Mapping relationships through notation, algebraic representations, and growth rate comparisons. Equips learners to transform functions, model contextual data, and solve exponential equations.
A comprehensive final assessment for Algebra 1 covering linear equations, systems, exponents, polynomials, and quadratic functions. Includes free response and graphing sections to evaluate deep understanding.
Focusing on the mechanics of exponential growth functions and identifying the 'a' and 'b' values in real-world scenarios.
A lesson where students model exponential growth through a hands-on activity using dried beans to simulate bacterial reproduction (binary fission). Students collect data, graph the resulting curve, and discuss the implications of rapid bacterial growth in health and science.
Students analyze the impact of reproductive rates on population recovery by comparing domestic cats to orangutans using mathematical modeling and graphing.
This lesson explores infinite geometric series, focusing on the conditions for convergence and the application of the infinite sum formula. Students will investigate Zeno's Paradox and learn to convert repeating decimals into fractions using series concepts.
A comprehensive lesson where Algebra 2 students distinguish between arithmetic and geometric sequences, identify common differences and ratios, and apply the explicit formula for geometric sequences to find specific terms.
A High School Pre-Calculus lesson exploring the relationships between arithmetic and geometric means through the lens of finding missing terms in sequences. Students will compare how these two mathematical averages create different patterns between the same endpoints.
A high-level mathematics lesson focused on distinguishing between sequences and series, determining convergence, and performing error analysis on complex geometric problems. Students will watch targeted practice segments and correct common mathematical misconceptions.
A 5th-grade math lesson focused on distinguishing between additive (y = x + a) and multiplicative (y = ax) patterns in function tables. Students watch a targeted video clip, participate in mental math, and create 'Imposter Rule' tables to challenge their peers.
A lesson focusing on the distinction between growth factors and percent change, specifically within the context of exponential models with differing units of time. Students learn to convert between these forms and adjust for unit changes using power rules.
This lesson teaches Algebra 2 students how to manipulate exponential bases to find effective growth or decay rates for different time intervals (e.g., converting annual rates to monthly or daily rates) using the power of a power property. Students will watch a targeted video, practice base conversion with a formulaic approach, and reflect on the relationship between time intervals and growth factors.
A lesson where students design exponential word problems with intentional 'unit traps' to master unit conversion in modeling. Includes video analysis, collaborative problem design, and peer solving.
A comprehensive lesson on distinguishing between arithmetic and geometric sequences, calculating means, and deriving explicit formulas for the nth term.
Students will synthesize their knowledge of arithmetic and geometric patterns to classify and analyze complex sequences and series through a rapid-fire video voting exercise and a collaborative sorting activity.
A Pre-Calculus lesson focused on deriving and applying partial sum formulas for arithmetic and geometric series through the lens of architectural blueprints and real-world construction scenarios.
Students will identify domain, range, and asymptotes for exponential and logarithmic functions and predict graph features using inverse relationships through a video-guided prediction activity and a gallery walk.
A Pre-Calculus lesson on infinite geometric series, focusing on determining convergence using the common ratio and calculating sums for convergent series. Includes a forensic-themed activity to engage students in mathematical analysis.
A Pre-Calculus lesson focused on distinguishing between arithmetic and geometric sequences and applying the finite geometric sum formula through visual analysis and active sorting.
A comprehensive lesson on sigma notation where students master arithmetic, geometric, and infinite series through a hands-on rotation activity and collaborative problem-solving.
A high school algebra lesson focusing on interpreting exponential growth factors and graphing population simulations. Students will learn to link decimal multipliers like 1.25 to percentage growth and use calculators to plot accurate exponential curves.
A targeted intervention session providing differentiated pathways for students based on their mastery of domain and range: enrichment projects, error analysis, and foundational reteaching.
A comprehensive lesson on graphing linear equations using slope-intercept form, featuring a technical blueprint theme to help 8th-grade students master the coordinate plane.
A comprehensive ACT Math preparation module focusing on core concepts, time management strategies, and targeted practice across all test categories.
