.A.1b | ||
---|---|---|
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). Grade levels |
2.NBT.A.2 | ||
---|---|---|
Count within 1000; skip-count by 5s, 10s, and 100s. Grade levels |
2.NBT.A.3 | ||
---|---|---|
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Grade levels |
2.NBT.A.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. Grade levels |
2.NBT.B | ||
---|---|---|
Grade 2 » Number & Operations in Base Ten » Use place value understanding and properties of operations to add and subtract. |
2.NBT.B.5 | ||
---|---|---|
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Grade levels |
2.NBT.B.6 | ||
---|---|---|
Add up to four two-digit numbers using strategies based on place value and properties of operations. Grade levels |
2.NBT.B.8 | ||
---|---|---|
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. Grade levels |
2.NBT.B.9 | ||
---|---|---|
Explain why addition and subtraction strategies work, using place value and the properties of operations.^{1} Grade levels |
2.OA.A | ||
---|---|---|
Grade 2 » Operations & Algebraic Thinking » Represent and solve problems involving addition and subtraction. |
2.OA.B | ||
---|---|---|
Grade 2 » Operations & Algebraic Thinking » Add and subtract within 20. |
2.OA.B.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. Grade levels |
2.OA.C | ||
---|---|---|
Grade 2 » Operations & Algebraic Thinking » Work with equal groups of objects to gain foundations for multiplication. |
3.G.A | ||
---|---|---|
Grade 3 » Geometry » Reason with shapes and their attributes. |
3.MD.A | ||
---|---|---|
Grade 3 » Measurement & Data » Solve problems involving measurement and estimation. |
3.MD.B | ||
---|---|---|
Grade 3 » Measurement & Data » Represent and interpret data. |
3.MD.C | ||
---|---|---|
Grade 3 » Measurement & Data » Geometric measurement: understand concepts of area and relate area to multiplication and to addition. |
3.MD.C.5 | ||
---|---|---|
Recognize area as an attribute of plane figures and understand concepts of area measurement. Grade levels |
3.MD.C.5a | ||
---|---|---|
A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. Grade levels |
3.MD.C.5b | ||
---|---|---|
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. Grade levels |
3.MD.C.6 | ||
---|---|---|
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Grade levels |
3.MD.C.7 | ||
---|---|---|
Relate area to the operations of multiplication and addition. Grade levels |
3.MD.C.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. Grade levels |
3.MD.D | ||
---|---|---|
Grade 3 » Measurement & Data » Geometric measurement: recognize perimeter. |
3.NBT.A | ||
---|---|---|
Grade 3 » Number & Operations in Base Ten » Use place value understanding and properties of operations to perform multi-digit arithmetic.¹ |
3.NBT.A.1 | ||
---|---|---|
Use place value understanding to round whole numbers to the nearest 10 or 100. Grade levels |
3.NBT.A.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. Grade levels |
3.NBT.A.3 | ||
---|---|---|
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. Grade levels |
3.NF.A | ||
---|---|---|
Grade 3 » Number & Operations—Fractions¹ » Develop understanding of fractions as numbers. |
3.NF.A.2 | ||
---|---|---|
Understand a fraction as a number on the number line; represent fractions on a number line diagram. Grade levels |
3.NF.A.3 | ||
---|---|---|
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Grade levels |
3.NF.A.3a | ||
---|---|---|
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Grade levels |
3.NF.A.3b | ||
---|---|---|
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. Grade levels |
3.OA.A | ||
---|---|---|
Grade 3 » Operations & Algebraic Thinking » Represent and solve problems involving multiplication and division. |
3.OA.B | ||
---|---|---|
Grade 3 » Operations & Algebraic Thinking » Understand properties of multiplication and the relationship between multiplication and division. |
3.OA.B.6 | ||
---|---|---|
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Grade levels |
3.OA.C | ||
---|---|---|
Grade 3 » Operations & Algebraic Thinking » Multiply and divide within 100. |
3.OA.D | ||
---|---|---|
Grade 3 » Operations & Algebraic Thinking » Solve problems involving the four operations, and identify and explain patterns in arithmetic. |
4.G.A | ||
---|---|---|
Grade 4 » Geometry » Draw and identify lines and angles, and classify shapes by properties of their lines and angles. |
4.G.A.1 | ||
---|---|---|
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Grade levels |
4.MD.A | ||
---|---|---|
Grade 4 » Measurement & Data » Solve problems involving measurement and conversion of measurements. |
