This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

The “Systems Are Everywhere” module was originally written for high school science teachers or counselors to use in any setting (in class or in extracurricular programs). However, during field-testing, we found that many elementary and middle school teachers were able to use these lessons successfully with their students. The module is made up of three lessons that serve to foster students’ understanding of systems, systems models, and systems thinking at every level of learning and across many content areas. Blended throughout the lessons are career connections that will introduce students to diverse systems thinkers in STEM, and provide context for how systems approaches are used in real life to address complex problems. The lessons and module can be used as a stand-alone set of activities or can be integrated into any course as an extension or enrichment.

The module begins with students modeling a complex system. Students will brainstorm and sketch the parts and connections of the system, then use an online tool (Loopy) to model the interactions of those parts and connections. Next, students will develop their understanding of systems thinking skills and their application for addressing problems and solutions. Then, students will apply their knowledge and skills to model a system of their choosing. Lastly, they will showcase their skills by creating a student profile and integrating their systems thinking skills into a resume.

Target Audience
This is our introductory module that we recommend teaching before each of our other modules to give students a background in systems and to help them understand the many careers available in STEM. This module can be applied easily to any content area and works best as written for students between 6th and 12th grades but can be adapted for other ages. It works very well when teaching virtually and in-person. If you are looking for an introduction to systems that can be delivered in-person with more kinesthetic activities, please see our Introduction to Systems module. The Intro to Systems module works best with 8-12 grade students, though can be used with some modifications for 6-7th graders. This Systems are Everywhere module can work well for elementary through secondary grades.

This unit consists of five lessons encouraging younger learners to engineer increasingly better towers using blocks and recycled materials. Each 30 minute lesson ("phase") includes goals, discussion, activity instructions, extensions, and student worksheets.

Phase 1: Paper Cut-Outs Activity
Phase 2: Building Blocks Activity
Phase 3: Number of Blocks Activity
Phase 4: Building within a Space Activity
Phase 5: Recycled Tower Activity

NGSS: K-2-ETS1-1, K-2-ETS1-2, K-2-ETS1-3

Common Core ELA: RI.2.1, W.2.6, W.2.8, SL.2.5

Common Core Math: MP.2, MP.4, MP.5, 2.MD.D.10

This lesson unit is intended to help teachers assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures: starting temperature + change in temperature = final temperature final temperature Đ change in temperature = starting temperature final temperature Đ starting temperature = change in temperature.

Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with known cross sections. These objects of complex shape defy standard procedures to compute volumes. Even calculus techniques depend on the ability to perform multiple measurements of the objects or find functional descriptions of their edges. During both guided and independent practice, students use (free GeoGebra) geometry software, a photograph of the object, a known dimension of it, a spreadsheet application and integral calculus techniques to calculate the volume of complex shape solids within a margin of error of less than 5%—an approach that can be used to compute the volumes of big or small objects. This activity is suitable for the end of the second semester of AP Calculus classes, serving as a major grade for the last six-week period, with students’ project results presentation grades used as the second semester final test.