6th Grade EOG Mathematics Test with Answer Key 2026-2027

 6th Grade Mathematics

End-of-Year Assessment

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Parent Preparation Guide & Complete Examination

 

 

Aligned To Texas TEKS Mathematics — Grade 6

Frameworks Used Bloom's Taxonomy Hess's Cognitive Rigor Matrix

 

FOR PARENTS: What Is This Document?   This guide contains a complete, rigorous 6th Grade mathematics examination aligned to the Texas Essential Knowledge and Skills (TEKS). It is designed to help parents understand what their child is expected to know by the end of 6th Grade and to prepare them for STAAR. Each question includes the specific TEKS standard, Bloom's Taxonomy level, Depth of Knowledge (DOK) level, a parent-friendly explanation of what the question measures, at-home support activities, and common mistakes to watch for.

 

 

 

PART 1: NUMBER & OPERATIONS / RATIONAL NUMBERS

 

Student Name: ___________________________    Date: _______________    Grade: 6

 

Directions: Read each question carefully. Show all your work. For multiple-choice questions, circle the letter of the best answer. For open-response questions, write your answer and explanation in the space provided.

 

Question 1   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.2A

Order the following numbers from least to greatest:     -3,   2.5,   -1/2,   0,   -2.75,   1

Answer: _______________________________________________

 

Question 2   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.3A

A submarine is at -240 feet (below sea level). It rises 95 feet. Then it dives 130 feet. What is its final depth?

A)  -275 feet B)  -145 feet C)  -275 feet D)  -465 feet

 

Question 3   Bloom's: Analyze  |  DOK: 3  |  TEKS: 6.2E

Which is greater: -4/5 or -0.75? Show your reasoning by converting to a common form and justify which is greater on a number line.

Answer: _______________________________________________

 

 

PART 2: PROPORTIONALITY & RATIOS

 

Question 4   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.4B

A car travels 270 miles in 4.5 hours at a constant speed. What is the unit rate in miles per hour? If the driver continues at the same rate, how far will she travel in 7 hours?

A)  60 mph; 420 miles B)  60 mph; 360 miles C)  54 mph; 378 miles D)  60 mph; 480 miles

 

Question 5   Bloom's: Analyze  |  DOK: 3  |  TEKS: 6.4E

A store sells 3 notebooks for $4.50. Another store sells 5 notebooks for $7.25.  Which store has the better unit price? Show your work and explain how you know.

Answer: _______________________________________________

 

Question 6   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.5A

The tax rate in a city is 8.25%. A family buys a bicycle for $185. What is the sales tax? What is the total price including tax?

Answer: _______________________________________________

 

 

PART 3: EXPRESSIONS, EQUATIONS & INEQUALITIES

 

Question 7   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.9A

Write and solve an equation for the following:  A phone plan costs $25 per month plus $0.10 per text message. Last month the total bill was $38.50. How many text messages were sent?

A)  138 texts B)  135 texts C)  135 texts D)  385 texts

 

Question 8   Bloom's: Analyze  |  DOK: 3  |  TEKS: 6.9B

Graph and interpret the inequality: 2x + 3 > 11  A) Solve for x. B) What does your solution mean in this context: 'A student must score more than 11 points total. Each question is worth 2 points and there is a 3-point bonus.'

Answer: _______________________________________________

 

Question 9   Bloom's: Evaluate  |  DOK: 3  |  TEKS: 6.10A

Two students are selling cookies at a bake sale:    Student A charges $0.75 per cookie.    Student B charges $1.00 per cookie but gives a free cookie for every 5 purchased.  For a purchase of 10 cookies, who offers the better deal? Show all calculations and justify your choice.

Answer: _______________________________________________

 

 

PART 4: GEOMETRY & MEASUREMENT

 

Question 10   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.8A

Find the area of a triangle with a base of 14 cm and a height of 9 cm. Then find the area of a parallelogram with a base of 14 cm and a height of 9 cm. What do you notice?

Answer: _______________________________________________

 

Question 11   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.8D

A storage box has a surface area to calculate. It is a rectangular prism: 10 cm × 6 cm × 4 cm. How many square centimeters of cardboard are needed to make the box? (Find the surface area.)