A 30-minute Tier 2 intervention lesson focused on graphing two-variable linear inequalities on a 4-quadrant coordinate plane, emphasizing boundary lines and half-plane shading.
A comprehensive lesson on graphing Sine and Cosine functions, featuring guided notes, instructional slides, and a detailed answer key. Students will learn to identify amplitude, period, midline, and phase shifts to accurately sketch periodic graphs.
A comprehensive introduction to parent functions and their transformations, designed for Algebraic Reasoning students to master shifts, stretches, and reflections.
A comprehensive lesson on variables, covering identification, simplification, solving multi-step equations, and graphing. Includes visual aids and collaborative task cards.
A comprehensive 20-question practice test and answer key designed to prepare students for the TSIA2 Mathematics assessment, focusing on algebraic, geometric, and statistical reasoning.
A 10th-grade Honors Algebra lesson focused on using domain restrictions ($B \ge 0$) to predict extraneous solutions in absolute value equations before solving. Students compare this proactive strategy with the traditional substitution method.
A lesson for 11th-grade students on identifying and understanding extraneous solutions in absolute value equations through algebraic methods and graphical verification.
Students will master adding, subtracting, multiplying, and composing functions through a combination of visual instruction and a hands-on station-based activity. This lesson focuses on the transition from basic polynomial arithmetic to formal function notation.
A lesson connecting quadratic algebra to graphical models. Students analyze vertex form word problems, identify key features like maximums and roots, and verify their algebraic work using graphing technology.
Students will master translating between recursive and explicit formulas for geometric sequences through a collaborative 'telephone' activity and visual notation analysis.
A comprehensive lesson for 10th Grade Honors Math focusing on determining positive and negative intervals of functions. Students transition from visual graph analysis to algebraic sign charts for polynomials and rational functions.
This lesson clarifies the common misconception that zero is a positive number and teaches students how to use parentheses in interval notation to exclude intercepts. It features a high-energy 'Zero is Lava' game to reinforce the concept of 'skipping' points on the number line.
Students will master the relationship between algebraic intervals and graphical behavior by 'reverse engineering' function sketches from specific positive and negative interval constraints. The lesson uses a technical drafting aesthetic to help students visualize the x-axis as a critical boundary and understand the impact of root multiplicity.
Students will learn to visually identify where linear and quadratic functions are positive (above the x-axis) and negative (below the x-axis) and represent these regions using interval notation. The lesson features a video-guided instruction phase and a hands-on 'Graph Highlighter' activity.
A 9th-grade algebra lesson where students act as 'secret agents' to decode patterns in tables and translate them into algebraic function rules. Students will transition from intuitive pattern recognition to formal equation writing.
A lesson designed to help English learners practice TELPAS speaking skills while comparing the solutions and characteristics of quadratic functions.
Students explore linear relationships through a business lens, graphing revenue and cost to identify the 'Sweet Spot' of maximum profit using marginal analysis.
A 10th-grade Math and Consumer Math lesson exploring price elasticity of demand. Students will visualize the 'stretch' of demand curves through graphing and analyze the relationship between price changes and total revenue.
A support-focused algebra lesson where students transition from identifying intercepts visually to 'reverse engineering' graphs from given x and y intercepts. The lesson uses a drafting/blueprint theme to engage students in the 'construction' of mathematical lines and curves.
A lesson for 8th Grade Algebra I students to discover that the slope of a line is constant between any two points. Includes a video-based hook, a collaborative graphing investigation, and a challenge on scaling slopes.
A high-energy 7th-grade math lesson that uses roller coaster physics to introduce slope as a rate of change. Students will visualize, physically model, and identify positive and negative slopes through video, movement, and real-world application.
Students explore the school environment to find physical examples of slope, measuring vertical rise and horizontal run to calculate real-world steepness and discuss ADA accessibility standards.
A lesson focused on calculating slope/rate of change from tables of values, featuring a rise-over-run warm-up, a video analysis of an airplane's ascent, and a 'Slope Detectives' unit rate activity.
