Maryland College and Career Ready Standards for Mathematics (2025)
Each standard below is explained in plain language, with lesson ideas and a free generator that builds a full lesson plan aligned to it. Standard text is verified against msde.maryland.gov.
Kindergarten
- K.AT.A.1
Represent addition and subtraction situations (presented with numerals or mathematical symbols) within 10 with objects, ...
- K.AT.A.2
Solve addition and subtraction problems in context (add to, take from, put together/take apart) within 10 and represent ...
- K.AT.B.3
Identify, extend, and create repeating patterns (AABAAB, ABCABC, or AABBCC) using concrete objects, drawings, sounds, or...
- K.DS.A.1
Organize data by classifying objects into given categories and counting the number of objects in each category (Limit th...
- K.DS.A.2
Analyze data sets by ordering the categories by count.
- K.GR.A.1
Describe measurable attributes of an object such as length, height, weight, and capacity using appropriate vocabulary (e...
- K.GR.A.3
Order up to 3 objects by a measurable attribute (e.g. greatest to least in height).
- K.GR.B.4
Describe the relative positions of objects using terms such as above, below, beside, in front of, behind, and next to.
- K.GR.B.5
Identify and describe given shapes and shapes of objects in everyday situations including two-dimensional shapes (circle...
- K.GR.B.8
Draw two dimensional shapes and build or create models of three-dimensional shapes.
- K.NOS.A.3
Count backwards from any given number within 20.
- K.NOS.A.4
Write numbers from 0 to 20.
- K.NOS.A.5
Represent a number of objects with a written numeral within 20 (with 0 representing a count of no objects).
- K.NOS.B.6
Use the relationship between numbers and quantities within 20 to count objects with one-to-one correspondence (arranged ...
- K.NOS.B.7
When counting objects within 20, recognize that each successive number name refers to a quantity that is one larger.
- K.NOS.B.8
Recognize the number of objects in a set without counting (subitizing) with both unfamiliar patterns within 6 and famili...
- K.NOS.C.10
Compare two quantities within 20 using greater than, equal to, or less than, with objects, location on number paths, and...
- K.NOS.C.9
Understand 10 as a group, collection, or bundle of ten ones called a “ten.”
- K.NOS.C.9.a
Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and equati...
- K.NOS.C.9.b
Describe a given number as one ten and the correct number of ones (e.g., 13 is one ten and three ones).
- K.NOS.D.11
Decompose numbers within 10 in more than one way, by using objects or drawings, and record each decomposition with a dra...
Grade 1
- 1.DS.A.1
Ask and answer questions by collecting, organizing and summarizing data.
- 1.DS.A.1.a
Craft a question that can be answered by collecting categorical data.
- 1.DS.A.1.b
Collect and organize categorical data (into up to three categories) using surveys or observations.
- 1.DS.A.1.c
Represent data by creating tally charts and picture graphs.
- 1.DS.A.1.d
Summarize the data presented in tally charts using “most,” “least,” “greater than,” “less than,” and “equal to”.
- 1.GR.A.2
Use non-standard units (with no gaps or overlaps) to measure the length of an object to the nearest whole unit.
- 1.GR.B.3
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g...
- 1.GR.C.5
Tell time in hours, half hours, and quarter hours using a digital clock or analog clock. Estimate time intervals (1 hour...
- 1.GR.C.6
Identify and know the value of coins (penny, nickel, dime, and quarter) and bills ($1, $5, $10, and $20).
- 1.NOS.A.1
Count forward and backward within 120.
- 1.NOS.A.1.a
Count forward and backwards by ones starting with any number.
- 1.NOS.A.1.b
Skip count forward and backwards by tens.
- 1.NOS.A.2
Read, write numerals, and represent a number of objects with a written numeral within 120.
- 1.NOS.B.3
Extend understanding of 10 as a group, collection, or bundle of ten ones, called a “ten,” to compose and decompose two-d...
- 1.NOS.B.3.a
Compose and decompose two-digit numbers into tens and ones using objects or drawings, and equations (e.g., 10 + 4 = 14; ...
- 1.NOS.B.3.b
Describe a given number as the correct number of tens and ones (e.g., 14 is one ten and four ones; 38 is three tens and ...
- 1.NOS.B.3.c
Compose and decompose two-digit numbers in more than one way (e.g. 46 = 41 + 5 or 46 = 23 + 23).
- 1.NOS.B.4
Represent whole numbers as lengths from 0 on a number line (horizontal and vertical) with equally spaced points correspo...
- 1.NOS.B.5
Compare two numbers within 100 by reasoning about values of tens and ones digits and the location of the numbers on a nu...
- 1.NOS.B.6
Estimate the location of numbers on a number line by reasoning about their relationship to benchmark numbers (e.g. 10, 5...
- 1.NOS.C.7
Apply the Commutative Property of Addition and Associative Property of Addition as a strategy to add.
- 1.NOS.C.8
Use the inverse relationship between addition and subtraction to subtract.
- 1.NOS.D.9
Recall or quickly derive addition and subtraction facts within 20.
- 1.NOS.D.9.a
Use the count on and count back strategies to add and subtract (e.g., 4 + 1, 7 – 2, etc.).
- 1.NOS.D.9.b
Use the make ten strategy to add and subtract with combinations of 10 (e.g., 7 + 3, 6 + 4, 10 – 3, 10 – 6, etc.).
- 1.NOS.D.9.c
Use the ten more and ten less strategies to add and subtract (including those with a difference of 10).
- 1.NOS.D.9.d
Use the doubles to add and subtract (e.g., 6 + 6 = 12, 14 – 7 = 7, etc.)
- 1.NOS.E.10
Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple o...
- 1.NOS.E.10.a
Use concrete models and drawings to add.
- 1.NOS.E.10.b
Use counting strategies and strategies based on place value (e.g., partial sums, making tens, etc.) to add.
- 1.NOS.E.10.c
Use properties of operations, and/or the inverse relationship between addition and subtraction to add.
- 1.NOS.E.10.d
Represent and explain the calculation by connecting the strategy used to the meaning of addition.
- 1.NOS.E.12
Subtract a multiple of 10 from another multiple of 10 within 90.
- 1.NOS.E.12.a
Use concrete models or drawings to subtract.
