Texas Essential Knowledge and Skills for Mathematics
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 tea.texas.gov.
Kindergarten
- K.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- K.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- K.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- K.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- K.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- K.1.E
create and use representations to organize, record, and communicate mathematical ideas
- K.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- K.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- K.2
The student applies mathematical process standards to understand how to represent and compare whole numbers, the relativ...
- K.2.A
count forward and backward to at least 20 with and without objects
- K.2.B
read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
- K.2.C
count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the se...
- K.2.D
recognize instantly the quantity of a small group of objects in organized and random arrangements
- K.2.E
generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a...
- K.2.F
generate a number that is one more than or one less than another number up to at least 20
- K.2.G
compare sets of objects up to at least 20 in each set using comparative language
- K.2.H
use comparative language to describe two numbers up to 20 presented as written numerals
- K.2.I
compose and decompose numbers up to 10 with objects and pictures
- K.3
The student applies mathematical process standards to develop an understanding of addition and subtraction situations in...
- K.3.A
model the action of joining to represent addition and the action of separating to represent subtraction
- K.3.B
solve word problems using objects and drawings to find sums up to 10 and differences within 10
- K.3.C
explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete an...
- K.4
The student applies mathematical process standards to identify coins in order to recognize the need for monetary transac...
- K.5
The student applies mathematical process standards to identify the pattern in the number word list. The student is expec...
- K.6
The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional...
- K.6.A
identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles
- K.6.B
identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world
- K.6.C
identify two-dimensional components of three-dimensional objects
- K.6.D
identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably
- K.6.E
classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or siz...
- K.6.F
create two-dimensional shapes using a variety of materials and drawings
- K.7
The student applies mathematical process standards to directly compare measurable attributes
- K.7.A
give an example of a measurable attribute of a given object, including length, capacity, and weight
- K.7.B
compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describ...
- K.8
The student applies mathematical process standards to collect and organize data to make it useful for interpreting infor...
- K.8.A
collect, sort, and organize data into two or three categories
- K.8.B
use data to create real-object and picture graphs
- K.8.C
draw conclusions from real-object and picture graphs
- K.9
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financia...
- K.9.A
identify ways to earn income
- K.9.B
differentiate between money received as income and money received as gifts
- K.9.C
list simple skills required for jobs
- K.9.D
distinguish between wants and needs and identify income as a source to meet one's wants and needs
Grade 1
- 1.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 1.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 1.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 1.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 1.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 1.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 1.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 1.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 1.2
The student applies mathematical process standards to represent and compare whole numbers, the relative position and ma...
- 1.2.A
recognize instantly the quantity of structured arrangements
- 1.2.B
use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, s...
- 1.2.C
use objects, pictures, and expanded and standard forms to represent numbers up to 120
- 1.2.D
generate a number that is greater than or less than a given whole number up to 120
- 1.2.E
use place value to compare whole numbers up to 120 using comparative language
- 1.2.F
order whole numbers up to 120 using place value and open number lines
- 1.2.G
represent the comparison of two numbers to 100 using the symbols >, <, or =
- 1.3
The student applies mathematical process standards to develop and use strategies for whole number addition and subtracti...
- 1.3.A
use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99
- 1.3.B
use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and ...
- 1.3.C
compose 10 with two or more addends with and without concrete objects
- 1.3.D
apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10
- 1.3.E
explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial model...
- 1.3.F
generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 2...
- 1.4
The student applies mathematical process standards to identify coins, their values, and the relationships among them in ...
- 1.4.A
identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them
- 1.4.B
write a number with the cent symbol to describe the value of a coin
- 1.4.C
use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or d...
- 1.5
The student applies mathematical process standards to identify and apply number patterns within properties of numbers an...
- 1.5.A
recite numbers forward and backward from any given number between 1 and 120
- 1.5.B
skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set
- 1.5.C
use relationships to determine the number that is 10 more and 10 less than a given number up to 120
- 1.5.D
represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models...