This lesson focuses on finding and interpreting the initial value (y-intercept) from linear tables by 'working backward' using the rate of change. Students watch a video demonstration, practice the calculation, and engage in a creative role-play activity to provide context for abstract data.
A comprehensive lesson for 8th-grade students on translating between tabular and graphical representations of linear functions, featuring a video-based exploration and a collaborative relay activity.
A remediation-focused lesson for 4th and 5th graders to master input/output tables by applying the 'Check Three' strategy to avoid common pattern traps.
A 4th-grade lesson where students become 'Pattern Detectives' to identify and apply addition and subtraction rules in input/output tables. Includes a hands-on 'Magic Box' warm-up and a video-guided investigation.
Strengthens geometric reasoning through 'Shape Sort' tasks, focusing on the properties and classification of polygons.
Develops data literacy through 'Story of a Graph' activities where students connect real-world scenarios to visual representations.
Explores the meaning of the equals sign and balanced expressions using 'True/False Equations' to move students toward algebraic reasoning.
Focuses on fraction fluency and conceptual understanding using 'Quick Images' and 'Number Line Talks' to build a solid foundation in part-to-whole relationships.
A comprehensive lesson on translating between tables, graphs, and verbal descriptions to construct linear equations in slope-intercept form. Students act as 'Equation Architects' to build mathematical models of real-world scenarios.
Students learn to model business costs using linear equations and graphs. They define fixed and variable costs through a video case study and apply these concepts to a custom sneaker business scenario.
A 10th-grade math lesson that bridges coordinate geometry with economics. Students interpret and construct line graphs (demand curves) and analyze how non-price factors cause parallel shifts in the graph.
Students will master projectile motion by applying the quadratic formula to solve for flight time. The lesson uses a volcano-themed scenario to bridge abstract algebra with physical kinematics, including a deep dive into interpreting mathematical results like negative time.
In this lesson, students bridge the gap between abstract Greek geometry and Renaissance physics by applying quadratic equations to projectile motion. Students watch a comprehensive breakdown of the kinematic-quadratic relationship, participate in historical-mathematical discussions, and design a catapult model that they must describe through theoretical algebraic modeling.
A lesson for Algebra II students to distinguish between function composition and multiplication, featuring video analysis and a 'Symbol Sort' activity.
This lesson focuses on the skill of decomposing composite functions, a prerequisite for the Chain Rule in Calculus. Students will analyze the relationship between 'inner' and 'outer' functions through video observation, algebraic reverse engineering, and conceptual discussion.
A high-school Pre-Calculus lesson exploring the non-commutative nature of function composition through algebraic manipulation, visual substitution logic, and the discovery of inverse functions.
A lesson focusing on the 'Inside-Out' method for numerically evaluating composite functions, featuring a Russian Nesting Doll analogy and a high-energy group relay activity.
A high-school algebra lesson focused on avoiding the 'power of a sum' error when expanding binomials within composite functions, featuring video-guided instruction and a hands-on expansion challenge.
A Pre-Calculus lesson focused on the relationship between exponential and logarithmic functions through the lens of domain and range swapping. Students analyze transformations, identify key features like asymptotes, and verify inverse relationships graphically.
Students will master the algebraic process of finding inverses for complex exponential and logarithmic functions involving shifts, stretches, and reflections. The lesson uses a station-rotation model to build complexity and includes a real-world video application.
Students explore inverse functions through the lens of geometric reflection across the line y=x, utilizing paper-folding, video analysis, and digital graphing tools to bridge the gap between algebraic manipulation and visual logic.
A lesson focusing on verifying inverse functions through algebraic composition, specifically targeting exponential and logarithmic functions. Students will explore how properties like \(b^{\log_b x} = x\) allow for simplification and proof of inverse relationships.
A high-level Algebra 1 lesson for Honors students focused on deriving the Point-Slope form from the Slope Formula, featuring algebraic manipulation and a Socratic seminar.
A Pre-Calculus lesson exploring the geometric relationship between exponential and natural logarithmic functions as inverses, featuring video analysis and side-by-side graphical comparisons.