Answer: _______________________________________________

 

 

PART 5: DATA ANALYSIS & STATISTICS

 

Question 12   Bloom's: Apply  |  DOK: 2  |  TEKS: 6.12A

Class scores: 72, 85, 91, 68, 85, 79, 95, 85, 70, 88  A) Find the mean, median, and mode. B) If the teacher adds 5 bonus points to every score, how does each measure change?

Answer: _______________________________________________

 

Question 13   Bloom's: Evaluate  |  DOK: 3  |  TEKS: 6.12C

A school reports the average teacher salary as $68,000. A news article claims: 'Teachers at this school are well-paid.' But the individual salaries are: $32,000, $34,000, $36,000, $40,000, $45,000, $195,000.  Is the news article's claim supported by the data? Which measure of center best represents the typical teacher's salary? Use evidence.

Answer: _______________________________________________

 

 

PART 6: EXTENDED PROBLEM SOLVING

 

Question 14   Bloom's: Analyze  |  DOK: 3  |  TEKS: 6.4/6.9

A small business sells handmade candles. Production costs:    Fixed costs: $120 per month (rent, tools)    Variable cost: $3.50 per candle    Selling price: $8 per candle  A) Write an equation for monthly PROFIT in terms of n candles sold. B) How many candles must be sold to break even (profit = $0)? C) What is the profit if 60 candles are sold?

Answer: _______________________________________________

 

Question 15   Bloom's: Create  |  DOK: 4  |  TEKS: All Domains

EXTENDED RESPONSE: You are a financial advisor for a day!  A 12-year-old client earns $50/month. Create a COMPLETE monthly budget that:    (1) Covers at least 3 types of expenses    (2) Includes savings (at least 15%)    (3) Does not exceed income    (4) Uses a table with amounts and percentages    (5) Justifies every budget decision with mathematical reasoning  Then: Project how much they will have saved after 6 months.

Answer: _______________________________________________

 

 

COMPLETE ANSWER KEY

For Parent and Educator Use

 

 

Q#	Answer	Explanation	TEKS
1	-3, -2.75, -1/2, 0, 1, 2.5	Negative numbers increase toward zero; positive numbers increase away. -3 < -2.75 < -0.5 < 0 < 1 < 2.5.	6.2A
2	A) -275 feet	-240 + 95 = -145. -145 - 130 = -275 feet.	6.3A
3	-0.75 > -4/5 because -4/5 = -0.80 and -0.75 > -0.80 (closer to zero).	-4/5 = -0.80. Comparing -0.80 and -0.75: since -0.75 is closer to 0, it is greater (-0.75 > -0.80).	6.2E
4	A) 60 mph; 420 miles	270 ÷ 4.5 = 60 mph. 60 × 7 = 420 miles.	6.4B
5	Store 1: $1.50/notebook. Store 2: $1.45/notebook. Store 2 is cheaper per notebook.	Store 1: $4.50÷3=$1.50 each. Store 2: $7.25÷5=$1.45 each. $1.45 < $1.50, so Store 2 is the better deal.	6.4E
6	Tax: $15.26. Total: $200.26.	Tax = 185 × 0.0825 = $15.2625 ≈ $15.26. Total = $185 + $15.26 = $200.26.	6.5A
7	B) 135 texts	25 + 0.10t = 38.50. 0.10t = 13.50. t = 135 texts.	6.9A
8	A) x > 4. B) The student must answer more than 4 questions correctly (at least 5).	2x+3>11 → 2x>8 → x>4. Context: x = questions answered correctly. x>4 means 5 or more correct answers needed.	6.9B
9	Student A: 10 × $0.75 = $7.50. Student B: 10 cookies but gets 2 free → pays for 8 → $8.00. Student A is a better deal by $0.50.	Student B: 10 cookies ÷ 5 = 2 free cookies. Pays for 8: 8×$1.00=$8.00. Student A: 10×$0.75=$7.50. Student A saves the buyer $0.50.	6.10A
10	Triangle: 63 cm². Parallelogram: 126 cm². The parallelogram has exactly double the area of the triangle with the same base and height.	Triangle = (1/2)bh = (1/2)(14)(9) = 63 cm². Parallelogram = bh = 14×9 = 126 cm². This illustrates why the triangle formula includes 1/2.	6.8A
11	Surface area = 248 cm².	SA = 2(lw + lh + wh) = 2(10×6 + 10×4 + 6×4) = 2(60+40+24) = 2(124) = 248 cm².	6.8D
12	A) Mean=81.8, Median=85, Mode=85. B) Each measure increases by exactly 5 points: Mean=86.8, Median=90, Mode=90.	Adding a constant to all values shifts the entire distribution by that amount — mean, median, and mode all increase by the same amount (5).	6.12A
13	The claim is misleading. The $195,000 outlier inflates the mean. Median = ($36,000+$40,000)/2 = $38,000, which better represents the typical teacher. Most teachers earn far below $68,000.	Mean: (32+34+36+40+45+195)÷6 = 382÷6 = $63,667 ≈ $68K. Median = $38K. The principal earns $195K and distorts the mean dramatically. 5 of 6 teachers earn below the mean.	6.12C
14	A) P = 8n - (120 + 3.5n) = 4.5n - 120. B) 4.5n = 120 → n ≈ 27 candles. C) P = 4.5(60) - 120 = $150.	Profit = Revenue - Costs. Revenue = 8n. Costs = 120 + 3.5n. Profit = 4.5n - 120. Break-even: 4.5n=120, n=26.67 → 27 candles. At 60: $150 profit.	6.4/6.9
15	Answers will vary. Full credit: complete budget totaling ≤$50, includes ≥3 categories, savings ≥$7.50, percentages shown, 6-month projection calculated.	Example: Savings $10 (20%), Snacks $12 (24%), Entertainment $15 (30%), School supplies $8 (16%), Misc $5 (10%). Total=$50. 6-month savings: $10×6=$60.	All Domains

