M102

Modeling with Linear Functions and Equations

About This Badge

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. Solving the equations gives us new and useful information about the situation. In M102 Modeling with Linear Functions and Equations, you will create function models in situations where changes in one quantity are assumed to be proportional to changes in another quantity. You will solve problems and interpret models to gain insight into situations involving a constant rate, such as the startup cost for a business, constant speed, uniform density, and many others. You will also create linear equations to model constraints in real-world problems, such as problems involving finite resources, spatial constraints, manufacturing specifications, or other conditions that must be satisfied. As you learn linear modeling, you will reason quantitatively using the relationships between the parts of a linear function model and the situation it describes. You will use technology as a tool to solve linear equations and to understand how the graphs of linear functions relate to their constituent parts. The work for this badge builds a foundation for the future study of topics such as quadratic and exponential function models. Modeling with linear functions and equations is useful for careers in a variety of fields, like science, engineering, medicine, business, and artificial intelligence.

Suggested prerequisites for this badge: comfort with solving simple equations and problems involving proportional relationships.

This badge may be offered concurrently with M101.

This badge is suggested as a prerequisite for: M103 Modeling with Functions of Quadratic Type; M104 Modeling with Functions of Exponential Type.

XQ has developed a project-based unit aligned to Badge 102 as a part of the XQ Math Algebra 1 course. Find a teacher guide, content overview, and project overview for _Module 3 - In The Zone_ under Learning Principles and Learning Activities, below. You can access the full folder of module materials HERE.

Learning Activities and Alignment Guidance

These resources provide learning activities that can supplement traditional coursework as well as guidance for aligning coursework to this badge.

Standards M102 2024

Points of Emphasis in M102

Introduction to Alignment Guidance Final

M102 Alignment Guidance x

Learning Principles 2024

Sample Learning Activities-teacher

Sample Activities - Student Version

XQ Math - Mod 3 Project Overview

XQ Math - Mod 3 - Overview

Welcome to XQ Math - Teacher Guide (2)

Assessment: Pre-/Post-Task

These tasks should be administered to students before launching instruction on a new badge and again once badge instruction is coming to a close. These tasks are designed to support students' understanding of what they have learned from the beginning to the end of each badge and to support teachers in making relevant, timely decisions about how they support student learning.

M102 PRE Task

M102 POST Task

M102 PRE TASK Teacher Scoring Guide

M102 Teacher-Facing Template

M102 Teacher-Facing Template

M102 Class Summary File

102 Class Summary File

Assessment: Performance Tasks

There are two available performance tasks for this badge. Each task has a teacher guide, scoring guidance, and student versions (docx format) in English and Spanish. Where available, samples of student work are also provided.

Evidence of Learning 2024

Introduction to Performance Assessments

M102A Cost of Driving Fast Teacher-Facing

Student Work M102A The Cost of Driving Fast

M102A Cost of Driving Fast Student-Facing (1)

M102A Cost of Driviing Fast Student-Facing

ESP M102A Cost of Driving FastStudent-Facing

ESP M102A Cost of Driving Fast Student

M102B Side Hustle Teacher-Facing Final

M102B Side Hustle Teacher-Facing Final

M102B Side Hustle Student-Facing Final

M102B Side Hustle Student-Facing Final

M102B Side Hustle Option A Scoring Guide (1)

M102B Side Hustle Option B Scoring Guide

Assessment: Portfolio Resources

IM Portfolio M102

Assessment: Professional Development Resources

M102 Baseline 2024 w student work

Baseline PL Handout M102 2024 w student work

M102 Baseline 2024 w student work

Baseline PL Handout M102 2024 w student work

Content and Practice Expectations

These resources explain the core content and practice expectations for this badge as well as how this badge aligns to content standards.