- 1.NOS.E.12.b
Use counting strategies, properties of operations, and/or the inverse relationship between addition and subtraction to s...
- 1.NOS.E.12.c
Represent and explain the calculation by connecting the strategy used to the meaning of subtraction.
- 1.NOS.E.13
Subtract a 1-digit number from a 2-digit number (without regrouping).
- 1.NOS.E.13.a
Use concrete models or drawings to subtract.
- 1.NOS.E.13.b
Use counting strategies, properties of operations, and/or the inverse relationship between addition and subtraction to s...
- 1.NOS.E.13.c
Represent and explain the calculation by connecting the strategy used to the meaning of subtraction.
- 1.NOS.F.14
Partition circles and rectangles into equal shares (halves and fourths) recognizing that decomposing into more equal sha...
Grade 2
- 2.AT.A.1
Use addition and subtraction within 100 to solve one-step problems in context involving an unknown in any situation or p...
- 2.AT.A.2
Use addition and/or subtraction within 100 to solve two-step problems in context involving any situation or position of ...
- 2.DS.A.1
Ask and answer questions by collecting, organizing and summarizing data.
- 2.DS.A.1.a
Craft a question that can be answered by collecting categorical and numerical data.
- 2.DS.A.1.b
Collect and organize data using surveys, making observations, or measuring.
- 2.DS.A.1.c
Represent categorical data using picture graphs and bar graphs. Represent numerical data using line plots.
- 2.DS.A.1.d
Summarize the data presented in data visualizations using “most,” “least,” “greater than,” “less than,” and “equal to” a...
- 2.GR.A.1
Measure the length of an object to the nearest whole unit by using appropriate tools (e.g., rulers, yardsticks, meter st...
- 2.GR.B.6
Explain that a line of symmetry for a two-dimensional figure is a line across the figure such that the figure can be fol...
- 2.GR.C.7
Tell and represent time to the nearest minute using multiple representations (e.g., digital clocks, analog clocks, numbe...
- 2.GR.C.8
Estimate and calculate elapsed time to the hour and half hour (e.g. If the school day begins at 8am and ends at 3 pm, th...
- 2.GR.C.9
Count mixed sets of coins and bills to solve problems in context (within $20.00) involving bills, quarters, dimes, nicke...
- 2.NOS.A.1
Use understanding of 100 as a bundle of ten tens, called a “hundred,” and compose and decompose three-digit numbers.
- 2.NOS.A.1.a
Compose and decompose three-digit numbers into hundreds, tens, and ones by using objects, drawings, and/or equations (e....
- 2.NOS.A.1.c
Compose and decompose three-digit numbers in more than one way (e.g., 439 = 400 + 39 or 439 = 435 + 4).
- 2.NOS.A.2
Count forward and backward within 1000 starting with any number.
- 2.NOS.A.2.a
Skip-count forward and backwards by 2s, 5s, 10s, and 100s.
- 2.NOS.A.2.b
Use skip-counting to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 colum...
- 2.NOS.A.4
Compare two numbers within 1000 by reasoning about the values of the hundreds, tens, and ones digits and/or the location...
- 2.NOS.A.5
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers (e.g. 10...
- 2.NOS.B.6
Recall or quickly derive addition and subtraction facts within 20.
- 2.NOS.B.6.a
Use counting, make ten, and ten more/less, doubling strategies to add and subtract.
- 2.NOS.B.6.b
Use the use ten strategy (e.g., think of 9 + 1 + 6 to solve 9 + 7) and doubles plus one strategy (e.g., think of 4 + 4 +...
- 2.NOS.B.6.c
Use the inverse operation to add and subtract (e.g. think of 7 + ? = 15 to solve 15 – 7 = ?).
- 2.NOS.C.7
Represent whole number sums and differences within 100 using lengths on a number line.
- 2.NOS.C.8
Fluently add and subtract within 100.
- 2.NOS.C.8.a
Use strategies based on counting (e.g., counting on, counting back) and place value (e.g., partial sums, making tens, et...
- 2.NOS.C.8.b
Use properties of operations, and the inverse relationship between addition and subtraction to add and subtract.
- 2.NOS.C.8.c
Determine and explain when a strategy is most efficient.
- 2.NOS.C.9
Add and subtract within 1000, recognizing that when adding or subtracting three-digit numbers, one adds or subtracts hun...
- 2.NOS.C.9.a
Use concrete models or drawings to add and subtract.
- 2.NOS.C.9.b
Use strategies based on place value (counting on, partial sums, making tens, etc.) to add and subtract.
- 2.NOS.C.9.c
Use properties of operations, and/or the relationship between addition and subtraction to add and subtract.
- 2.NOS.C.9.d
Represent and explain the calculation by connecting the strategy used to the meaning of addition and subtraction.
- 2.NOS.D.11
Partition circles and rectangles into equal shares (halves, thirds, and fourths) recognizing that equal shares do not ne...
Grade 3
- 3.AT.A.1
Use multiplication and division within 100 to solve one-step problems in context involving equal groups, arrays, and are...
- 3.AT.A.2
Use the four operations to solve two-step problems in context (within number limits for each operation as stated in 3.NO...
- 3.AT.A.2.a
Represent these problems using equations with a letter standing for the unknown quantity.
- 3.AT.A.2.b
Assess the reasonableness of answers in terms of context, using mental computation and estimation strategies including, ...
- 3.DS.A.1
Ask and answer questions by collecting, organizing and summarizing data, recognizing the importance of context when anal...
- 3.DS.A.1.a
Create a scaled data visualization (e.g., picture graph, bar graph for categorial data; line plot with fraction units of...
- 3.DS.A.1.b
Summarize data presented in scaled data visualizations (e.g., picture graph, bar graph for categorial data; line plot fo...
- 3.DS.A.1.c
Identify patterns in the data and evaluate whether these patterns might apply to different contexts or situations.
- 3.GR.A.1
Measure the length of an object to the nearest half and quarter unit by using appropriate tools (e.g., rulers, yardstick...
- 3.GR.A.2
Solve problems in context that involve addition and subtraction of time intervals in minutes (e.g., represent and solve ...
- 3.GR.A.3
Measure and estimate liquid volumes and masses of objects using standard units of liters(l), grams (g), and kilograms (k...