- 1.5.E
understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the ...
- 1.5.F
determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three o...
- 1.5.G
apply properties of operations to add and subtract two or three numbers
- 1.6
The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional...
- 1.6.A
classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language
- 1.6.B
distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not defi...
- 1.6.C
create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses,...
- 1.6.D
identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses...
- 1.6.E
identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triang...
- 1.6.F
compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if ...
- 1.6.G
partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words
- 1.6.H
identify examples and non-examples of halves and fourths
- 1.7
The student applies mathematical process standards to select and use units to describe length and time
- 1.7.A
use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement;
- 1.7.B
illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no ga...
- 1.7.C
measure the same object/distance with units of two different lengths and describe how and why the measurements differ
- 1.7.D
describe a length to the nearest whole unit using a number and a unit
- 1.7.E
tell time to the hour and half hour using analog and digital clocks
- 1.8
The student applies mathematical process standards to organize data to make it useful for interpreting information and s...
- 1.8.A
collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts
- 1.8.B
use data to create picture and bar-type graphs
- 1.8.C
draw conclusions and generate and answer questions using information from picture and bar-type graphs
- 1.9
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financia...
- 1.9.A
define money earned as income
- 1.9.B
identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs
- 1.9.C
distinguish between spending and saving
- 1.9.D
consider charitable giving
Grade 2
- 2.10.A
explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data ...
- 2.10.B
organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more
- 2.10.C
write and solve one-step word problems involving addition or subtraction using data represented within pictographs and b...
- 2.10.D
draw conclusions and make predictions from information in a graph
- 2.11.A
calculate how money saved can accumulate into a larger amount over time
- 2.11.B
explain that saving is an alternative to spending
- 2.11.C
distinguish between a deposit and a withdrawal
- 2.11.D
identify examples of borrowing and distinguish between responsible and irresponsible borrowing
- 2.11.E
identify examples of lending and use concepts of benefits and costs to evaluate lending decisions
- 2.11.F
differentiate between producers and consumers and calculate the cost to produce a simple item
- 2.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 2.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 2.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 2.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 2.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 2.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 2.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 2.2.A
use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many ...
- 2.2.B
use standard, word, and expanded forms to represent numbers up to 1,200
- 2.2.C
generate a number that is greater than or less than a given whole number up to 1,200
- 2.2.D
use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, o...
- 2.2.E
locate the position of a given whole number on an open number line
- 2.2.F
name the whole number that corresponds to a specific point on a number line
- 2.3.A
partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words
- 2.3.B
explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, t...
- 2.3.C
use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equa...
- 2.3.D
identify examples and non-examples of halves, fourths, and eighths
- 2.4.A
recall basic facts to add and subtract within 20 with automaticity
- 2.4.B
add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledg...
- 2.4.C
solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategie...
- 2.4.D
generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of who...
- 2.5.A
determine the value of a collection of coins up to one dollar; and
- 2.5.B
use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins.
- 2.6.A
model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined
- 2.6.B
model, create, and describe contextual division situations in which a set of concrete objects is separated into equivale...
- 2.7.A
determine whether a number up to 40 is even or odd using pairings of objects to represent the number
- 2.7.B
use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,2...
- 2.7.C
represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem
- 2.8.A
create two-dimensional shapes based on given attributes, including number of sides and vertices
- 2.8.B
classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as ...
- 2.8.C
classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and...
- 2.8.D
compose two-dimensional shapes and three-dimensional solids with given properties or attributes
- 2.8.E
decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitionin...
- 2.9.A
find the length of objects using concrete models for standard units of length
- 2.9.B
describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an ...
- 2.9.C
represent whole numbers as distances from any given location on a number line
- 2.9.D
determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes
- 2.9.E
determine a solution to a problem involving length, including estimating lengths
- 2.9.F
use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to...
- 2.9.G
read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and...
