Module 9: Factors & Number Structure

Investigate the multiplicative structure of whole numbers through factors, primes, divisibility, and shared numerical relationships.

Prime vs. Composite Numbers - Distinguish prime and composite numbers by examining the number and structure of their factors.

Factors & Prime Factorizations - Break whole numbers into factors and represent them uniquely as products of prime numbers.

Divisibility & Divisibility Rules - Use place-value patterns and number properties to determine whether one number divides evenly into another.

Greatest Common Factors - Identify the largest factor shared by two or more numbers and connect it to their underlying factor structure.

Least Common Multiples - Find the smallest multiple shared by two or more numbers and explore how common multiples arise from number structure.

Module 10: Angles, Lines, & Geometric Language

Build the language and reasoning needed to describe geometric relationships precisely, with a focus on angles, lines, attributes, and mathematical definitions.

Angle Measurement - Understand angles as measures of rotation and use degrees, benchmarks, and tools such as protractors to describe their size.

Lines & Angles - Explore how lines, rays, segments, and intersecting lines create important angle relationships.

Interior & Exterior Angles - Investigate relationships among angles inside and outside polygons and use those relationships to determine unknown measures.

Attributes - Identify and describe the measurable and defining characteristics that can be used to compare and classify geometric figures.

Describing Geometry Using Precise Mathematical Language - Practice using definitions, attributes, and geometric vocabulary to describe shapes and relationships clearly and accurately.

Module 11: Two-Dimensional Shapes

Examine the properties and relationships of two-dimensional figures while developing a flexible, hierarchical understanding of geometric classification.

Polygons - Identify and classify polygons using defining attributes such as straight sides, closure, regularity, and convexity.

Quadrilaterals - Explore the properties and relationships among four-sided figures, including parallelograms, rectangles, rhombi, squares, and trapezoids.

Triangles - Classify triangles by their sides and angles while examining the properties that all triangles share.

Circles - Understand circles through radius, diameter, circumference, area, and the defining idea of equal distance from a center.

Hierarchical Classification of Shapes - Organize shapes into nested categories to understand how one figure can belong to several geometric classes at the same time.

Properties vs. Definitions - Distinguish characteristics that are always true of a shape from the minimum attributes needed to define that shape.

Module 12: Perimeter, Area, & Measurement

Develop measurement as a process of comparing quantities to units while exploring perimeter, area, unit conversions, and the reasoning behind familiar formulas.

Perimeter & Area - Compare the distance around a figure with the amount of surface it covers and explore how these measurements can vary independently.

Conversions - Use relationships among units to convert measurements while reasoning about why numerical values change when units change.

Units & Iteration - Understand measurement as repeatedly applying a chosen unit to determine the size of a length, area, or other quantity.

Why Area Formulas Work - Use decomposition, rearrangement, and visual models to explain the reasoning behind common area formulas.

Module 13: Three-Dimensional Geometry

Extend geometric and measurement reasoning into three dimensions by examining solids, nets, surface area, volume, and the relationships among different types of measurement.

Polyhedra - Identify and classify three-dimensional figures by examining their faces, edges, vertices, and other defining properties.

Surface Area - Measure the total area covering the outside of a three-dimensional figure by connecting its faces to two-dimensional area.

Volume - Understand volume as the amount of three-dimensional space a solid occupies, measured using cubic units.

Nets of Three-Dimensional Figures - Explore how two-dimensional arrangements of faces can fold to form three-dimensional objects.

Connecting Area, Surface Area, & Volume - Compare linear, square, and cubic measurement to understand how area, surface area, and volume are related but measure different attributes.

Module 14: Transformations, Congruence, & Similarity

Explore how figures can move, change size, and remain mathematically related through transformations, symmetry, congruence, similarity, and scale.

Transformations & Symmetry - Explore ways figures can move or map onto themselves while identifying patterns of reflectional and rotational symmetry.

Congruency & Similarity - Compare figures to determine whether they have exactly the same size and shape or the same shape at different sizes.

Translations, Rotations, & Reflections - Examine the three rigid transformations and describe how each changes a figure’s position or orientation without changing its size or shape.

Scale Factor - Use multiplicative relationships to describe how corresponding lengths change when figures are enlarged or reduced.

Module 15: Ratios & Proportional Reasoning

Develop proportional reasoning by comparing quantities, examining rates, and representing relationships with tables, graphs, models, and equations.

Defining Ratios - Understand ratios as comparisons between quantities and explore the different ways ratio relationships can be represented and interpreted.

Solving Ratios - Use scaling, equivalent ratios, and visual models to determine unknown quantities while preserving a proportional relationship.

Rates & Unit Rates - Compare quantities measured in different units and use unit rates to describe how much of one quantity corresponds to one unit of another.

Proportional vs. Nonproportional Relationships - Distinguish proportional relationships from other relationships by examining how quantities change relative to one another.

Tables, Graphs, & Double Number Lines for Ratios - Represent ratio relationships in multiple ways and connect the same proportional structure across tables, graphs, and double number lines.

Module 16: Percent Reasoning

Build a flexible understanding of percent as a proportional relationship and connect percents to fractions, decimals, estimation, and real-world changes.

Reasoning About Percent - Understand percent as a comparison to 100 and use part-whole relationships to solve a variety of percent problems.

Percent Increase & Decrease - Analyze how quantities change by a given percent and distinguish the original amount, amount of change, and resulting value.

Connecting Fractions, Decimals, Ratios, & Percents - Recognize fractions, decimals, ratios, and percents as interconnected ways of representing the same quantitative relationships.

Benchmark Percents & Estimation - Use familiar percents such as 1%, 10%, 25%, 50%, and 100% to estimate and reason efficiently about unfamiliar percentages.