4.MD.B | ||
---|---|---|
Grade 4 » Measurement & Data » Represent and interpret data. |
4.MD.C | ||
---|---|---|
Grade 4 » Measurement & Data » Geometric measurement: understand concepts of angle and measure angles. |
4.MD.C.5 | ||
---|---|---|
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: Grade levels |
4.MD.C.5b | ||
---|---|---|
An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Grade levels |
4.MD.C.6 | ||
---|---|---|
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Grade levels |
4.NBT.A | ||
---|---|---|
Grade 4 » Number & Operations in Base Ten¹ » Generalize place value understanding for multi-digit whole numbers. |
4.NBT.A.3 | ||
---|---|---|
Use place value understanding to round multi-digit whole numbers to any place. Grade levels |
4.NBT.B | ||
---|---|---|
Grade 4 » Number & Operations in Base Ten¹ » Use place value understanding and properties of operations to perform multi-digit arithmetic. |
4.NBT.B.4 | ||
---|---|---|
Fluently add and subtract multi-digit whole numbers using the standard algorithm. Grade levels |
4.NF.A | ||
---|---|---|
Grade 4 » Number & Operations—FractionsÂ¹ » Extend understanding of fraction equivalence and ordering. |
4.NF.B | ||
---|---|---|
Grade 4 » Number & Operations—FractionsÂ¹ » Build fractions from unit fractions. |
4.NF.B.3 | ||
---|---|---|
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Grade levels |
4.NF.B.3a | ||
---|---|---|
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Grade levels |
4.NF.B.4 | ||
---|---|---|
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Grade levels |
4.NF.C | ||
---|---|---|
Grade 4 » Number & Operations—FractionsÂ¹ » Understand decimal notation for fractions, and compare decimal fractions. |
4.NF.C.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. Grade levels |
4.OA.A | ||
---|---|---|
Grade 4 » Operations & Algebraic Thinking » Use the four operations with whole numbers to solve problems. |
4.OA.B | ||
---|---|---|
Grade 4 » Operations & Algebraic Thinking » Gain familiarity with factors and multiples. |
4.OA.C | ||
---|---|---|
Grade 4 » Operations & Algebraic Thinking » Generate and analyze patterns. |
5.G.A | ||
---|---|---|
Grade 5 » Geometry » Graph points on the coordinate plane to solve real-world and mathematical problems. |
5.G.B | ||
---|---|---|
Grade 5 » Geometry » Classify two-dimensional figures into categories based on their properties. |
5.G.B.4 | ||
---|---|---|
Classify two-dimensional figures in a hierarchy based on properties. Grade levels |
5.MD.A | ||
---|---|---|
Grade 5 » Measurement & Data » Convert like measurement units within a given measurement system. |
5.MD.B | ||
---|---|---|
Grade 5 » Measurement & Data » Represent and interpret data. |
5.MD.C | ||
---|---|---|
Grade 5 » Measurement & Data » Geometric measurement: understand concepts of volume. |
5.MD.C.3 | ||
---|---|---|
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Grade levels |
5.MD.C.3a | ||
---|---|---|
A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. Grade levels |
5.MD.C.3b | ||
---|---|---|
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. Grade levels |
5.MD.C.4 | ||
---|---|---|
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Grade levels |
5.MD.C.5 | ||
---|---|---|
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Grade levels |
5.NBT.A | ||
---|---|---|
Grade 5 » Number & Operations in Base Ten » Understand the place value system. |
5.NBT.A.2 | ||
---|---|---|
5.NBT.A.3 | ||
---|---|---|
Read, write, and compare decimals to thousandths. Grade levels |
5.NBT.A.3b | ||
---|---|---|
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Grade levels |
5.NBT.A.4 | ||
---|---|---|
Use place value understanding to round decimals to any place. Grade levels |
5.NBT.B | ||
---|---|---|
Grade 5 » Number & Operations in Base Ten » Perform operations with multi-digit whole numbers and with decimals to hundredths. |
5.NBT.B.5 | ||
---|---|---|
Fluently multiply multi-digit whole numbers using the standard algorithm. Grade levels |
5.NF.A | ||
---|---|---|
Grade 5 » Number & Operations—Fractions » Use equivalent fractions as a strategy to add and subtract fractions. |
5.NF.B | ||
---|---|---|
Grade 5 » Number & Operations—Fractions » Apply and extend previous understandings of multiplication and division. |
5.NF.B.4 | ||
---|---|---|
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Grade levels |
5.NF.B.4a | ||
---|---|---|
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Grade levels |
5.NF.B.5 | ||
---|---|---|
Interpret multiplication as scaling (resizing), by: Grade levels |