Grade 3
- 3.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 3.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 3.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 3.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 3.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 3.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 3.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 3.2.A
compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so m...
- 3.2.B
describe the mathematical relationships found in the base-10 place value system through the hundred thousands place
- 3.2.C
represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use word...
- 3.2.D
compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =
- 3.3.A
represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concret...
- 3.3.B
determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, an...
- 3.3.C
explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into ...
- 3.3.D
compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/...
- 3.3.E
solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial represe...
- 3.3.F
represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, i...
- 3.3.G
explain that two fractions are equivalent if and only if they are both represented by the same point on the number line ...
- 3.3.H
compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying...
- 3.4.A
solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based...
- 3.4.B
round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems
- 3.4.C
determine the value of a collection of coins and bills
- 3.4.D
determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 b...
- 3.4.E
represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, a...
- 3.4.F
recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts
- 3.4.G
use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. S...
- 3.4.H
determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects...
- 3.4.I
determine if a number is even or odd using divisibility rules
- 3.4.J
determine a quotient using the relationship between multiplication and division
- 3.4.K
solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects;...
- 3.5
The student applies mathematical process standards to analyze and create patterns and relationships
- 3.5.A
represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models...
- 3.5.B
represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and ...
- 3.5.C
describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24
- 3.5.D
determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknow...
- 3.5.E
represent real-world relationships using number pairs in a table and verbal descriptions
- 3.6
The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop...
- 3.6.B
use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals...
- 3.6.C
determine the area of rectangles with whole number side lengths in problems using multiplication related to the number o...
- 3.6.D
decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original f...
- 3.6.E
decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit ...
- 3.7
The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems ...
- 3.7.A
represent fractions of halves, fourths, and eighths as distances from zero on a number line
- 3.7.B
determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems
- 3.7.C
determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial mode...
- 3.7.D
determine when it is appropriate to use measurements of liquid volume (capacity) or weight
- 3.7.E
determine liquid volume (capacity) or weight using appropriate units and tools
- 3.8
The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpre...
- 3.8.A
summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled in...
- 3.8.B
solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar...
- 3.9
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financia...
- 3.9.A
explain the connection between human capital/labor and income
- 3.9.B
describe the relationship between the availability or scarcity of resources and how that impacts cost
- 3.9.C
identify the costs and benefits of planned and unplanned spending decisions
- 3.9.D
explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility t...
- 3.9.E
list reasons to save and explain the benefit of a savings plan, including for college
- 3.9.F
identify decisions involving income, spending, saving, credit, and charitable giving
Grade 4
- 4.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 4.10
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financia...
- 4.10.A
distinguish between fixed and variable expenses
- 4.10.B
calculate profit in a given situation
- 4.10.C
compare the advantages and disadvantages of various savings options
- 4.10.D
describe how to allocate a weekly allowance among spending; saving, including for college; and sharing
- 4.10.E
describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending
- 4.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 4.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 4.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 4.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 4.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 4.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 4.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 4.2
The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and under...
- 4.2.A
interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of ...
- 4.2.B
represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded no...
- 4.2.C
compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =
- 4.2.D
round whole numbers to a given place value through the hundred thousands place
- 4.2.E
represent decimals, including tenths and hundredths, using concrete and visual models and money
- 4.2.F
compare and order decimals using concrete and visual models to the hundredths
- 4.2.G
relate decimals to fractions that name tenths and hundredths
- 4.2.H
determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line
- 4.3
The student applies mathematical process standards to represent and generate fractions to solve problems
- 4.3.A
represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b
- 4.3.B
decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial...
- 4.3.C
determine if two given fractions are equivalent using a variety of methods
- 4.3.D
compare two fractions with different numerators and different denominators and represent the comparison using the symbol...
- 4.3.E
represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models tha...
- 4.3.F
evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, refe...
