Lenny LearningLenny
Create
Explore
Workspace
LoginSign up
MathEnglish Language ArtsScience & EngineeringSocial StudiesGlobal LanguagesHealth & Physical EducationSpecial EducationCounseling & Life SkillsArts & CreativityESL
Lenny LearningLenny
Lenny Learning
About
Training
Pricing
Support
Contact
© 2026 Lenny Learning Inc.

Ratios

SequencesLessonsMaterialsVideos
  1. Math

Ratios

SequencesLessonsMaterialsVideos
SequencesLessonsMaterialsVideos

Comparisons of quantities using unit rates and proportional reasoning. Connects tables, graphs, and equations to represent constant rates of change.

Ratios and ProportionsProportional relationships, unit rates, and constant of proportionality. Develops strategies for solving multi-step problems involving scale, percentages, and equivalent ratios.
Proportional RelationshipsAnalysis of equivalent ratios and the constant of proportionality across tables, graphs, and equations. Connects unit rates to linear relationships and real-world scaling applications.
Unit RateCalculation and comparison of rates where the second quantity is one unit. Applies division strategies to solve real-world problems involving constant speed, unit pricing, and measurement conversions.
MathNumbers & CountingCounting ObjectsNumber NamesComparing NumbersNumber OperationsCounting SequenceNumbers 0-10Place Value Understanding and SystemAdd and Subtract Within 20Addition and Subtraction ConceptsAddition and Subtraction EquationsAddition and Subtraction ProblemsFoundations for MultiplicationMultiplication and Division PropertiesMultiply and Divide Within 100Multiplication and Division ProblemsFactors and MultiplesProperties of OperationsPatterns and RelationshipsGenerate and Analyze PatternsMulti-Digit ArithmeticPlace Value OperationsMulti-Digit and Decimal OperationsNumerical ExpressionsFour Operations and PatternsFour Operations Problem SolvingMeasurement & DataMeasurable AttributesMeasuring LengthsMeasure and Estimate Lengths in Standard UnitsRelate Addition and Subtraction to LengthClassifying and Counting ObjectsTime and MoneyArea Concepts and MeasurementPerimeter and Area MeasuresAngle Concepts and MeasurementTime, Volume, and MassMeasurement Unit ConversionsGeometryIdentifying ShapesShapes and AttributesShape Attributes and ReasoningShapes and CompositionClassifying 2D FiguresGeometric Figures and RelationshipsLines, Angles, and ShapesAngle, Area, and VolumeGeometric MeasurementVolume of 3D ShapesCoordinate Plane ApplicationsTransformations in the PlaneCongruence and SimilarityUnderstand congruence in terms of rigid motionsSimilarity and TransformationsProve Theorems Involving SimilarityPythagorean TheoremTrigonometry for General TrianglesMake Geometric ConstructionsProve Geometric TheoremsTheorems About CirclesFind Arc Lengths And Areas of Sectors of CirclesVolume FormulasRelationships Between Two-Dimensional and Three-Dimensional ObjectsProve Simple Geometric Theorems AlgebraicallyTranslate Between Geometric Description and Equation for Conic SectionApply Geometric Concepts in Modeling SituationsFractions & DecimalsFractions as NumbersBuilding FractionsFraction Equivalence and OrderingAdding and Subtracting FractionsMultiplying and Dividing FractionsDividing FractionsDecimal FractionsMulti-Digit Computation and FactorsAdd, Subtract, Multiply, and Divide Rational NumbersRational Number SystemIrrational Numbers and ApproximationsRatiosRatios and ProportionsProportional RelationshipsUnit RateAlgebraAlgebraic ExpressionsGenerate Equivalent ExpressionsQuantitative RelationshipsProportional Relationships and Linear EquationsEquations and InequalitiesEquation Solving and ReasoningLinear Equations and SystemsGraph Equations and InequalitiesSystems of EquationsReal-World Algebraic ProblemsQuantitative Reasoning with UnitsExpression StructureEquivalent Expression FormsRadicals and Integer ExponentsRational ExponentsRational and Irrational NumbersPolynomial OperationsPolynomial IdentitiesPolynomial Zeros and FactorsRational ExpressionsComplex Number OperationsComplex Numbers in PolynomialsComplex Numbers on PlaneStatistics & ProbabilityRepresent and Interpret DataData DistributionsStatistical VariabilityProbability ModelsCompound Event ProbabilitiesStatistical SamplingInterpret Categorical and Quantitative DataBivariate Data PatternsInterpret Linear ModelsComparing Two PopulationsRandom Processes in StatisticsIndependence and Conditional ProbabilityExpected ValuesProbability-Based Decision MakingStatistical Inference and ConclusionsFunctionsFunction Concepts and NotationDefine and Compare FunctionsInterpret Functions in ContextAnalyze Function RepresentationsModel Relationships with FunctionsIdentify Linear vs Exponential GrowthDistinguish Between Function TypesCompare Growth RatesInterpret Function ExpressionsBuild Functions from RelationshipsConstruct and Model FunctionsTransform and Combine FunctionsModel Comparison and SelectionSolve Exponential EquationsTrigonometryTrigonometric Ratios Involving Right TrianglesTrigonometric Functions and Unit CircleModel with Trigonometric FunctionsTrigonometric IdentitiesVectors & MatricesIntroduction to Vectors and MatricesVector QuantitiesVector OperationsMatrix OperationsCalculusLimits and ContinuityDerivative Concepts and NotationDerivative Rules and TechniquesApplications of DerivativesOptimization ProblemsRelated RatesCurve Sketching and AnalysisIntegration Concepts and NotationAntiderivatives and Indefinite IntegralsDefinite Integrals and AreaFundamental Theorem of CalculusIntegration TechniquesApplications of IntegrationDifferential EquationsSequences and SeriesParametric and Polar FunctionsVector-Valued Functions
Material
Relationship Review Practice Answer Key