 

 

PARENT GUIDE

Understanding Every Question: What It Measures & How to Help

 

 

Q1: Ordering Rational Numbers Including Negatives TEKS 6.2A  |  Bloom's: Apply | DOK: 2

What This Question Measures: 6th grade introduces the complete rational number system — integers, fractions, decimals, both positive and negative. Ordering these requires a solid mental number line extending in both directions. How to Help Your Child at Home: Draw a number line together from -5 to 5. Place the numbers on it physically. Temperature scales (thermometers) and bank account balances are excellent real-world models for negative numbers. Watch For / Common Mistakes: Students often think -3 is greater than -1/2 because 3 > 1/2. In the negatives, the number farther from zero is SMALLER (colder temperatures, deeper debt). Use a thermometer analogy.

 

Q2: Integer Operations in Context TEKS 6.3A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students add and subtract integers in a multi-step real-world context — applying the rules for integer operations (rising = positive, diving = negative) to a navigation problem. How to Help Your Child at Home: Use an elevator model: floor 0 = sea level, basement floors = negative. 'Start at floor -4, go up 3, then go down 6.' What floor are you on? Elevators make integer arithmetic concrete. Watch For / Common Mistakes: Students may add all three absolute values without considering direction, or may forget that subtracting a positive moves further negative. A number line drawn physically helps prevent sign errors.

 

Q3: Comparing Negative Fractions and Decimals TEKS 6.2E  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students compare negative rational numbers in mixed forms — requiring conversion to a common form AND understanding of negative number ordering, two skills working simultaneously. How to Help Your Child at Home: Convert and draw. Make your child write both as decimals, then place both on a number line. The one closer to zero is always greater. This is counterintuitive and requires practice. Watch For / Common Mistakes: Students may correctly compute -4/5 = -0.80 but then say -0.80 > -0.75 because '80 > 75.' The negative sign reverses the order. Always use a number line to double-check negative comparisons.

 

Q4: Unit Rates and Proportional Reasoning TEKS 6.4B  |  Bloom's: Apply | DOK: 2

What This Question Measures: Unit rates (speed, price per unit, efficiency) are a cornerstone of 6th grade proportional reasoning. Students find and apply a unit rate — a skill that connects to science, economics, and everyday decision-making. How to Help Your Child at Home: Check unit prices on grocery shelves (price per ounce). Calculate which size is the better deal. Use GPS apps — discuss: 'If we're going 65 mph for 3 hours, how far will we go?' Watch For / Common Mistakes: Students may divide 4.5 ÷ 270 instead of 270 ÷ 4.5, getting a rate less than 1 mph. Unit rate = miles per hour = miles ÷ hours. Always divide in the direction the unit label reads.

