## Monthly Budget – Introduction

## Helping students understand and implement a monthly budget is challenging, especially for students with disabilities that make it harder for students to conceptualize abstract ideas. I previously posted about a full budget activity. This post shows a means of scaffolding the concept of partitioning money in a budget context. The idea is to keep it simple for now and build from there.

### Set Up

A parent of a student I support came up with the following idea. We start with a couple major budget items (rent, groceries, utilities) and the temporary idea that the remaining money is discretionary (not the word we use with the student). Money is printed (legal if the printed bills are small enough and only 1 sided) in lieu of fake money that does not look like the bills they would see.

The activity is guided by slides on a Google Slides presentation (link at bottom of this post). Note: the activity can be rerun as needed and the Google Slides slides can be copied, pasted, and information removed. This allows you to keep a record of each trial with this activity.

### Job and Pay

The student can either search for a job on a site like Indeed.com or an ad for a job can be provided. The hourly rate is established and the student is prompted to compute the total pay on Google Calculator to allow a screenshot to be produced.

The student then uses the chart to provide a visual and scaffolding to compute the total pay for a month. I go with 4 weeks of 5 work days each, with no taxes to keep it simple.

The student counts out the money, first by grouping hundreds together to get a $1,000. Then the total is moved next to the envelopes.

The pay is entered into a bank balance table to provide practice with the format of a check register. This helps provide structure and having the money counted out on the table allows the student to see a concrete representation of the bank balance table. (Note: I slide the money to the left to allow space to move the money to the envelopes as the student pays bills.)

### Paying Bills

The first bill is rent. The student is prompted to search for an apartment on a website like Apartment.com, take a screenshot, and paste into a slide.

The student then pays the bill by counting out the money and sliding the money towards the envelope.

The student then enters the rent into the bank balance. I then point to the money pile on the right in image above and refer to it as rent. I then point to the rent entry into the bank balance. Similarly, I point to the pile on the left, refer to it as the balance and count it out, then point to the new balance in the table. This provides a concrete representation for the bank balance.

I found a website that provides average bill amounts for our state. The student clicks on the link, takes a screen shot of the average costs, and pastes it into the slide.

We focused only on heat and electricity. The student identifies both amounts (I round to the nearest 5 to keep it simple) and then pays both by moving the money over.

Both bills are entered into the bank balance. I then point to the two piles of money used to pay the bills, point to the entries into the table below, point to the pile of remaining money, and point to the entry into the balance in the table below.

Finally, the student makes a shopping list of food items for all 3 meals for the week. To make it easy, we can assume the the same meal each day. The student is provided a lot of leeway in what he or she chooses and what amounts. The amounts they choose may not be enough for a week. That can be addressed in grocery shopping activities conducted in isolation.

The student shops online for the items and takes a screenshot of the cart.

The student completes the table to determine the total cost for a month.

The student moves the money over and then this total cost is entered into the bank balance. The same comparisons between money piles and cost and balance are presented. Then the remaining money is free to use for whatever the student wants. At this point, you can have the student go shopping for clothes or whatever.

### The Google Slides File

Here is the Link to the Google Slides file. You can make a copy to access it.

## Simplify Rational Monomial Expressions

## This post provides details about a handout for simplifying rational monomial expressions. It incorporates a couple strategies to make the simplification of rational monomial expressions more accessible. The strategies include address prerequisites skills ahead of time, chunking, and scaffolding. This incrementally walks the students through the steps.

### The Pages of the Handout

The handout has 3 pages.

- Page 1 is an initiation with two parts. There is a review of prerequisite skills aligned with the new topic. There is also a preview of the new topic with scaffolding to separate the factors into individual fractions.
- Page 2 provides a Before and Now to draw upon student prior knowledge of simplifying using exponents rules. This is followed by scaffolded steps to separate the expression into individual fractions for each type of term (e.g., Xs). This provides a load reduction for what the student has to focus on.
- Page 3 involves negative and 0 exponents with an additional step to address each.

### Access to Handout

Here is a link to the handout.

## 0 and Negative Exponents – Scaffolded

## This post presents a scaffolded and meaning making approach to exponents that are 0 or negatives.

### Handout

The slide show below presents all 4 pages.

- The handout starts with an initiation to preview the prerequisites for what is presented in the lesson. It also introduces a chart that will be used for discovery.
- Page 2 presents a discovery activity of following a pattern of dividing by 2 down to the 0 exponent. The concept of exponents is presented as the number of occurrences of the base. This leads to the idea of a 0 exponent indicating the base is no longer present, but there is still 1.
- Similarly, on the 3rd page the pattern of dividing continues into negative exponents to show the resulting fractions. The negative exponents are then presented as reciprocals.
- For terms with multiple factors (e.g., 5x vs just x) the students are presented steps to write the factors separately. This unpacks the reason why the negative exponent acts only on one of the factors (unless both are grouped with parentheses).