- 4.3.G
represent fractions and decimals to the tenths or hundredths as distances from zero on a number line
- 4.4
The student applies mathematical process standards to develop and use strategies and methods for whole number computatio...
- 4.4.A
add and subtract whole numbers and decimals to the hundredths place using the standard algorithm
- 4.4.B
determine products of a number and 10 or 100 using properties of operations and place value understandings
- 4.4.C
represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through ...
- 4.4.D
use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit nu...
- 4.4.E
represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models,...
- 4.4.F
use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit di...
- 4.4.G
round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers
- 4.4.H
solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders
- 4.5
The student applies mathematical process standards to develop concepts of expressions and equations
- 4.5.A
represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a...
- 4.5.B
represent problems using an input-output table and numerical expressions to generate a number pattern that follows a giv...
- 4.5.C
use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special ...
- 4.5.D
solve problems related to perimeter and area of rectangles where dimensions are whole numbers
- 4.6
The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations ...
- 4.6.A
identify points, lines, line segments, rays, angles, and perpendicular and parallel lines
- 4.6.B
identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure
- 4.6.C
apply knowledge of right angles to identify acute, right, and obtuse triangles
- 4.6.D
classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or ...
- 4.7
The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees
- 4.7.A
illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" ...
- 4.7.B
illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cut...
- 4.7.C
determine the approximate measures of angles in degrees to the nearest whole number using a protractor
- 4.7.D
draw an angle with a given measure
- 4.7.E
determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures
- 4.8
The student applies mathematical process standards to select appropriate customary and metric units, strategies, and too...
- 4.8.A
identify relative sizes of measurement units within the customary and metric systems
- 4.8.B
convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or ...
- 4.8.C
solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition,...
- 4.9
The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpre...
- 4.9.A
represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions
- 4.9.B
solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, ...
Grade 5
- 5.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 5.10
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financia...
- 5.10.A
define income tax, payroll tax, sales tax, and property tax
- 5.10.B
explain the difference between gross income and net income
- 5.10.C
identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and...
- 5.10.D
develop a system for keeping and using financial records
- 5.10.E
describe actions that might be taken to balance a budget when expenses exceed income
- 5.10.F
balance a simple budget
- 5.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 5.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 5.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 5.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 5.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 5.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 5.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 5.2
The student applies mathematical process standards to represent, compare, and order positive rational numbers and unders...
- 5.2.A
represent the value of the digit in decimals through the thousandths using expanded notation and numerals
- 5.2.B
compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =
- 5.2.C
round decimals to tenths or hundredths
- 5.3
The student applies mathematical process standards to develop and use strategies and methods for positive rational numbe...
- 5.3.A
estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication,...
- 5.3.B
multiply with fluency a three-digit number by a two-digit number using the standard algorithm
- 5.3.C
solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the stan...
- 5.3.D
represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area ...
- 5.3.E
solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-...
- 5.3.F
represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using...
- 5.3.G
solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using...
- 5.3.H
represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using ob...
- 5.3.I
represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pict...
- 5.3.J
represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/...
- 5.3.K
add and subtract positive rational numbers fluently
- 5.3.L
divide whole numbers by unit fractions and unit fractions by whole numbers
- 5.4
The student applies mathematical process standards to develop concepts of expressions and equations
- 5.4.A
identify prime and composite numbers
- 5.4.B
represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter s...
- 5.4.C
generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph
- 5.4.D
recognize the difference between additive and multiplicative numerical patterns given in a table or graph
- 5.4.E
describe the meaning of parentheses and brackets in a numeric expression
- 5.4.F
simplify numerical expressions that do not involve exponents, including up to two levels of grouping
- 5.4.G
use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the s...
- 5.4.H
represent and solve problems related to perimeter and/or area and related to volume
- 5.5
The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The...
- 5.6
The student applies mathematical process standards to understand, recognize, and quantify volume
- 5.6.A
recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-d...
