Mathematics, grade 6
58 things Texas expects by the end of grade 6, in the state's own words and ours.
This sheet is grade 6. Grades 4 and 5 are named here by title only; the wording in full is on their own sheets: grade 4, grade 5. Grades 1–3 sit further back still, on their own sheets: grade 1, grade 2, grade 3.
How to go at a problem, rather than which problems. These run underneath all the rest.
- 6.1.A Apply mathematics to real-world problems Close
6.1.A · Grade 6
Apply mathematics to real-world problems
apply mathematics to problems arising in everyday life, society, and the workplace
Example
- A campground charges $32 a night. Ask what four nights comes to, then hand over the receipt and ask whether it matches.
- Ask how many packs of 8 water bottles it takes to get 40 bottles into the cooler.
- 6.1.B Use a problem-solving model Close
6.1.B · Grade 6
Use a problem-solving model
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
Example
- Give a two-step problem and ask what they would do first, before any arithmetic happens.
- After an answer, ask why it is reasonable. Listen for a reason rather than a re-check of the steps.
Part of the problem solving topic
- 6.1.C Select tools and techniques for problems Close
6.1.C · Grade 6
Select tools and techniques for problems
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
Example
- Ask for 5 x 60 and watch whether they reach for paper. Reaching for it at this size is the thing worth noticing.
- Ask which is easier for 47 x 6, mental math or writing it down, and why.
Part of the problem solving topic
- 6.1.D Communicate ideas in multiple representations Close
6.1.D · Grade 6
Communicate ideas in multiple representations
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
Example
- Ask them to show 6 x 7 two ways: with a drawing, and with a number sentence.
- Ask them to explain a division out loud, without pointing at the page.
Part of the graphs and data topic
- 6.1.E Create and use representations Close
6.1.E · Grade 6
Create and use representations
create and use representations to organize, record, and communicate mathematical ideas
Example
- Ask them to keep a tally of something on a drive and turn it into a table at the end.
- 6.1.F Analyze relationships; connect and communicate Close
6.1.F · Grade 6
Analyze relationships; connect and communicate
analyze mathematical relationships to connect and communicate mathematical ideas
Example
- Ask what 6 x 4 has to do with 6 x 40.
- Ask why knowing 5 x 8 helps with 6 x 8.
- 6.1.G Display, explain, and justify precisely Close
6.1.G · Grade 6
Display, explain, and justify precisely
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
Example
- Ask them to convince you that one third is bigger than one fourth, using the word "parts". Listen for whether the bigger bottom number pulls them the wrong way.
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
What numbers are, how big they are, and how they come apart and go back together.
- 6.2.A Sort number sets with a Venn diagram Close
6.2.A · Grade 6
Sort number sets with a Venn diagram
classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
Example
- Draw three nested circles for whole numbers, integers, and rational numbers, and ask them to place -4, 0, 3, three fourths, and -1.2 in the smallest circle each one fits.
- Ask whether -6 belongs with the whole numbers, the integers, or both, and where it sits on the diagram.
- 6.2.B A number, its opposite, its absolute value Close
6.2.B · Grade 6
A number, its opposite, its absolute value
identify a number, its opposite, and its absolute value
Example
- Give -7 and ask for its opposite and its absolute value.
- Give 4.5 and -4.5 and ask what the two share: opposites, and the same absolute value.
- 6.2.C Order integers and rationals on a line Close
6.2.C · Grade 6
Order integers and rationals on a line
locate, compare, and order integers and rational numbers using a number line
Example
- Mark -3, 1, -1.5, and two thirds on a number line and ask them to lay the four out smallest first.
- Mark -2 and 3 on a number line and ask which is greater, and how the positions show it.
- 6.2.D Order rational numbers from real contexts Close
6.2.D · Grade 6
Order rational numbers from real contexts
order a set of rational numbers arising from mathematical and real-world contexts
Example
- Three morning temperatures read -4, -1, and -7 degrees. Ask them to put the three in order from coldest to warmest.
