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Texas Standards

5th Grade Math TEKS

All 46 Texas math standards for 5th grade, each explained in plain English. The official wording is one click away under each one.

46 standards

Mathematical process standards

7 standards
The student uses mathematical processes to acquire and demonstrate mathematical understanding.
5.1(A)
Use math to solve problems from everyday life, society and work, like comparing prices per item to find the better buy.
Official wording
apply mathematics to problems arising in everyday life, society, and the workplace;
5.1(B)
Work through problems by analyzing the information, planning, solving, then justifying the answer and judging whether it is reasonable, like checking with an estimate.
Official wording
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;
5.1(C)
Choose suitable tools and techniques for a problem, like grid paper, a calculator, mental math, estimation or number sense.
Official wording
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;
5.1(D)
Communicate math reasoning and what follows from it with symbols, diagrams, graphs and words, like showing a decimal product on an area model.
Official wording
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
5.1(E)
Create and use models like tables, graphs and diagrams to organize, record and share math ideas, like a coordinate grid for a pattern.
Official wording
create and use representations to organize, record, and communicate mathematical ideas;
5.1(F)
Analyze relationships between math ideas and use them to explain, like seeing how multiplying by 0.1 relates to dividing by 10.
Official wording
analyze mathematical relationships to connect and communicate mathematical ideas; and
5.1(G)
Explain and defend math reasoning in writing or speech using precise words like numerator, quotient, prime and volume.
Official wording
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Number and operations

15 standards
The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place value.
5.2(A)
Write decimals through the thousandths in expanded form and as numerals, like 4.326 = 4 + 0.3 + 0.02 + 0.006.
Official wording
represent the value of the digit in decimals through the thousandths using expanded notation and numerals;
5.2(B)
Decide which of two decimals to the thousandths is greater, put them in order and record it with >, < or =, like 0.457 < 0.47.
Official wording
compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =; and
5.2(C)
Round decimals to the nearest tenth or hundredth, like 3.468 rounding to 3.5 or 3.47.
Official wording
round decimals to tenths or hundredths.
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.
5.3(A)
Estimate answers to math and real-world problems with any of the four operations, like rounding 4.8 x 19 to 5 x 20.
Official wording
estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division;
5.3(B)
Use the standard algorithm fluently to multiply three-digit numbers by two-digit numbers, like 382 x 47.
Official wording
multiply with fluency a three-digit number by a two-digit number using the standard algorithm;
5.3(C)
Find quotients when dividing up to four-digit numbers by two-digit numbers, with strategies or the standard algorithm, like 2,568 ÷ 24 = 107.
Official wording
solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm;
5.3(D)
Show multiplying decimals with products to hundredths using objects and area models, like 0.3 x 0.4 as a shaded grid of 0.12.
Official wording
represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models;
5.3(E)
Multiply decimals to the hundredths, including money problems, using place value, properties and links to whole-number multiplying, like 2.5 x 1.2 = 3.
Official wording
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;
5.3(F)
Use objects and area models to show a decimal with up to four digits divided by a whole number with up to two digits, like 4.8 ÷ 12 = 0.4.
Official wording
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;
5.3(G)
Divide a decimal with up to four digits by a whole number with up to two digits, using strategies or the standard algorithm, like 25.65 ÷ 15 = 1.71.
Official wording
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;
5.3(H)
Model and solve adding and subtracting fractions with unlike denominators, like 1/2 + 1/3 = 5/6, using objects, drawings and properties.
Official wording
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;
5.3(I)
Model and solve multiplying a whole number by a fraction with objects and area models, like 3 x 2/5 = 6/5.
Official wording
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;
5.3(J)
Use objects or area models to show problems like 1/4 ÷ 2, sharing a unit fraction among groups, and 2 ÷ 1/4, counting unit fractions in a whole.
Official wording
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;
5.3(K)
Fluently find sums and differences of positive fractions and decimals, like 2/3 + 3/4 or 6.2 - 1.85.
Official wording
add and subtract positive rational numbers fluently; and
5.3(L)
Compute quotients like 3 ÷ 1/5 = 15 and 1/5 ÷ 3 = 1/15, dividing between whole numbers and unit fractions.
Official wording
divide whole numbers by unit fractions and unit fractions by whole numbers.

