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Public Practice Guides

Grade-by-grade word problem guides families can inspect before signup

MathRoutine publishes 218 public learning guides and 654 difficulty-specific pages so the product is not just a landing page claim. Each guide shows reasoning focus, common mistakes, sample word problems, and the type of AI support students receive after they try the problem.

12 grades

Grade 1-12 coverage without adding topics that do not belong in a grade's curriculum.

218 learning guides

Grade, topic, and curriculum-strand pages show reasoning patterns, common mistakes, sample problems, and support previews.

654 difficulty pages

Core, Stretch, and Challenge pages clarify what changes as cognitive demand increases.

Popular Free Practice

High-intent math pages families search for first

Start with the guides that match common search intent: worksheets with answers, homework help, step-by-step word problems, Algebra practice, and AP Calculus examples.

Algebra 1 Practice Problems With Answers

Free examples, answers, AI support preview

Algebra 2 Practice Problems With Answers

Free examples, answers, AI support preview

AP Calculus AB Word Problems With Answers

Free examples, answers, AI support preview

AP Calculus Derivative Word Problems With Answers

Free examples, answers, AI support preview

Grade 4 Equivalent Fractions Word Problems With Answers

Free examples, answers, AI support preview

Grade 5 Fraction Homework Help With Answers

Free examples, answers, AI support preview

Grade 5 Fraction Word Problems With Answers

Free examples, answers, AI support preview

Grade 6 Dividing Fractions Word Problems With Answers

Free examples, answers, AI support preview

Grade 6 Fraction Word Problems With Answers

Free examples, answers, AI support preview

Grade 6 Percent Word Problems With Answers

Free examples, answers, AI support preview

Grade 6 Ratio Word Problems With Answers

Free examples, answers, AI support preview

Grade 7 Algebra Homework Help With Answers

Free examples, answers, AI support preview

Grade 7 Percent Word Problems With Answers

Free examples, answers, AI support preview

Grade 7 Ratio Word Problems With Answers

Free examples, answers, AI support preview

Grade 8 Algebra Practice Problems With Answers

Free examples, answers, AI support preview

Grade 8 Algebra Word Problems With Answers

Free examples, answers, AI support preview

AP Calculus Accumulation Integrals With Answers

Free examples, answers, AI support preview

AP Calculus BC Interval of Convergence With Answers

Free examples, answers, AI support preview

Grade 1

8 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 1 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 1 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 1 Addition Word Problems With Answers

part-part-whole + counting on

Grade 1 Subtraction Word Problems With Answers

take-away + left over

Grade 1 Missing Addend Stories Word Problems

unknown addend + part-whole story

Grade 1 Comparison Word Problems Word Problems

comparison gap + larger-minus-smaller

Grade 1 Number Bond Word Problems With Answers

part-part-whole + missing addend

Grade 1 Making Ten Word Problems With Answers

make-ten strategy + part decomposition

Grade 2

12 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 2 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 2 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 2 Time Word Problems

elapsed-time chains + crossing the hour

Grade 2 Measurement Word Problems

unit conversion + missing dimension

Grade 2 Math Word Problems With Answers

part-whole + change story

Grade 2 Two-Digit Addition Word Problems

two-part total + place-value combine

Grade 2 Telling Time Word Problems

time forward + time backward

Grade 2 Measurement Word Problems

same-unit compare + length total

Grade 2 Two-Step Addition Stories Word Problems

combine then add + state tracking

Grade 2 Length Comparison Stories Word Problems

measurement gap + same-unit comparison

Grade 2 Subtraction With Regrouping Word Problems

take-away change + two-digit regrouping

Grade 2 Elapsed Time Word Problems With Answers

clock interval + friendly-time jump

Grade 3

19 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 3 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 3 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 3 Multiplication Word Problems

