Focus Skills™

Count aloud the number names from 1 to 10

CCSS.Math.Content.K.CC.A.1

Count orally to ten by ones, saying the number names in standard order

1

Read a whole number from 0 to 10

CCSS.Math.Content.K.CC.A.3

Read a whole number from 0 to 10

2

Identify written numerals 0 to 9 in environment

CCSS.Math.Content.K.CC.A.3

Identify the written numerals 0 to 9 in the everyday environment

3

Understand relationship: counting / quantities

CCSS.Math.Content.K.CC.B.4

Understand the relationship between counting and quantities

4

Count out 0 to 10 objects given oral directions

CCSS.Math.Content.K.CC.A.1

Count out a number of objects from 0 to 10 given oral directions

5

Compare sets of up to 5 objects

CCSS.Math.Content.K.CC.C.6

Compare sets of up to 5 objects

11

Identify the position in sequences, up to 5th

CCSS.Math.Content.K.CC.B.4

Identify positions of objects in sequences (e.g., first, second) up to fifth

14

Model addition within 5 using objects

CCSS.Math.Content.K.OA.A.1

Model addition within 5 using objects

15

Model subtraction within 5 using objects

CCSS.Math.Content.K.OA.A.1

Model subtraction within 5 using objects

16

Identify actual objects using position words

CCSS.Math.Content.K.G.A.1

Identify objects in the environment based on position words

13

Compare / sort common 2-D shapes

CCSS.Math.Content.K.G.B.4

Compare and sort common 2-dimensional shapes by comparing their attributes

19

Sort objects according to one attribute

CCSS.Math.Content.K.MD.B.3

Sort objects according to one attribute

18

Count out a given number of objects from 1 to 20

CCSS.Math.Content.K.CC.B.5

Count out a given number of objects from 1 to 20

26

Count aloud by 1s from a number less than 100

CCSS.Math.Content.K.CC.A.2

Count on orally by ones from a number less than 100

30

Write numbers from 0 to 20 given oral directions

CCSS.Math.Content.K.CC.A.3

Write a number from 0 to 20 when given oral directions

32

Represent 0 to 20 grouped objects with a numeral

CCSS.Math.Content.K.CC.A.3

Represent the total number of objects in a group from 0 to 20 with a numeral

33

Compare with words: 2 groups with up to 20 items

CCSS.Math.Content.K.CC.C.6

Compare two groups containing up to 20 objects each using words

35

Find the number that is 1 larger than, within 20

CCSS.Math.Content.K.CC.B.4.c

Determine the number that is one larger than a given number within 20

37

Compose number from 11 to 19 using pictures

CCSS.Math.Content.K.NBT.A.1

Compose a number from 11 to 19 from ten ones and some further ones, using pictures or objects

58

Add numbers with a sum to 10: pictures / objects

CCSS.Math.Content.K.OA.A.2

Add numbers with a sum up to 10, using pictures or objects

48

Subtract numbers using objects: minuend up to 10

CCSS.Math.Content.K.OA.A.2

Subtract numbers with a minuend up to 10, using pictures or objects

49

Add numbers with sum up to 10

CCSS.Math.Content.K.OA.A.2

Add numbers with a sum up to 10

52

Decompose number 10 or less into pairs: pictures

CCSS.Math.Content.K.OA.A.3

Decompose a number less than or equal to 10 into pairs, using pictures or objects

53

Find number to make 10 when added: picture

CCSS.Math.Content.K.OA.A.4

Determine the number that makes 10 when added to a number from 1 to 9, using pictures or objects

55

Identify a 2-dimensional shape

CCSS.Math.Content.K.G.A.2

Identify a 2-dimensional shape

69

Identify a shape regardless of orientation / size

CCSS.Math.Content.K.G.A.2

Correctly identify a shape regardless of orientation or overall size

70

Identify a 2-D or 3-D shape as flat or solid

CCSS.Math.Content.K.G.A.3

Identify a 2-dimensional or 3-dimensional shape as flat or solid

72

Identify attributes of a 2-dimensional shape

CCSS.Math.Content.K.G.B.4

Identify attributes of a 2-dimensional shape

73

Describe measurable attributes of an object

CCSS.Math.Content.K.MD.A.1

Describe several measurable attributes of an object

61

Count aloud up to 120 from a smaller number

CCSS.Math.Content.1.NBT.A.1

Count orally up to 120 from a number less than 120

81

Count on by ones from a number within 120

CCSS.Math.Content.1.NBT.A.1

Count on by ones from a number within 120

82

Represent numbers of objects by numerals: 0-120

CCSS.Math.Content.1.NBT.A.1

Represent the total number of objects in a group from 0 to 120 with a numeral

85

Understand 2-digit number digits: 10s and 1s

CCSS.Math.Content.1.NBT.B.2

Understand that the digits of a 2-digit number represent amounts of tens and ones

92

Recognize a number from a model of 10s / 1s to 100

CCSS.Math.Content.1.NBT.B.2

Recognize a number from a model of tens and ones to 100

93

Determine a digit's value in a 2-digit number

CCSS.Math.Content.1.NBT.B.2

Determine the value of a digit in a 2-digit number

94

Compare 2-digit numbers using standard symbols

CCSS.Math.Content.1.NBT.B.3

Compare two 2-digit numbers using standard symbols

96

Add 10 to a 2-digit number using mental math

CCSS.Math.Content.1.NBT.C.5

Add 10 to a 2-digit number using mental math

105

Subtract 10 from a 2-digit number: mental math

CCSS.Math.Content.1.NBT.C.5

Subtract 10 from a 2-digit number using mental math

106

Subtract multiple of 10 from 10 to 90: various

CCSS.Math.Content.1.NBT.C.6

Subtract a multiple of 10 from a multiple of 10 in the range 10 to 90, using various methods

