rates, ratios, proportions
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Unit Rate Problems using Manipulatives and Visuals
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Intro to Percent Change on Jamboard
This post provides details about an artifact that has a manipulative and visual representation of tax rate and discount rate. These contexts are used as an introduction to percent change. The manipulatives are presented on a Google Jamboard. Overview The price or original price is presented as dollar bill. The bill is cut into proportional…
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Intro to Solving Proportions
Solving division equation proportions is challenging for two reasons. First, it involves fractions. Second, for some reason, many students struggle with solving division equations and a proportion is a more complex version. This post outlines a scaffolded handout to guide students through solving by multiplying both sides. Overview The handout provides support in two ways.…
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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 Ratios using Jamboard
Below are images from a Google Jamboard for a hands on introduction to ratios. (See image at the bottom for how to make a copy in order to use it.) The images are from Clever Cat Creations and provide a visual representation. The moveable items engage the students kinesthetically. It also helps unpack the concept…
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Solving Proportions – Scaffolded and Jamboard
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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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Unit Cost and Actual Shopping
I previously shared that grocery shopping has a lot of tasks that are overlooked. One is working with unit costs. There are two math tasks related to unit cost, interpreting what a unit cost is and computing the total cost for buying multiple items. When I take a student into a grocery store to work…