equal-group modeling + scaling

Grade 3 Division Word Problems

unknown group size + remainder reasoning

Grade 3 Fractions Word Problems

unit fraction reasoning + fraction of a whole

Grade 3 Time Word Problems

elapsed-time chains + crossing the hour

Grade 3 Money Word Problems

budget tracking + change and refund logic

Grade 3 Measurement Word Problems

unit conversion + missing dimension

Grade 3 Word Problem Mixed Word Problems

operation choice + multi-constraint setup

Grade 3 Math Homework Help Word Problems

equal groups + two-step total

Grade 3 Addition Worksheet With Answers

place-value addition + three-part total

Grade 3 Subtraction Worksheet With Answers

take-away + comparison gap

Grade 3 Multiplication Word Problems With Answers

equal groups + array model

Grade 3 Division Word Problems With Answers

equal sharing + number of groups

Grade 3 Money Word Problems With Answers

total cost + change from payment

Grade 3 Equal Groups With Extras Word Problems

equal groups + add-on quantity

Grade 3 Remainders in Context Word Problems

full groups + leftover amount

Grade 3 Array Word Problems With Answers

rectangular array + equal groups

Grade 3 Fractions on a Number Line With Answers

equal partition + unit fraction distance

Grade 4

20 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 4 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 4 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 4 Multiplication Word Problems

equal-group modeling + scaling

Grade 4 Division Word Problems

unknown group size + remainder reasoning

Grade 4 Fractions Word Problems

unit fraction reasoning + fraction of a whole

Grade 4 Time Word Problems

elapsed-time chains + crossing the hour

Grade 4 Money Word Problems

budget tracking + change and refund logic

Grade 4 Measurement Word Problems

unit conversion + missing dimension

Grade 4 Word Problem Mixed Word Problems

operation choice + multi-constraint setup

Grade 4 Math Practice Problems With Answers

multiply then subtract + divide with remainder

Grade 4 Multiplication Worksheet With Answers

array multiplication + equal groups

Grade 4 Division Worksheet With Answers

equal sharing + full groups

Grade 4 Multiplication Word Problems With Answers

multi-digit equal groups + array total

Grade 4 Division Word Problems With Remainders

full groups + leftover amount

Grade 4 Area and Perimeter Word Problems

formula choice + missing side

Grade 4 Multi-Step Word Problems

multiply then subtract + add then divide

Grade 4 Unlike Denominator Stories Word Problems

common denominator + part-whole total

Grade 4 Area and Perimeter Traps Word Problems

formula selection + dimension tracking

Grade 4 Equivalent Fractions Word Problems With Answers

fraction scaling + common partition

Grade 4 Measurement Conversion Word Problems With Answers

unit conversion + mixed-unit comparison

Grade 5

21 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 5 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 5 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 5 Multiplication Word Problems

equal-group modeling + scaling

Grade 5 Division Word Problems

unknown group size + remainder reasoning

Grade 5 Fractions Word Problems

unit fraction reasoning + fraction of a whole

Grade 5 Time Word Problems

elapsed-time chains + crossing the hour

Grade 5 Money Word Problems

budget tracking + change and refund logic

Grade 5 Measurement Word Problems

unit conversion + missing dimension

Grade 5 Word Problem Mixed Word Problems

operation choice + multi-constraint setup

Grade 5 Fraction Homework Help With Answers

fraction of quantity + unlike denominators

Grade 5 Decimal Word Problems With Answers

decimal measurement + money total

Grade 5 Two-Step Word Problems With Answers

multiply then subtract + add then divide

Grade 5 Fraction Word Problems With Answers

fraction of quantity + unlike denominators

Grade 5 Mixed Number Word Problems

mixed-number addition + mixed-number subtraction

Grade 5 Common Core Math Word Problems

operation choice + fraction-whole relationship

Grade 5 Fraction of a Quantity Word Problems

fraction of whole + remaining part

Singapore Math Word Problems Grade 5

part-whole model + comparison bar

ESL Math Word Problems

vocabulary-to-operation bridge + given-goal-trap scan

Grade 5 Multi-Step Word Problem Planning Word Problems

operation sequence + intermediate result

Grade 5 Decimal Money Word Problems With Answers

decimal multiplication + decimal addition

Grade 5 Rectangular Prism Volume Problems With Answers

volume multiplication + missing factor

Grade 6

20 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 6 Addition Word Problems