108

Understand composing a 10: add / subtract to 100

CCSS.Math.Content.1.NBT.C.4

Understand when it is necessary to compose a ten when adding or subtracting within 100

110

Add within 100

CCSS.Math.Content.1.NBT.C.4

Add within 100 using one of various strategies

114

Add within 20 using place value strategy

CCSS.Math.Content.1.OA.C.6

Add within 20 using strategies based on place value

99

Subtract within 20 using any strategy

CCSS.Math.Content.1.OA.C.6

Subtract within 20 using any strategy

102

Subtract within 20 using any strategy

CCSS.Math.Content.1.OA.B.3

Subtract within 20 using any strategy

102

Solve a problem: addition / subtraction within 20

CCSS.Math.Content.1.OA.A.1

Solve a problem involving addition or subtraction of numbers within 20

103

Find an unknown: addition / subtraction fact to 20

CCSS.Math.Content.1.OA.D.8

Determine an unknown whole number in an addition or subtraction equation within 20

111

Draw a shape with given attributes

CCSS.Math.Content.1.G.A.1

Draw a shape with given attributes

122

Compose a composite shape from 2-D shapes

CCSS.Math.Content.1.G.A.2

Compose a composite shape from 2-dimensional shapes

125

Partition a 2-D figure into 2 / 4 equal shares

CCSS.Math.Content.1.G.A.3

Partition a 2-dimensional figure into two or four equal shares

131

Order three objects by length

CCSS.Math.Content.1.MD.A.1

Order three objects by length

119

Recognize length: exact number of spanning units

CCSS.Math.Content.1.MD.A.2

Understand length measurement of an object as the number of same-size length units that span it with no gaps or overlaps

120

Count on by ones from a number within 1000

CCSS.Math.Content.2.NBT.A.2

Count on by ones from a number within 1000

136

Understand 3-digit number represents 100s / 10s / 1s

CCSS.Math.Content.2.NBT.A.1

Understand that the digits of a 3-digit number represent amounts of hundreds, tens, and ones

140

Read a whole number to 1000

CCSS.Math.Content.2.NBT.A.3

Read a whole number to 1000

141

Write a whole number in standard form up to 1000

CCSS.Math.Content.2.NBT.A.3

Write a whole number in standard form up to 1000

144

Write a whole number in expanded form up to 1000

CCSS.Math.Content.2.NBT.A.3

Write a whole number in expanded form up to 1000

146

Compare two 3-digit numbers: standard symbols

CCSS.Math.Content.2.NBT.A.4

Compare two 3-digit numbers using standard symbols, emphasizing the meanings of hundreds, tens, and ones

147

Understand when to regroup: add / subtract to 1000

CCSS.Math.Content.2.NBT.B.7

Understand when it is necessary to compose a ten and/or a hundred when adding or subtracting within 1000

164

Add within 1000

CCSS.Math.Content.2.NBT.B.7

Add within 1000 using one of various strategies

167

Subtract within 1000: place-value strategies

CCSS.Math.Content.2.NBT.B.7

Subtract within 1000 using strategies based on place value

168

Know basic addition facts within 20

CCSS.Math.Content.2.OA.B.2

Know basic addition facts within 20

148

Solve a problem: open sentence to model context

CCSS.Math.Content.2.OA.A.1

Represent a situation with an open sentence to solve a problem

151

Solve addition / subtraction problem within 100

CCSS.Math.Content.2.OA.A.1

Solve a 1- or 2-step problem in any addition or subtraction situation within 100

152

Partition a rectangle / circle into equal parts

CCSS.Math.Content.2.G.A.3

Partition a rectangle or circle into equal-sized parts

187

Name rectangle / circle parts cut equally in 2 / 3 / 4

CCSS.Math.Content.2.G.A.3

Describe the shares of a rectangle or circle partitioned into two, three, or four equal shares

188

Draw a shape with specified attributes

CCSS.Math.Content.2.G.A.1

Draw a shape with specified attributes

193

Solve a problem: open sentence to model context

CCSS.Math.Content.2.MD.B.5

Represent a situation with an open sentence to solve a problem

151

Know ruler units equal in size / span with no gaps

CCSS.Math.Content.2.MD.A.1

Understand that the units on a ruler or number line are equal in size and span it with no gaps or overlaps

171

Know ruler units equal in size / span with no gaps

CCSS.Math.Content.2.MD.B.6

Understand that the units on a ruler or number line are equal in size and span it with no gaps or overlaps

171

Measure / find difference in length in whole units

CCSS.Math.Content.2.MD.A.4

Measure in whole units to determine how much longer one object is than another

177

Generate data: measure length using whole units

CCSS.Math.Content.2.MD.D.9

Generate measurement data by measuring lengths using whole-number units

178

Add / subtract to 100 to solve a length problem

CCSS.Math.Content.2.MD.B.5

Add or subtract within 100 to solve a problem involving lengths that are given in the same units

180

Tell / write time to nearest 5 minutes

CCSS.Math.Content.2.MD.C.7

Tell and write time to the nearest five minutes, including indication of a.m. and p.m.