5.NF.B.5a | ||
---|---|---|
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. Grade levels |
5.NF.B.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. Grade levels |
5.NF.B.7 | ||
---|---|---|
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.^{1} Grade levels |
5.NF.B.7a | ||
---|---|---|
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Grade levels |
5.NF.B.7b | ||
---|---|---|
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Grade levels |
5.OA.A | ||
---|---|---|
Grade 5 » Operations & Algebraic Thinking » Write and interpret numerical expressions. |
5.OA.A.1 | ||
---|---|---|
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Grade levels |
5.OA.B | ||
---|---|---|
Grade 5 » Operations & Algebraic Thinking » Analyze patterns and relationships. |
6.EE.A | ||
---|---|---|
Grade 6 » Expressions & Equations » Apply and extend previous understandings of arithmetic to algebraic expressions. |
6.EE.A.1 | ||
---|---|---|
Write and evaluate numerical expressions involving whole-number exponents. Grade levels |
6.EE.A.2 | ||
---|---|---|
Write, read, and evaluate expressions in which letters stand for numbers. Grade levels |
6.EE.A.2a | ||
---|---|---|
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y. Grade levels |
6.EE.A.2c | ||
---|---|---|
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 = s^{3} and A = 6 s^{2} to find the volume and surface area of a cube with sides of length s = 1/2. Grade levels |
6.EE.B | ||
---|---|---|
Grade 6 » Expressions & Equations » Reason about and solve one-variable equations and inequalities. |
6.EE.B.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. Grade levels |
6.EE.B.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. Grade levels |
6.EE.C | ||
---|---|---|
Grade 6 » Expressions & Equations » Represent and analyze quantitative relationships between dependent and independent variables. |
6.EE.C.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. Grade levels |
6.G.A | ||
---|---|---|
Grade 6 » Geometry » Solve real-world and mathematical problems involving area, surface area, and volume. |
6.NS.A | ||
---|---|---|
Grade 6 » The Number System » Apply and extend previous understandings of multiplication and division to divide fractions by fractions. |
6.NS.A.1 | ||
---|---|---|
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. Grade levels |
6.NS.B | ||
---|---|---|
Grade 6 » The Number System » Compute fluently with multi-digit numbers and find common factors and multiples. |
6.NS.B.2 | ||
---|---|---|
Fluently divide multi-digit numbers using the standard algorithm. Grade levels |
6.NS.B.3 | ||
---|---|---|
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Grade levels |
6.NS.C | ||
---|---|---|
Grade 6 » The Number System » Apply and extend previous understandings of numbers to the system of rational numbers. |
6.NS.C.7 | ||
---|---|---|
Understand ordering and absolute value of rational numbers. Grade levels |
6.RP.A | ||
---|---|---|
Grade 6 » Ratios & Proportional Relationships » Understand ratio concepts and use ratio reasoning to solve problems. |
6.RP.A.1 | ||
---|---|---|
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Grade levels |
6.RP.A.2 | ||
---|---|---|
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."^{1} Grade levels |
6.RP.A.3d | ||
---|---|---|
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Grade levels |
6.SP.A | ||
---|---|---|
Grade 6 » Statistics & Probability » Develop understanding of statistical variability. |
6.SP.A.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. Grade levels |
6.SP.B | ||
---|---|---|
Grade 6 » Statistics & Probability » Summarize and describe distributions. |
6.SP.B.4 | ||
---|---|---|
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Grade levels |
6.SP.B.5 | ||
---|---|---|
Summarize numerical data sets in relation to their context, such as by: Grade levels |
6.SP.B.5a | ||
---|---|---|
Reporting the number of observations. Grade levels |
6.SP.B.5b | ||
---|---|---|
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Grade levels |
6.SP.B.5d | ||
---|---|---|
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. Grade levels |
7.EE.A | ||
---|---|---|
Grade 7 » Expressions & Equations » Use properties of operations to generate equivalent expressions. |
7.EE.A.1 | ||
---|---|---|
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Grade levels |
7.EE.B | ||
---|---|---|
Grade 7 » Expressions & Equations » Solve real-life and mathematical problems using numerical and algebraic expressions and equations. |
7.EE.B.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. Grade levels |