A high-level lesson on mastering the Table Method for graphing exponential and natural logarithmic functions using Euler's number (e). Students analyze a tutorial video, create procedural flowcharts, and participate in a collaborative 'Graphing Relay' to solidify their understanding of asymptotes and key points.
A comprehensive lesson for Algebra II students on graphing exponential functions with base 'e', featuring a video-led tutorial, pair activities, and domain/range analysis.
A lesson for Algebra II students on graphing natural log transformations (h, k) and identifying vertical asymptotes. Includes a video analysis, hands-on stations, and graphing practice.
Students will learn to use the R-squared value in GeoGebra to mathematically justify the choice between linear and exponential regression models through a competitive 'Regression Battle' activity.
A lesson introducing students to regression and the 'line of best fit' by moving from manual estimation to computer-aided modeling using real-world messy data.
Students transition from textbook-perfect functions to real-world data analysis using GeoGebra. They will learn to perform linear and exponential regressions, interpret the R-squared value to determine the best fit, and apply these skills to distinguish between population growth and linear accumulation.
A technical, hands-on lesson teaching 11th-grade students how to perform linear and exponential regressions using GeoGebra, transitioning from textbook examples to messy real-world data analysis.
A high school interdisciplinary lesson connecting physics and algebra. Students analyze real-world lab data using linear and exponential regression in GeoGebra, exploring why experimental data rarely fits perfect mathematical models and how R-squared measures the quality of a fit.
Students use their constructed models to extrapolate and answer questions about future events, solving trigonometric inequalities graphically.
Students use graphing calculators or regression software to fit trigonometric equations to data sets. They compare their hand-calculated models to the regression models.
Focusing on the x-axis, students determine the period of real-world cycles. They calculate the horizontal scaling factor and determine appropriate horizontal shifts.
Students learn the algebraic techniques to extract the midline and amplitude from a data table. They practice these calculations on various environmental data sets.
Students plot given data sets and identify the periodic nature of the data. They sketch a 'best fit' curve by hand to estimate the maximums, minimums, and cycle length.
Students synthesize their knowledge by fitting power functions to real-world data sets, comparing square root and cube root models to find the best fit for physical phenomena.
Students apply fractional exponents to compound interest formulas to calculate returns over partial time intervals, such as months or days within a year.
Students investigate the mathematical structure of the musical scale, where frequency steps are governed by the 12th root of 2, connecting geometric sequences to rational exponents.
Students analyze Kepler’s Third Law to relate planetary orbital periods to distance from the sun using the 3/2 power, practicing conversions between radical and exponential forms.
Students explore the relationship between animal mass and metabolic rate using Kleiber's Law (3/4 power rule), introducing the concept of fractional powers in biological systems.
The sequence concludes with Information Theory metrics, using Mutual Information to detect non-monotonic, complex associations that correlation coefficients miss.
This lesson focuses on locally weighted scatterplot smoothing (LOESS) to visualize trends without pre-defined parametric functions, exploring bandwidth selection and smoothing.
Students explore modeling curvature using polynomial terms and splines, while addressing the bias-variance tradeoff and the risks of overfitting.
This lesson introduces Spearman’s rho and Kendall’s tau for assessing monotonic relationships in ordinal and non-normal continuous data.
Students analyze Anscombe's Quartet and other pathological datasets to demonstrate where Pearson’s r fails, focusing on the distinction between linearity and general association.
A lesson for 11th-12th grade physics and math students focused on the practical application of inverse functions. Students learn why traditional variable swapping is avoided in scientific formulas and practice isolating independent variables in real-world exponential and logarithmic contexts.
A comprehensive lesson on solving quadratic equations when the leading coefficient is greater than 1, emphasizing fraction arithmetic and collaborative problem-solving through a relay activity.
Students learn to simplify exponential functions with fractional exponents (like x/2 or x/3) by converting them into radical notation. This transformation allows students to graph functions with fractional periods more easily by finding the growth factor for a single unit of x.