184

Read / write a number up to 10,000: standard form

CCSS.Math.Content.3.NBT.A.1

Read and write a whole number in standard form up to 10,000

201

Compare whole numbers up to 10,000 using < / > / =

CCSS.Math.Content.3.NBT.A.1

Compare whole numbers up to 10,000 using the symbols <, >, and =

202

Multiply 1-digit by multiple of 10 up to 90

CCSS.Math.Content.3.NBT.A.3

Multiply a 1-digit whole number by a multiple of 10 within 90

223

Understand the structure of a fraction

CCSS.Math.Content.3.NF.A.1

Understand the structure of a fraction

231

Represent a unit fraction on a number line

CCSS.Math.Content.3.NF.A.2.a

Represent a unit fraction on a number line

235

Generate simple equivalent fractions

CCSS.Math.Content.3.NF.A.3.b

Generate simple equivalent fractions

240

Explain fraction equivalence with fraction model

CCSS.Math.Content.3.NF.A.3.b

Explain why two fractions are equivalent using a visual fraction model

241

Interpret product fact: sum of equal groups

CCSS.Math.Content.3.OA.A.1

Interpret a multiplication fact as the sum of equal groups

204

Represent a multiplication fact various ways

CCSS.Math.Content.3.OA.A.1

Represent a multiplication fact using a variety of approaches

206

Interpret quotient as partitioning into shares

CCSS.Math.Content.3.OA.A.2

Interpret the whole-number quotient of a division fact as a partitioning into equal shares

207

Solve problem within 100 involving equal groups

CCSS.Math.Content.3.OA.A.3

Solve a problem within 100 involving equal groups

211

Fluently multiply within 100, using basic facts

CCSS.Math.Content.3.OA.C.7

Fluently multiply within 100, using basic facts

214

Multiply whole numbers within 100

CCSS.Math.Content.3.OA.B.5

Multiply whole numbers within 100 using strategies based on properties of operations

215

Fluently divide within 100, using basic facts

CCSS.Math.Content.3.OA.C.7

Fluently divide within 100, using basic facts

216

Solve 2-step problem: whole numbers / 4 operations

CCSS.Math.Content.3.OA.D.8

Solve a 2-step problem with whole numbers using any of the four operations

217

Determine the unknown: multiplication equation

CCSS.Math.Content.3.OA.A.4

Determine the unknown in a multiplication equation

218

Determine the unknown in a division equation

CCSS.Math.Content.3.OA.A.4

Determine the unknown in a division equation

219

Partition a shape into parts with equal areas

CCSS.Math.Content.3.G.A.2

Partition a shape into parts with equal areas

230

Express area of a part of shape as unit fraction

CCSS.Math.Content.3.G.A.2

Express the area of a part of a shape as a unit fraction

232

Tell / write time to the nearest minute

CCSS.Math.Content.3.MD.A.1

Tell and write time to the nearest minute, including indication of a.m. and p.m.

247

Perimeter of a polygon given side lengths

CCSS.Math.Content.3.MD.D.8

Find the perimeter of a polygon given the side lengths

261

Show tiling / length times width yield same area

CCSS.Math.Content.3.MD.C.7.a

Demonstrate that the area of a rectangle is the same using tiling or multiplying side lengths

271

Find rectangle's area: multiplying side lengths

CCSS.Math.Content.3.MD.C.7.b

Find the area of a rectangle by multiplying side lengths

272

Make length measurement data (nearest 1 / 4 in.)

CCSS.Math.Content.3.MD.B.4

Generate measurement data by measuring lengths using rulers with halves and fourths of an inch

283

Read / write number: expanded form up to 1,000,000

CCSS.Math.Content.4.NBT.A.2

Read and write a whole number in expanded form up to 1,000,000

287

Compare two whole numbers up to 1,000,000

CCSS.Math.Content.4.NBT.A.2

Compare two whole numbers up to 1,000,000

288

Round number within 1,000,000

CCSS.Math.Content.4.NBT.A.3

Round a whole number within 1,000,000 to a specified place

289

Fluently add whole numbers within 1,000,000

CCSS.Math.Content.4.NBT.B.4

Fluently add whole numbers within 1,000,000

290

Fluently subtract whole numbers within 1,000,000

CCSS.Math.Content.4.NBT.B.4

Fluently subtract whole numbers within 1,000,000

291

Multiply 1-digit by 2- / 4-digit: place value

CCSS.Math.Content.4.NBT.B.5

Multiply a 1-digit whole number by a 2- to 4-digit whole number using strategies based on place value and properties of operations

293

Multiply two 2-digit whole numbers various ways

CCSS.Math.Content.4.NBT.B.5

Multiply two 2-digit whole numbers using various strategies

294

Divide 4-digit number / 1-digit: relationships

CCSS.Math.Content.4.NBT.B.6

Divide a number of up to four digits by a 1-digit number using strategies based on place value and the relationship between multiplication and division

296

Create equivalent fractions by multiplying by 1

CCSS.Math.Content.4.NF.A.1

Generate equivalent fractions by multiplying the numerator and denominator of a fraction by the same number

315

Compare fractions with unlike denominators

CCSS.Math.Content.4.NF.A.2

Compare fractions with unlike denominators

318

Write fraction: sum of like fractions many ways

CCSS.Math.Content.4.NF.B.3.b

Decompose a fraction into a sum of fractions with the same denominator in more than one way