- One trail drops 12.5 feet below the start and another climbs 8.25 feet above it. Ask them to order -12.5, 0, and 8.25.
- 6.2.E Read a/b as a divided by b Close
6.2.E · Grade 6
Read a/b as a divided by b
extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0
Example
- Write three fourths and ask them to work out 3 divided by 4, then say what the fraction bar was doing all along.
- Write 7 over 2 and ask for its value as a division, then as a mixed number.
Part of the fractions topic
- 6.3.A Dividing equals multiplying by the reciprocal Close
6.3.A · Grade 6
Dividing equals multiplying by the reciprocal
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
Example
- Ask for 6 divided by one half, then for 6 times 2, and ask what they notice about the two answers.
- Ask for two thirds divided by four fifths two ways: by the division, and by multiplying two thirds by five fourths.
Part of the multiplication and division topic
- 6.3.B Does a fraction grow or shrink it Close
6.3.B · Grade 6
Does a fraction grow or shrink it
determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one
Example
- Ask whether 48 times three fourths comes out bigger or smaller than 48, before working anything out.
- Ask whether 20 times five fourths comes out bigger or smaller than 20, then work it out to check.
- Ask them to sort one half, five fourths, and 1 into growers and shrinkers for multiplication, then test each one on 60.
Part of the fractions topic
- 6.3.C From integer models to standard algorithms Close
6.3.C · Grade 6
From integer models to standard algorithms
represent integer operations with concrete models and connect the actions with the models to standardized algorithms
Example
- Lay out 5 red counters and take away 8, bringing in zero-pairs to make it possible, and ask them to connect each move to the subtraction 5 - 8.
- Model -3 plus -4 with counters of one color, then ask them to write the addition the model shows.
- 6.3.D Fluent integer arithmetic, all four operations Close
6.3.D · Grade 6
Fluent integer arithmetic, all four operations
add, subtract, multiply, and divide integers fluently
Example
- Ask for -6 plus 11, -6 minus 11, -6 times 11, and -66 divided by 11.
- Ask for 8 minus -3 and -8 minus 3, and notice the two answers are not the same.
Part of the adding and subtracting topic
- 6.3.E Fluently multiply, divide positive rationals Close
6.3.E · Grade 6
Fluently multiply, divide positive rationals
multiply and divide positive rational numbers fluently
Example
- Ask for three eighths times four ninths.
- Ask for 2.5 divided by 0.5, then for 5 times 0.5, and ask what they notice about the two answers.
Part of the multiplication and division topic
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
- 6.4.A Additive or multiplicative? Compare four ways Close
6.4.A · Grade 6
Additive or multiplicative? Compare four ways
compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships
Example
- Give the rules y = 3x and y = x + 3 with tables for x = 1 through 4, and ask which one grows by adding and which by multiplying.
- Graph y = 2x and y = x + 2 on the same axes and ask them to say in words how the two lines climb differently.
Part of the graphs and data topic
- 6.4.B Predict and compare with ratios and rates Close
6.4.B · Grade 6
Predict and compare with ratios and rates
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates
Example
- Two bags of trail mix sell at the same price: one holds 12 ounces, the other 18. Ask which is the better buy and how they know without dividing.
- A car covers 240 miles on 8 gallons. Ask how far it goes on 12 gallons at the same rate.
Part of the problem solving topic
- 6.4.C A ratio compares two like quantities Close
6.4.C · Grade 6
A ratio compares two like quantities
give examples of ratios as multiplicative comparisons of two quantities describing the same attribute
Example
- A recipe uses 3 cups of flour for every 1 cup of sugar. Ask them to state the ratio and what it compares.
- A campsite holds 12 campers and 4 counselors. Ask for the ratio of campers to counselors as a multiplicative comparison.
- 6.4.D A rate compares two unlike quantities Close
6.4.D · Grade 6
A rate compares two unlike quantities
give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients
Example
- A hiker covers 9 miles in 3 hours. Ask for the rate as a quotient, in miles per hour.
