proportional relationships
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Word Problems with Unit Rates
Word problems are challenging. In middle school and high school, word problems for proportional relationships and linear functions are particularly challenging. This post shows an visualization approach to unpacking the unit rate component of such word problems. Visualizing Unit Rate Below is an excerpt from a handout used to introduce such word problems. It starts…
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Intro to Linear Functions and Proportionality Equations Using Context, Tables, and Graphs.
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Intro Linear & Proportional Relationship
This post provides a handout to introduce linear functions and proportional relationships. Multiple instructional strategies are implemented. There is context that draws upon prior knowledge, scaffolding, and visual representations. Graph and table representations of the functions are used as an entry point, without the use of equations. Overview There is a difference between proportional relationships…
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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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Intro to Ratio Tables
If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. To introduce ratio tables, I draw upon a relevant prior knowledge for a child. Food, especially pizza is a go to context for me. Use a CRA approach by using manipulatives (concrete), pictures (representational),…
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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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Multiplication, Proportional Relationships, and Slope Word Problems Updated
I posted previously about unpacking word problems involving multiplication or Slope. Here is an update. I have students draw a picture for the quantities identified. The multiplication situations become apparent when groups of objects are arise through the drawing, in contrast to an addition problem (right). This also helps algebra students visualize the rate and…
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Multiplication, Proportional Relationships, and Slope Word Problems Updated
I posted previously about unpacking word problems involving multiplication or Slope. Here is an update. I have students draw a picture for the quantities identified. The multiplication situations become apparent when groups of objects are arise through the drawing, in contrast to an addition problem (right). This also helps algebra students visualize the rate and…
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Intro to Constant of Proportionality Using Hourly Pay
An effective instructional strategy is to make the new math topic meaningful. A fellow Facebook group member asked about teaching the topic constant of proportionality. My suggestion is to use hourly wages as an introduction. I created a handout that starts with students finding a job with an hourly pay stated and then completing a…