This alignment shows the Media4Math resources that support the standards shown below. Click on a grade to see the TEKS standards for that grade. Then click on a specific standard to see all the Media4Math resources that support it.

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# TEKS Standards Alignment: K-5

## Kindergarten

2. Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system. The student is expected to:

Standard Description
2A count forward and backward to at least 20 with and without objects
2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
2C count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order
2D recognize instantly the quantity of a small group of objects in organized and random arrangements
2E generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20
2F generate a number that is one more than or one less than another number up to at least 20
2G compare sets of objects up to at least 20 in each set using comparative language
2H use comparative language to describe two numbers up to 20 presented as written numeral
2I compose and decompose numbers up to 10 with objects and pictures

3. Number and operations. The student applies mathematical process standards to develop an understanding of addition and subtraction situations in order to solve problems. The student is expected to:

Standard Description
3A model the action of joining to represent addition and the action of separating to represent subtraction
3B solve word problems using objects and drawings to find sums up to 10 and differences within 10
3C explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences

6.Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

Standard Description
6A identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles
6B identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world
6C identify two-dimensional components of three-dimensional objects
6D identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably
6E classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size
6F create two-dimensional shapes using a variety of materials and drawings

7. Geometry and measurement. The student applies mathematical process standards to directly compare measurable attributes. The student is expected to:

Standard Description
7A give an example of a measurable attribute of a given object, including length, capacity, and weight
7B compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference

8. Data analysis. The student applies mathematical process standards to collect and organize data to make it useful for interpreting information. The student is expected to:

Standard Description
8A collect, sort, and organize data into two or three categories
8B use data to create real-object and picture graphs
8C draw conclusions from real-object and picture graphs

9. Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to:

Standard Description
9A identify ways to earn income
9C list simple skills required for jobs
9D distinguish between wants and needs and identify income as a source to meet one's wants and needs

2. Number and operations. The student applies mathematical process standards to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:

Standard Description
2A recognize instantly the quantity of structured arrangements
2B use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones
2C use objects, pictures, and expanded and standard forms to represent numbers up to 120
2D generate a number that is greater than or less than a given whole number up to 120
2E use place value to compare whole numbers up to 120 using comparative language
2F order whole numbers up to 120 using place value and open number lines
2G represent the comparison of two numbers to 100 using the symbols >, <, or

3. Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to:

Standard Description
3A use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99
3B use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3
3C compose 10 with two or more addends with and without concrete objects
3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10
3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences
3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20

4. Number and operations. The student applies mathematical process standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The student is expected to:

Standard Description
4A identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them
4B write a number with the cent symbol to describe the value of a coin
4C use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

5. Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:

Standard Description
5A recite numbers forward and backward from any given number between 1 and 120
5B skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set
5C use relationships to determine the number that is 10 more and 10 less than a given number up to 120
5D represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences
5E understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s)
5F determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation
5G apply properties of operations to add and subtract two or three numbers

6. Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

Standard Description
6A classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language
6B distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape
6C create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons
6D identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language
6E identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language
6F compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible
6G partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words
6H identify examples and non-examples of halves and fourths

7. Geometry and measurement. The student applies mathematical process standards to select and use units to describe length and time. The student is expected to:

Standard Description
7A use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement
7B illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other
7C measure the same object/distance with units of two different lengths and describe how and why the measurements differ
7D describe a length to the nearest whole unit using a number and a unit
7E tell time to the hour and half hour using analog and digital clocks

8. Data analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:

Standard Description
8A collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts
8B use data to create picture and bar-type graphs
8C draw conclusions and generate and answer questions using information from picture and bar-type graphs

9. Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

Standard Description
9A define money earned as income
9B identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs
9C distinguish between spending and saving
9D consider charitable giving

2. Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:

Standard Description
2A 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 thousands, hundreds, tens, and ones
2B use standard, word, and expanded forms to represent numbers up to 1,200
2C generate a number that is greater than or less than a given whole number up to 1,200
2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)
2E locate the position of a given whole number on an open number line
2F name the whole number that corresponds to a specific point on a number line

3. Number and operations. The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to:

Standard Description
3A partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words
3B explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part
3C use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole
3D identify examples and non-examples of halves, fourths, and eighths

4. Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve addition and subtraction problems with efficiency and accuracy. The student is expected to:

Standard Description
4A recall basic facts to add and subtract within 20 with automaticity
4B add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations
4C solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms
4D generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

5. Number and operations. The student applies mathematical process standards to determine the value of coins in order to solve monetary transactions. The student is expected to:

Standard Description
5A determine the value of a collection of coins up to one dollar
5B use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

6. Number and operations. The student applies mathematical process standards to connect repeated addition and subtraction to multiplication and division situations that involve equal groupings and shares. The student is expected to:

Standard Description
6A model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined
6B model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

7. Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:

Standard Description
7A determine whether a number up to 40 is even or odd using pairings of objects to represent the number
7B use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200
7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

8. Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

Standard Description
8A create two-dimensional shapes based on given attributes, including number of sides and vertices
8B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language
8C classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices
8D compose two-dimensional shapes and three-dimensional solids with given properties or attributes
8E decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

9. Geometry and measurement. The student applies mathematical process standards to select and use units to describe length, area, and time. The student is expected to:

Standard Description
9A find the length of objects using concrete models for standard units of length
9B describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object
9C represent whole numbers as distances from any given location on a number line
9D determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes
9E determine a solution to a problem involving length, including estimating lengths
9F use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit
9G read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m