- A faucet fills 20 gallons in 4 minutes. Ask for the unit rate and what each single unit means.
Part of the multiplication and division topic
- 6.4.E Model ratios and percents three ways Close
6.4.E · Grade 6
Model ratios and percents three ways
represent ratios and percents with concrete models, fractions, and decimals
Example
- Shade 30 squares of a 10-by-10 grid and ask them to name the shaded part as a ratio, a fraction, a decimal, and a percent.
- Ask them to show 1 to 4 with counters, then write it as a fraction and a decimal.
Part of the fractions topic
- 6.4.F Benchmark fractions and percents on grids Close
6.4.F · Grade 6
Benchmark fractions and percents on grids
represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers
Example
- Shade 25 squares of a 10-by-10 grid and ask what fraction and what percent that is.
- Shade one third of a strip diagram and ask what benchmark percent it matches.
- On a number line from 0 to 100, ask them to mark 1%, 10%, 50%, and 75%, and name the fraction each one matches.
Part of the fractions topic
- 6.4.G Same value as fraction, decimal, percent Close
6.4.G · Grade 6
Same value as fraction, decimal, percent
generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money
Example
- A $40 shirt is marked 25% off. Ask for the discount three ways: as a fraction of 40, as a decimal times 40, and in dollars.
- Ask them to write three fourths as a decimal and a percent first, then work out how many cents three quarters of a dollar is.
Part of the fractions topic
- 6.4.H Convert units within one measurement system Close
6.4.H · Grade 6
Convert units within one measurement system
convert units within a measurement system, including the use of proportions and unit rates
Example
- Ask how many inches are in 5 feet, set up as a proportion.
- A recipe calls for 3 quarts of water. Ask how many gallons that is, worked out with a unit rate.
Part of the measurement topic
- 6.5.A Model ratio and rate problems four ways Close
6.5.A · Grade 6
Model ratio and rate problems four ways
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions
Example
- A map uses 1 inch for every 25 miles. Ask them to build a table for 1, 2, 3, and 4 inches, graph the pairs, then read off the miles for 3.5 inches.
- A recipe for 2 doubles to serve 6. Ask for the scale factor, then set up the proportion that scales one ingredient and apply it to the rest.
Part of the graphs and data topic
- 6.5.B Find the part, whole, or percent Close
6.5.B · Grade 6
Find the part, whole, or percent
solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models
Example
- 30 campers are 25% of the group. Ask for the whole group, using a strip diagram cut into fourths.
- Ask for 10% of an $80 bill, then for what percent $20 is of $80.
Part of the problem solving topic
- 6.5.C Equal parts as fraction, decimal, percent Close
6.5.C · Grade 6
Equal parts as fraction, decimal, percent
use equivalent fractions, decimals, and percents to show equal parts of the same whole
Example
- Shade one half of one circle, two fourths of a second, and five tenths of a third, and ask what the three shadings share.
- Ask them to write 0.2 as a fraction and a percent, then shade that share of a grid.
Part of the fractions topic
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
- 6.6.A Spot the independent and dependent quantity Close
6.6.A · Grade 6
Spot the independent and dependent quantity
identify independent and dependent quantities from tables and graphs
Example
- Show a table of hours driven and miles covered and ask which quantity depends on the other.
- Show a graph of a plant’s height over weeks and ask which axis holds the independent quantity.
Part of the graphs and data topic
- 6.6.B Write the equation behind a table Close
6.6.B · Grade 6
Write the equation behind a table
write an equation that represents the relationship between independent and dependent quantities from a table
Example
- Give a table pairing 1, 2, and 3 shirts with $12, $24, and $36, and ask for the equation linking shirts to cost.
- Give a table pairing 1 through 4 hours with $9, $18, $27, and $36 of pay, and ask for the equation linking hours to pay.