7.G.A | ||
---|---|---|
Grade 7 » Geometry » Draw construct, and describe geometrical figures and describe the relationships between them. |
7.G.A.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. Grade levels |
7.G.B | ||
---|---|---|
Grade 7 » Geometry » Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. |
7.G.B.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. Grade levels |
7.NS.A | ||
---|---|---|
Grade 7 » The Number System » Apply and extend previous understandings of operations with fractions. |
7.NS.A.1a | ||
---|---|---|
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. Grade levels |
7.NS.A.1d | ||
---|---|---|
Apply properties of operations as strategies to add and subtract rational numbers. Grade levels |
7.NS.A.2 | ||
---|---|---|
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Grade levels |
7.NS.A.2c | ||
---|---|---|
Apply properties of operations as strategies to multiply and divide rational numbers. Grade levels |
7.NS.A.2d | ||
---|---|---|
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. Grade levels |
7.NS.A.3 | ||
---|---|---|
Solve real-world and mathematical problems involving the four operations with rational numbers.^{1} Grade levels |
7.RP.A | ||
---|---|---|
Grade 7 » Ratios & Proportional Relationships » Analyze proportional relationships and use them to solve real-world and mathematical problems. |
7.RP.A.2 | ||
---|---|---|
Recognize and represent proportional relationships between quantities. Grade levels |
7.RP.A.2b | ||
---|---|---|
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Grade levels |
7.SP.A | ||
---|---|---|
Grade 7 » Statistics & Probability » Use random sampling to draw inferences about a population. |
7.SP.B | ||
---|---|---|
Grade 7 » Statistics & Probability » Draw informal comparative inferences about two populations. |
7.SP.C | ||
---|---|---|
Grade 7 » Statistics & Probability » Investigate chance processes and develop, use, and evaluate probability models. |
7.SP.C.8 | ||
---|---|---|
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Grade levels |
7.SP.C.8a | ||
---|---|---|
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. Grade levels |
8.EE.A | ||
---|---|---|
Grade 8 » Expressions & Equations » Expressions and Equations Work with radicals and integer exponents. |
8.EE.A.1 | ||
---|---|---|
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^{2} × 3^{-5} = 3^{-3} = 1/3^{3} = 1/27. Grade levels |
8.EE.A.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 Grade levels |
8.EE.B | ||
---|---|---|
Grade 8 » Expressions & Equations » Understand the connections between proportional relationships, lines, and linear equations. |
8.EE.C | ||
---|---|---|
Grade 8 » Expressions & Equations » Analyze and solve linear equations and pairs of simultaneous linear equations. |
8.EE.C.7 | ||
---|---|---|
Solve linear equations in one variable. Grade levels |
8.EE.C.8 | ||
---|---|---|
Analyze and solve pairs of simultaneous linear equations. Grade levels |
8.EE.C.8a | ||
---|---|---|
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. Grade levels |
8.EE.C.8b | ||
---|---|---|
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. Grade levels |
8.EE.C.8c | ||
---|---|---|
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. Grade levels |
8.F.A | ||
---|---|---|
Grade 8 » Functions » Define, evaluate, and compare functions. |
8.F.A.1 | ||
---|---|---|
8.F.A.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. Grade levels |
8.F.A.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. Grade levels |
8.F.B | ||
---|---|---|
Grade 8 » Functions » Use functions to model relationships between quantities. |
8.F.B.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. Grade levels |
8.F.B.5 | ||
---|---|---|
8.G.A | ||
---|---|---|
Grade 8 » Geometry » Understand congruence and similarity using physical models, transparencies, or geometry software. |
8.G.A.1 | ||
---|---|---|
Verify experimentally the properties of rotations, reflections, and translations: Grade levels |
8.G.A.1a | ||
---|---|---|
Lines are taken to lines, and line segments to line segments of the same length. Grade levels |
8.G.A.1b | ||
---|---|---|
Angles are taken to angles of the same measure. Grade levels |
8.G.A.1c | ||
---|---|---|
Parallel lines are taken to parallel lines. Grade levels |
8.G.A.3 | ||
---|---|---|
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Grade levels |
8.G.B | ||
---|---|---|
Grade 8 » Geometry » Understand and apply the Pythagorean Theorem. |
8.G.B.6 | ||
---|---|---|
Explain a proof of the Pythagorean Theorem and its converse. Grade levels |
