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Math Assessment Activity: The Continuity Principle

Intersecting circles investigation: students solve two circle equations for their meeting points, then show algebraically that the points become complex numbers once one circle is translated apart.
Grades
Grades 8–12, Middle School, High School
File type
PDF
Preparation
Print ready

Updated Oct 13, 2026

Topic
math assessments, continuity
Resource types
Teacher Tools, Assessments
Preparation
Print ready

About this resource

What's inside this resource

Discover "The Continuity Principle: A Math Assessment Activity" - an innovative and captivating digital tool designed to enhance your students' problem-solving abilities in mathematics. This 40-minute timed evaluation is expertly crafted to test not only their mathematical skills, but also their critical thinking prowess.

As educators ourselves, we recognize the value of evaluating our students through activities that promote self-reflection and intellectual growth. The Continuity Principle assessment consists of 7 diverse tasks, delving into various facets of mathematics - such as logical reasoning, data analysis, identifying patterns, and real-world applications.

This resource is provided as a single PDF file with 4 easy-to-print pages. Developed by experienced teachers who have spent years in the classroom environment, this unique math activity facilitates meaningful learning while adhering to academic standards. Its flexible design allows it to be adapted for different teaching approaches and cater to each student's individual learning style.

Upgrade your math lessons with our Continuity Principle Assessment Activity – a brilliant supplement for your digital teaching collection! Offer your students the chance to surprise both themselves and you with this engaging math challenge from TeachSimple.com!

In the classroom

Teaching tips & learning objectives

Learning objectives

  • Solve simultaneous equations of two circles
  • Show that non-intersecting circles give complex solutions

Teaching tips

  • Students need a computer with GeoGebra or Desmos for the final locus task.

Skills covered

  • Solving systems — finding intersection points from two circle equations
  • Visualizing loci — tracing complex intersection points with GeoGebra or Desmos

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Resource details

Concepts & topics

Core concepts

  • Equations of circles
  • Simultaneous equations
  • Complex numbers
  • Translation
  • Locus

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