- 3.GR.A.4
Add, subtract, multiply, or divide to solve one-step problems in measurement contexts involving masses or volumes that a...
- 3.GR.B.5
Explain that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having...
- 3.GR.C.6
Identify area as an attribute of a two-dimensional figure and measure area of rectangular space by counting square units...
- 3.GR.C.7.a
Determine the area of a rectangle with whole-number side lengths by tiling and connecting the visual representation to m...
- 3.GR.C.7.c
Determine the area of composite rectilinear figures by decomposing them into non-overlapping rectangles and adding the a...
- 3.GR.C.8
Identify perimeter as an attribute of two-dimensional figures and measure the distance around the outside of a figure by...
- 3.GR.C.9
Solve problems in contexts involving perimeters of polygons, including finding the perimeter given the side lengths, fin...
- 3.NOS.A.1
Apply and extend place value understanding to whole numbers within 10,000.
- 3.NOS.A.1.a
Read and write whole numbers using base-ten numerals, number names, and expanded form.
- 3.NOS.A.1.b
Compose and decompose whole numbers.
- 3.NOS.A.1.c
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rou...
- 3.NOS.A.1.d
Compare two whole numbers by reasoning about the values of the digits and the location of the numbers on a number line. ...
- 3.NOS.B.2
Represent and interpret multiplication of two factors (0- 10) as equal groups or as a composed unit that can be repeated...
- 3.NOS.B.3
Represent and interpret whole-number quotients (0-10) as dividing an amount into known number of groups (partitive) or a...
- 3.NOS.C.4
Identify and apply the Commutative Property of Multiplication, Associative Property of Multiplication, and Distributive ...
- 3.NOS.C.5
Explain and use the inverse relationship between multiplication and division to determine the unknown whole number in a ...
- 3.NOS.D.6
Estimate sums and differences within 1,000 using benchmark numbers and front-end estimation. Determine when an estimate ...
- 3.NOS.D.7
Fluently add and subtract within 1,000.
- 3.NOS.D.7.a
Use computational strategies efficiently (e.g., decomposition, partials sums, compensation, make ten/hundred/thousand) t...
- 3.NOS.D.7.b
Use properties of operations, and/or the inverse relationship between addition and subtraction.
- 3.NOS.D.7.c
Determine and explain when a strategy is most efficient.
- 3.NOS.E.9
Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotie...
- 3.NOS.E.9.a
Skip count (2s, 5s, 10s) and apply properties of operations (0s, 1s) to derive foundational facts.
- 3.NOS.E.9.b
Derive unknown facts from known facts using double facts (e.g., to solve 4 × 3, double 3 to get 6 and double 6 to get 12...
- 3.NOS.E.9.c
Use properties of operations (e.g., to solve 8 × 7, think of (5 × 7) + (3 × 7)) to multiply.
- 3.NOS.E.9.d
Use the inverse relationship between multiplication and division (e.g., think of 4 × ? = 28 to solve 28 ÷ 4 = ?) to mult...
- 3.NOS.F.10
Recognize and explain that a fraction represents a part of a whole.
- 3.NOS.F.10.b
Explain that a fraction 1/d represents one part of a whole that is divided into d equal parts, and that a fraction c/d r...
- 3.NOS.F.11
Explain a fraction of a set c/d as the quantity formed by c items as part of the given set of d objects.
- 3.NOS.F.13
Explain equivalence of fractions and compare fractions by reasoning about their size, recognizing that comparisons are v...
- 3.NOS.F.13.a
Represent two fractions as equivalent if they are the same size, or they represent the same point on the number line.
- 3.NOS.F.13.b
Identify and generate equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3.) and explain why the fractions are equivalent u...
- 3.NOS.F.13.d
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Record the results ...
Grade 4
- 4.AT.A.1
Interpret a multiplication situation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as ma...
- 4.AT.A.2
Multiply or divide to solve multiplicative comparison problems in context by using drawings and equations with a symbol ...
- 4.AT.A.3
Distinguish multiplicative comparison from additive comparison.
- 4.AT.A.4
Solve multistep problems in context involving whole numbers and having whole number answers using the four operations, i...
- 4.AT.A.4.a
Represent these problems using equations with a letter standing for the unknown quantity.
- 4.AT.A.4.b
Assess the reasonableness of answers in terms of context, including interpreting remainders.
- 4.DS.A.1
Ask and answer questions by collecting, organizing and summarizing data, recognizing the importance of context when anal...
- 4.DS.A.1.a
Create scaled data visualization (e.g. bar graphs for categorical data; line plots with fraction units of halves, fourth...
- 4.DS.A.1.b
Summarize data presented in scaled data visualizations (e.g. bar graphs, line plots) and draw conclusions about the data...
- 4.DS.A.1.c
Compare and contrast different data visualizations of the same data by varying attributes (e.g., reordering bars, changi...
- 4.GR.A.1
Apply the relationship between measurement units within a given measurement system (customary: in, ft, yd, oz, lb, sec, ...
- 4.GR.A.2
Use the four operations to solve problems in context involving distances, intervals of time, liquid volumes, masses of o...
- 4.GR.A.4
Relate the area of a triangle to the area of a rectangle using decomposition and visual models. Derive and apply the for...
- 4.GR.B.5
Identify angles as geometric figures formed by two rays that share a common endpoint and describe angle size as the amou...
- 4.GR.B.6
Measure angles in whole-number degrees using a protractor. Estimate and sketch angles of specified measures.
- 4.GR.B.7
Explain that when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the an...
- 4.NOS.A.1
Apply and extend place value understanding to multi-digit whole numbers within 1,000,000.
- 4.NOS.A.1.a
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
- 4.NOS.A.1.b
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rou...
- 4.NOS.A.1.c
Compare two multi-digit numbers by reasoning about the values of the digits and the location of the numbers on a number ...
- 4.NOS.A.2
Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to...
- 4.NOS.B.3
Fluently add and subtract multi-digit whole numbers within 1,000,000.
- 4.NOS.B.3.a
Apply estimation strategies to estimate sums and differences.
- 4.NOS.B.3.b
Use computational strategies (e.g., decomposition, partials sums) efficiently.