Relationship Review Practice Answer Key

Teacher answer key for Day 4 Relationship Review Practice Set. Includes solutions for unit rate interpretation and origin meaning. Revised for robust variable rendering, better labels, and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Relationship Review Answer Key

Relationship Review Answer Key

Teacher answer key for Day 4 Relationship Review student worksheet. Includes solutions for interpreting (1, r) and (0, 0) on a graph. Revised for better spacing, higher contrast labels, and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Proportional Site Practice Answer Key

Proportional Site Practice Answer Key

Teacher answer key for Day 3 Proportional Site Practice Set. Includes solutions for constant k, table completion, and proportionality identification. Revised with robust variable rendering and improved grid alignment.

AG

Anna Gomez

Other
4/29
Material
Proportional Plots Answer Key

Proportional Plots Answer Key

Teacher answer key for Day 3 Proportional Plots student worksheet. Includes solutions for constant k calculations, table completion, and graphing rules. Revised for better page consolidation and clear visual reference.

AG

Anna Gomez

Other
4/29
Material
Equation Assembly Practice Answer Key

Equation Assembly Practice Answer Key

Teacher answer key for Day 2 Equation Assembly Practice Set. Includes solutions for one-step and two-step equation practice. Revised for robust variable rendering and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Equation Assembly Answer Key

Equation Assembly Answer Key

Teacher answer key for Day 2 Equation Assembly student worksheet. Includes solutions for one-step and two-step equations and substitution checks. Revised for better page consolidation and high-contrast printing.

AG

Anna Gomez

Other
4/29
Material
Expression Site Practice Answer Key

Expression Site Practice Answer Key

Teacher answer key for Day 1 Expression Site Practice Set. Includes solutions for independent practice on combining like terms and distributive property. Revised for robust variable rendering and fixed page consolidation.