- 5.6.B
determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers t...
- 5.7
The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems ...
- 5.8
The student applies mathematical process standards to identify locations on a coordinate plane
- 5.8.A
describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection ...
- 5.8.B
describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane
- 5.8.C
graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world pr...
- 5.9
The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpr...
- 5.9.A
represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements i...
- 5.9.B
represent discrete paired data on a scatterplot
- 5.9.C
solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterp...
Grade 6
- 6.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 6.10
The student applies mathematical process standards to use equations and inequalities to solve problems
- 6.10.A
model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
- 6.10.B
determine if the given value(s) make(s) one-variable, one-step equations or inequalities true
- 6.11
The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The stud...
- 6.12
The student applies mathematical process standards to use numerical or graphical representations to analyze problems
- 6.12.A
represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots
- 6.12.B
use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution
- 6.12.C
summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and in...
- 6.12.D
summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each cat...
- 6.13
The student applies mathematical process standards to use numerical or graphical representations to solve problems
- 6.13.A
interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots
- 6.13.B
distinguish between situations that yield data with and without variability
- 6.14
The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in ...
- 6.14.A
compare the features and costs of a checking account and a debit card offered by different local financial institutions
- 6.14.B
distinguish between debit cards and credit cards
- 6.14.C
balance a check register that includes deposits, withdrawals, and transfers
- 6.14.D
explain why it is important to establish a positive credit history
- 6.14.E
describe the information in a credit report and how long it is retained
- 6.14.F
describe the value of credit reports to borrowers and to lenders
- 6.14.G
explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-stu...
- 6.14.H
compare the annual salary of several occupations requiring various levels of post-secondary education or vocational trai...
- 6.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 6.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 6.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 6.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 6.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 6.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 6.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 6.2
The student applies mathematical process standards to represent and use rational numbers in a variety of forms
- 6.2.A
classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe ...
- 6.2.B
identify a number, its opposite, and its absolute value
- 6.2.C
locate, compare, and order integers and rational numbers using a number line
- 6.2.D
order a set of rational numbers arising from mathematical and real-world contexts
- 6.2.E
extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b...
- 6.3
The student applies mathematical process standards to represent addition, subtraction, multiplication, and division whil...
- 6.3.A
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
- 6.3.B
determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, inc...
- 6.3.C
represent integer operations with concrete models and connect the actions with the models to standardized algorithms
- 6.3.D
add, subtract, multiply, and divide integers fluently
- 6.3.E
multiply and divide positive rational numbers fluently
- 6.4
The student applies mathematical process standards to develop an understanding of proportional relationships in problem ...
- 6.4.A
compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to di...
- 6.4.B
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios ...
- 6.4.C
give examples of ratios as multiplicative comparisons of two quantities describing the same attribute
- 6.4.D
give examples of rates as the comparison by division of two quantities having different attributes, including rates as q...
- 6.4.E
represent ratios and percents with concrete models, fractions, and decimals
- 6.4.F
represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 g...
- 6.4.G
generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involv...
- 6.4.H
convert units within a measurement system, including the use of proportions and unit rates
- 6.5
The student applies mathematical process standards to solve problems involving proportional relationships
- 6.5.A
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and propo...
- 6.5.B
solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the perce...
- 6.5.C
use equivalent fractions, decimals, and percents to show equal parts of the same whole
- 6.6
The student applies mathematical process standards to use multiple representations to describe algebraic relationships
- 6.6.A
identify independent and dependent quantities from tables and graphs
- 6.6.B
write an equation that represents the relationship between independent and dependent quantities from a table
- 6.6.C
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
- 6.7
The student applies mathematical process standards to develop concepts of expressions and equations
- 6.7.A
generate equivalent numerical expressions using order of operations, including whole number exponents and prime factoriz...
- 6.7.B
distinguish between expressions and equations verbally, numerically, and algebraically
- 6.7.C
determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations
- 6.7.D
generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and dis...