- 6.6.C One situation, four representations Close
6.6.C · Grade 6
One situation, four representations
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
Example
- A taxi charges $3 plus $2 a mile. Ask them to describe it in words, make a table for 1 through 4 miles, graph the pairs, and write the equation.
- A recipe triples cups of flour per bag of sugar. Ask for the table, the graph, and the equation, each in the form the rule names.
Part of the graphs and data topic
- 6.7.A Rewrite expressions with exponents and factors Close
6.7.A · Grade 6
Rewrite expressions with exponents and factors
generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
Example
- Ask them to simplify 3 + 4 × 2².
- Ask for the prime factorization of 36, then use it to simplify 2² × 3².
- 6.7.B Tell an expression from an equation Close
6.7.B · Grade 6
Tell an expression from an equation
distinguish between expressions and equations verbally, numerically, and algebraically
Example
- Show 4x + 5 and 4x + 5 = 13 side by side and ask which one can be solved, and why.
- Give "three less than twice a number" and ask them to say it, write it, work out its value at 4, then write "it equals 10" and test whether that claim is true at 4 — and say which one is the expression and which the equation.
- 6.7.C Test two expressions for equivalence Close
6.7.C · Grade 6
Test two expressions for equivalence
determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations
Example
- Ask whether 3(x + 2) and 3x + 6 are equivalent, using tiles, a drawing, and algebra.
- Ask whether 5 + 2x and 7x are equivalent, and show the answer two ways.
- 6.7.D Use the properties to rewrite expressions Close
6.7.D · Grade 6
Use the properties to rewrite expressions
generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties
Example
- Ask them to use the distributive property to rewrite 4(x + 3).
- Ask them to rewrite 7 + 5 + 3 two ways, once with the commutative property and once with the associative property, then check both give 15.
- Ask them to work out 8 + 0 and 8 × 1, then 5 + (-5) and 6 × one sixth, and name which pair shows the identity property and which shows the inverse property.
- 6.8.A Angles, sides, and what makes a triangle Close
6.8.A · Grade 6
Angles, sides, and what makes a triangle
extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle
Example
- Give two angles of a triangle, 50° and 60°, and ask for the third.
- Ask whether sides 3, 4, and 8 can form a triangle, and why not.
- Give a triangle with sides 5, 5, and 8 and ask which two angles are equal.
Part of the measurement topic
- 6.8.B Build area formulas by rearranging shapes Close
6.8.B · Grade 6
Build area formulas by rearranging shapes
model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes
Example
- Cut a paper parallelogram and rearrange it into a rectangle, then ask what that says about its area formula.
- Fit two copies of a triangle together into a parallelogram, then ask what that says about the triangle’s area formula.
- Cut a paper trapezoid into two triangles and ask what the two triangle areas add up to say about the trapezoid’s area formula.
Part of the shapes and geometry topic
- 6.8.C Write equations for area and volume Close
6.8.C · Grade 6
Write equations for area and volume
write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers
Example
- A rectangle measures 4.5 by 2. Ask for the equation that gives its area.
- A right rectangular prism measures 3 by 2 by 5. Ask for the equation that gives its volume.
- A parallelogram has base 6 and height 4, a trapezoid has bases 6 and 10 and height 4, and a triangle has base 7.5 and height 4. Ask for the equation that gives each area.
Part of the shapes and geometry topic
- 6.8.D Solve area and volume problems Close
6.8.D · Grade 6
Solve area and volume problems
determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers
Example
- A trapezoid has bases 6 and 10 and height 4. Ask for its area.
- A triangle has base 7.5 and height 4. Ask for its area.
- A rectangle measures 4.5 by 2, a parallelogram has base 6 and height 4, and a right rectangular prism measures 3 by 2 by 5. Ask for each area and the volume.
Part of the shapes and geometry topic
- 6.9.A Write a one-step equation or inequality Close
6.9.A · Grade 6
Write a one-step equation or inequality
write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
Example
- A ride admits riders at least 48 inches tall. Ask them to write the inequality for height h.