322

Add or subtract fractions with like denominators

CCSS.Math.Content.4.NF.B.3.c

Add or subtract fractions with like denominators

326

Understand fraction as multiple of unit fraction

CCSS.Math.Content.4.NF.B.4.a

Understand a fraction as a multiple of a unit fraction

330

Multiply a fraction by a whole number

CCSS.Math.Content.4.NF.B.4

Multiply a fraction by a whole number

333

Write fractions, denominator 10 / 100, as decimals

CCSS.Math.Content.4.NF.C.6

Express a fraction with a denominator of 10 or 100 as a decimal

337

Compare decimals to 100ths using <, >, =

CCSS.Math.Content.4.NF.C.7

Compare two decimals through hundredths using standard symbols

340

Interpret multiplication equation as comparison

CCSS.Math.Content.4.OA.A.1

Interpret a multiplication equation as a comparison

298

Multiply / divide: multiplicative comparison

CCSS.Math.Content.4.OA.A.2

Multiply or divide in a given situation involving multiplicative comparison

301

Solve problems: whole numbers with 4 operations

CCSS.Math.Content.4.OA.A.3

Solve a multi-step problem with whole numbers involving the four operations

303

Interpret remainder in a multi-step word problem

CCSS.Math.Content.4.OA.A.3

Interpret the remainder in a multi-step word problem

304

Draw a line of symmetry

CCSS.Math.Content.4.G.A.3

Draw a line of symmetry

361

Convert larger to smaller unit: single system

CCSS.Math.Content.4.MD.A.1

Convert a larger unit to a smaller unit within a single measurement system

343

Solve problems: area / perimeter rectangle formula

CCSS.Math.Content.4.MD.A.3

Solve a problem using the area or perimeter formulas for rectangles

362

Fluently multiply multi-digit whole numbers

CCSS.Math.Content.5.NBT.B.5

Fluently multiply multi-digit whole numbers

365

Divide up to 4-digit by 2-digit using strategies

CCSS.Math.Content.5.NBT.B.6

Divide a whole number of up to four digits by a 2-digit whole number using one of various strategies

366

Explain x / ÷ by power of 10 in decimals

CCSS.Math.Content.5.NBT.A.2

Explain the pattern in the placement of the decimal point when multiplying or dividing decimals by powers of 10

395

Read and write a decimal through thousandths

CCSS.Math.Content.5.NBT.A.3.a

Read and write a decimal through thousandths in any form

398

Compare two decimals through thousandths

CCSS.Math.Content.5.NBT.A.3.b

Compare two decimals through thousandths

399

Add decimals through hundredths

CCSS.Math.Content.5.NBT.B.7

Add decimals through hundredths using one of various strategies

402

Subtract decimals through hundredths

CCSS.Math.Content.5.NBT.B.7

Subtract decimals through hundredths using one of various strategies

404

Multiply decimals through hundredths

CCSS.Math.Content.5.NBT.B.7

Multiply decimals through hundredths using one of various strategies

408

Divide decimals through hundredths

CCSS.Math.Content.5.NBT.B.7

Divide decimals through hundredths using one of various strategies

410

Add / subtract fractions referring to same whole

CCSS.Math.Content.5.NF.A.2

Solve problems involving addition or subtraction of fractions referring to the same whole

372

Multiply a fraction by a fraction

CCSS.Math.Content.5.NF.B.4

Multiply a fraction by a fraction

379

Multiply fractional lengths for rectangular area

CCSS.Math.Content.5.NF.B.4.b

Multiply fractional side lengths of a rectangle to find its area

380

Multiply fractions and mixed numbers in context

CCSS.Math.Content.5.NF.B.6

Multiply fractions and mixed numbers in a given situation

383

Interpret unit fraction divided by whole number

CCSS.Math.Content.5.NF.B.7.a

Interpret division of a unit fraction by a nonzero whole number

384

Divide a unit fraction by a nonzero whole number

CCSS.Math.Content.5.NF.B.7.a

Divide a unit fraction by a nonzero whole number

385

Divide a whole number by a unit fraction

CCSS.Math.Content.5.NF.B.7.b

Divide a whole number by a unit fraction

388

Evaluate numerical expression: grouping symbols

CCSS.Math.Content.5.OA.A.1

Evaluate a numerical expression containing grouping symbols

412

Evaluate an expression using order of operations

CCSS.Math.Content.5.OA.A.1

Evaluate a numerical expression involving four or more operations, using order of operations

414

Graph a point in the first quadrant

CCSS.Math.Content.5.G.A.2

Graph a point in the first quadrant of the coordinate plane

423

Understand volume measurement using unit cubes

CCSS.Math.Content.5.MD.C.3.b

Understand that volume can be measured using unit cubes

432

Find volume of prism by multiplying edges

CCSS.Math.Content.5.MD.C.5.a

Find the volume of a right rectangular prism by multiplying edge lengths

435

Solve problem using volume formula for prism

CCSS.Math.Content.5.MD.C.5.b

Find the volume of a right rectangular prism to solve a problem, using a formula

436

Describe a ratio relationship between quantities

CCSS.Math.Content.6.RP.A.1

Describe a ratio relationship between two quantities

456

Determine a unit rate

CCSS.Math.Content.6.RP.A.2

Determine a unit rate

458

Solve a unit rate problem

CCSS.Math.Content.6.RP.A.3.b

Solve a unit rate problem

460

Solve a problem: parts / wholes / percentages

CCSS.Math.Content.6.RP.A.3.c

Solve a problem involving parts, wholes, and percentages

464

Factor a numerical sum via the distributive law

CCSS.Math.Content.6.NS.B.4

Express the sum of two whole numbers in factored form using the distributive property

446

Divide mixed numbers and fractions

CCSS.Math.Content.6.NS.A.1

Divide mixed numbers or fractions

450

Solve problem: multiply decimals to thousandths

CCSS.Math.Content.6.NS.B.3

Solve a problem involving multiplication of two decimal numbers to thousandths

454

Recognize where opposites are on a number line

CCSS.Math.Content.6.NS.C.6.a

Recognize that opposite numbers are located on opposite sides of zero on a number line

475

Convert between fractions and decimals

CCSS.Math.Content.6.NS.C.7

Convert between fractions and decimals

478

Understand coordinate signs determine quadrants

CCSS.Math.Content.6.NS.C.6.b

Understand signs of numbers in ordered pairs as indicating locations in the quadrants of the coordinate plane