8.G.B.7 | ||
---|---|---|
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Grade levels |
8.G.B.8 | ||
---|---|---|
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Grade levels |
8.G.C | ||
---|---|---|
Grade 8 » Geometry » Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. |
8.G.C.9 | ||
---|---|---|
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Grade levels |
8.NS.A | ||
---|---|---|
Grade 8 » The Number System » Know that there are numbers that are not rational, and approximate them by rational numbers. |
8.SP.A | ||
---|---|---|
Grade 8 » Statistics & Probability » Investigate patterns of association in bivariate data. |
8.SP.A.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. Grade levels |
8.SP.A.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? Grade levels |
HSA-APR.B.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. Grade levels |
HSA-APR.C.5 | ||
---|---|---|
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^{n} in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.^{1} Grade levels |
HSA-CED.A.2 | ||
---|---|---|
HSA-REI.A.2 | ||
---|---|---|
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Grade levels |
HSA-REI.B.3 | ||
---|---|---|
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Grade levels |
HSA-REI.B.4 | ||
---|---|---|
Solve quadratic equations in one variable. Grade levels |
HSA-REI.C.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. Grade levels |
HSA-REI.C.6 | ||
---|---|---|
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Grade levels |
HSA-REI.C.7 | ||
---|---|---|
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x^{2} + y^{2} = 3. Grade levels |
HSA-REI.C.8 | ||
---|---|---|
(+) Represent a system of linear equations as a single matrix equation in a vector variable. Grade levels |
HSA-REI.C.9 | ||
---|---|---|
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). Grade levels |
HSA-REI.D.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). Grade levels |
HSA-REI.D.12 | ||
---|---|---|
HSA-SSE.A.1 | ||
---|---|---|
Interpret expressions that represent a quantity in terms of its context.^{*} Grade levels |
HSA-SSE.A.1a | ||
---|---|---|
Interpret parts of an expression, such as terms, factors, and coefficients. Grade levels |
HSA-SSE.A.2 | ||
---|---|---|
Use the structure of an expression to identify ways to rewrite it. For example, see x^{4} - y^{4} as (x^{2})^{2} - (y^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (x^{2} - y^{2})(x^{2} + y^{2}). Grade levels |
HSA-SSE.B.3 | ||
---|---|---|
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.^{*} Grade levels |
HSA-SSE.B.3a | ||
---|---|---|
Factor a quadratic expression to reveal the zeros of the function it defines. Grade levels |
HSA-SSE.B.3b | ||
---|---|---|
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Grade levels |
HSA.APR.A | ||
---|---|---|
High School: Algebra » Arithmetic with Polynomials & Rational Expressions » Perform arithmetic operations on polynomials. |
HSA.APR.B | ||
---|---|---|
High School: Algebra » Arithmetic with Polynomials & Rational Expressions » Understand the relationship between zeros and factors of polynomials. |
HSA.APR.C | ||
---|---|---|
High School: Algebra » Arithmetic with Polynomials & Rational Expressions » Use polynomial identities to solve problems. |
HSA.APR.D | ||
---|---|---|
High School: Algebra » Arithmetic with Polynomials & Rational Expressions » Rewrite rational expressions. |
HSA.CED.A | ||
---|---|---|
High School: Algebra » Creating Equations✭ » Create equations that describe numbers or relationships. |
HSA.REI.A | ||
---|---|---|
High School: Algebra » Reasoning with Equations & Inequalities » Understand solving equations as a process of reasoning and explain the reasoning. |
HSA.REI.B | ||
---|---|---|
High School: Algebra » Reasoning with Equations & Inequalities » Solve equations and inequalities in one variable. |
HSA.REI.C | ||
---|---|---|
High School: Algebra » Reasoning with Equations & Inequalities » Solve systems of equations. |
HSA.REI.D | ||
---|---|---|
High School: Algebra » Reasoning with Equations & Inequalities » Represent and solve equations and inequalities graphically. |
HSA.SSE.A | ||
---|---|---|
High School: Algebra » Seeing Structure in Expressions » Interpret the structure of expressions. |
HSA.SSE.B | ||
---|---|---|
High School: Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems. |
HSF-BF.A.1 | ||
---|---|---|
Write a function that describes a relationship between two quantities.^{*} Grade levels |
HSF-BF.A.1a | ||
---|---|---|
