Math Unit – Geometry is a homeschool math curriculum for ages 11–13 that develops geometric reasoning through similarity, congruence, coordinate transformations, angle relationships, the Pythagorean Theorem, and volume. Students begin by comparing figures and using scale factors, then move into reflections, translations, rotations, dilations, and multistep transformation sequences on the coordinate plane. Activities such as “Help Tessa Travel,” “Reflecting Points and Lines,” and “Drawing Triangles to Find Slope” style visual reasoning are replaced here by geometry-specific work with transformations, triangle-angle proofs, and three-dimensional measurement.

At a Glance

Age Range: Ages 11–13 (usually 7th grade)
Estimated Time Commitment: 19 lessons, approximately 45 minutes each
Prerequisites: Ability to graph coordinates, calculate with fractions and decimals, and understand proportions and scale factors
Student Independence: Designed for students to work independently, with parent support as needed
Includes: Student-directed lessons, Parent Plan sections, Student Activity Pages, answer keys, and unit assessment materials
Required items: Math Materials Kit sold separately

This unit is part of the age 11-13 full year math program, which covers approximately half of the seventh-grade math standards and all of the eight-grade standards.

Key Features

• Transformation Geometry: Students reflect, translate, rotate, and dilate figures on the coordinate plane while tracking how coordinates change. In “Help Tessa Travel,” they move a triangle through a sequence of transformations, record intermediate and final coordinates, and verify that rigid transformations preserve congruence.
• Similarity and Scale: Students distinguish congruent, similar, and unrelated figures using side lengths, angle markings, and proportional relationships. They use scale factors to solve missing-side problems and connect dilations with enlargements, reductions, and similar figures.
• Angle Reasoning and Proof: Students calculate missing interior and exterior angles, apply Angle-Angle similarity, and identify angle relationships formed by parallel lines and a transversal. They also cut out and rearrange triangle angles and complete a visual proof showing that the interior angles of a triangle total 180°.
• Pythagorean Problem-Solving: Students use (a^2+b^2=c^2) to find missing sides and apply the converse to determine whether a triangle is right. They then extend the theorem to real-world situations, coordinate-grid distance, proof, and three-dimensional problems.
• Measurement and Volume: Students calculate the volume of cylinders, cones, and spheres and compare how the formulas apply to different three-dimensional solids. “Working with Volume” brings these formulas together through additional practice across all three shapes.

Learning Outcomes

By the end of this unit, students will be able to:

• Distinguish congruent, similar, and non-similar figures using geometric evidence.
  
• Use scale factors to determine corresponding side lengths in similar figures.
• Perform and describe reflections, translations, rotations, and dilations on the coordinate plane.
• Analyze multistep sequences of transformations and track changes in position, orientation, and size.
• Calculate missing interior and exterior angles and apply Angle-Angle similarity.
• Identify angle relationships created by parallel lines and a transversal.
• Apply the Pythagorean Theorem and its converse to numerical, coordinate, real-world, and three-dimensional problems.
• Calculate the volume of cylinders, cones, and spheres.

Math Unit – Geometry connects visual, numerical, and coordinate-based geometry across two- and three-dimensional problems. Through transformation sequences, scale-factor reasoning, angle proofs, Pythagorean applications, and volume work, students use geometric relationships to explain, calculate, and represent how figures behave.

This item includes free online access to Beyond the Page Online for 18 months. This includes Learning Gates, Portfolio and any curriculum or student activity pages that you have purchased.