513

Evaluate an expression with whole-number powers

CCSS.Math.Content.6.EE.A.1

Evaluate a numerical expression involving whole-number exponents

488

Evaluate an expression given values of variables

CCSS.Math.Content.6.EE.A.2.c

Evaluate an expression for specific values of its variables

493

Relate a graph / table to a 2-variable equation

CCSS.Math.Content.6.EE.C.9

Relate a graph or a table showing the relationship between two variables to an equation

508

Solve problem: x + p = q or px = q (rationals)

CCSS.Math.Content.6.EE.B.7

Solve a problem involving an equation of the form x + p = q or px = q with nonnegative rational numbers

510

Solve problem: area of triangle/square/rectangle

CCSS.Math.Content.6.G.A.1

Determine the area of a triangle, square or rectangle to solve a problem

518

Find polygon area from triangle / rectangle areas

CCSS.Math.Content.6.G.A.1

Find the area of polygons including special quadrilaterals composed of triangles and/or rectangles

520

Apply volume formula for prism: fractional length

CCSS.Math.Content.6.G.A.2

Solve a problem using a formula to find the volume of a right rectangular prism with fractional-edge lengths

527

Draw a net of a 3-dimensional object

CCSS.Math.Content.6.G.A.4

Draw a net of a 3-dimensional object

529

Understand data sets by center / spread / shape

CCSS.Math.Content.6.SP.A.2

Understand a statistical distribution by its center, spread, and overall shape

533

Display data on a dot / box plot / histogram

CCSS.Math.Content.6.SP.B.4

Display numerical data in dot plots, histograms, and box plots

536

Summarize a data set in relation to its context

CCSS.Math.Content.6.SP.B.5

Summarize a numerical data set in relation to its context

537

Compute a unit rate from a ratio of fractions

CCSS.Math.Content.7.RP.A.1

Compute the unit rate associated with a ratio of fractions

576

Decide if variables are in a linear relationship

CCSS.Math.Content.7.RP.A.2.a

Determine if the variables in a situation are in a proportional or linear non-proportional relationship given a table, a graph, or an equation

577

Identify the constant of proportionality

CCSS.Math.Content.7.RP.A.2.b

Identify the constant of proportionality

578

Explain ordered pair: proportional relationship

CCSS.Math.Content.7.RP.A.2.d

Interpret the meaning of an ordered pair on a graph that shows a proportional relationship in a given situation

580

See subtraction as adding the additive inverse

CCSS.Math.Content.7.NS.A.1.c

Understand subtraction of rational numbers as adding the additive inverse

550

Add integers

CCSS.Math.Content.7.NS.A.1.d

Add integers

556

Subtract integers

CCSS.Math.Content.7.NS.A.1.d

Subtract integers

557

Add rational numbers

CCSS.Math.Content.7.NS.A.1.d

Add rational numbers

560

Subtract rational numbers

CCSS.Math.Content.7.NS.A.1.d

Subtract rational numbers

561

Divide integers

CCSS.Math.Content.7.NS.A.2.c

Divide integers

569

Multiply or divide integers to solve a problem

CCSS.Math.Content.7.NS.A.3

Multiply or divide integers to solve a problem

570

Multiply rational numbers

CCSS.Math.Content.7.NS.A.2.c

Multiply rational numbers

571

Divide rational numbers

CCSS.Math.Content.7.NS.A.2.c

Divide rational numbers

572

Convert between rational numbers in any form

CCSS.Math.Content.7.NS.A.2.d

Convert between rational numbers in any form

573

Solve problems with rationals and 4 operations

CCSS.Math.Content.7.NS.A.3

Solve a real-world problem with rational numbers involving any of the four operations

575

Add / subtract to simplify a linear expression

CCSS.Math.Content.7.EE.A.1

Add or subtract to simplify a linear expression with rational coefficients

585

Compare different forms of an expression

CCSS.Math.Content.7.EE.A.2

Understand that different forms of an expression can show how its various quantities are related

588

Solve problems: px + q = r or p(x + q) = r

CCSS.Math.Content.7.EE.B.4.a

Fluently solve equations of the form px + q = r or p(x + q) = r

590

Graph solutions of inequalities with rationals

CCSS.Math.Content.7.EE.B.4.b

Graph the solution set of an inequality involving rational numbers

596

Find the measure of an unknown angle in a figure

CCSS.Math.Content.7.G.B.5

Determine the measure of an unknown angle in a geometric figure

602

Solve problems: apply area / circumference formula

CCSS.Math.Content.7.G.B.4

Solve a problem involving the area or circumference of a circle using the appropriate formula

604

Solve a problem with surface area or volume

CCSS.Math.Content.7.G.B.6

Solve a problem involving the surface area or volume of a 3-dimensional object composed of cubes and/or right prisms

607

Determine 2-D cross-sections of 3-D shapes

CCSS.Math.Content.7.G.A.3

Determine the 2-dimensional figure that results from slicing a 3-dimensional shape

610

Use data from a random sample to draw inferences

CCSS.Math.Content.7.SP.A.2

Use data from a random sample to draw inferences about a population

614

Make comparative inferences from random samples

CCSS.Math.Content.7.SP.B.4

Make comparative inferences about two populations using measures of center and measures of variability from random samples

618

Predict approximate frequency given probability

CCSS.Math.Content.7.SP.C.6

Predict the approximate relative frequency of a chance event given its probability

622

Understand the probability of a compound event

CCSS.Math.Content.7.SP.C.8.a

Understand that the probability of a compound event is the fraction of the outcomes in the sample space for which the compound event occurs

632

Approximate an irrational on a number line

CCSS.Math.Content.8.NS.A.2

Approximate the location of an irrational number on a number line

641

Make equivalent integer exponent expressions

CCSS.Math.Content.8.EE.A.1

Generate an equivalent expression using properties of integer exponents

645

Perform basic operations: scientific notation

CCSS.Math.Content.8.EE.A.4

Perform operations with numbers written in scientific notation

650

Use square / cube root symbols for solutions

CCSS.Math.Content.8.EE.A.2

Represent a solution of a simple quadratic or cubic equation using a square root or cube root symbol