- Three friends split a $27 bill evenly. Ask for the equation for one share s.
- 6.9.B Graph the solution on a number line Close
6.9.B · Grade 6
Graph the solution on a number line
represent solutions for one-variable, one-step equations and inequalities on number lines
Example
- Ask them to graph x > 4 on a number line, with the open circle in the right place.
- Ask them to graph x = 7 and x ≤ 7 on two lines and say what differs.
- 6.9.C Write the story problem for an equation Close
6.9.C · Grade 6
Write the story problem for an equation
write corresponding real-world problems given one-variable, one-step equations or inequalities
Example
- Give the equation n + 5 = 12 and ask for a story it could tell.
- Give the inequality t < 30 and ask for a real situation it fits.
- 6.10.A Model and solve one-step problems Close
6.10.A · Grade 6
Model and solve one-step problems
model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
Example
- Model x + 6 = 14 with tiles and ask for x.
- A rectangle has area 36 and length 9. Ask them to model 9w = 36 with a drawing and solve for the width.
Part of the problem solving topic
- 6.10.B Check whether a value works Close
6.10.B · Grade 6
Check whether a value works
determine if the given value(s) make(s) one-variable, one-step equations or inequalities true
Example
- Ask whether 7 makes x + 5 = 12 true, and whether it makes x + 5 > 12 true.
- Ask which of 3, 4, and 5 make 2n ≥ 8 true.
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
- 6.11 Graph ordered pairs in every quadrant Close
6.11 · Grade 6
Graph ordered pairs in every quadrant
The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers
Example
- Ask them to plot (2, 3), (3, -2), (-4, 5), and (-1.5, -2.5), naming the quadrant each one lands in.
- Ask them to plot (0, 4) and (2.5, 0) and say why neither point sits inside any quadrant.
Part of the graphs and data topic
- 6.12.A Graph numeric data four ways Close
6.12.A · Grade 6
Graph numeric data four ways
represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots
Example
- Give the values 12, 13, 13, 15, 18, and 21 and ask for a dot plot.
- Give the same six values and ask for a stem-and-leaf plot, then a histogram, then a box plot.
Part of the graphs and data topic
- 6.12.B Center, spread, and shape from a graph Close
6.12.B · Grade 6
Center, spread, and shape from a graph
use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution
Example
- Show a dot plot bunched at 6 through 8 with one point out at 20, and ask what that single point does to the center, the spread, and the shape.
Part of the graphs and data topic
- 6.12.C Mean, median, range, and IQR Close
6.12.C · Grade 6
Mean, median, range, and IQR
summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution
Example
- Give the data 4, 6, 7, 7, and 11 and ask for the mean, the median, and the range, then ask what the three say about the center, the spread, and the shape.
- Give the data 2, 5, 6, 8, 9, and 12 and ask for the median and the interquartile range, then ask what the two say about the center and the spread.
Part of the graphs and data topic
- 6.12.D Categorical data: mode and percent bars Close
6.12.D · Grade 6
Categorical data: mode and percent bars
summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution
Example
- Take a vote on favorite fruit and ask for the mode, a relative frequency table, and a percent bar graph of the result, then ask what the three summaries say about how the vote split.
Part of the graphs and data topic
- 6.13.A Read numeric data off a plot Close
6.13.A · Grade 6
Read numeric data off a plot
interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots
Example
- Show a box plot of quiz scores with the median marked and ask what share of the class scored above it.
- Show a histogram of daily temperatures and ask which range holds the most days.
- Show a dot plot of pets per family and ask how many families have more than two pets, then show a stem-and-leaf plot of spelling scores and ask for the highest score and how many scored above 90.
Part of the graphs and data topic
- 6.13.B Data that varies, data that does not Close
6.13.B · Grade 6
Data that varies, data that does not
distinguish between situations that yield data with and without variability
Example
- Ask whether "the ages of dogs at a shelter" yields data with variability, and whether "the number of days in June" does.
