slope
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Graphing Linear Function Using Slope-Intercept – Steps
This document walks students through the steps for plotting the y-intercept and then using run and rise to plot additional points to draw a line. The handout starts with a review of prerequisite skills of identify slope and intercept in the equation. Below are slides from a Google Slides version. Link to handout here. Link…
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Intro to Writing Equations for Linear Functions – Pizza and Toppings
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Proportional Relationship (with k) vs Linear Function (with m)
There have been interesting discussions on various Facebook Teacher pages about proportional relationships vs linear functions. This mirrors discussion about the constant of proportionality vs slope vs unit rates. The difference between the proportional relationships and slope is context and the ratios. The ratio for the former addresses the variables themselves. The ratio for the…
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Group Model for Proportional Relationships and Slope Application
If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. In my experience, many students struggle with translating word problems modeled by a proportional relationship or a linear function into a algebraic expression or equation. (Image below.) Here is a link to a Jamboard…
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Slope, Constant of Proportionality, Unit Rate, Rate, Rate of Change
A question was posed recently that I find intriguing and important. The question was, “what is the difference between slope, constant of proportionality, unit rate, and rate of change?” I researched the answer to this to evaluate my own understanding of these terms. Here is what I found (and am open to feedback as my…
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CCSS MATH Coherence Map – 3rd Grade Groups of Objects to HS Slope
A hidden treasure is the Common Core of State Standards Math Coherence Map. It is an interactive flow chart that shows connections between the various standards. If you are teaching math, you can see the connections between what you are teaching, what was taught previously, and how you are preparing students for their future math…
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CCSS MATH Coherence Map – 3rd Grade Groups of Objects to HS Slope
A hidden treasure is the Common Core of State Standards Math Coherence Map. It is an interactive flow chart that shows connections between the various standards. If you are teaching math, you can see the connections between what you are teaching, what was taught previously, and how you are preparing students for their future math…
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Multiplication Problems as Intro to Unit Rates and Slope (follow up)
I previously related elementary school word problems with math topics in secondary schools. The photo below shows a method to help elementary school students unpack the multiplication problem, to help middle school students identify the unit rate, and to help algebra students identify slope (you can focus on simple problems like this as an entry…
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Handouts for Multiplication and Unit Rate Word Problems
Here are excerpts from two handouts I use to help students understand how to write multiplication and rate word problems as math expressions. The image, below at top, shows a problem from the first handout I present. The students draw a single group represented by the rate expression (for elementary school word problems the term…
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Slippery Slope – 3rd Grade Multiplication Word Problems to Slope in Algebra
Top left is a scaffolding I use to help students learn to solve math problems using multiplication (3rd grade). The situations are typically rate problems (e.g., 5 pumpkins per plant or $2 per slice of pizza) although the term “rate” is not used yet. The same concept of rate plays out in high school with…