- 4.NOS.B.3.c
Use a standard algorithm
- 4.NOS.B.3.d
Determine and explain when a strategy or algorithm is most efficient.
- 4.NOS.B.4
Extend place value understanding and basic facts to multiply a multi-digit whole number by a multiple of ten.
- 4.NOS.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.
- 4.NOS.B.5.a
Apply estimation strategies to estimate products.
- 4.NOS.B.5.b
Use strategies based on place value (e.g., partial products) to multiply.
- 4.NOS.B.5.c
Use properties of operations (e.g., use doubling and halving strategy to think of 12 × 32 as 6 × 64) to multiply.
- 4.NOS.B.5.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of ...
- 4.NOS.B.6
Divide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders.
- 4.NOS.B.6.a
Apply estimation strategies to estimate quotients.
- 4.NOS.B.6.b
Use strategies based on place value (e.g., partial quotients) to divide.
- 4.NOS.B.6.c
Use properties of operations and/or the inverse relationship between multiplication and division to divide.
- 4.NOS.B.6.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of ...
- 4.NOS.C.7
Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotie...
- 4.NOS.C.7.a
Skip count (2s, 5s, 10s) and apply properties of operations (0s, 1s) to derive foundational facts.
- 4.NOS.C.7.b
Derive unknown facts from known facts using double facts (e.g., to solve 4 × 3, double 3 to get 6 and double 6 to get 12...
- 4.NOS.C.7.c
Use properties of operations (e.g., to solve 8 × 7, think of (5 × 7 + (3 × 7)) to multiply.
- 4.NOS.C.7.d
Use the inverse relationship between multiplication and division (e.g., think of 4 × ? = 28 to solve 28 ÷ 4 = ?) to mult...
- 4.NOS.C.8
Explain and apply concepts of factors, multiples, and prime and composite numbers for whole numbers in the range of 1-10...
- 4.NOS.C.8.a
Identify factor pairs for a whole number in the range of 1–100.
- 4.NOS.C.8.b
Determine whether a given whole number in the range of 1–100 is a multiple of a one-digit number.
- 4.NOS.C.8.c
Distinguish between factors and multiples and explain how they relate to a given number.
- 4.NOS.C.8.d
Determine whether a given whole number in the range of 1–100 is prime, composite, or neither.
- 4.NOS.D.10
Compare two fractions with different numerators and different denominators, understanding that comparisons are valid onl...
- 4.NOS.D.10.a
Use benchmark numbers (e.g., 1/2, 1), common numerators, and common denominators to compare.
- 4.NOS.D.10.b
Record comparisons with symbols >, =, <.
- 4.NOS.D.10.c
Justify comparisons using representations and reasoning.
- 4.NOS.D.9
Understand and generate equivalent fractions.
- 4.NOS.D.9.a
Identify and generate equivalent fractions using representations and the Identity Property of Multiplication.
- 4.NOS.D.9.b
Explain why fractions are equivalent (c/d = (n × c)/(n × d)).
- 4.NOS.E.11
Apply understanding of a fraction c/d with d > 1 as a sum of unit fractions (1/d) to decompose a fraction (including fra...
- 4.NOS.E.12
Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with ...
- 4.NOS.E.12.b
Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 3/4 + 3/4...
- 4.NOS.E.12.c
Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compe...
- 4.NOS.E.12.d
Solve problems in context involving addition and subtraction of fractions using visual fraction models and equations to ...
- 4.NOS.E.13.a
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 4 × 1/2 will be less ...
- 4.NOS.E.13.b
Use understanding of multiplication as equal groups to multiply a unit fraction by whole number (e.g., interpret b × 1/d...
- 4.NOS.E.13.c
Use understanding of multiplication as equal groups to multiply a fraction by whole number (e.g., interpret b × c/d as b...
- 4.NOS.E.13.d
Solve problems in context involving multiplication of a fraction by a whole number, using visual fraction models and equ...
Grade 5
- 5.AT.A.1
Interpret and evaluate numerical expressions with grouping symbols (e.g. parentheses, brackets, or braces).
- 5.AT.A.2
Write expressions that record calculations with numbers and interpret numerical expressions without evaluating them.
- 5.AT.B.3
Generate and analyze number patterns.
- 5.AT.B.3.a
Generate a number pattern that follows a given rule and identify relationships between the numbers within the pattern.
- 5.AT.B.3.b
Generate two numerical patterns using two given rules and identify relationships between corresponding terms.
- 5.AT.B.3.c
Use tables, ordered pairs, and graphs to represent the relationship between quantities.
- 5.DS.A.1
Ask and answer questions by collecting, organizing and summarizing data, recognizing the importance of context when anal...
- 5.DS.A.1.a
Create scaled data visualization (e.g. bar graphs for categorical data; line plots with fraction units of halves, fourth...
- 5.DS.A.1.b
Summarize data presented in scaled visualizations (e.g. bar graphs, circle graphs, line plots, line graphs) by identifyi...
- 5.DS.A.1.c
Evaluate whether a data visualization accurately represents the data and allows for accurate interpretation given the co...
- 5.GR.A.1
Apply the relationship between measurement units within a given measurement system to convert among different-sized stan...
- 5.GR.B.2
Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that cate...
- 5.GR.B.3.a
Classify triangles based on properties (e.g., angle measure, side lengths).
- 5.GR.B.3.b
Classify quadrilaterals in a hierarchy based on properties (e.g., side lengths, angle measures, presence of parallel or ...
- 5.GR.C.4
Identify volume as an attribute of three-dimensional figures and measure volume by counting cubic units (e.g., non-stand...
- 5.GR.C.5
Relate volume to the operations of multiplication and addition and solve problems in context.
- 5.GR.C.5.a
Find the volume of a right rectangular prism with whole-number side lengths by filling it with unit cubes in layers and ...
- 5.GR.C.5.b
Apply the formulas V = (l)(w)(h) and V = (B)(h) for rectangular prisms to find volumes of right rectangular prisms with ...
- 5.GR.C.5.c
Determine the volumes of composite figures by decomposing them into non-overlapping right rectangular prisms and adding ...
- 5.GR.D.6
Define the coordinate system as a pair of perpendicular lines called axes that intersect at the origin. Use understandin...
- 5.NOS.A.1
Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to ...