A math intervention lesson focused on identifying extraneous solutions and building the habit of checking work to avoid 'math catastrophes.' Students act as 'Quality Control' engineers to grade fictional work and reflect on the necessity of verification.
A 9th-grade Algebra I lesson focused on solving rational equations and identifying extraneous solutions through verification and domain analysis. Students use a video investigation and a 'Valid or Invalid?' lab-style worksheet to master the concept of non-reversible operations.
This lesson explores the logical pitfalls of non-reversible algebraic operations, teaching students to identify 'risky' steps like multiplying by variables or squaring, which can lead to extraneous solutions. Students will learn to map the logical flow of equations and account for domain restrictions through visual logic branching.
A high school math lesson where students create a visual reference guide (anchor chart) for exponent properties and use it to solve complex exponential equations with common bases. The lesson centers on a step-by-step video tutorial and hands-on project work.
A math intervention lesson focused on identifying and correcting misconceptions when solving exponential equations by matching bases. Students act as 'Math Detectives' to find and fix errors in algebraic work.
A comprehensive Algebra 1 lesson focusing on solving exponential equations by identifying common bases and applying exponent rules. Includes a video-guided note-taking session, partner practice, and conceptual discussion.
A lesson where 11th-grade students learn to solve complex algebraic equations involving rational exponents by treating the equation as a series of operations to be reversed, featuring a video-guided 'blueprint' method.
A lesson focused on solving for function inputs using inverse operations, featuring varied variables and a 'Variable Switch' partner activity.
Students discover the relationship between powers and logarithms through pattern recognition, trial and error, and a competitive card game. The lesson focuses on evaluating logs without calculators by converting them to exponential form.
Students will translate between logarithmic and exponential forms, practicing the 'inverse' relationship through guided video analysis and a collaborative domino matching activity.
An introductory lesson on logarithms where students learn to convert logarithmic equations into exponential form using the 'Loop Method'. Includes mental math warm-ups, video-guided notes, and practice problems focusing on the relationship between bases, exponents, and results.
A Pre-Calculus lesson where students master logarithmic to exponential conversions by designing their own challenging problems, ranging from basic integers to complex rational exponents.
Students investigate the behavior of functions with oscillating discontinuities, specifically focusing on the limit of \(\sin(1/x)\) as \(x \to 0\) compared to bounded oscillating functions like \(x \cdot \sin(1/x)\). The lesson uses a combination of video analysis and digital graphing tools to explore the formal definition of limit failure due to oscillation.
An intensive review lesson for 11th-grade Pre-Calculus students focusing on rapid synthesis of quadratic transformations. Students will master the 'over 1, up a' technique to graph complex vertex-form equations and connect these transformations to calculus-ready concepts like rate of change.
This Pre-Algebra lesson helps students differentiate between linear growth (multiplication) and exponential growth (powers) using a weightlifter analogy and hands-on graphing. Students will explore the 'power' of exponents through tables of values and visual comparison.
A lesson where students discover that quadratic sequences have a constant second difference, connecting the visual pattern of differences to the algebraic presence of n-squared.
Students investigate geometric sequences that involve negative and fractional common ratios through a 'Pattern Detective' theme, focusing on how these ratios affect the behavior of the sequence (decreasing or alternating signs).
A lesson where students discover the visual differences between linear and exponential growth by plotting data and analyzing the 'steepness' of resulting graphs. Students compare constant rates of change (addition) with multiplicative rates of change (multiplication).
Students will investigate the visual and numerical differences between linear and exponential models through a data-matching card sort and real-world scenario analysis.
A lesson exploring why linear slopes fail to model exponential growth, featuring a visual analysis of changing rates of change.
A 9th-grade algebra lesson where students explore the visual differences between linear and exponential growth models through storytelling, data creation, and graphing.
An introductory algebra lesson for 8th-grade students focused on recursive formulas through the Fibonacci sequence. Students explore patterns, watch an instructional video, build their own sequences using the Fibonacci rule, and graph the results to observe non-linear growth.