AG

Anna Gomez

Other
4/29
Material
Expression Engineering Answer Key

Expression Engineering Answer Key

Teacher answer key for Day 1 Expression Engineering student worksheet. Includes solutions for combining like terms, the distributive property, and multi-step simplification. Revised for higher contrast, better page breaks, and print-ready styles.

AG

Anna Gomez

Other
4/29
Material
Similarity Blueprint Reference Sheet

Similarity Blueprint Reference Sheet

A student-friendly reference sheet for similarity concepts. Includes formulas for scale factor, similarity criteria (AAA, SSS, SAS), and a visual guide for shadow trigonometry.

DE

Donia ElSayed

Math Teacher
4/28
Material
Project Master Rubric Teacher Guide

Project Master Rubric Teacher Guide

A comprehensive teacher's rubric for the Similarity Superstars project. Covers poster, art, and presentation components with specific grading criteria for data, logic, and polish.

DE

Donia ElSayed

Math Teacher
4/28
Material
Similarity Showdown Presentation Guide

Similarity Showdown Presentation Guide

A digital slide presentation template and guide for students. Covers similarity criteria (AAA, SAS, SSS), presentation requirements, and slide layout templates.

DE

Donia ElSayed

Math Teacher
4/28
Material
Artful Proportions Art Guide

Artful Proportions Art Guide

A guide for students to create similarity-based art and tessellations. Includes sections for base shape design, scale factor definitions, and artistic requirements.

DE

Donia ElSayed

Math Teacher
4/28
Material
Shadow Sleuths Poster Guide

Shadow Sleuths Poster Guide

A project guide for students to conduct indirect measurement using shadows. Includes data collection tables, a ratio setup guide, and poster requirements.

DE

Donia ElSayed

Math Teacher
4/28
Material
Relationship Review Practice Set

Relationship Review Practice Set

Independent practice worksheet for Day 4 focusing on interpreting proportional relationships. Revised with robust variable rendering, improved solving layout, and high-contrast work areas. Consolidated into a clean two-page format.

AG

Anna Gomez

Other
4/28
Material
Proportional Site Practice Set

Proportional Site Practice Set

Independent practice worksheet for Day 3 focusing on proportional relationships. Includes calculating the constant k, completing tables, graphing, and identifying proportional equations. Revised with robust variable rendering, better grid alignment, and fixed page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Practice Set

Equation Assembly Practice Set

Independent practice worksheet for Day 2 focusing on solving equations. Includes sections for one-step equations, two-step equations, and a substitution check. Revised for robust variable rendering, better vertical solving layout, and page consolidation.

AG

Anna Gomez

Other
4/28
Material
Expression Site Practice Set

Expression Site Practice Set

Independent practice worksheet for Day 1 focusing on algebraic expression simplification. Includes sections for combining like terms, distributive property, and multi-step simplification. Revised for better page breaks, work area spacing, and robust variable rendering.

AG

Anna Gomez

Other
4/28
Material
Relationship Review Worksheet

Relationship Review Worksheet

Student worksheet for Day 4 of the Foundations Blueprint sequence, focusing on interpreting proportional relationships on a graph. Revised with white background work areas and improved layout.

AG

Anna Gomez

Other
4/28
Material
Proportional Plots Worksheet

Proportional Plots Worksheet

Student worksheet for Day 3 of the Foundations Blueprint sequence, focusing on proportional relationships. Revised for accurate grid scaling and better page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Worksheet

Equation Assembly Worksheet

Student worksheet for Day 2 of the Foundations Blueprint sequence, focusing on solving equations. Revised for better page breaks and clear labeling of variables.

