Foundational fraction equivalence, ordering, and operations across the rational number system. Addresses multi-digit computation, decimal conversions, and the distinction between rational and irrational numbers.
A comprehensive math series designed to prepare students for HSED exams by focusing on essential arithmetic skills applied to real-world workplace and adult life scenarios. Topics include multi-digit operations, decimals, fractions, and percentages.
A comprehensive Tier 2 intervention sequence focused on multiplying and dividing rational numbers. Students move from concrete modeling with fraction tiles to abstract long division and fluency practice.
A math unit focused on understanding and applying ratios and proportions through visual methods, mental math strategies, and algorithmic problem-solving.
A series of lessons focused on mastering algebraic and numerical fractions through visual strategies and structural simplification.
A specialized math support sequence for 8th-grade students, focusing on the conceptual understanding of fractions, decimals, and operations through the use of physical and virtual manipulatives. This sequence uses a 'Blueprint & Construction' theme to make abstract rational number concepts concrete and applicable to real-world design.
A comprehensive 5-lesson unit on rational expressions, covering domain restrictions, simplification, arithmetic operations, and solving equations with a focus on extraneous solutions.
This mastery-based sequence focuses on the algebraic side of probability, specifically utilizing the multiplication rule for complex problems. Students progress from visual models to abstract formulas, covering independent and dependent events, 'at least one' scenarios using complements, and mixed strategy application.
This sequence guides 7th-grade students from visual probability models (tree diagrams, area models) to the abstract Multiplication Rule for independent and dependent events. Students will discover the rule through inquiry, apply it to increasingly complex multi-stage scenarios, and master the distinction between replacement and non-replacement contexts.
This sequence explores the differences between independent and dependent events through hands-on simulations, comparative analysis, and multi-step calculations. Students learn to adjust sample spaces and numerators based on whether items are replaced, building a strong foundation for compound probability.
A comprehensive 9th-grade unit on mastering arithmetic operations with signed rational numbers (fractions and decimals). The sequence moves from visual number line models to abstract algorithms and complex order of operations, emphasizing the 'why' behind sign rules.
A comprehensive 7th-grade unit that builds a deep conceptual understanding of fraction division, moving from visual modeling to the standard algorithm and real-world application. Students investigate reciprocals, handle mixed numbers, and solve complex multi-step problems.
This sequence guides students from conceptual modeling of fraction division to applying the standard algorithm with mixed numbers in complex geometric and real-world contexts. Students will explore the 'why' behind the reciprocal before mastering the 'how' and applying it to find missing dimensions and unit rates.
This inquiry-based sequence utilizes geometric area models to conceptualize the distributive property. Students move from concrete arithmetic to abstract algebraic manipulation, eventually fluently expanding linear expressions with rational coefficients.
An 8th-grade algebra sequence focused on the precision of expression simplification, covering negative distribution, nested grouping symbols, and fractional coefficients through a technical blueprint theme.
Students transition from rote arithmetic to applying fraction operations within the context of architectural design and resource management, culminating in a blueprint design project.
This 8th-grade sequence bridges ratio concepts with linear functions by exploring unit rates as the slope of proportional relationships. Students progress from complex fraction calculations to graphing, comparing multiple representations, and modeling real-world scenarios with equations, culminating in a logistics optimization challenge.
This project-based sequence guides students through the practical application of unit rates in financial and physical contexts. Students calculate basic unit prices, solve complex fraction rates, and analyze constant speed through graphing, culminating in a consumer analysis project.
A high-stakes financial modeling unit where students apply rational number arithmetic to track net worth, allocate assets, and forecast long-term growth. Students take on the role of financial planners using signed decimals and fractions to navigate market volatility and interest rates.
A project-based unit where 8th-grade students apply rational number operations (fractions and decimals) to scale blueprints and budget materials for a 'Tiny House' architectural design project.
This sequence moves students from visual models to standard algorithms for multiplying and dividing fractions. Students build a deep conceptual understanding through scaling, area models, and physical manipulatives before mastering the standard algorithm and applying it to real-world scaling and design projects.
A comprehensive 3-day review sequence for the Algebra I Regents examination, focusing on foundations, systems, and polynomial operations. Each 75-minute lesson provides a balance of guided instruction and independent practice with problems modeled after the NYS Interim Assessment.
A targeted intervention sequence for Grade 8 students to master estimating irrational numbers like square roots and pi, placing them accurately on number lines between rational benchmarks.
A specialized intervention sequence focused on the Number System for Grade 8, specifically identifying rational and irrational numbers through their decimal expansions and converting between forms.
A targeted Tier 2 intervention sequence focused on helping students master rational approximations of irrational numbers. Students move from 'sandwiching' square roots between perfect squares to estimating complex expressions and comparing values on a number line.
A Tier 2 intervention unit focused on distinguishing between rational and irrational numbers through pattern recognition and algebraic conversion. Students explore decimal expansions, long division models, and number line placement to master Colorado standard 8.NS.A.1.
A specialized intervention sequence designed for Grade 8 students to build a conceptual foundation in the real number system, focusing on the distinction between rational (repeating/terminating) and irrational numbers using CRA methods.
A specialized intervention sequence focused on helping 8th-grade students master the approximation and comparison of irrational numbers using visual models and estimation strategies.