Determine an explicit expression, a recursive process, or steps for calculation from a context. Grade levels |
HSF-BF.A.1b | ||
---|---|---|
HSF-BF.A.1c | ||
---|---|---|
HSF-BF.A.2 | ||
---|---|---|
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.^{*} Grade levels |
HSF-BF.B.4 | ||
---|---|---|
Find inverse functions. Grade levels |
HSF-BF.B.4a | ||
---|---|---|
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x^{3} or f(x) = (x+1)/(x-1) for x ≠ 1. Grade levels |
HSF-BF.B.4b | ||
---|---|---|
(+) Verify by composition that one function is the inverse of another. Grade levels |
HSF-BF.B.4c | ||
---|---|---|
HSF-BF.B.4d | ||
---|---|---|
HSF-BF.B.5 | ||
---|---|---|
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Grade levels |
HSF-IF.A.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). Grade levels |
HSF-IF.A.2 | ||
---|---|---|
HSF-IF.B.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.^{*} Grade levels |
HSF-IF.B.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.^{*} Grade levels |
HSF-IF.B.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.^{*} Grade levels |
HSF-IF.C.7 | ||
---|---|---|
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.^{*} Grade levels |
HSF-IF.C.7a | ||
---|---|---|
Graph linear and quadratic functions and show intercepts, maxima, and minima. Grade levels |
HSF-IF.C.7b | ||
---|---|---|
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Grade levels |
HSF-IF.C.7c | ||
---|---|---|
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Grade levels |
HSF-IF.C.7d | ||
---|---|---|
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Grade levels |
HSF-IF.C.7e | ||
---|---|---|
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Grade levels |
HSF-IF.C.8 | ||
---|---|---|
HSF-IF.C.8a | ||
---|---|---|
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. Grade levels |
HSF-IF.C.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. Grade levels |
HSF-LE.A.1 | ||
---|---|---|
Distinguish between situations that can be modeled with linear functions and with exponential functions. Grade levels |
HSF-LE.A.1a | ||
---|---|---|
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Grade levels |
HSF-LE.A.1b | ||
---|---|---|
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Grade levels |
HSF-LE.A.1c | ||
---|---|---|
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Grade levels |
HSF-LE.A.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. Grade levels |
HSF-LE.B.5 | ||
---|---|---|
Interpret the parameters in a linear or exponential function in terms of a context. Grade levels |
HSF-TF.A.1 | ||
---|---|---|
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Grade levels |
HSF-TF.A.4 | ||
---|---|---|
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Grade levels |
HSF-TF.B.5 | ||
---|---|---|
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^{*} Grade levels |
HSF-TF.B.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. Grade levels |
HSF-TF.C.9 | ||
---|---|---|
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Grade levels |
HSF.BF.A | ||
---|---|---|
High School: Functions » Building Functions » Build a function that models a relationship between two quantities. |
HSF.BF.B | ||
---|---|---|
High School: Functions » Building Functions » Build new functions from existing functions. |
HSF.IF.A | ||
---|---|---|
High School: Functions » Interpreting Functions » Understand the concept of a function and use function notation. |
HSF.IF.B | ||
---|---|---|
High School: Functions » Interpreting Functions » Interpret functions that arise in applications in terms of the context. |
HSF.IF.C | ||
---|---|---|
High School: Functions » Interpreting Functions » Analyze functions using different representations. |
HSF.LE.B | ||
---|---|---|
High School: Functions » Linear, Quadratic, & Exponential Models* » Interpret expressions for functions in terms of the situation they model. |
HSF.TF.A | ||
---|---|---|
High School: Functions » Trigonometric Functions » Extend the domain of trigonometric functions using the unit circle. |
HSF.TF.B | ||
---|---|---|
High School: Functions » Trigonometric Functions » Model periodic phenomena with trigonometric functions. |
HSF.TF.C | ||
---|---|---|
High School: Functions » Trigonometric Functions » Prove and apply trigonometric identities. |
HSG-C.A.1 | ||
---|---|---|
Prove that all circles are similar. Grade levels |
HSG-C.A.3 | ||
---|---|---|
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Grade levels |
HSG-C.A.4 | ||
---|---|---|
(+) Construct a tangent line from a point outside a given circle to the circle. Grade levels |
HSG-CO.A.3 | ||
---|---|---|