AG

Anna Gomez

Other
4/28
Material
Relationship Review Practice Answer Key

Relationship Review Practice Answer Key

Teacher answer key for Day 4 Relationship Review Practice Set. Includes solutions for unit rate interpretation and origin meaning. Revised for robust variable rendering, better labels, and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Relationship Review Answer Key

Relationship Review Answer Key

Teacher answer key for Day 4 Relationship Review student worksheet. Includes solutions for interpreting (1, r) and (0, 0) on a graph. Revised for better spacing, higher contrast labels, and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Proportional Site Practice Answer Key

Proportional Site Practice Answer Key

Teacher answer key for Day 3 Proportional Site Practice Set. Includes solutions for constant k, table completion, and proportionality identification. Revised with robust variable rendering and improved grid alignment.

AG

Anna Gomez

Other
4/29
Material
Proportional Plots Answer Key

Proportional Plots Answer Key

Teacher answer key for Day 3 Proportional Plots student worksheet. Includes solutions for constant k calculations, table completion, and graphing rules. Revised for better page consolidation and clear visual reference.

AG

Anna Gomez

Other
4/29
Material
Equation Assembly Practice Answer Key

Equation Assembly Practice Answer Key

Teacher answer key for Day 2 Equation Assembly Practice Set. Includes solutions for one-step and two-step equation practice. Revised for robust variable rendering and fixed page breaks.

AG

Anna Gomez

Other
4/29
Material
Equation Assembly Answer Key

Equation Assembly Answer Key

Teacher answer key for Day 2 Equation Assembly student worksheet. Includes solutions for one-step and two-step equations and substitution checks. Revised for better page consolidation and high-contrast printing.

AG

Anna Gomez

Other
4/29
Material
Expression Site Practice Answer Key

Expression Site Practice Answer Key

Teacher answer key for Day 1 Expression Site Practice Set. Includes solutions for independent practice on combining like terms and distributive property. Revised for robust variable rendering and fixed page consolidation.

AG

Anna Gomez

Other
4/29
Material
Expression Engineering Answer Key

Expression Engineering Answer Key

Teacher answer key for Day 1 Expression Engineering student worksheet. Includes solutions for combining like terms, the distributive property, and multi-step simplification. Revised for higher contrast, better page breaks, and print-ready styles.

AG

Anna Gomez

Other
4/29
Material
Relationship Review Practice Set

Relationship Review Practice Set

Independent practice worksheet for Day 4 focusing on interpreting proportional relationships. Revised with robust variable rendering, improved solving layout, and high-contrast work areas. Consolidated into a clean two-page format.

AG

Anna Gomez

Other
4/28
Material
Proportional Site Practice Set

Proportional Site Practice Set

Independent practice worksheet for Day 3 focusing on proportional relationships. Includes calculating the constant k, completing tables, graphing, and identifying proportional equations. Revised with robust variable rendering, better grid alignment, and fixed page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Practice Set

Equation Assembly Practice Set

Independent practice worksheet for Day 2 focusing on solving equations. Includes sections for one-step equations, two-step equations, and a substitution check. Revised for robust variable rendering, better vertical solving layout, and page consolidation.

AG

Anna Gomez

Other
4/28
Material
Expression Site Practice Set

Expression Site Practice Set

Independent practice worksheet for Day 1 focusing on algebraic expression simplification. Includes sections for combining like terms, distributive property, and multi-step simplification. Revised for better page breaks, work area spacing, and robust variable rendering.

AG

Anna Gomez

Other
4/28
Material
Relationship Review Worksheet

Relationship Review Worksheet

Student worksheet for Day 4 of the Foundations Blueprint sequence, focusing on interpreting proportional relationships on a graph. Revised with white background work areas and improved layout.

AG

Anna Gomez

Other
4/28
Material
Proportional Plots Worksheet

Proportional Plots Worksheet

Student worksheet for Day 3 of the Foundations Blueprint sequence, focusing on proportional relationships. Revised for accurate grid scaling and better page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Worksheet

Equation Assembly Worksheet

Student worksheet for Day 2 of the Foundations Blueprint sequence, focusing on solving equations. Revised for better page breaks and clear labeling of variables.