hidden quantity + part-whole reasoning

Grade 6 Subtraction Word Problems

reverse reasoning + comparison logic

Grade 6 Multiplication Word Problems

equal-group modeling + scaling

Grade 6 Division Word Problems

unknown group size + remainder reasoning

Grade 6 Fractions Word Problems

unit fraction reasoning + fraction of a whole

Grade 6 Time Word Problems

elapsed-time chains + crossing the hour

Grade 6 Money Word Problems

budget tracking + change and refund logic

Grade 6 Measurement Word Problems

unit conversion + missing dimension

Grade 6 Word Problem Mixed Word Problems

operation choice + multi-constraint setup

Grade 6 Math Homework Help With Answers

ratio scale + percent of whole

Grade 6 Unit Rate Word Problems With Answers

unit rate + ratio table

Grade 6 Word Problem Worksheet With Answers

operation sequence + ratio then compare

Grade 6 Ratio Word Problems With Answers

ratio table + scale factor

Grade 6 Percent Word Problems With Answers

part-whole percent + discount

Grade 6 Fraction Word Problems With Answers

fraction multiplication + fraction division

Grade 6 Multi-Step Word Problems

ratio scale then compare + percent of whole

Grade 6 Ratio Table Word Problems Word Problems

ratio table + scale factor

Grade 6 Percent of a Whole Stories Word Problems

part-whole-percent + base amount

Grade 6 Unit Price Word Problems With Answers

unit rate + rate comparison

Grade 6 Dividing Fractions Word Problems With Answers

fraction measurement division + reciprocal operation

Grade 7

18 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 7 Expressions & Equations Word Problems

equation setup + reverse reasoning

Grade 7 Ratios & Proportions Word Problems

unit rate + scale factor

Grade 7 Percents Word Problems

part-whole-percent triangle + percent change

Grade 7 Inequalities Word Problems

limit modeling + boundary values

Grade 7 Geometry & Formulas Word Problems

missing measurement + formula setup

Grade 7 Algebra Homework Help With Answers

two-step equation + unknown recovery

Grade 7 Discount and Markup Word Problems With Answers

percent of whole + discount amount

Grade 7 Two-Step Equations With Answers

fixed amount plus rate + unknown recovery

Grade 7 Percent Word Problems With Answers

percent of whole + markup and discount

Grade 7 Inequality Word Problems With Answers

budget boundary + included endpoint

Grade 7 Ratio Word Problems With Answers

unit rate + ratio table

Grade 7 Area and Volume Word Problems With Answers

formula choice + missing measurement

Grade 7 Unit Rate Word Problems

unit-rate bridge + ratio table

Grade 7 Percent Change Word Problems

changing base + percentage points

Grade 7 Two-Step Inequality Word Problems

budget boundary + at least or at most

Grade 7 Circle and Area Word Problems Word Problems

radius-diameter distinction + area formula

Grade 7 Proportional Relationship Tables With Answers

ratio invariance + constant of proportionality

Grade 7 Scale Drawing Problems With Answers

scale proportion + drawing-to-actual conversion

Grade 8

21 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 8 Linear Equations Word Problems