Algebraic reasoning

8 standards
The student applies mathematical process standards to develop concepts of expressions and equations.
5.4(A)
Identify numbers as prime, with exactly two factors, or composite, with more than two, like 13 is prime and 15 is composite.
Official wording
identify prime and composite numbers;
5.4(B)
Write and solve an equation with a letter for the unknown to model a multi-step whole-number word problem, like 4 x n + 12 = 40.
Official wording
represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity;
5.4(C)
Make a number pattern from a rule like y = 3x or y = x + 4 and graph the pairs on a coordinate grid.
Official wording
generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph;
5.4(D)
Tell additive patterns, which add the same amount, from multiplicative patterns, which multiply by the same amount, in a table or graph.
Official wording
recognize the difference between additive and multiplicative numerical patterns given in a table or graph;
5.4(E)
Describe what parentheses and brackets do in a numeric expression, like showing which part to work out before the rest.
Official wording
describe the meaning of parentheses and brackets in a numeric expression;
5.4(F)
Simplify expressions without exponents that have up to two levels of grouping, like a set of parentheses inside brackets, working in the right order.
Official wording
simplify numerical expressions that do not involve exponents, including up to two levels of grouping;
5.4(G)
Use cubes and drawings to discover the volume formulas for a rectangular prism, V = l x w x h and V = Bh, and for a cube, V = s x s x s.
Official wording
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); and
5.4(H)
Model and solve problems involving perimeter, area or volume, like fencing a yard, tiling a floor or filling a box with cubes.
Official wording
represent and solve problems related to perimeter and/or area and related to volume.

Geometry and measurement

7 standards
The student applies mathematical process standards to classify two-dimensional figures by attributes and properties.
5.5
Classify flat shapes in a diagram of groups and subgroups based on their properties, like squares within rectangles within parallelograms.
Official wording
classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.
The student applies mathematical process standards to understand, recognize, and quantify volume.
5.6(A)
Recognize that a cube 1 unit on each side holds 1 cubic unit, and that a solid's volume is how many such cubes fill it without gaps or overlaps.
Official wording
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
5.6(B)
Find how many cubic units fill a box with whole-number edges by multiplying the cubes in one base layer by the number of layers, like 12 x 5 = 60.
Official wording
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.
The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving measurement.
5.7
Solve problems by converting units within one system, customary or metric, like changing 3.5 kilograms to grams or 2 gallons to quarts.
Official wording
solve problems by calculating conversions within a measurement system, customary or metric.
The student applies mathematical process standards to identify locations on a coordinate plane.
5.8(A)
Describe the coordinate plane as two perpendicular axes meeting at the origin, where the first number of a pair moves across and the second moves up.
Official wording
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;
5.8(B)
Describe the steps for plotting an ordered pair in the first quadrant, like starting at 0, moving right 3, then up 5.
Official wording
describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane; and
5.8(C)
Plot ordered pairs in the first quadrant that come from math or real-world problems, number patterns or input-output tables, like hours worked and pay.
Official wording
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.

Data analysis

3 standards
The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.
5.9(A)
Display category data in bar graphs or frequency tables and number data, including fraction or decimal measurements, in dot plots or stem-and-leaf plots.
Official wording
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;
5.9(B)
Graph pairs of separate data values on a scatterplot, like each student's hours of reading and number of books finished.
Official wording
represent discrete paired data on a scatterplot; and
5.9(C)
Answer one- and two-step questions by reading scatterplots, bar graphs, dot plots, stem-and-leaf plots and frequency tables, like finding a range or total.
Official wording
solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.

Personal financial literacy

6 standards
The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.
5.10(A)
Define taxes on income, on payroll, on sales and on property, like the sales tax added to a purchase at the register.
Official wording
define income tax, payroll tax, sales tax, and property tax;
5.10(B)
Explain the difference between gross income, pay before deductions, and net income, the take-home pay left after taxes.
Official wording
explain the difference between gross income and net income;
5.10(C)
Identify the pros and cons of paying by check, credit card, debit card or electronic payment, like debit cards using money you already have.
Official wording
identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments;
5.10(D)
Set up a way to track money coming in and going out, like a simple ledger or spreadsheet of receipts and bills.
Official wording
develop a system for keeping and using financial records;
5.10(E)
Describe steps to fix a budget when spending is more than income, like cutting extras or finding ways to earn more.
Official wording
describe actions that might be taken to balance a budget when expenses exceed income; and
5.10(F)
Balance a simple budget so planned spending and saving match the money coming in.
Official wording
balance a simple budget.

The official Texas documents

Texas Essential Knowledge and Skills for Mathematics, 19 Texas Administrative Code Chapter 111, adopted by the Texas State Board of Education.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.