659

Interpret a unit rate as the slope of a graph

CCSS.Math.Content.8.EE.B.5

Interpret a unit rate as the slope of a graph

665

Derive the slope-intercept equation for a line

CCSS.Math.Content.8.EE.B.6

Derive the equation y = mx + b for a line intercepting the vertical axis at b

669

Solve rational coefficient linear equations

CCSS.Math.Content.8.EE.C.7.b

Solve a linear equation with rational coefficients

675

Solve 2-variable linear systems algebraically

CCSS.Math.Content.8.EE.C.8.b

Solve a system of two linear equations in two variables algebraically

683

Apply Pythagorean theorem to find unknown side

CCSS.Math.Content.8.G.B.7

Find an unknown side length of a right triangle, using the Pythagorean theorem

656

Use the Pythagorean theorem to find distance

CCSS.Math.Content.8.G.B.8

Find the distance between two points, using the Pythagorean theorem

658

Perform a rotation, reflection, or translation

CCSS.Math.Content.8.G.A.3

Perform a rotation, reflection, or translation

698

Understand congruence via rigid transformations

CCSS.Math.Content.8.G.A.2

Understand congruence through rigid transformations

702

Understand similarity through transformations

CCSS.Math.Content.8.G.A.4

Understand similarity through transformations

706

Angle facts from parallels and transversals

CCSS.Math.Content.8.G.A.5

Establish facts about the angles created by parallel lines and a transversal

709

Solve problems with cone / cylinder / sphere volume

CCSS.Math.Content.8.G.C.9

Solve a real-world or mathematical problem involving the volume of a cone, cylinder, or sphere

713

Construct a scatter plot

CCSS.Math.Content.8.SP.A.1

Construct a scatter plot

688

Know graph as ordered pairs of inputs / outputs

CCSS.Math.Content.8.F.A.1

Understand that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output

661

Find rate of change / initial value of a function

CCSS.Math.Content.8.F.B.4

Determine the rate of change or initial value of a function from a description of a relationship or from two (x, y) values

670

Write a function to model a linear relationship

CCSS.Math.Content.8.F.B.4

Write a function to model a linear relationship between two quantities

672

Compare linear functions shown different ways

CCSS.Math.Content.8.F.A.2

Compare two linear functions each represented in a different way

676

Know y = mx + b as linear (straight-line graph)

CCSS.Math.Content.8.F.A.3

Recognize the equation y = mx + b as defining a linear function whose graph is a straight line

677

Find a sequence to transform a figure to another

CCSS.Math.Content.HSG-CO.A.5

Identify a sequence of transformations that will carry a given figure onto another figure

885

Tell if figures are congruent via rigid motions

CCSS.Math.Content.HSG-CO.B.6

Determine if two figures are congruent using the definition of congruence in terms of rigid motions

889

Show triangle congruence: corresponding parts

CCSS.Math.Content.HSG-CO.B.7

Show two triangles are congruent if corresponding sides and angles are congruent

891

Tell if figures are similar via transformations

CCSS.Math.Content.HSG-SRT.A.2

Determine if two figures are similar by using similarity transformations

908

Prove the Pythagorean theorem using similarity

CCSS.Math.Content.HSG-SRT.B.4

Prove the Pythagorean theorem using triangle similarity

913

Solve problems: congruence / similarity criteria

CCSS.Math.Content.HSG-SRT.B.5

Solve a problem using congruence and similarity criteria

914

Define trig ratios: similar triangle side ratios

CCSS.Math.Content.HSG-SRT.C.6

Understand that the side ratios in similar right triangles define the trigonometric ratios

920

Relate / use: sine / cosine of complementary angles

CCSS.Math.Content.HSG-SRT.C.7

Use the relationship between the sine and cosine of complementary angles to solve a problem