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Grade levels |
HSG-CO.A.4 | ||
---|---|---|
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Grade levels |
HSG-CO.B.8 | ||
---|---|---|
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Grade levels |
HSG-CO.D.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. Grade levels |
HSG-CO.D.13 | ||
---|---|---|
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Grade levels |
HSG-GMD.A.2 | ||
---|---|---|
(+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. Grade levels |
HSG-GMD.A.3 | ||
---|---|---|
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.^{*} Grade levels |
HSG-GPE.A.2 | ||
---|---|---|
Derive the equation of a parabola given a focus and directrix. Grade levels |
HSG-GPE.A.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. Grade levels |
HSG-GPE.B.6 | ||
---|---|---|
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Grade levels |
HSG-GPE.B.7 | ||
---|---|---|
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.^{*} Grade levels |
HSG-MG.A.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).^{*} Grade levels |
HSG-MG.A.2 | ||
---|---|---|
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).^{*} Grade levels |
HSG-MG.A.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).^{*} Grade levels |
HSG-SRT.A.1 | ||
---|---|---|
Verify experimentally the properties of dilations given by a center and a scale factor: Grade levels |
HSG-SRT.A.1a | ||
---|---|---|
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. Grade levels |
HSG-SRT.A.1b | ||
---|---|---|
The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Grade levels |
HSG-SRT.A.3 | ||
---|---|---|
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Grade levels |
HSG-SRT.B.5 | ||
---|---|---|
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Grade levels |
HSG-SRT.C.7 | ||
---|---|---|
Explain and use the relationship between the sine and cosine of complementary angles. Grade levels |
HSG-SRT.C.8 | ||
---|---|---|
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.^{*} Grade levels |
HSG-SRT.D.10 | ||
---|---|---|
(+) Prove the Laws of Sines and Cosines and use them to solve problems. Grade levels |
HSG-SRT.D.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. Grade levels |
HSG.C.A | ||
---|---|---|
High School: Geometry » Circles » Understand and apply theorems about circles |
HSG.C.B | ||
---|---|---|
High School: Geometry » Circles » Find arc lengths and areas of sectors of circles |
HSG.CO.A | ||
---|---|---|
High School: Geometry » Congruence » Experiment with transformations in the plane |
HSG.CO.B | ||
---|---|---|
High School: Geometry » Congruence » Understand congruence in terms of rigid motions |
HSG.CO.C | ||
---|---|---|
High School: Geometry » Congruence » Prove geometric theorems |
HSG.CO.D | ||
---|---|---|
High School: Geometry » Congruence » Make geometric constructions |
HSG.GMD | ||
---|---|---|
High School: Geometry » Geometric Measurement & Dimension |
HSG.GMD.A | ||
---|---|---|
High School: Geometry » Geometric Measurement & Dimension » Explain volume formulas and use them to solve problems |
HSG.GMD.B | ||
---|---|---|
High School: Geometry » Geometric Measurement & Dimension » Visualize relationships between two-dimensional and three-dimensional objects |
HSG.GPE.A | ||
---|---|---|
High School: Geometry » Expressing Geometric Properties with Equations » Translate between the geometric description and the equation for a conic section |
HSG.GPE.B | ||
---|---|---|
High School: Geometry » Expressing Geometric Properties with Equations » Use coordinates to prove simple geometric theorems algebraically |
HSG.MG.A | ||
---|---|---|
High School: Geometry » Modeling with Geometry » Apply geometric concepts in modeling situations |
HSG.SRT.A | ||
---|---|---|
High School: Geometry » Similarity, Right Triangles, & Trigonometry » Understand similarity in terms of similarity transformations |
HSG.SRT.B | ||
---|---|---|
High School: Geometry » Similarity, Right Triangles, & Trigonometry » Prove theorems involving similarity |
HSG.SRT.C | ||
---|---|---|
High School: Geometry » Similarity, Right Triangles, & Trigonometry » Define trigonometric ratios and solve problems involving right triangles |
HSG.SRT.D | ||
---|---|---|
High School: Geometry » Similarity, Right Triangles, & Trigonometry » Apply trigonometry to general triangles |
HSN-CN.A.1 | ||
---|---|---|
Know there is a complex number i such that i^{2} = -1, and every complex number has the form a + bi with a and b real. Grade levels |
HSN-CN.A.2 | ||
---|---|---|
Use the relation i^{2} = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Grade levels |