AG

Anna Gomez

Other
4/28
Material
Expression Engineering Worksheet

Expression Engineering Worksheet

Student worksheet for Day 1 of the Foundations Blueprint sequence, focusing on algebraic expressions. Includes sections for a Do Now, combining like terms, the distributive property, and an exit ticket. Revised for better spacing and formatting.

AG

Anna Gomez

Other
4/28
Material
Championship Milestone Assessment Answer Key

Championship Milestone Assessment Answer Key

Revised 1-page answer key for the Milestone Assessment. Standardized all layouts to a stacked vertical format with border dividers. Standardized the 'Final Answer' format to text-xl across all six problems and tightened spacing to ensure all content fits on one sheet. Improved math entity rendering.

AG

Anna Gomez

Other
4/28
Material
Championship Milestone Assessment Student Copy

Championship Milestone Assessment Student Copy

Revised Milestone Assessment with fixed page breaks (Question 3 kept together). Improved work area labels with higher contrast and better alignment. SVG for triangle area adjusted for perfect visibility. Removed decorative artifacts from work areas.

AG

Anna Gomez

Other
4/28
Material
Data Dash Practice Set Answer Key

Data Dash Practice Set Answer Key

Revised 1-page answer key for Week 7 practice set. Added x/y axis labels to graph thumbnail, consolidated all content onto a single page to avoid orphaned text, and improved math rendering clarity. Badge alignment fixed.

AG

Anna Gomez

Other
4/28
Material
Data Dash Warm-Ups Answer Key

Data Dash Warm-Ups Answer Key

Revised 1-page answer key for Week 7 warm-ups. Standardized capitalization for mathematical terms, increased font size for calculations, and ensured all 5 days fit on one sheet with improved text contrast.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Answer Key

Equation Assembly Answer Key

Teacher answer key for Day 2 Equation Assembly student worksheet. Includes solutions for one-step and two-step equations and substitution checks. Revised for better page consolidation and high-contrast printing.

AG

Anna Gomez

Other
4/29
Material
Expression Site Practice Answer Key

Expression Site Practice Answer Key

Teacher answer key for Day 1 Expression Site Practice Set. Includes solutions for independent practice on combining like terms and distributive property. Revised for robust variable rendering and fixed page consolidation.

AG

Anna Gomez

Other
4/29
Material
Expression Engineering Answer Key

Expression Engineering Answer Key

Teacher answer key for Day 1 Expression Engineering student worksheet. Includes solutions for combining like terms, the distributive property, and multi-step simplification. Revised for higher contrast, better page breaks, and print-ready styles.

AG

Anna Gomez

Other
4/29
Material
Similarity Blueprint Reference Sheet

Similarity Blueprint Reference Sheet

A student-friendly reference sheet for similarity concepts. Includes formulas for scale factor, similarity criteria (AAA, SSS, SAS), and a visual guide for shadow trigonometry.

DE

Donia ElSayed

Math Teacher
4/28
Material
Project Master Rubric Teacher Guide

Project Master Rubric Teacher Guide

A comprehensive teacher's rubric for the Similarity Superstars project. Covers poster, art, and presentation components with specific grading criteria for data, logic, and polish.

DE

Donia ElSayed

Math Teacher
4/28
Material
Similarity Showdown Presentation Guide

Similarity Showdown Presentation Guide

A digital slide presentation template and guide for students. Covers similarity criteria (AAA, SAS, SSS), presentation requirements, and slide layout templates.

DE

Donia ElSayed

Math Teacher
4/28
Material
Artful Proportions Art Guide

Artful Proportions Art Guide

A guide for students to create similarity-based art and tessellations. Includes sections for base shape design, scale factor definitions, and artistic requirements.

DE

Donia ElSayed

Math Teacher
4/28
Material
Shadow Sleuths Poster Guide

Shadow Sleuths Poster Guide

A project guide for students to conduct indirect measurement using shadows. Includes data collection tables, a ratio setup guide, and poster requirements.