### Access to Handouts

Here is a link to the student handout, and a link to the teacher handout.

## Intro to Concept of Functions

## Functions are perhaps the most prevalent and important topic covered in secondary math, aside from maybe 1 variable linear equations. The concept of a mathematical function is challenging for many students. This post provides details about a meaning making approach to introducing functions.

### Overview

The introduction is presented on a Google Jamboard, to allow for movement in the pairing of inputs and outputs. It starts with analogies pairing of items using a gumball machine and a Coke machine and proceeds incrementally towards the various representations. The functions are contrasted with examples of relationships that are not functions.

### Slides of the Jamboard

- Slides1 and 2 present the gumball and Coke machines. Students can move the items to see how a quarter can result in 2 different color gumballs while the Coke button results in only 1 output.
- In slides 3 and 4, the use of an hourly wage introduces input and output with quantities. Slide 4 shows two different pay amounts for the same number of hours worked. This taps into prior knowledge.
- The sequencing progresses through
- function machines
- equations
- tables
- graphs

- Each includes an example and a non-example.
- The last slide provides a sorting activity.

### Access to Jamboard

Here is the link. To access the Jamboard, you need to make a copy.

## Prerequisite Skills and Current Content

## The effort to provide intervention to fill in gaps is challenging for different reasons. One reason is the effort to balance support for current content while filling in gaps. This post shows an example of how to fill in gaps while working through the current topic.

### Overview

Various rubrics used to assess teacher instruction includes an effort to build on or connect to prior knowledge. If the student has gaps with prior knowledge, the lesson becomes less accessible for students with the gaps. Previously, I addressed how to support both current content and fill in gaps. The idea is to systematically fill in gaps by addressing prerequisite skills as they arise in new lessons.

### Example

The handout out below shows an example of how this can play out. The first page is used as a do now for the content presented on page 2. If you are teaching a student how to solve 1 step equations and are moving into integers, page 1 is a a means of supporting the new content while filling in possible gaps. The first image shows the student will need to evaluate -13 – 3 as part of the solving in the lesson. This can be addressed in the do now, as shown in the 2nd image, page on the right. (Notice all the problems on page 1 are steps to solve on page 2 problems.) This is useful for students with special needs and for differentiation.

## 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 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

### Access to Jamboard

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

## Base 10 Blocks on Jamboard for Subtraction

## This post provides access to and details about a Google Jamboard with scaffolded background to support multi-digit subtraction with regrouping.

### The Jamboard

The Jamboard has images of basic base 10 blocks. The background provides side by side tables for numbers and for blocks. Additional blocks are set aside for regrouping. Here is a FB Reel and a YouTube video showing how to use this artifact.

### Access to the Jamboard

Here is a link. You need to make a copy to access it

## Introduction to Perimeter and Area

## This post provides a conceptual approach to understanding perimeter and area.

### Overview

Students are prompted to build an rectangular animal pen for some farm animals. The number of fences represents the perimeter. The number of squared segments of grass inside the pen represents the area.

### Google Jamboard

The slides are presented below. This video shows how the manipulatives work.

### Access to Jamboard.

Here is a link to the Jamboard. Need to make a copy to use it.

## Intro to Graphing Linear Functions using Jamboard

## Graphing linear functions may be the most important topic in Algebra 1. While proportional reasoning is a prelude to functions, this is the first formally identified function presented to them. The graphing leads to slope and intercepts, beyond the entry point for graphical representations to functions. This post presents an activity that can serve as the entry point for linear functions.

### Overview

The activity is presented on a Google Jamboard, which provides manipulatives. It begins with a relevant context for students, money and being paid for a job. This allows them to engage the function using money. Before using numbers, they engage the work context through images. They are presented the table and then graph representations of the function before getting into the equation. Here is a FB Reel showing the movement of the images.

### The Slides

There are 3 categories of slides. Here is a description of each.

- Table and graph clocks for hours and dollar bill for the money.
- They graph the whole hours first, then fractional hours (1/2 and 1/4) to see that there are points “squeezed in between each other. This leads to the idea of infinite number of points. In turn, this leads to the idea of the line are a visual means to present all the points. The points can be presented as solutions. Hence, the graph presents all the solutions for the function.

- Table and graph with numbers on sticky notes that can be moved from the table to ordered pairs to positions on the coordinate plane.
- The equation, with sticky notes to show numbers substituted in for the variables and then moved to ordered pairs with parentheses.

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