- 5.NOS.A.3.b
Estimate decimal quantities by reasoning about their location on a number line, their relationship to benchmark numbers ...
- 5.NOS.A.3.c
Compare two decimals to thousandths by reasoning about the values of the digits and the location on the number line. Rec...
- 5.NOS.B.4
Fluently multiply multi-digit whole numbers.
- 5.NOS.B.4.a
Apply estimation strategies to estimate products.
- 5.NOS.B.4.b
Use computational strategies (e.g., partial products, doubling and halving) efficiently to multiply.
- 5.NOS.B.4.c
Use a standard algorithm to multiply.
- 5.NOS.B.4.d
Determine and explain when a strategy or algorithm is most efficient.
- 5.NOS.B.5
Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.
- 5.NOS.B.5.a
Apply estimation strategies to estimate quotients.
- 5.NOS.B.5.b
Use partial quotients efficiently to divide.
- 5.NOS.B.5.c
Use properties of operations and/or the inverse relationship between multiplication and division to divide.
- 5.NOS.B.5.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of ...
- 5.NOS.B.6
Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract decimals to hun...
- 5.NOS.B.6.a
Apply estimation strategies to estimate sums and differences of decimals.
- 5.NOS.B.6.b
Use concrete models, drawings, strategies based on place value (e.g., partial sums), properties of operations and/or the...
- 5.NOS.B.6.c
Use an algorithm to add and subtract decimals.
- 5.NOS.B.6.d
Determine and explain when a strategy or algorithm is most efficient.
- 5.NOS.B.7
Apply and extend previous understanding of multiplication and division of whole numbers to multiply and divide decimals ...
- 5.NOS.B.7.a
Apply estimation strategies to estimate products and quotients.
- 5.NOS.B.7.b
Use concrete models, drawings, and arrays to multiply and divide.
- 5.NOS.B.7.c
Use strategies based on place value (e.g., partial products, partial quotients) to multiply and divide.
- 5.NOS.B.7.d
Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.
- 5.NOS.B.7.e
Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multip...
- 5.NOS.C.8
Add and subtract fractions with unlike denominators.
- 5.NOS.C.8.a
Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 2/3 + 3/4...
- 5.NOS.C.8.b
Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compe...
- 5.NOS.C.8.c
Use equivalent fractions to produce an equivalent sum or difference of fractions with like denominators (e.g. 2/3 + 5/4 ...
- 5.NOS.C.9
Solve problems in context involving addition and subtraction of fractions referring to the same whole, including cases o...
- 5.NOS.D.10
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b) in context using visual fraction mode...
- 5.NOS.D.11
Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b).
- 5.NOS.D.11.a
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 3/4 × 2 will be less ...
- 5.NOS.D.11.b
Multiply a whole number by a fraction (e.g., interpret c/d × b as c/d of b when c/d is greater than or less than 1).
- 5.NOS.D.12
Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.
- 5.NOS.D.12.a
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 1/2 × 3/4 will be les...
- 5.NOS.D.12.b
Apply and extend whole number multiplication strategies (e.g. area models).
- 5.NOS.D.12.c
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fractio...
- 5.NOS.D.13
Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factor...
- 5.NOS.D.13.a
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.
- 5.NOS.D.13.b
Apply and extend whole number multiplication strategies (e.g. area model, partial products).
- 5.NOS.D.14
Interpret multiplication as scaling (sizing) in context.
- 5.NOS.D.16
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit...
- 5.NOS.D.16.a
Apply estimation strategies to estimate quotients and assess reasonableness of answers.
- 5.NOS.D.16.b
Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute...
- 5.NOS.D.16.c
Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotient...
- 5.NOS.D.16.d
Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division w...
Grade 6
- 6.AT.A.1
Use ratio language in context (e.g., “__ to __,” “for every,” “per”) to describe a ratio relationship between two quanti...
- 6.AT.A.2
Represent and use unit rates, written as fractions (a/b, b ≠ 0) with whole number numerators and denominators, in contex...
- 6.AT.A.2.a
Use unit rate language in the context of a ratio relationship (e.g., “The recipe has a ratio of 3 cups of flour to 4 cup...
- 6.AT.A.3
Use ratio and rate reasoning to solve problems in context by reasoning about tables of equivalent ratios, tape diagrams,...
- 6.AT.A.3.a
Generate, compare and find missing values of equivalent ratios and unit rates using multiple representations.
- 6.AT.A.3.b
Plot the pairs of values on the Coordinate Plane (in quadrant 1) to represent unit rates and make connections between re...
- 6.AT.A.4
Find a percent of a quantity in context as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity), inc...
- 6.AT.B.5
Write numerical expressions involving whole number exponents and positive rational number bases. Use technology to evalu...
- 6.AT.B.6.c
Evaluate expressions given specific values of their variables in context. Include expressions that involve arithmetic op...
- 6.AT.B.7
Apply the properties of operations (e.g., distributive, associative, commutative, etc.) to generate equivalent algebraic...
- 6.AT.C.10
Solve problems in context by writing and solving inequalities and interpreting solution sets in context.
- 6.AT.C.10.a
Explain that a variable can represent an unknown number in a set and use substitution to determine whether a given numbe...
- 6.AT.C.10.b
Write and solve one-step inequalities of the form x + p > q, x − p > q, px > q and x/p > q (using ≥, >, ≤, <) where p an...
- 6.AT.C.10.c
Represent solutions of such inequalities on a number line.
- 6.AT.C.8
Solve problems in context by writing and solving equations and interpreting the solutions in context.
- 6.AT.C.8.a
Explain that a variable can represent an unknown number and use substitution to determine whether a given number makes a...
- 6.AT.C.8.b
Write and solve one-step equations of the form x + p = q, x − p = q, px = q and x/p = q for cases in which p, q and x ar...
- 6.AT.C.8.c
Represent solutions of such equations on a number line.
- 6.AT.C.9
Write an inequality of the form x > c (using ≥, >, ≤, <) represent a constraint or condition in context. Recognize that ...
- 6.AT.D.11
Use variables to represent two quantities in context that change in relationship to one another.
- 6.AT.D.11.a
Write an equation (one-step) to express one quantity, thought of as the dependent variable, in terms of the other quanti...