In this lesson, 8th-grade students explore the Fibonacci sequence and the fascinating way its consecutive ratios converge to the Golden Ratio (1.618). Through a combination of video analysis, manual calculation, and graphical visualization, students discover how math models beauty in nature.
A conceptual 8th-grade math lesson comparing linear and exponential decay using an airplane landing analogy and real-world scenarios. Students analyze graphs, watch an instructional video, and sort scenarios based on their decay patterns.
A high-school level enrichment lesson exploring the hierarchy of operations, focusing on tetration and the explosive growth of hyper-operations compared to addition, multiplication, and exponentiation.
A high-level Pre-Calculus lesson exploring tetration and its inverse, the super root, through logical deduction and video-guided inquiry. Students transition from familiar inverse operations to the frontier of fast-growing functions.
Students explore the intersection of physics and algebra by modeling volcanic projectile motion using quadratic functions, focusing on parameter manipulation and real-world interpretation of the discriminant.
Students will learn to navigate quadratic word problems by identifying whether they need to find the vertex, roots, or y-intercept based on specific keywords and context. The lesson includes a warm-up, a video-based discussion, a feature-sorting activity, and guided problem-solving.
Students will analyze real-world linear scenarios from a video and then design their own word problems using Standard and Slope-Intercept forms. The lesson culminates in a peer-review 'Linear Life Project' where students solve each others' scenarios.
Students learn to translate word problems into linear equations by identifying slopes, y-intercepts, and totals using a detective-themed 'deconstruction' method.
Students will learn to extract rates and points from real-world scenarios to write linear equations in point-slope form, utilizing a taxi-themed video and a scavenger hunt activity.
A lesson where students use point-slope form to model real-world statistics, research their own data points, and forecast future trends.
Students will learn to translate business 'flat fees' and 'per-unit' rates into point-slope equations by treating the starting value as the coordinate point (0, y). This lesson uses real-world party planning scenarios to solidify the connection between word problems and linear functions.
A lesson focused on interpreting x-intercepts as 'end points' or zero values in real-world scenarios with negative slopes, using a 'leaking pool' video and a 'countdown' group activity.
A lesson focused on finding the real and complex zeros of polynomial functions using various algebraic methods like factoring and synthetic division.
This lesson helps students determine the most efficient linear form (Standard, Slope-Intercept, or Point-Slope) based on real-world context and 'clues' within word problems. It features a video analysis, a collaborative anchor chart creation, and a hands-on 'Form Sort' activity.
A comprehensive 10th-grade Algebra 2 lesson focused on distinguishing between increasing/decreasing intervals and positive/negative intervals using a 'Cartographer' aesthetic. Students rotate through stations to 'map' polynomial functions and analyze tricky cases where functions touch the axis.
A high-school math lesson where students use visual and algebraic methods to solve for x and y intercepts through a "Function Detective" crime-solving simulation.
A lesson connecting quadratic factoring to x-intercepts on a graph using visual and algebraic methods. Students explore why factors reveal the 'roots' of a parabola through the Zero Product Property.
Students step into the role of 'Story Producers' to create their own quadratic word problems in vertex form. They will analyze the three key features of quadratics (vertex, roots, and y-intercept) and design a narrative around a real-world scenario that moves 'up and down'.
A high school physics and math lesson exploring the application of quadratic vertex form to projectile motion, featuring a video-based investigation and a data-modeling lab.
Students explore the sweet spot of business pricing by solving quadratic functions in vertex form to find break-even points and maximum profit.
Students will apply mathematical function rules to real-world scenarios by creating word problems, input/output tables, and identifying independent and dependent variables.
A 9th-grade Algebra I lesson focused on writing linear equations in point-slope form when given two points. Students will master the transition from the slope formula to the point-slope equation through video analysis, peer collaboration in the 'Two-Point Pass' activity, and reflective writing.
A targeted remediation lesson for 10th-grade students focusing on Point-Slope Form. This lesson features a diagnostic warm-up, a video-guided note-taking session, and a rigorous error analysis activity to combat common sign-related misconceptions in linear equations.