 

Q5: Comparing Unit Prices — Consumer Math TEKS 6.4E  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students compute and compare unit rates in a consumer context — one of the most practically useful math skills. This is exactly the kind of reasoning needed at grocery stores, online shopping, and budget planning. How to Help Your Child at Home: Make unit price calculation a grocery store game. For each item bought in bulk vs. individual, compute the price per unit. Who can find the best deal? This is real financial literacy in action. Watch For / Common Mistakes: Students may compare total prices ($4.50 < $7.25) rather than unit prices. The larger package isn't always cheaper per unit. The point is to find the cost for ONE item to make a fair comparison.

 

Q6: Calculating Sales Tax and Total Cost TEKS 6.5A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply percent to compute sales tax — a ubiquitous real-world application of proportional reasoning. This is explicitly required by TEKS 6.5A and directly reflects adult financial literacy. How to Help Your Child at Home: On every purchase, have your child estimate and then calculate the tax. 'The item is $40. At 8% tax, about how much is tax?' Then check the receipt. Make it a habit before reaching the register. Watch For / Common Mistakes: Students may calculate 8.25% of the total INCLUDING tax (circular reasoning) or forget to ADD the tax to the original price. Clarify: tax is calculated on the PRE-TAX price, then added.

 

Q7: Writing and Solving One-Step/Two-Step Equations TEKS 6.9A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students write and solve a linear equation from a word problem — the core of 6th grade algebra. This mirrors how mathematicians and scientists model real-world situations. How to Help Your Child at Home: Look at a real phone or utility bill together. Identify the fixed cost and the variable cost. Write the equation. Solve for the unknown. This makes algebra immediately relevant. Watch For / Common Mistakes: Students may set up the equation correctly but then divide 13.50 ÷ 0.10 incorrectly (getting 13.5 instead of 135). Decimal division with small divisors requires care — encourage students to verify by substituting back.

 

Q8: Solving and Interpreting Inequalities TEKS 6.9B  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students solve a two-step inequality AND interpret the solution in a real context — requiring both procedural skill and conceptual understanding of what 'x > 4' means in practice. How to Help Your Child at Home: Create inequality scenarios: 'You need to earn MORE than $50 for a reward. You earn $8 per hour. Write and solve the inequality.' Discuss: why is x > 4 different from x = 4? Watch For / Common Mistakes: Students may solve the equation (x=4) and stop, forgetting the inequality symbol changes. Also: the solution 'x > 4' means 5, 6, 7... questions — not 4.1, 4.2... Discuss what makes sense in context.

 

Q9: Evaluating Pricing Deals — Multi-Variable Consumer Math TEKS 6.10A  |  Bloom's: Evaluate | DOK: 3

What This Question Measures: Students evaluate a complex pricing scenario requiring multi-step reasoning and comparison — excellent preparation for real consumer decisions and for the extended STAAR problem types. How to Help Your Child at Home: Look for 'buy X get Y free' deals at the grocery store. Calculate: 'Is this actually cheaper per item?' Often the unit price still favors the single-item price. Develop critical consumer thinking. Watch For / Common Mistakes: Students may think Student B is better because '$1 each with free ones sounds good.' The math must win: calculate ACTUAL cost for the specific quantity. The appeal of 'free' often obscures the real price.

 

Q10: Area of Triangles and Parallelograms — Understanding the Relationship TEKS 6.8A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply area formulas for triangles and parallelograms AND discover the conceptual relationship between them — the triangle formula is literally half the parallelogram formula. How to Help Your Child at Home: Cut a parallelogram from cardboard. Cut it diagonally into two triangles. Show that two triangles make one parallelogram. This is WHY we divide by 2 for triangles — a conceptual understanding, not just a memorized formula. Watch For / Common Mistakes: Students often forget the 1/2 in the triangle formula or use the slant side instead of the height. The HEIGHT is always perpendicular to the base — it may not be a side of the triangle.