Part of the graphs and data topic
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
Money: earning it, saving it, and choosing between two things.
- 6.14.A Compare checking accounts and debit cards Close
6.14.A · Grade 6
Compare checking accounts and debit cards
compare the features and costs of a checking account and a debit card offered by different local financial institutions
Example
- Pull up two local banks’ checking pages and ask them to compare the monthly fees and minimum balances side by side.
- Ask what a debit card from each bank costs to use at the other bank’s machine.
- 6.14.B Debit card or credit card Close
6.14.B · Grade 6
Debit card or credit card
distinguish between debit cards and credit cards
Example
- Ask them to explain the difference between a debit card and a credit card: whose money moves in each case.
- Show a $20 purchase made both ways and ask what happens to the bank balance that same day in each case.
Part of the personal finance topic
- 6.14.C Balance a check register Close
6.14.C · Grade 6
Balance a check register
balance a check register that includes deposits, withdrawals, and transfers
Example
- Give a register starting at $200 with a $50 deposit, a $30 withdrawal, and a $20 transfer out, and ask for the ending balance.
- Give a register with three entries and one arithmetic mistake, and ask them to find it and fix the balance.
- 6.14.D Why a good credit history matters Close
6.14.D · Grade 6
Why a good credit history matters
explain why it is important to establish a positive credit history
Example
- Ask them to explain why a landlord or a lender cares about on-time payments going back years. Listen for the future looking at the past.
Part of the personal finance topic
- 6.14.E What a credit report holds, how long Close
6.14.E · Grade 6
What a credit report holds, how long
describe the information in a credit report and how long it is retained
Example
- Show a sample credit report and ask what kinds of information appear on it, and how long each kind stays.
Part of the personal finance topic
- 6.14.F Credit reports, for borrower and lender Close
6.14.F · Grade 6
Credit reports, for borrower and lender
describe the value of credit reports to borrowers and to lenders
Example
- Ask what a lender learns from a credit report that a borrower cannot just say about themselves.
Part of the personal finance topic
- 6.14.G Ways to pay for college Close
6.14.G · Grade 6
Ways to pay for college
explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study
Example
- Ask them to name five ways to pay for college — savings, grants, scholarships, student loans, work-study — and sort them into money earned, money given, and money borrowed.
Part of the money topic
- 6.14.H How training level changes lifetime income Close
6.14.H · Grade 6
How training level changes lifetime income
compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income
Example
- Compare a $45,000 delivery-driver salary needing no post-secondary schooling with a $55,000 electrician salary needing a two-year certificate and a $65,000 nursing salary needing a four-year degree, and ask for the lifetime gaps over 40 years.
- Ask how that gap changes if the higher-paying job needs four years of tuition paid first.