A 7th-grade unit exploring the divide between rational and irrational numbers. Students use long division patterns, geometric square models, and number line approximation to master the real number system.
This high school mathematics sequence guides students from the decimal representation of rational and irrational numbers through the formal logic of proof by contradiction, culminating in the classic proof of the irrationality of the square root of 2 and the exploration of closure properties in the real number system.
An 8th-grade geometry sequence focusing on the algebraic manipulation of volume formulas for cylinders, cones, and spheres. Students progress from simple calculations to solving for missing dimensions (height and radius) using inverse operations, square roots, and cube roots.
This sequence bridges the conceptual gap between basic arithmetic definitions and rigorous algebraic understanding of the real number system. Students move from decimal expansion to formal proofs by contradiction, geometric construction, and iterative approximation algorithms.
A high-school level exploration of irrational numbers, covering geometric origins, formal proofs by contradiction, decimal classification, and high-precision estimation techniques. Students move from historical context to rigorous algebraic reasoning and numerical analysis.
This sequence guides 8th-grade students from the basics of perfect squares to the complex task of approximating and ordering irrational numbers on the real number line. Students will use geometric models, decimal expansion analysis, and systematic bounding techniques to master the real number system.
This sequence guides 9th-grade students through the conceptual shift from rational to irrational numbers. Students explore decimal expansions, geometric models of square roots, estimation techniques using perfect square benchmarks, and precision plotting on the real number line, culminating in the comparison and ordering of real numbers in various formats.
Students transition from understanding rational numbers to exploring the concept of irrationality through square roots. They develop estimation strategies using perfect square benchmarks to approximate values to the nearest integer and tenth, culminating in ordering a mix of real numbers on a number line.
A comprehensive Tier 2 intervention designed to move 7th graders from foundational one-step equations to complex multi-step real-world problems using a 'structural engineering' theme.
A specialized intervention sequence focused on mastering linear expressions through visual models and properties of operations. Students move from concrete algebra tiles to abstract manipulation of rational coefficients.
A comprehensive math review sequence focusing on foundational middle school skills including fraction conversions and decimal operations. This unit is designed to bridge conceptual understanding with procedural fluency.
A comprehensive math unit focusing on applying percentage calculations, sales tax, and multi-step budgeting to real-world scenarios. students act as event planners to manage a fixed budget while accounting for specific tax rates.
A unit focused on applying percentages to real-world financial contexts, including discounts, markups, and interest.
A lesson sequence focusing on financial literacy and the practical application of percentage decrease through real-world shopping scenarios and discount calculations.
A middle school mathematics unit focused on proportional reasoning, ratio analysis, and multi-representation of numerical relationships.
This 8th-grade sequence focuses on fundamental math fluency using manipulatives. Students redefine base-10 blocks for decimals, engage in regrouping simulations, visualize division, and perform error analysis to solidify their understanding of place value and operations.
This financial literacy sequence for 6th-grade students focuses on consumer skills, specifically unit pricing, discount evaluation, brand comparison, and hidden costs. Students apply mathematical strategies to real-world shopping scenarios, culminating in a comprehensive grocery store simulation.
A 7th-grade entrepreneurship sequence focused on the financial math and operational logic behind a business plan. Students progress from estimating startup costs to conducting break-even analysis and managing a simulated month of profitability.
This sequence guides 7th-grade students through the process of factoring linear expressions, starting with finding the GCF of algebraic terms and progressing to factoring negatives, rationals, and interpreting expressions in real-world contexts. Students develop 'bidirectional fluency' between expanded and factored forms, viewing algebra through the lens of structural decomposition.
A 5-lesson unit where 8th-grade students act as financial analysts to master operations with rational numbers through real-world simulations of bank ledgers, stock markets, and debt division.
A comprehensive 8th-grade math sequence that bridges the gap between basic fraction division and algebraic reasoning. It covers visual proofs, rational number rules, complex fractions, fractional coefficients in equations, and real-world rate applications.
This sequence applies fraction multiplication and division to architectural design and spatial planning, moving from visual area models to complex multi-step scaling and design challenges. Students master operations with rational numbers through the lens of a professional architect.
A comprehensive math sequence where students become prospectors to master arithmetic, word problems, geometry, and probability through engaging, game-based challenges.
A series of inquiry-based lessons exploring the deep connection between prime factorization and decimal representations. Students move from predicting decimal types to mental conversion strategies and advanced simplification.
A comprehensive math intervention sequence for 6th-grade students, focusing on four key domains: Numbers & Operations, Algebraic Thinking, Measurement & Data, and Geometry. This sequence uses high-leverage strategies from the All Learners Network (ALN) and aligns with i-Ready prerequisite modules to bridge conceptual gaps.
A unit focused on mastering the number system, starting with integer basics and moving toward complex operations and coordinate planes.
A project-based unit where 7th-grade students act as data consultants to solve school-wide problems. They learn to identify bias, design sampling plans, collect data, and present data-backed recommendations to administration.
This sequence explores how different algebraic structures represent real-world scenarios, specifically focusing on percents, geometry, and financial modeling. Students learn to translate verbal descriptions, analyze equivalent expressions, and apply their knowledge to a final project as financial consultants.
This sequence introduces 6th-grade students to one-step equations using the concept of inverse operations. Students explore the logic of 'undoing' actions, apply properties of equality to solve equations involving all four operations, and master the skill of verifying their solutions through substitution.
