## 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.

## Scaffolding Percent Discount and Tax

This is a snippet of a handout that is a follow up to a previous percent activity that I posted. It walks students through the mathematical steps including subtracting the price. I found that the cutting part of the previous activity was effective but the steps were not as clear. This handout is an attempt to clarify the steps.

What is surprising is how confused and challenged students are by simply computing the new price. Part of it is working memory and part of it, I believe, is learned behavior. Students are trained in math to simply follow steps without understanding the meaning of the steps. I ask them what the 6 represents in the problem above and many are unclear.

Here are the full handouts worked out by this student. The tax part of the first handout has the discount rate and not the tax rate listed – error. I corrected this after the lesson.

BTW, this student has autism and struggles to complete work in class. He took a long time to complete it. One problem is that he doesn’t have the personal experience and prior knowledge about discounts and taxes. To supplement this he would be given money and an item to buy and act out the actual purchase of the item to see how he pays less money.

## Conceptual Understanding

I gave a student a pop quiz on percent change – find discount and tax – after she completed Â independent practice on this objective. The student followed the steps very well, as you can see in the photo (I added the ink later) up to the very end. At that point she added the tax to 6 for a total cost of \$9.36 – good deal for an \$80 coat!

This is hardly uncommon if not typical in education both at the secondary and post-secondary level. The focus is largely on steps and not concept building. I asked her follow up questions (as opposed to telling her what to do to fix it) to flesh out the concept. “What did you do first and why?” “What does discount mean?” “What did you do here (pointing to the 6/100 part)?” “What do you pay the cashier?” She was confused because she wasn’t thinking real life situation but got caught in the weeds of the math steps.

What often happens is that students give up when pressed to think. I often have students tell me “can’t you just tell me the answer?” and “you’re the teacher, you’re supposed to teach me.” I respond “Yes, I can show you and I already taught you; now it’s your turn.”