923

Find length: special right triangle properties

CCSS.Math.Content.HSG-SRT.C.8

Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

925

Solve right triangles: trig / Pythagorean theorem

CCSS.Math.Content.HSG-SRT.C.8

Solve a right triangle using trigonometric ratios and/or the Pythagorean theorem

928

Know and apply the law of sines

CCSS.Math.Content.HSG-SRT.D.11

Know and apply the law of sines

932

Know and apply the law of sines

CCSS.Math.Content.HSG-SRT.D.10

Know and apply the law of sines

932

Know and apply the law of cosines

CCSS.Math.Content.HSG-SRT.D.11

Know and apply the law of cosines

934

Know and apply the law of cosines

CCSS.Math.Content.HSG-SRT.D.10

Know and apply the law of cosines

934

Apply inscribed angle / radius / chord relationships

CCSS.Math.Content.HSG-C.A.2

Apply relationships among inscribed angles, radii, and chords

941

Find the length of an arc of a circle

CCSS.Math.Content.HSG-C.B.5

Find the length of an arc of a circle

947

Find the area of a sector of a circle

CCSS.Math.Content.HSG-C.B.5

Find the area of a sector of a circle

950

Compute the area of a triangle or rectangle

CCSS.Math.Content.HSG-GPE.B.7

Compute the area of a triangle or rectangle

874

Apply pyramid / cone / cylinder / sphere volumes

CCSS.Math.Content.HSG-GMD.A.3

Solve a problem involving the volume of a pyramid, cone, cylinder, and/or sphere

964

Understand the meaning of independent events

CCSS.Math.Content.HSS-CP.A.2

Understand the meaning of independent events in terms of probability

973

Understand what conditional probability means

CCSS.Math.Content.HSS-CP.A.3

Understand the meaning of conditional probability

976

Construct a two-way frequency table of data

CCSS.Math.Content.HSS-CP.A.4

Construct a two-way frequency table of data

979

Find the conditional probability of an event

CCSS.Math.Content.HSS-CP.B.6

Determine the conditional probability of an event A given an event B

985

Solve a problem using permutations

CCSS.Math.Content.HSS-CP.B.9

Solve a problem using permutations

992

Solve a problem using combinations

CCSS.Math.Content.HSS-CP.B.9

Solve a problem using combinations

994

Analyze a strategy using basic probability ideas

CCSS.Math.Content.HSS-MD.B.7

Analyze a decision or a strategy using simple probability concepts

996

Interpret a linear expression by parts

CCSS.Math.Content.HSA-SSE.A.1.b

Interpret a linear expression by viewing one or more of its parts as a single entity

739

Interpret an exponential expression by parts

CCSS.Math.Content.HSA-SSE.A.1.b

Interpret an exponential expression by viewing one or more of its parts as a single entity

778

Use exponent properties to modify an exponential

CCSS.Math.Content.HSA-SSE.B.3.c

Use the properties of exponents to write an equivalent form of an exponential function

786

Complete the square: find the max / min value

CCSS.Math.Content.HSA-SSE.B.3.b

Complete the square in a quadratic expression to find the maximum or minimum value of the function it defines

824

Solve problems: 1-variable linear inequality

CCSS.Math.Content.HSA-CED.A.1

Solve a real-world problem involving a multi-step linear inequality in one variable

729

Solve a formula for a linear variable

CCSS.Math.Content.HSA-CED.A.4

Rearrange a formula to isolate a variable of interest where the formula is linear in that variable

730

Graph a linear equation using coordinate axes

CCSS.Math.Content.HSA-CED.A.2

Graph a linear equation using coordinate axes

734

Show conditions by linear equations / inequalities

CCSS.Math.Content.HSA-CED.A.3

Represent constraints using linear equations or inequalities

768

Graph an exponential equation: coordinate axes

CCSS.Math.Content.HSA-CED.A.2

Graph an exponential equation using coordinate axes

780

Solve a linear equation / inequality in 1 variable

CCSS.Math.Content.HSA-REI.B.3

Solve a linear equation or inequality in one variable

724

Know graph as all solutions of equation

CCSS.Math.Content.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

733

Solve 2-variable linear systems using any method

CCSS.Math.Content.HSA-REI.C.6

Solve a system of linear equations in two variables using any method

763

Graph solution to system of linear inequalities

CCSS.Math.Content.HSA-REI.D.12

Graph the solution set to a system of linear inequalities in two variables

767

Solve a quadratic equation by factoring

CCSS.Math.Content.HSA-REI.B.4.b

Solve a quadratic equation by factoring

811

Solve a quadratic using the quadratic formula

CCSS.Math.Content.HSA-REI.B.4.b

Solve a quadratic equation by using the quadratic formula

815

Solve system of linear / quadratic: algebraically

CCSS.Math.Content.HSA-REI.C.7

Solve a system of equations consisting of a linear equation and a quadratic equation, algebraically

827

Find the linear function of best fit for data

CCSS.Math.Content.HSS-ID.B.6.a

Determine the linear function of best fit for data on a scatter plot

754

Find the linear function of best fit for data

CCSS.Math.Content.HSS-ID.B.6.c

Determine the linear function of best fit for data on a scatter plot

754

Solve problems using best fit linear functions

CCSS.Math.Content.HSS-ID.B.6.a

Solve a problem using a linear function of best fit

759

Summarize data in a 2-way frequency table

CCSS.Math.Content.HSS-ID.B.5

Summarize categorical data for two categories in a two-way frequency table

861

Evaluate a function for a given input

CCSS.Math.Content.HSF-IF.A.2

Evaluate a function for a given input

722

Graph a linear equation using coordinate axes

CCSS.Math.Content.HSF-IF.C.7.a

Graph a linear equation using coordinate axes

734

Interpret features of a linear function

CCSS.Math.Content.HSF-IF.B.4

Interpret features of a linear function that models a relationship between two quantities

741

Interpret features of an exponential function

CCSS.Math.Content.HSF-IF.B.4

Interpret features of an exponential function that models a relationship between two quantities

781

Interpret exponentials using exponent properties

CCSS.Math.Content.HSF-IF.C.8.b

Interpret an expression for an exponential function using the properties of exponents

788

Graph exponentials with intercepts / end behavior

CCSS.Math.Content.HSF-IF.C.7.e

Graph an exponential function showing intercepts and end behavior

790

Relate domain of quadratic function in context

CCSS.Math.Content.HSF-IF.B.5

Relate the domain of a quadratic function to the quantitative relationship the function describes

831

Graph a quadratic showing intercepts / max / min

CCSS.Math.Content.HSF-IF.C.7.a

Graph a quadratic function, showing its intercepts and maximum or minimum

834

Interpret critical values of quadratic: context

CCSS.Math.Content.HSF-IF.C.8.a

Interpret zeros, maxima or minima, and axis of symmetry of a quadratic function, given a context

835

Interpret critical values of quadratic: context

CCSS.Math.Content.HSF-IF.B.4

Interpret zeros, maxima or minima, and axis of symmetry of a quadratic function, given a context

835

f(x+k), f(x)+k, kf(x), or f(kx) on linear graph

CCSS.Math.Content.HSF-BF.B.3

Identify the effect of replacing f(x) with f(x + k), f(x) + k, kf(x), or f(kx) on the graph of a linear function

748

f(x+k), f(x)+k, kf(x), or f(kx) on exp graph

CCSS.Math.Content.HSF-BF.B.3

Identify the effect of replacing f(x) with f(x + k), f(x) + k, kf(x), or f(kx) on the graph of an exponential function