- 6.8
The student applies mathematical process standards to use geometry to represent relationships and solve problems
- 6.8.A
extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship...
- 6.8.B
model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes
- 6.8.C
write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and...
- 6.8.D
determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume ...
- 6.9
The student applies mathematical process standards to use equations and inequalities to represent situations
- 6.9.A
write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
- 6.9.B
represent solutions for one-variable, one-step equations and inequalities on number lines
- 6.9.C
write corresponding real-world problems given one-variable, one-step equations or inequalities
Grade 7
- 7.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 7.10
The student applies mathematical process standards to use one-variable equations and inequalities to represent situation...
- 7.10.A
write one-variable, two-step equations and inequalities to represent constraints or conditions within problems
- 7.10.B
represent solutions for one-variable, two-step equations and inequalities on number lines
- 7.10.C
write a corresponding real-world problem given a one-variable, two-step equation or inequality
- 7.11
The student applies mathematical process standards to solve one-variable equations and inequalities
- 7.11.A
model and solve one-variable, two-step equations and inequalities
- 7.11.B
determine if the given value(s) make(s) one-variable, two-step equations and inequalities true
- 7.11.C
write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationship...
- 7.12
The student applies mathematical process standards to use statistical representations to analyze data
- 7.12.A
compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spre...
- 7.12.B
use data from a random sample to make inferences about a population
- 7.12.C
compare two populations based on data in random samples from these populations, including informal comparative inference...
- 7.13
The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in ...
- 7.13.A
calculate the sales tax for a given purchase and calculate income tax for earned wages
- 7.13.B
identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies...
- 7.13.C
create and organize a financial assets and liabilities record and construct a net worth statement
- 7.13.D
use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to m...
- 7.13.E
calculate and compare simple interest and compound interest earnings
- 7.13.F
analyze and compare monetary incentives, including sales, rebates, and coupons
- 7.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 7.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 7.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 7.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 7.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 7.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 7.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 7.2
The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The stu...
- 7.3
The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and jus...
- 7.3.A
add, subtract, multiply, and divide rational numbers fluently
- 7.3.B
apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, an...
- 7.4
The student applies mathematical process standards to represent and solve problems involving proportional relationships
- 7.4.A
represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, gr...
- 7.4.B
calculate unit rates from rates in mathematical and real-world problems
- 7.4.C
determine the constant of proportionality (k = y/x) within mathematical and real-world problems
- 7.4.D
solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and perce...
- 7.4.E
convert between measurement systems, including the use of proportions and the use of unit rates
- 7.5
The student applies mathematical process standards to use geometry to describe or solve problems involving proportional ...
- 7.5.A
generalize the critical attributes of similarity, including ratios within and between similar shapes
- 7.5.B
describe π as the ratio of the circumference of a circle to its diameter
- 7.5.C
solve mathematical and real-world problems involving similar shape and scale drawings
- 7.6
The student applies mathematical process standards to use probability and statistics to describe or solve problems invol...
- 7.6.A
represent sample spaces for simple and compound events using lists and tree diagrams
- 7.6.B
select and use different simulations to represent simple and compound events with and without technology
- 7.6.C
make predictions and determine solutions using experimental data for simple and compound events
- 7.6.D
make predictions and determine solutions using theoretical probability for simple and compound events
- 7.6.E
find the probabilities of a simple event and its complement and describe the relationship between the two
- 7.6.F
use data from a random sample to make inferences about a population
- 7.6.G
solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-p...
- 7.6.H
solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and
- 7.6.I
determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.
- 7.7
The student applies mathematical process standards to represent linear relationships using multiple representations. The...
- 7.8
The student applies mathematical process standards to develop geometric relationships with volume
- 7.8.A
model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases a...
- 7.8.B
explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid hav...
- 7.8.C
use models to determine the approximate formulas for the circumference and area of a circle and connect the models to th...