HSN-CN.A.3 | ||
---|---|---|
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Grade levels |
HSN-CN.C.7 | ||
---|---|---|
Solve quadratic equations with real coefficients that have complex solutions. Grade levels |
HSN-CN.C.8 | ||
---|---|---|
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^{2} + 4 as (x + 2i)(x - 2i). Grade levels |
HSN-CN.C.9 | ||
---|---|---|
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Grade levels |
HSN-Q.A.2 | ||
---|---|---|
Define appropriate quantities for the purpose of descriptive modeling. Grade levels |
HSN-Q.A.3 | ||
---|---|---|
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Grade levels |
HSN-RN.A.2 | ||
---|---|---|
Rewrite expressions involving radicals and rational exponents using the properties of exponents. Grade levels |
HSN-VM.A.2 | ||
---|---|---|
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Grade levels |
HSN-VM.A.3 | ||
---|---|---|
(+) Solve problems involving velocity and other quantities that can be represented by vectors. Grade levels |
HSN-VM.B.4 | ||
---|---|---|
(+) Add and subtract vectors. Grade levels |
HSN-VM.B.4b | ||
---|---|---|
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Grade levels |
HSN-VM.B.4c | ||
---|---|---|
Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. Grade levels |
HSN-VM.B.5 | ||
---|---|---|
(+) Multiply a vector by a scalar. Grade levels |
HSN-VM.B.5a | ||
---|---|---|
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v_{x}, v_{y}) = (cv_{x}, cv_{y}). Grade levels |
HSN-VM.C.12 | ||
---|---|---|
(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. Grade levels |
HSN-VM.C.6 | ||
---|---|---|
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Grade levels |
HSN-VM.C.7 | ||
---|---|---|
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. Grade levels |
HSN-VM.C.8 | ||
---|---|---|
(+) Add, subtract, and multiply matrices of appropriate dimensions. Grade levels |
HSN.CN.A | ||
---|---|---|
High School: Number and Quantity » The Complex Number System » Perform arithmetic operations with complex numbers. |
HSN.CN.B | ||
---|---|---|
High School: Number and Quantity » The Complex Number System » Represent complex numbers and their operations on the complex plane. |
HSN.CN.C | ||
---|---|---|
High School: Number and Quantity » The Complex Number System » Use complex numbers in polynomial identities and equations. |
HSN.Q.A | ||
---|---|---|
High School: Number and Quantity » Quantities* » Reason quantitatively and use units to solve problems. |
HSN.RN | ||
---|---|---|
High School: Number and Quantity » The Real Number System |
HSN.RN.A | ||
---|---|---|
High School: Number and Quantity » The Real Number System » Extend the properties of exponents to rational exponents. |
HSN.RN.B | ||
---|---|---|
High School: Number and Quantity » The Real Number System » Use properties of rational and irrational numbers. |
HSN.VM.A | ||
---|---|---|
High School: Number and Quantity » Vector & Matrix Quantities » Represent and model with vector quantities. |
HSN.VM.B | ||
---|---|---|
High School: Number and Quantity » Vector & Matrix Quantities » Perform operations on vectors. |
HSN.VM.C | ||
---|---|---|
High School: Number and Quantity » Vector & Matrix Quantities » Perform operations on matrices and use matrices in applications. |
HSS-CP.B.6 | ||
---|---|---|
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. Grade levels |
HSS-CP.B.7 | ||
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Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. Grade levels |
HSS-CP.B.8 | ||
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(+) 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. Grade levels |
HSS-CP.B.9 | ||
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(+) Use permutations and combinations to compute probabilities of compound events and solve problems. Grade levels |
HSS-IC.A.1 | ||
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Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Grade levels |
HSS-IC.B.3 | ||
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Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Grade levels |
HSS-IC.B.4 | ||
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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. Grade levels |
HSS-IC.B.5 | ||
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Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Grade levels |
HSS-IC.B.6 | ||
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Evaluate reports based on data. Grade levels |
HSS-ID.A.1 | ||
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