795

Explain transformations on a quadratic's graph

CCSS.Math.Content.HSF-BF.B.3

Explain the effects of transformations on the graph of a quadratic function

851

Combine functions to describe a relationship

CCSS.Math.Content.HSF-BF.A.1.b

Write a function that describes a relationship between two quantities by combining functions, using arithmetic operations

852

Find a linear function from given information

CCSS.Math.Content.HSF-LE.A.2

Determine an equation of a linear function, using given information

751

Exponential growth will exceed polynomial growth

CCSS.Math.Content.HSF-LE.A.3

Recognize that exponential growth eventually exceeds linear, quadratic, and polynomial growth

853

Rewrite expression: radical / rational exponents

CCSS.Math.Content.HSN-RN.A.2

Rewrite an expression involving radicals and rational exponents using properties of exponents

771

Perform the 4 operations on radical expressions

CCSS.Math.Content.HSN-RN.A.2

Perform the four operations on algebraic radical expressions

772

Determine accuracy of measurement

CCSS.Math.Content.HSN-Q.A.3

Choose a level of precision appropriate to limitations on measurement

716

Convert a rate to an equivalent rate

CCSS.Math.Content.HSN-Q.A.1

Convert a rate to an equivalent rate

718

Select / interpret unit form of a formula quantity

CCSS.Math.Content.HSN-Q.A.1

Select or interpret the unit form of a quantity in a formula

719

Find a process for solving problems using units

CCSS.Math.Content.HSN-Q.A.1

Determine the process for solving a multi-step problem using the units involved

720

Interpret the meaning: graph's origin or scale

CCSS.Math.Content.HSN-Q.A.1

Interpret the meaning of the origin or scale for a graph or data display

731

Choose the scale for a graph or data display

CCSS.Math.Content.HSN-Q.A.1

Choose the scale for a graph or data display

732

Rewrite a polynomial in an equivalent form

CCSS.Math.Content.HSA-SSE.A.2

Rewrite a polynomial expression in equivalent forms, using the structure of the expression

1020

Use polynomial identities to get numerical facts

CCSS.Math.Content.HSA-APR.C.4

Describe a numerical relationship using polynomial identities

1004

Know and apply the Remainder theorem

CCSS.Math.Content.HSA-APR.B.2

Know and apply the Remainder theorem

1012

Add or subtract rational expressions

CCSS.Math.Content.HSA-APR.D.7

Add or subtract rational expressions

1017

Multiply or divide rational expressions

CCSS.Math.Content.HSA-APR.D.7

Multiply or divide rational expressions

1018

Graph a nonlinear equation using coordinate axes

CCSS.Math.Content.HSA-CED.A.2

Graph a nonlinear equation using coordinate axes

1044

Solve quadratic equations with complex solutions

CCSS.Math.Content.HSA-REI.B.4.b

Solve a quadratic equation that has complex solutions

1002

Solve a rational equation in one variable

CCSS.Math.Content.HSA-REI.A.2

Solve a rational equation in one variable

1023

Solve a radical equation in one variable

CCSS.Math.Content.HSA-REI.A.2

Solve a radical equation in one variable

1024

Fit a data set to a normal distribution

CCSS.Math.Content.HSS-ID.A.4

Fit a data set to a normal distribution

1089

Estimate population proportions from sample data

CCSS.Math.Content.HSS-IC.B.4

Estimate a population mean or proportion, using data from a sample survey

1098

Evaluate a report based on data

CCSS.Math.Content.HSS-IC.B.6

Evaluate a report based on data

1102

Graph polynomial function: end behavior / zeros

CCSS.Math.Content.HSF-IF.C.7.c

Graph a polynomial function showing the end behavior and zeros where appropriate

1015

Graph a trigonometric function in context

CCSS.Math.Content.HSF-IF.C.7.e

Determine the graph of a trigonometric function that represents a specific context or situation

1035

Graph an exponential or log function in context

CCSS.Math.Content.HSF-IF.C.7.e

Determine a graph of an exponential or logarithmic function that represents a specific context or situation

1050

Relate domain to the function's context

CCSS.Math.Content.HSF-IF.B.5

Relate the domain of a function to the quantitative relationship the function describes

1055

Estimate an average rate of change given a graph

CCSS.Math.Content.HSF-IF.B.6

Estimate the average rate of change of a function over a specified interval on a graph

1058

Represent a function in multiple symbolic ways

CCSS.Math.Content.HSF-IF.C.8

Represent a function symbolically in multiple ways

1065

Compare properties of functions in unlike forms

CCSS.Math.Content.HSF-IF.C.9

Compare the properties of two functions each represented in a different way

1066

Find the inverse of a function

CCSS.Math.Content.HSF-BF.B.4.a

Find the inverse of a function

1069

Solve an exponential equation using logarithms

CCSS.Math.Content.HSF-LE.A.4

Solve an exponential equation using logarithms

1047

Relate radian measure of an angle to arc length

CCSS.Math.Content.HSF-TF.A.1

Understand radian measure of an angle and how it relates to arc length

1031

Model a situation with a trigonometric function

CCSS.Math.Content.HSF-TF.B.5

Model a situation with a trigonometric function

1036

Use the Pythagorean identity to find trig values

CCSS.Math.Content.HSF-TF.C.8

Use the Pythagorean identity to find trigonometric values

1038

Know the standard form of complex numbers

CCSS.Math.Content.HSN-CN.A.1

Know the standard form of complex numbers

998

Solve quadratic equations with complex solutions

CCSS.Math.Content.HSN-CN.C.7

Solve a quadratic equation that has complex solutions

1002