M153:ReasoningandProofthroughSimilarity
Have you ever zoomed in on a photo and noticed how the shapes stay the same, just bigger? That's similarity in action: when shapes grow or shrink but keep the same angles and proportions. Architects use it to design buildings. Animators use it to make movement look real. Scientists use it to study shadows and reflections.
In M153 Geometry: Reasoning and Proof through Similarity, you will:
• Construct and critique logical arguments as you explore relationships between geometric figures
• Perform geometric constructions and describe sequences of transformations to prove that one figure is similar to another
• Test and apply theorems to reason about relationships between figures and construct visual representations using segments, angles, triangles, and quadrilaterals
• Use technology to aid in performing transformations
Examples of careers that use M153 concepts: graphic design, animation, art, and physics.
Associated Badges
Prerequisites for This Badge
Basic understanding of angles, triangles, and quadrilaterals
Badges This Is a Prerequisite For
Learning Goals
Content & Practice Expectations
Each badge framework describes the mathematics skills and understandings that students will need to demonstrate to earn each badge through a set of Content & Practice Expectations (CPEs).
Alignment Guidance
Guidance for aligning badge standards (CPEs) to your existing curriculum and mathematical standards can be found in the documents shared below.
Points of Emphasis
This document highlights key mathematical concepts that should be emphasized in this badge.
Intro to Alignment Guidance
This document describes the structure of the alignment guidance documents provided with each badge.
Alignment Guidance
Guidance for aligning this badge to the open-source Illustrative Mathematics (IM) curriculum.
Intersection of Badge Content with CCSS Clusters
A mapping of each badge to the relevant Common Core State Standards for Mathematics (CCSSM).
Curricular Resources
Learning Activities
These resources provide learning activities that can supplement traditional coursework.
Learning Principles
Descriptions of the XQ Math Badging Learning Principles, which should undergird instructional materials.
M153 Learning Activities Teacher-Facing.pdf
Teacher guide for the sample activities provided with this badge.
M153 Learning Activities Student-Facing.docx
Student-facing worksheets provided for classroom implementation of the sample learning activities.
Assessments
Introduction to Badge Assessments
This document provides an overview of the different badging forms of assessment.
Pre-/Post-Task
These tasks should be administered before instruction begins on a new badge and again as badge instruction comes to a close. The pre-task gives students an opportunity to see where their learning is headed, identify any relevant background knowledge or skills they already possess, and establish a starting point for the badge. The post-task provides an opportunity for students to demonstrate what they have learned and compare their new thinking to their original responses. Together, these tasks help students recognize their growth over time while providing teachers with meaningful information to guide instruction and support learning.
Portfolio Resources
A portfolio of evidence consists of student-produced artifacts that demonstrate proficiency against a badge’s CPEs. The portfolio development process involves students selecting and reflecting on artifacts that showcase their understanding of badge CPEs, followed by iterative teacher review and student-teacher conferencing until the work demonstrates proficiency.
Professional Learning Resources
Download a sample Professional Learning presentation for this badge that you may copy and customize to suit your needs. When available, samples of student work are provided for discussion.
Baseline Professional Learning
A modifiable presentation to introduce teachers to key concepts of math badging, illustrated through sample math tasks for this badge.
Baseline Professional Learning - Student Work
A collection of student work samples with teacher feedback, to aide in assessment of student learning for this badge.
Baseline Professional Learning Handout
A handout to accompany the professional learning session for this badge.