- 6.AT.D.11.b
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to th...
- 6.DS.A.2
Use the language of probability (e.g., likely, unlikely, certain, impossible) to describe the likelihood of possible out...
- 6.DS.A.3
Explain how a set of data collected to answer a statistical question has a distribution which can be described by its ce...
- 6.DS.B.5
Interpret numerical data in plots on a number line, including line plots, histograms, and box plots.
- 6.DS.B.6.c
Give quantitative measures of center (median and/or mean) and variability (interquartile range), as well as describing o...
- 6.GR.A.1
Find the area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and ...
- 6.GR.A.2
Find the volume of a right rectangular prism with fractional edge lengths.
- 6.GR.A.2.a
By packing prisms with unit cubes and using estimation to show that the volume can be found by multiplying the edge leng...
- 6.GR.A.2.b
Apply the formulas V = lwh and V = B · h (B is the area of the base) to find the volumes of right rectangular prisms wit...
- 6.GR.A.4
Represent three-dimensional figures (triangular prism, rectangular prism, pyramid) using nets made up of rectangles and ...
- 6.NOS.A.1
Divide fractions by fractions in context.
- 6.NOS.A.1.a
Extend estimation strategies to estimate and assess the reasonableness of quotients.
- 6.NOS.A.1.b
Use and connect concrete and visual fraction models (e.g., linear, regional/area, and set models) and equations to divid...
- 6.NOS.A.1.c
Represent and explain the calculation by connecting fraction models, and/or equations to the meaning of division.
- 6.NOS.B.2
Fluently divide multi-digit numbers.
- 6.NOS.B.2.a
Extend estimation strategies to estimate and assess the reasonableness of quotients.
- 6.NOS.B.2.b
Use strategies (e.g., partial quotients, inverse relationship between multiplication and division) to divide.
- 6.NOS.B.2.c
Use a standard algorithm to divide.
- 6.NOS.B.2.d
Determine and explain when a strategy or algorithm is most efficient.
- 6.NOS.B.3
Fluently multiply and divide multi-digit decimals to the thousandths in context.
- 6.NOS.B.3.a
Extend estimation strategies to estimate and assess the reasonableness of products and quotients.
- 6.NOS.B.3.b
Generalize whole number strategies to multiply and divide decimals.
- 6.NOS.B.3.c
Use a standard algorithm to multiply and divide decimals.
- 6.NOS.B.3.d
Determine and explain when a strategy or algorithm is most efficient.
- 6.NOS.B.4
Identify the common factors and multiples of two whole numbers.
- 6.NOS.B.4.a
Identify the greatest common factor of two whole numbers within 100.
- 6.NOS.B.4.b
Identify the least common multiple of two whole numbers within 12.
- 6.NOS.B.4.c
Express the sum of two whole numbers within 100 using the distributive property to factor out the common factor of the a...
- 6.NOS.C.5
Use understanding of rational numbers as positive and negative numbers to describe quantities having opposite directions...
- 6.NOS.C.6
Represent a rational number as a point on vertical or horizontal number lines. Represent points on a number line with ne...
- 6.NOS.C.6.a
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and by ...
- 6.NOS.C.6.b
Locate and interpret the positions of rational numbers on a number line.
- 6.NOS.C.6.c
Recognize and locate opposite signs of rational numbers as indicating locations on opposite sides of 0 on the number lin...
- 6.NOS.C.7
Intersect perpendicular number lines at the point (0,0) as the x-axis and y-axis to introduce the four quadrants of the ...
- 6.NOS.C.7.a
Use understanding of the relationship between signs and value of coordinates in ordered pairs to reason about the locati...
- 6.NOS.C.7.b
Locate and interpret the positions of rational numbers on the Coordinate Plane, including how changes in the signs of or...
- 6.NOS.C.8
Order and identify the absolute value of rational numbers.
- 6.NOS.C.9
Solve problems in context by graphing points (with the same first coordinate or the same second coordinate) in all four ...
- 6.NOS.C.9.a
Explain that points with the same x-coordinate or y-coordinate are located on same vertical or horizontal line respectiv...
- 6.NOS.C.9.b
Use absolute value to calculate length of vertical and horizontal lines on Coordinate Plane.
Grade 7
- 7.AT.A.2
Identify proportional relationships between quantities.
- 7.AT.A.3
Represent proportional relationships between quantities.
- 7.AT.A.4
Solve ratio and percent problems in context (e.g., simple interest, tax, markups and markdowns, tips, commissions, fees,...
- 7.AT.B.5
subtract, factor, and expand linear expressions with rational coefficients.
- 7.AT.B.6
Rewrite an expression in different forms to shed light on the represented context and how the quantities in it are relat...
- 7.AT.C.7
Analyze contextual situations to determine whether an equation or inequality best represents the relationship between qu...
- 7.AT.C.8
Use variables to represent quantities and write and solve equations to model and reason about relationships in context.
- 7.AT.C.8.a
Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
- 7.AT.C.8.b
Solve equations of these forms flexibly and efficiently. Explain the solution process and how it connects to the origina...
- 7.AT.C.8.c
Solve word problems leading to equations of these forms and interpret the solution in terms of the context.
- 7.AT.C.9
Use variables to represent quantities and write and solve inequalities to model and reason about constraints and conditi...
- 7.AT.C.9.a
Write inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
- 7.AT.C.9.b
Solve inequalities of these forms and graph the solution set on a number line.
- 7.AT.C.9.c
Interpret the solution set in terms of the context by describing what values are possible or reasonable in the given sit...
- 7.DS.A.1
Determine when generalizations about a population are appropriate based on how the sample was selected.
- 7.DS.A.1.a
Decide whether a sample is representative of a population by explaining how it was selected and how that selection affec...
- 7.DS.A.1.b
Explain how a random sample increases the likelihood that the sample represents the population.
- 7.DS.A.2
Use data from random samples to make and evaluate estimates or predictions about a population.
- 7.DS.A.2.a
Use data from a single random sample to estimate an unknown characteristic of a population.
- 7.DS.A.2.b
Generate and compare multiple random samples of the same size and use the variability across samples to assess how relia...
- 7.DS.B.3
Compare two numerical data distributions using visual displays and numerical measures to draw inferences about differenc...