- 7.9
The student applies mathematical process standards to solve geometric problems
- 7.9.A
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyram...
- 7.9.B
determine the circumference and area of circles
- 7.9.C
determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, tria...
- 7.9.D
solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular pris...
Grade 8
- 8.1
The student uses mathematical processes to acquire and demonstrate mathematical understanding
- 8.10
The student applies mathematical process standards to develop transformational geometry concepts
- 8.10.A
generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-di...
- 8.10.B
differentiate between transformations that preserve congruence and those that do not
- 8.10.C
explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360...
- 8.10.D
model the effect on linear and area measurements of dilated two-dimensional shapes
- 8.11
The student applies mathematical process standards to use statistical procedures to describe data
- 8.11.A
construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, a...
- 8.11.B
determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean ...
- 8.11.C
simulate generating random samples of the same size from a population with known characteristics to develop the notion o...
- 8.12
The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in ...
- 8.12.A
solve real-world problems comparing how interest rate and loan length affect the cost of credit
- 8.12.B
calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of intere...
- 8.12.C
explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time
- 8.12.D
calculate and compare simple interest and compound interest earnings
- 8.12.E
identify and explain the advantages and disadvantages of different payment methods
- 8.12.F
analyze situations to determine if they represent financially responsible decisions and identify the benefits of financi...
- 8.12.G
estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic sa...
- 8.1.A
apply mathematics to problems arising in everyday life, society, and the workplace
- 8.1.B
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- 8.1.C
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, in...
- 8.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, dia...
- 8.1.E
create and use representations to organize, record, and communicate mathematical ideas
- 8.1.F
analyze mathematical relationships to connect and communicate mathematical ideas
- 8.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral co...
- 8.2
The student applies mathematical process standards to represent and use real numbers in a variety of forms
- 8.2.A
extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of re...
- 8.2.B
approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that ra...
- 8.2.C
convert between standard decimal notation and scientific notation
- 8.2.D
order a set of real numbers arising from mathematical and real-world contexts
- 8.3
The student applies mathematical process standards to use proportional relationships to describe dilations
- 8.3.A
generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
- 8.3.B
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
- 8.3.C
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimension...
- 8.4
The student applies mathematical process standards to explain proportional and non-proportional relationships involving ...
- 8.4.A
use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-value...
- 8.4.B
graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
- 8.4.C
use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world p...
- 8.5
The student applies mathematical process standards to use proportional and non-proportional relationships to develop fou...
- 8.5.A
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
- 8.5.B
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
- 8.5.C
contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a lin...
- 8.5.D
use a trend line that approximates the linear relationship between bivariate sets of data to make predictions
- 8.5.E
solve problems involving direct variation
- 8.5.F
distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx ...
- 8.5.G
identify functions using sets of ordered pairs, tables, mappings, and graphs
- 8.5.H
identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems
- 8.5.I
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, ...
- 8.6
The student applies mathematical process standards to develop mathematical relationships and make connections to geometr...
- 8.6.A
describe the volume formula V = Bh of a cylinder in terms of its base area and its height
- 8.6.B
model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect t...
- 8.6.C
use models and diagrams to explain the Pythagorean theorem
- 8.7
The student applies mathematical process standards to use geometry to solve problems
- 8.7.A
solve problems involving the volume of cylinders, cones, and spheres
- 8.7.B
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determ...
- 8.7.C
use the Pythagorean Theorem and its converse to solve problems
- 8.7.D
determine the distance between two points on a coordinate plane using the Pythagorean Theorem
- 8.8
The student applies mathematical process standards to use one-variable equations or inequalities in problem situations
- 8.8.A
write one-variable equations or inequalities with variables on both sides that represent problems using rational number ...
- 8.8.B
write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides o...
- 8.8.C
model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and re...
- 8.8.D
use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when p...
- 8.9
The student applies mathematical process standards to use multiple representations to develop foundational concepts of s...