unknown setup + two-step solving

Grade 8 Linear Functions Word Problems

slope as rate + initial value

Grade 8 Systems of Equations Word Problems

two-variable modeling + intersection meaning

Grade 8 Exponents & Scientific Notation Word Problems

place value scale + power comparison

Grade 8 Algebraic Modeling Word Problems

variable definition + multi-constraint modeling

Grade 8 Quadratic Equations Word Problems

area modeling + factoring structure

Grade 8 Algebra Practice Problems With Answers

fixed fee plus rate + linear input recovery

Grade 8 Linear Function Practice With Answers

rate plus start + slope units

Grade 8 Systems of Equations Worksheet With Answers

count and value + substitution

Grade 8 Linear Equations With Answers

linear model + input recovery

Grade 8 Slope-Intercept Word Problems

initial value plus rate + slope units

Grade 8 Systems of Equations Word Problems With Answers

count and value + substitution

Grade 8 Scientific Notation Word Problems With Answers

power-of-ten comparison + coefficient adjustment

Grade 8 Algebra Word Problems With Answers

budget model + comparison model

Grade 8 Slope-Intercept Model Word Problems

fixed amount plus rate + function notation

Grade 8 Systems of Equations Word Problems

count and value + two relationships

Grade 8 Scientific Notation Word Problems

power-of-ten scale + ratio comparison

Grade 8 Quadratic Modeling Word Problems

area product + projectile height

Grade 8 Variable Definition Word Problems Word Problems

setup-first modeling + constraint equation

Grade 8 Slope From a Table Problems With Answers

difference quotient + constant slope

Grade 8 Break-Even Systems Word Problems With Answers

two-model system + equal-output condition

Grade 9

20 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 9 Geometry Reasoning Word Problems

similarity scale factors + coordinate distance

Grade 9 Polynomials Word Problems

distribution structure + binomial products

Grade 9 Exponential & Logarithmic Models Word Problems

repeated multiplication + decay thresholds

Grade 9 Function Transformations Word Problems

vertical shifts + horizontal shifts

Algebra 1 Practice Problems With Answers

binomial product + factor relationship

Grade 9 Similar Triangles Worksheet With Answers

similarity scale + proportion setup

Grade 9 Geometry Word Problems With Answers

similarity scale + angle relationship

Grade 9 Polynomial Word Problems With Answers

area model + factored form

Grade 9 Exponential Function Word Problems With Answers

growth factor + decay factor

Grade 9 Function Transformation Practice With Answers

horizontal shift + vertical shift

Grade 9 Similar Triangles Word Problems

similarity ratio + area scale factor

Grade 9 Polynomial Products Word Problems

area model + distribution

Grade 9 Exponential Growth and Decay Word Problems

multiplicative change + decay factor

Grade 9 Function Shifts Word Problems

horizontal shift + vertical shift

Grade 9 Exponential Threshold Word Problems Word Problems

growth factor + threshold inequality

Grade 9 Transformation Reverse Questions Word Problems

reverse transformation + branch choice

Grade 9 Coordinate Geometry Proofs With Answers

coordinate proof + parallel-side evidence

Grade 9 Factoring Polynomials Word Problems With Answers

quadratic factorization + area model

Grade 9 Triangle Congruence Proofs With Answers

SAS congruence + correspondence order

Grade 9 Polynomial Zeros and Multiplicity With Answers

factor-to-zero connection + multiplicity parity

Grade 10

24 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 10 Algebraic Modeling Word Problems

