M102:ModelingwithLinearFunctionsandEquations
Which cell phone plan holds the best value for me? How do I keep track of my costs if I want to start a t-shirt business? Modeling with functions is a powerful way to gain insight into the world around us. Nature, society, business, and everyday life are full of situations in which a certain quantity depends on other measurable quantities. Function models enable us to describe, analyze, optimize, and predict what could happen in these situations. Meanwhile, equation models allow us to express real-world constraints in mathematical language, giving us new and useful information about a situation.
In M102 Modeling with Linear Functions and Equations, you will:
• Create function models in situations where changes in one quantity are proportional to changes in another, such as startup costs for a business, constant speed, and uniform density
• Create linear equations to model real-world constraints, such as finite resources, spatial constraints, or manufacturing specifications
• Use technology to solve linear equations and explore how the graphs of linear functions relate to their constituent parts
Examples of careers that use M102 concepts: science, engineering, medicine, business, and artificial intelligence.
Associated Badges
Prerequisites for This Badge
Comfort with solving simple equations and problems involving proportional relationships (may be offered concurrently with M101)
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.
Sample Learning Activities - Teacher
Teacher guide for the sample activities provided with this badge.
Sample Learning Activities - Student
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.
Performance Assessments
Each task has a teacher guide, scoring guidance, and student versions (docx format) in English and Spanish.
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.