## 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 pieces to show the increase or decrease amount, visually, as a part of the original amount. The pieces can be moved around the Jamboard and replaced by other denominations.

### Slides

The slides are presented in the slide show below. They are arranged in the following order. the slides show the different positions of the manipulatives, e.g., how the \$20 bill is cut into discount and sales price.

• Slide 1: 5% Tax Rate for \$20 price – compute the total to pay
• Slide 2: 20% off discount for \$20 original price – compute the sales price
• Slide 3: generic tax rate
• Slide 4: generic discount rate

Here is a link to the Jamboard. You must make a copy to access it.

## Making Discount Meaningful

Educators teaching math typically start with the “mathy” stuff first. For example, for finding the sales price teachers may start with showing students the stepsÂ to calculate (photo below).

I start with the concept, either with a pictorial representation or actual objectsÂ to represent the underlying concept. In the photo above, I show an object (related to the student’s interest – this student is into weight training) on sale. The \$50 circled in yellow represent the original price. I explain the concept of being on sale and discount and show that 20% is \$10 to take awayÂ (marked out). This leaves \$40 (in green) which is the sales price. This allows for conceptual understanding before showing him the “mathy” way of doing the problem.