variable definition + multi-constraint modeling

Grade 10 Quadratic Equations Word Problems

area modeling + factoring structure

Grade 10 Polynomials Word Problems

distribution structure + binomial products

Grade 10 Exponential & Logarithmic Models Word Problems

repeated multiplication + decay thresholds

Grade 10 Function Transformations Word Problems

vertical shifts + horizontal shifts

Grade 10 Rational & Radical Functions Word Problems

domain restrictions + radical evaluation

Grade 10 Complex Numbers Word Problems

component tracking + i squared as negative one

Grade 10 Sequences & Series Word Problems

common difference + common ratio

Algebra 2 Practice Problems With Answers

quadratic area model + function transformation

Grade 10 Complex Numbers Worksheet With Answers

component separation + i squared sign change

Grade 10 Quadratic Word Problems With Answers

area product + projectile return

Grade 10 Rational and Radical Equations With Answers

input recovery + domain exclusion

Grade 10 Polynomial Functions With Answers

zero-factor link + factored form

Grade 10 Sequence and Series Problems With Answers

arithmetic nth term + geometric nth term

Grade 10 Rational Functions Word Problems

asymptote shift + excluded value

Grade 10 Radical Equations Word Problems

domain restriction + inverse operation

Grade 10 Complex Roots Word Problems

discriminant signal + complex conjugates

Grade 10 Arithmetic and Geometric Sequences Word Problems

nth-term indexing + geometric multiplier

Grade 10 Logarithmic Thresholds Word Problems

reverse exponent + first exceed

Grade 10 Remainder Theorem Word Problems Word Problems

remainder theorem + parameter system

Grade 10 Completing the Square Word Problems With Answers

quadratic form selection + vertex extraction

Grade 10 Rational Function Asymptotes With Answers

domain restriction + vertical asymptote

Grade 10 Polynomial Long Division With Answers

polynomial division + degree reduction

Grade 10 Radical Equations With Extraneous Solutions

radical isolation + equation squaring

Grade 11

15 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 11 Precalculus Word Problems

function representation shifts + inverse and parameter recovery

Precalculus Homework Help With Answers

trig model features + inverse recovery

Grade 11 Precalculus Word Problems With Answers

trigonometric model + inverse function

Grade 11 Trigonometry Word Problems With Answers

periodic context + amplitude-midline

Grade 11 Inverse Function Problems With Answers

input recovery + function inverse

Grade 11 Trigonometric Models Word Problems

sinusoidal features + periodic context

Grade 11 Inverse Functions Word Problems

function reversal + input recovery

Grade 11 Polar Coordinates Word Problems

x-y components + squared radius

Grade 11 Precalculus Rational Models Word Problems

vertical asymptote + parameter recovery

Grade 11 Piecewise Function Models Word Problems

interval condition + rule selection

Grade 11 Logarithmic Scale Models Word Problems

log reverse reasoning + base interpretation

Precalculus Sinusoidal Modeling Problems With Answers

periodic model construction + phase shift

Precalculus Logarithmic Composition Problems With Answers

function composition + logarithmic domain

Precalculus Law of Sines Ambiguous Case Problems

SSA ambiguity + inverse-sine branch

Precalculus Trigonometric Equations With Answers

trigonometric substitution + factored equation

Grade 12

20 learning guides

Each page is indexable and includes sample problems, reasoning patterns, likely mistakes, and support examples.

Grade 12 Calculus AB Word Problems

instantaneous rate + net accumulation

Grade 12 Calculus BC Word Problems

series convergence + parametric and polar interpretation

Calculus Homework Help With Answers

derivative interpretation + related rates

AP Calculus Derivative Word Problems With Answers

instantaneous rate + derivative sign

AP Calculus AB Word Problems With Answers

related rates + net change

AP Calculus BC Series Practice With Answers

ratio test + endpoint testing

AP Calculus Related Rates With Answers

chain rule over time + instantaneous relationship

AP Calculus Accumulation Integrals With Answers

FTC interpretation + signed area

AP Calculus BC Interval of Convergence With Answers

ratio test + endpoint behavior

AP Calculus BC Parametric Calculus With Answers

parametric slope + component-rate ratio

Grade 12 Related Rates Word Problems

implicit rate relationship + chain rule

Grade 12 Accumulation Integrals Word Problems

net accumulation + FTC interpretation

Grade 12 Convergence Tests Word Problems

ratio test + alternating series

Grade 12 Taylor Series Word Problems

centered approximation + first omitted term

Grade 12 Optimization Word Problems Word Problems

objective function + constraint substitution

Grade 12 Parametric Motion Word Problems

parametric derivative + component rates

AP Calculus FTC and Chain Rule Problems With Answers

accumulation derivative + chain rule

AP Calculus BC Taylor Polynomial Problems With Answers

series coefficient structure + polynomial truncation

AP Calculus Separable Differential Equations With Answers

variable separation + implicit integration

AP Calculus BC Polar Area Problems With Answers

polar curve tracing + one-half r-squared integral

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