Part of the money topic
19 TAC §111.26 · the rule text · archived · verified 2026-09-05
Grade 4 53
- 4.1.A Apply mathematics to real-world problems
- 4.1.B Use a problem-solving model
- 4.1.C Select tools and techniques for problems
- 4.1.D Communicate ideas in multiple representations
- 4.1.E Create and use representations
- 4.1.F Analyze relationships; connect and communicate
- 4.1.G Display, explain, and justify precisely
- 4.2.A Ten times right, one-tenth left
- 4.2.B Expanded notation to a billion and hundredths
- 4.2.C Compare and order to a billion
- 4.2.D Round to the hundred thousands place
- 4.2.E Model decimals with objects and money
- 4.2.F Compare and order decimals to hundredths
- 4.2.G Decimals as tenths and hundredths fractions
- 4.2.H Find the decimal at a number-line point
- 4.3.A Build a/b from 1/b, even past one
- 4.3.B Decompose a fraction several ways
- 4.3.C Test two fractions for equivalence
- 4.3.D Compare fractions with unlike denominators
- 4.3.E Add and subtract fractions, same denominator
- 4.3.F Check fraction answers against benchmarks
- 4.3.G Place fractions and decimals on a line
- 4.4.A Add and subtract with the standard algorithm
- 4.4.B Multiply by 10 and 100
- 4.4.C Model two-digit products and perfect squares
- 4.4.D Multiply four-digit and two-digit numbers
- 4.4.E Model a four-digit quotient
- 4.4.F Divide four digits by one digit
- 4.4.G Round to the nearest thousand to estimate
- 4.4.H One- and two-step problems with remainders
- 4.5.A Use strip diagrams and letter equations
- 4.5.B Generate patterns from input-output tables
- 4.5.C Build the perimeter and area formulas
- 4.5.D Solve rectangle perimeter and area problems
- 4.6.A Name points, lines, rays, and angles
- 4.6.B Find and draw lines of symmetry
- 4.6.C Sort triangles as acute, right, or obtuse
- 4.6.D Classify figures by lines and angles
- 4.7.A See an angle as a circle slice
- 4.7.B A degree as 1/360 of a circle
- 4.7.C Measure angles with a protractor
- 4.7.D Draw an angle to a measure
- 4.7.E Find an unknown adjacent angle
- 4.8.A Rank customary and metric units by size
- 4.8.B Convert units within one system
- 4.8.C Solve length, time, volume, and money problems
- 4.9.A Show data on plots and tables
- 4.9.B Answer questions from a data display
- 4.10.A Tell fixed from variable expenses
- 4.10.B Work out the profit
- 4.10.C Weigh different savings options
- 4.10.D Split an allowance three ways
- 4.10.E What financial institutions are for
Grade 5 46
- 5.1.A Apply mathematics to real-world problems
- 5.1.B Use a problem-solving model
- 5.1.C Select tools and techniques for problems
- 5.1.D Communicate ideas in multiple representations
- 5.1.E Create and use representations
- 5.1.F Analyze relationships; connect and communicate
- 5.1.G Display, explain, and justify precisely
- 5.2.A Name a digit's value to thousandths
- 5.2.B Compare and order decimals to thousandths
- 5.2.C Round to the tenth or hundredth
- 5.3.A Estimate solutions across all four operations
- 5.3.B Multiply three-digit by two-digit fluently
- 5.3.C Divide four digits by two digits
- 5.3.D Model decimal products with area models
- 5.3.E Multiply decimals to hundredths, with money
- 5.3.F Model decimal quotients with area models
- 5.3.G Divide decimals to the hundredths
- 5.3.H Add and subtract unlike-denominator fractions
- 5.3.I Multiply a whole number by a fraction
- 5.3.J Model unit-fraction division both ways
- 5.3.K Fluently add and subtract rational numbers
- 5.3.L Divide with unit fractions, both ways
- 5.4.A Tell prime from composite
- 5.4.B Multi-step problems with a letter unknown
- 5.4.C Graph a pattern from a rule
- 5.4.D Tell additive from multiplicative patterns
- 5.4.E What parentheses and brackets mean
- 5.4.F Simplify expressions, two levels of grouping
- 5.4.G Build the volume formulas for a prism
- 5.4.H Perimeter, area, and volume problems
- 5.5 Sort 2-D figures into sets and subsets
- 5.6.A Volume as a count of unit cubes
- 5.6.B Volume as layers times the base area
- 5.7 Solve problems by converting units
- 5.8.A Axes, origin, and how coordinates move
- 5.8.B How to plot an ordered pair
- 5.8.C Plot points from problems and tables
- 5.9.A Display categorical and numerical data
- 5.9.B A scatterplot for paired data
- 5.9.C One- and two-step problems from a display
- 5.10.A Four kinds of tax, defined
- 5.10.B Tell gross income from net income
- 5.10.C Ways to pay, and their trade-offs
- 5.10.D Set up a records system
- 5.10.E What to do when spending exceeds income
- 5.10.F Bring a budget into balance