DE

Donia ElSayed

Math Teacher
4/28
Material
Relationship Review Practice Set

Relationship Review Practice Set

Independent practice worksheet for Day 4 focusing on interpreting proportional relationships. Revised with robust variable rendering, improved solving layout, and high-contrast work areas. Consolidated into a clean two-page format.

AG

Anna Gomez

Other
4/28
Material
Proportional Site Practice Set

Proportional Site Practice Set

Independent practice worksheet for Day 3 focusing on proportional relationships. Includes calculating the constant k, completing tables, graphing, and identifying proportional equations. Revised with robust variable rendering, better grid alignment, and fixed page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Practice Set

Equation Assembly Practice Set

Independent practice worksheet for Day 2 focusing on solving equations. Includes sections for one-step equations, two-step equations, and a substitution check. Revised for robust variable rendering, better vertical solving layout, and page consolidation.

AG

Anna Gomez

Other
4/28
Material
Expression Site Practice Set

Expression Site Practice Set

Independent practice worksheet for Day 1 focusing on algebraic expression simplification. Includes sections for combining like terms, distributive property, and multi-step simplification. Revised for better page breaks, work area spacing, and robust variable rendering.

AG

Anna Gomez

Other
4/28
Material
Relationship Review Worksheet

Relationship Review Worksheet

Student worksheet for Day 4 of the Foundations Blueprint sequence, focusing on interpreting proportional relationships on a graph. Revised with white background work areas and improved layout.

AG

Anna Gomez

Other
4/28
Material
Proportional Plots Worksheet

Proportional Plots Worksheet

Student worksheet for Day 3 of the Foundations Blueprint sequence, focusing on proportional relationships. Revised for accurate grid scaling and better page breaks.

AG

Anna Gomez

Other
4/28
Material
Equation Assembly Worksheet

Equation Assembly Worksheet

Student worksheet for Day 2 of the Foundations Blueprint sequence, focusing on solving equations. Revised for better page breaks and clear labeling of variables.

AG

Anna Gomez

Other
4/28
Material
Expression Engineering Worksheet

Expression Engineering Worksheet

Student worksheet for Day 1 of the Foundations Blueprint sequence, focusing on algebraic expressions. Includes sections for a Do Now, combining like terms, the distributive property, and an exit ticket. Revised for better spacing and formatting.

AG

Anna Gomez

Other
4/28
Material
Championship Milestone Assessment Answer Key

Championship Milestone Assessment Answer Key

Revised 1-page answer key for the Milestone Assessment. Standardized all layouts to a stacked vertical format with border dividers. Standardized the 'Final Answer' format to text-xl across all six problems and tightened spacing to ensure all content fits on one sheet. Improved math entity rendering.

AG

Anna Gomez

Other
4/28
Material
Championship Milestone Assessment Student Copy

Championship Milestone Assessment Student Copy

Revised Milestone Assessment with fixed page breaks (Question 3 kept together). Improved work area labels with higher contrast and better alignment. SVG for triangle area adjusted for perfect visibility. Removed decorative artifacts from work areas.

AG

Anna Gomez

Other
4/28
Material
Data Dash Practice Set Answer Key

Data Dash Practice Set Answer Key

Revised 1-page answer key for Week 7 practice set. Added x/y axis labels to graph thumbnail, consolidated all content onto a single page to avoid orphaned text, and improved math rendering clarity. Badge alignment fixed.

AG

Anna Gomez

Other
4/28
Material
Data Dash Warm-Ups Answer Key

Data Dash Warm-Ups Answer Key

Revised 1-page answer key for Week 7 warm-ups. Standardized capitalization for mathematical terms, increased font size for calculations, and ensured all 5 days fit on one sheet with improved text contrast.

AG

Anna Gomez

Other
4/28