 

Q11: Surface Area of Rectangular Prisms TEKS 6.8D  |  Bloom's: Apply | DOK: 2

What This Question Measures: Surface area (total outside area of a 3D shape) is a new 6th grade concept. It applies directly to packaging design, painting, and wrapping — real-world manufacturing and engineering contexts. How to Help Your Child at Home: Unfold a cereal box into its net (flat shape). Measure each face. Calculate the area of each rectangle. Add them all up — that's the surface area. This is exactly how packaging engineers work. Watch For / Common Mistakes: Students may confuse surface area with volume. Surface area = outside covering. Volume = inside space. Painting a box → surface area. Filling a box → volume. One uses square units, one uses cubic units.

 

Q12: Measures of Center and Effect of Adding a Constant TEKS 6.12A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students compute measures of center AND analyze how adding a constant affects the entire distribution — an important statistical concept that lays groundwork for transformations and data analysis. How to Help Your Child at Home: Record temperatures for a week. Then 'add 10 degrees' to simulate a heat wave. What happens to the average? The middle? Does the most common temperature change? Explore this transformation. Watch For / Common Mistakes: Students may correctly compute the original measures but recompute from scratch after adding 5 — missing the elegant insight that adding a constant shifts all measures equally. This shortcut is worth teaching explicitly.

 

Q13: Statistical Reasoning — Evaluating Claims from Data TEKS 6.12C  |  Bloom's: Evaluate | DOK: 3

What This Question Measures: DOK 3 Evaluate — students must analyze a real-world claim, identify how an outlier distorts the mean, and argue for a more appropriate measure. This is genuine media and statistical literacy. How to Help Your Child at Home: Look at news articles together that use averages. Ask: 'Is the mean the right number here? Could one very high or low number be pulling it up or down?' This builds lifelong critical thinking about statistics. Watch For / Common Mistakes: Students may accept the news claim because '$68,000 sounds high.' The job here is to look behind the headline. Require evidence: 'How many teachers earn MORE than the mean? Less?' (5 of 6 earn less — that tells the story.)

 

Q14: Profit, Break-Even Analysis — Business Math with Algebra TEKS 6.4/6.9  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students write a profit equation, solve for break-even, and evaluate profit — integrating expressions, equations, and proportional reasoning in a real business context that connects to economics and entrepreneurship. How to Help Your Child at Home: Plan a lemonade stand or bake sale together. Calculate real fixed costs and variable costs. Ask: 'How many do we need to sell to make money? How much profit will we earn if we sell 50?' This is the most real-world applicable math in 6th grade. Watch For / Common Mistakes: Students may write Revenue = Profit (ignoring costs) or may correctly write the equation but then fail to solve it algebraically. Encourage: 'Write the equation FIRST, then solve.'

 

Q15: Design a Complete Budget — Financial Literacy Capstone TEKS All Domains  |  Bloom's: Create | DOK: 4

What This Question Measures: Bloom's CREATE at DOK 4 — the capstone financial literacy task. Students design, justify, and project a complete budget using ratios, percents, operations, and algebraic thinking. This integrates all 6th grade domains. How to Help Your Child at Home: Create a real budget for your child's actual monthly money (allowance, gifts, earnings). Make it official — write it down, revisit it monthly. Discuss: 'Did we stick to the budget? What needs to change?' Real budgeting is the most important financial education a parent can provide. Watch For / Common Mistakes: Students may create a budget that doesn't add up to exactly $50 or that omits the savings requirement. Encourage them to check: 'Do all my percentages add to 100%? Do all my dollar amounts add to $50?'

 

 

Scoring Guide & Next Steps

 

 

Score	Performance Level	Recommended Action
27–30	Masters Grade Level	Excellent! Focus on enrichment and extension. Explore real-world applications and the next grade's preview topics.
22–26	Meets Grade Level	Strong! Review missed questions by domain. Use the Parent Guide tips for weak areas.
16–21	Approaches Grade Level	Spend 15 minutes daily on the domains where most questions were missed. Use hands-on activities from the guide.
0–15	Developing Foundational Skills	Schedule time with the teacher. Focus on the first two TEKS domains — they are the foundation for everything else.

 

 

 

This guide was developed using Texas TEKS Mathematics standards for Grade 6, Bloom's Revised Taxonomy, and Hess's Cognitive Rigor Matrix. All questions are original and written to mirror STAAR-aligned rigor. Designed to bridge classroom learning and home support.