- 7.DS.B.3.a
Use histograms and other visualizations to describe similarities and differences in the range, shape, and clustering of ...
- 7.DS.B.3.b
Use measures of center (e.g., mean or median) and measures of variability (e.g., range or interquartile range) to descri...
- 7.DS.B.3.c
Use both visual and numerical comparisons to describe how different the two groups are and whether the difference is mea...
- 7.DS.C.4
Explain that a probability of 0 means the event is impossible, 1 means it is certain, and values closer to 0 or 1 indica...
- 7.DS.C.5
Understand and apply long-run relative frequency to approximate probabilities and make predictions about chance events.
- 7.DS.C.5.a
Use data collection or simulation to approximate the probability of a chance event by observing its long-run relative fr...
- 7.DS.C.5.b
Use a known or estimated probability to evaluate whether the number of outcomes in a given number of simulation trials i...
- 7.DS.C.5.c
Use visual representations (e.g., bar graphs, circle graphs) to compare and interpret probabilities.
- 7.DS.C.6
Develop and use probability models to find probabilities of events and compare them to observed results.
- 7.DS.C.6.c
Compare probabilities from a model to observed data and explain possible reasons for any differences.
- 7.GR.A.2
Describe the two-dimensional figures that result from slicing three-dimensional figures (e.g., right rectangular prisms,...
- 7.GR.B.3
Apply the formulas for the area and circumference of a circle to solve problems in context. Use informal reasoning and v...
- 7.GR.B.4
Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensio...
- 7.GR.B.4.a
Solve problems involving area, surface area, and volume of polygonal figures and polyhedral solids, including triangles,...
- 7.GR.B.4.b
Solve problems involving volume of curved-surface solids, including cones, cylinders, and spheres—figures without edges.
- 7.GR.B.4.c
Interpret and justify solutions in context by comparing different geometric representations, estimating or checking for ...
- 7.NOS.A.1
Add and subtract rational numbers using multiple strategies and representations.
- 7.NOS.A.1.b
Model the addition of rational numbers as movement along a number line, where the direction and distance depend on the s...
- 7.NOS.A.1.c
Rewrite subtraction as addition using the additive inverse (p − q = p + (−q)). Use strategies such as number lines and a...
- 7.NOS.A.1.d
Model and solve multistep contextual problems involving addition and subtraction of rational numbers, using efficient an...
- 7.NOS.A.2
Multiply and divide rational numbers using multiple strategies and representations.
- 7.NOS.A.2.a
Model multiplication of rational numbers using number lines, arrays, or area models to show how properties of operations...
- 7.NOS.A.2.b
Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as ...
- 7.NOS.A.2.c
Use properties of operations to multiply and divide rational numbers flexibly and efficiently.
- 7.NOS.A.2.d
Analyze the decimal representation of a quotient resulting from dividing rational numbers to determine whether it termin...
- 7.NOS.A.2.e
Model and solve multistep contextual problems involving multiplication and division of rational numbers, using efficient...
- 7.NOS.A.3
Solve multistep problems involving positive and negative rational numbers in any form (i.e., fractions, decimals, percen...
- 7.NOS.A.3.a
Apply properties of operations to efficiently compute with rational numbers and convert between forms when appropriate t...
- 7.NOS.A.3.b
Evaluate the reasonableness of solutions using estimation, mental math, and understanding of the context.
Grade 8
- 8.AT.A.1
Analyze and compare proportional relationships using slope.
- 8.AT.A.1.a
Graph proportional relationships and interpret the unit rate as the slope of the graph.
- 8.AT.A.1.b
Compare proportional relationships represented in different forms (e.g., graphs, equations, and tables) by analyzing the...
- 8.AT.A.2
Use proportional reasoning to identify slope and represent linear relationships.
- 8.AT.A.2.a
Use proportional reasoning to explain why the slope m is the same between any two points on a non-vertical line by showi...
- 8.AT.A.2.b
Use this relationship to write equations of lines in the form y = mx for lines that pass through the origin, and in the ...
- 8.AT.B.3.a
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solution. Justify ...
- 8.AT.B.4
Solve linear inequalities in one variable.
- 8.AT.B.4.a
Solve inequalities including those requiring the use of the distributive property and combining like terms.
- 8.AT.B.4.b
Represent the solution set on a number line and describe the set of possible values in the context of the problem.
- 8.AT.B.5.a
Interpret the solution to a system of two linear equations as the point where their graphs intersect and verify that the...
- 8.AT.B.5.b
Solve systems of two linear equations by graphing and substitution. When using graphing, find an approximate or exact so...
- 8.AT.B.5.c
Use structure to determine when a system has no solution, one solution, or infinitely many solutions and justify the con...
- 8.AT.B.5.d
Model and solve contextual problems using systems of two linear equations.
- 8.AT.C.6
Determine whether a relationship is a function by analyzing whether each input is assigned to exactly one output.
- 8.AT.C.6.a
Given a clearly defined set of input-output pairs in a table, mapping, or real-world description, determine whether the ...
- 8.AT.C.6.b
Given a graph, identify input-output pairs and determine whether the graph represents a function.
- 8.AT.C.7
Compare the properties (i.e., rate of change, intercepts) of two linear functions each represented in a different way (a...
- 8.AT.C.8
Identify whether a function is linear or non-linear given equations, graphs, or input-output pairs, and provide a justif...
- 8.AT.D.10
Construct and interpret a linear function to model a relationship between two quantities.
- 8.AT.D.10.a
Given two input-output pairs, a graph, a table, or a description of a relationship, determine the rate of change and ini...
- 8.AT.D.10.b
Interpret the rate of change and initial value in the context of the problem.
- 8.AT.D.9
Interpret the graph of a linear function in the form y = mx + b
- 8.AT.D.9.a
Given the graph of a linear function, identify the slope and y-intercept.
- 8.AT.D.9.b
Match a linear equation in the form y = mx + b to its graph.
- 8.DS.A.1
Evaluate predictions and conclusions drawn from bivariate data.
- 8.DS.A.1.a
Determine whether observed associations in sample data justify generalizations about a broader population.
- 8.DS.A.1.b
Identify limitations or potential bias in data collection or interpretation when analyzing trends in scatter plots.
