Texas Essential Knowledge and Skills (TEKS): Grade 5
Skills available for Texas fifth-grade math standards
Strand
Print skill plan
1
Mathematical process standards
1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
A apply mathematics to problems arising in everyday life, society, and the workplace;
Whole numbers
Fractions
Decimals
Money
Measurement
Coordinate plane
Data and graphs
Perimeter, area, and volume
Financial literacy
A apply mathematics to problems arising in everyday life, society, and the workplace;
Whole numbers
Fractions
Decimals
Money
Measurement
Coordinate plane
Data and graphs
Perimeter, area, and volume
Financial literacy
B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Addition and subtraction
Division
Multi-step problems
Order of operations
Data and graphs
B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Addition and subtraction
Division
Multi-step problems
Order of operations
Data and graphs
C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Add and subtract fractions
Multiply fractions
Divide fractions
Add and subtract decimals
Multiply decimals
Divide decimals
Coordinate plane
Data and graphs
C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Add and subtract fractions
Multiply fractions
Divide fractions
Add and subtract decimals
Multiply decimals
Divide decimals
Coordinate plane
Data and graphs
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Fractions
Decimals
Multi-step problems
Patterns
Data and graphs
Two-dimensional figures
Volume
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Fractions
Decimals
Multi-step problems
Patterns
Data and graphs
Two-dimensional figures
Volume
E create and use representations to organize, record, and communicate mathematical ideas;
Add and subtract fractions
Multiply and divide fractions
Multiply decimals
Multi-step problems
Patterns
Data and graphs
Financial literacy
E create and use representations to organize, record, and communicate mathematical ideas;
Add and subtract fractions
Multiply and divide fractions
Multiply decimals
Multi-step problems
Patterns
Data and graphs
Financial literacy
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Place value
Patterns
Two-dimensional shapes
Data analysis
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Place value
Patterns
Two-dimensional shapes
Data analysis
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Division
Multi-step problems
Patterns
Coordinate plane
Two-dimensional shapes
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Division
Multi-step problems
Patterns
Coordinate plane
Two-dimensional shapes
2-3
Number and operations
2 The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value.
A represent the value of the digit in decimals through the thousandths using expanded notation and numerals;
Read and write decimals
Expanded notation
A represent the value of the digit in decimals through the thousandths using expanded notation and numerals;
Read and write decimals
Expanded notation
B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =; and
Compare decimals
Order decimals
Application problems
B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =; and
Compare decimals
Order decimals
Application problems
C round decimals to tenths or hundredths.
C round decimals to tenths or hundredths.
3 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.
A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division;
Whole numbers
Decimals
Fractions and mixed numbers
A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division;
Whole numbers
Decimals
Fractions and mixed numbers
B multiply with fluency a three-digit number by a two-digit number using the standard algorithm;
B multiply with fluency a three-digit number by a two-digit number using the standard algorithm;
C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm;
Division facts
Division strategies
Divide by 1-digit numbers
Divide by 2-digit numbers
C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm;
Division facts
Division strategies
Divide by 1-digit numbers
Divide by 2-digit numbers
D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models;
D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models;
E 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;
Multiplication strategies
Multiply decimals by whole numbers
Multiply two decimals
E 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;
Multiplication strategies
Multiply decimals by whole numbers
Multiply two decimals
F 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;
F 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;
G 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;
Division strategies
Divide by whole numbers
G 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;
Division strategies
Divide by whole numbers
H 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;
Use objects
Use models
Use properties
H 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;
Use objects
Use models
Use properties
I 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;
Number lines
Area models
Arrays
Find and sort products
I 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;
Number lines
Area models
Arrays
Find and sort products
J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models;
Divide unit fractions by whole numbers
Divide whole numbers by unit fractions
Mixed division with unit fractions
J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models;
Divide unit fractions by whole numbers
Divide whole numbers by unit fractions
Mixed division with unit fractions
K add and subtract positive rational numbers fluently; and
Whole numbers
Decimals
Fractions with like denominators
Fractions with unlike denominators
Mixed numbers with like denominators
Mixed numbers with unlike denominators
Fractions and decimals
K add and subtract positive rational numbers fluently; and
Whole numbers
Decimals
Fractions with like denominators
Fractions with unlike denominators
Mixed numbers with like denominators
Mixed numbers with unlike denominators
Fractions and decimals
L divide whole numbers by unit fractions and unit fractions by whole numbers.
L divide whole numbers by unit fractions and unit fractions by whole numbers.
4
Algebraic reasoning
4 The student applies mathematical process standards to develop concepts of expressions and equations.
A identify prime and composite numbers;
A identify prime and composite numbers;
B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity;
Variable equations
Multi-step word problems
B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity;
Variable equations
Multi-step word problems
C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph;
Complete a table
Graph patterns
Compare patterns
C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph;
Complete a table
Graph patterns
Compare patterns
D recognize the difference between additive and multiplicative numerical patterns given in a table or graph;
D recognize the difference between additive and multiplicative numerical patterns given in a table or graph;
E describe the meaning of parentheses and brackets in a numeric expression;
E describe the meaning of parentheses and brackets in a numeric expression;
F simplify numerical expressions that do not involve exponents, including up to two levels of grouping;
F simplify numerical expressions that do not involve exponents, including up to two levels of grouping;
G 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 × w × h, V = s × s × s, and V = Bh); and
G 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 × w × h, V = s × s × s, and V = Bh); and
H represent and solve problems related to perimeter and/or area and related to volume.
Perimeter
Area
Area and perimeter
Volume
H represent and solve problems related to perimeter and/or area and related to volume.
Perimeter
Area
Area and perimeter
Volume
5-8
Geometry and measurement
5 The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The student is expected to classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.
Polygons
Triangles
Quadrilaterals
6 The student applies mathematical process standards to understand, recognize, and quantify volume.
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-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; and
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-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; and
B 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.
B 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.
7 The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving measurement. The student is expected to solve problems by calculating conversions within a measurement system, customary or metric.
Customary units
Metric units
Multi-step word problems
Time
8 The student applies mathematical process standards to identify locations on a coordinate plane.
A 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;
A 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;
B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane; and
B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane; and
C 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.
C 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
9 The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.
A 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;
Bar graphs
Frequency tables
Line plots
Stem-and-leaf plots
A 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;
Bar graphs
Frequency tables
Line plots
Stem-and-leaf plots
B represent discrete paired data on a scatterplot; and
B represent discrete paired data on a scatterplot; and
C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.
Frequency tables
Dot plots
Bar graphs
Stem-and-leaf plots
Scatter plots
Two-step problems
C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.
Frequency tables
Dot plots
Bar graphs
Stem-and-leaf plots
Scatter plots
Two-step problems
10
Personal financial literacy
10 The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.
A define income tax, payroll tax, sales tax, and property tax;
A define income tax, payroll tax, sales tax, and property tax;
B explain the difference between gross income and net income;
B explain the difference between gross income and net income;
C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments;
C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments;
D develop a system for keeping and using financial records;
D develop a system for keeping and using financial records;
E describe actions that might be taken to balance a budget when expenses exceed income; and
E describe actions that might be taken to balance a budget when expenses exceed income; and
F balance a simple budget.
F balance a simple budget.
Printable activity: Creating financial records