10. Data analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:

Standard Description
10A explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category
10B organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more
10C write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one
10D draw conclusions and make predictions from information in a graph

11. Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

Standard Description
11A calculate how money saved can accumulate into a larger amount over time
11B explain that saving is an alternative to spending
11C distinguish between a deposit and a withdrawal
11D identify examples of borrowing and distinguish between responsible and irresponsible borrowing
11E identify examples of lending and use concepts of benefits and costs to evaluate lending decisions
11F differentiate between producers and consumers and calculate the cost to produce a simple item

2. Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:

Standard Description
2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate
2B describe the mathematical relationships found in the base-10 place value system through the hundred thousands place
2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers
2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

3. Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

Standard Description
3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines
3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line
3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number
3D 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/b
3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8
3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines
3G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model
3H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

4. Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. The student is expected to:

Standard Description
4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction
4B round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems
4C determine the value of a collection of coins and bills
4D determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10
4E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting
4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts
4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties
4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally
4I determine if a number is even or odd using divisibility rules
4J determine a quotient using the relationship between multiplication and division
4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

5. Algebraic reasoning. The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to:

Standard Description
5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations
5B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations
5C describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24
5D determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product
5E represent real-world relationships using number pairs in a table and verbal descriptions

6. Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is expected to:

Standard Description
6A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language
6B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row
6D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area
6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

7. Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement. The student is expected to:

Standard Description
7A represent fractions of halves, fourths, and eighths as distances from zero on a number line
7B determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems
7C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes
7D determine when it is appropriate to use measurements of liquid volume (capacity) or weight
7E determine liquid volume (capacity) or weight using appropriate units and tools

8. Data analysis. The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to:

Standard Description
8A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals
8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

9. Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

Standard Description
9A explain the connection between human capital/labor and income
9B describe the relationship between the availability or scarcity of resources and how that impacts cost
9C identify the costs and benefits of planned and unplanned spending decisions
9D explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest
9E list reasons to save and explain the benefit of a savings plan, including for college
9F identify decisions involving income, spending, saving, credit, and charitable giving

2. Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to:

Standard Description
2A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left
2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals
2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =
2D round whole numbers to a given place value through the hundred thousands place
2E represent decimals, including tenths and hundredths, using concrete and visual models and money
2F compare and order decimals using concrete and visual models to the hundredths
2G relate decimals to fractions that name tenths and hundredths
2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

3. Number and operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to:

Standard Description
3A 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
3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations
3C determine if two given fractions are equivalent using a variety of methods
3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <
3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations
3F evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole
3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

4. Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to:

Standard Description
4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm
4B determine products of a number and 10 or 100 using properties of operations and place value understandings
4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15
4D use strategies and algorithms, including the standard algorithm, to multiply up to a four- digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties
4E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations
4F use strategies and algorithms, including the standard algorithm, to divide up to a four- digit dividend by a one-digit divisor
4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers
4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

5. Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:

Standard Description
5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity
5B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence
5C use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w)
5D solve problems related to perimeter and area of rectangles where dimensions are whole numbers

6. Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:

Standard Description
6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines
6B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure
6C apply knowledge of right angles to identify acute, right, and obtuse triangles
6D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

7. Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:

Standard Description
7A 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" by the rays of the angle. Angle measures are limited to whole numbers
7B illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers
7C determine the approximate measures of angles in degrees to the nearest whole number using a protractor
7D draw an angle with a given measure
7E determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures

8. Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:

Standard Description
8A identify relative sizes of measurement units within the customary and metric systems
8B convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table
8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

9. Data analysis. The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to:

Standard Description
9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions
9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

10. Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

Standard Description
10A distinguish between fixed and variable expenses
10B calculate profit in a given situation
10D describe how to allocate a weekly allowance among spending; saving, including for college; and sharing
10E describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending

2. Number and operations. The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to:

Standard Description
2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals
2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =
2C round decimals to tenths or hundredths

3. Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to:

Standard Description
3A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division
3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm
3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm
3D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models
3E solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers
3F represent quotients of decimals to the hundredths, up to four-digit dividends and two- digit whole number divisors, using objects and pictorial models, including area models
3G solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm
3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations
3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models
3J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models

3K

add and subtract positive rational numbers fluently
3L divide whole numbers by unit fractions and unit fractions by whole numbers

4. Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:

Standard Description
4A identify prime and composite numbers
4B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity
4C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph
4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph
4E describe the meaning of parentheses and brackets in a numeric expression
4F simplify numerical expressions that do not involve exponents, including up to two levels of grouping
4G use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh)
4H represent and solve problems related to perimeter and/or area and related to volume

6. Geometry and measurement. The student applies mathematical process standards to understand, recognize, and quantify volume. The student is expected to:

Standard Description
6A 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-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible
6B determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base

8. Geometry and measurement. The student applies mathematical process standards to identify locations on a coordinate plane. The student is expected to:

Standard Description
8A describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin
8B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane
8C graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table

9. Data analysis. The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to:

Standard Description
9A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and- leaf plots
9B represent discrete paired data on a scatterplot
9C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot

10. Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

Standard Description
10A define income tax, payroll tax, sales tax, and property tax
10B explain the difference between gross income and net income
10C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments
10D develop a system for keeping and using financial records
10E describe actions that might be taken to balance a budget when expenses exceed income
10F balance a simple budget