- 8.DS.B.3
Compare the fit of different linear models shown on scatter plots of the same data by describing the overall pattern and...
- 8.DS.B.4
Use a provided linear model to make predictions based on bivariate measurement data. Interpret the meaning of the slope ...
- 8.DS.C.6
Find probabilities of compound events by representing or simulating the sample space or simulating events.
- 8.DS.C.6.a
Represent the sample space for a compound event using organized lists, tables, or tree diagrams. Given an event describe...
- 8.DS.C.6.b
Determine the probability of a compound event as a fraction of outcomes in the sample space that result in the event.
- 8.GR.A.1
Use the relationships between supplementary, complementary, vertical, and adjacent angles to write and solve equations f...
- 8.GR.A.2
Draw or build triangles using tools (ruler, protractor, technology, or physical manipulatives) given three measures of a...
- 8.GR.A.3
Use informal arguments to verify that the sum of the interior angles of a triangle is 180 degrees and why an exterior an...
- 8.GR.B.4
Understand and reason about the Pythagorean Theorem and its extensions.
- 8.GR.B.4.a
Use diagrams, examples, or informal reasoning to explain the Pythagorean Theorem and why it applies to all right triangl...
- 8.GR.B.4.b
Use the converse of the Pythagorean Theorem to determine whether a set of three side lengths forms a right triangle, and...
- 8.GR.B.5
Apply the Pythagorean Theorem to solve problems in context.
- 8.GR.B.5.a
Determine unknown side lengths in right triangles.
- 8.NOS.A.1
Identify a number as irrational when its decimal expansion neither terminates nor repeats, and explain that irrational n...
- 8.NOS.A.2
Use rational approximations of irrational numbers to estimate their locations on a number line, compare their size, and ...
- 8.NOS.B.4
Use square and cube roots to represent solutions to equations and describe numbers.
- 8.NOS.B.4.a
Use square and cube roots symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positi...
- 8.NOS.B.4.b
Evaluate square roots of perfect squares from 1 to 100 and cube roots of perfect cubes from 1 to 125 by inspection.
- 8.NOS.B.5
Apply scientific notation to represent and compare very large and very small quantities in context, and use technology t...
- 8.NOS.B.5.a
Express numbers as a single digit times an integer power of 10 to estimate and compare magnitudes.
- 8.NOS.B.5.b
Use scientific notation to model and compute with real-world quantities, choose appropriate units, and interpret their m...
High School
- A.CED.A.1.a
Create equations and inequalities in one variable and use them to solve problems.
- A.CED.A.1.b
Create polynomial equations given roots.
- A.REI.C.7.a
Solve systems of equations comprised of various combinations of all algebraic and transcendental functions in two variab...
- A.SSE.A.2.a
Analyze the structure of the general form of a second degree equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0, to identify th...
- A.SSE.B.3.d
Choose and produce an equivalent form of a second degree equation, Ax² + Cy² + Dx + Ey + F = 0, to reveal and explain pr...
- A.SSE.B.3.e
Translate between the standard and general form, Ax² + Cy² + Dx + Ey + F = 0, of a second degree equation.
- A.SSE.B.4.a
Express the sums in a series using sigma notation.
- A.SSE.B.5
Determine the sum, if it exists, of an infinite geometric series.
- F.BF.A.1.c
Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the he...
- F.BF.B.4.e
Build inverse trigonometric functions.
- F.IF.A.2.a
Extend evaluating functions to include operations with composite functions, e.g. f(x + 2) − f(x).
- F.IF.C.10
Describe the behavior of a sequence.
- F.IF.C.7.f
Graph all functions including piecewise-defined functions, step functions and absolute value functions
- F.IF.C.7.g
Determine the end behavior of the graph of a polynomial function using the degree and leading coefficient.
- F.IF.C.8.c
Interpret the behavior of the graph of a function using the concept of limits.
- F.IF.C.8.d
Estimate limits algebraically, numerically and graphically.
- F.LE.A.1.d
Distinguish between situations that can be modeled with exponential functions and logistic functions.
- F.LE.A.4.a
Use properties of logarithms, including both common and natural logarithms, to rewrite and solve exponential models.
- F.LE.B.5.a
Interpret the parameters in a logistic function in terms of a context.
- F.LE.B.6
Build and interpret logistic functions to model real-world problems.
- F.LE.B.6.a
Sketch and analyze the graphs of logistic functions.
- F.LE.B.6.b
Compare and contrast the exponential, logarithmic, and logistic models.
- F.LE.B.6.c
Apply understanding of logarithmic and logistic functions to solve real-world problems.
- F.TF.A.3
Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6 and use the u...
- F.TF.C.9.a
Use trigonometric identities to rewrite expressions and as a tool when solving trigonometric equations.
- G.GMD.A.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, py...
- G.GMD.B.4.a
Identify the shapes of two-dimensional cross-sections of a right double cone.
- G.GPE.C.10
Plot points on a polar coordinate grid.
- G.GPE.C.8
Understand the relationship between polar coordinates and Cartesian coordinates.
- G.GPE.C.9
Convert between polar and rectangular coordinates.
- G.GPE.D.11
Convert equations between polar and rectangular forms.
- G.GPE.D.12
Graph polar equations by hand and using technology.
- G.GPE.D.13
Solve systems of polar equations.
- N.OA.A.1
Use the notation for the factorial of a non-negative integer, n!, to evaluate expressions.
- N.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitat...
- N.VM.B.5.c
Determine the dot product of two vectors.
- P.CED.A.1
Create a single equation, using rectangular coordinates, that is equivalent to a pair of parametric equations.
- P.CED.A.2
Given a data set, create a parametric equation and a single equation using rectangular coordinates to fit the data.
- P.IPE.A.1
Sketch the curve defined by parametric equations.
- P.IPE.A.2
Use parametric equations to model and solve motion problems.
- S.IC.A.1.a
Introduce sampling distributions as a means to explore variability in sample statistics and ultimately evaluate a claim ...
- S.IC.B.7
Conduct statistical investigations.
- S.IC.B.7.a
Conduct observational studies.
- S.IC.B.7.b
Conduct statistical experiments.
- S.ID.B.6.d
Fit a function to data represented by a scatterplot; use functions fitted to data to solve problems in the context of th...