Online Personalized Consumer Math Board Game

The game is played on a Jamboard. There are moveable game pieces on the left (Lego figures chosen to mirror the players – no hair is me), along with movable bills. There is a white rectangle partially covering the cashier’s money. It is a moveable rectangle I use to reveal the money when the cashier pays out money to a player. The money is subsequently covered again. When money is paid, the appropriate number of bills are moved to the cashier’s counter. Change can be computed and given. (technical note: you can click on an object on Jamboard to change its order, e.g., click on the bills to move them back, behind the rectangle.)

The game is a version of the Allowance Game, which is appears to be a version of Monopoly. The goal is to simulate budgeting and real life spending situations in an interactive and gamified way. The spaces can be revised to cater to the interests and reality of the players. The activities are all ones that I have used in isolation with students I help. The game can be played online and with multiple players who need to learn consumer math topics. (When you share the Jamboard with others, you can make them editors which allows them to move pieces.)

Players start with money in a bank account (center of the board) and then roll a virtual die and move accordingly. If a player does not have enough money for a spending activity, the activity cannot be completed. For some experiences, they are limited in what they can spend, e.g., buying a birthday present. (For rent, I will use an IOU until the player makes enough money – obviously a lot to possibly unpack in this scenario.) Spaces have an activity that falls into one of three categories:

  • earn money at a job by rolling dice for the number of hours worked
  • have a static money experience, e.g., get $20 from birthday or spend $12 on tooth brush
  • have a dynamic money experience, e.g., spend money on Amazon or attend a baseball game and the player goes to a related website (for example, a player buys a Red Sox ticket and a YouTube video of highlights of a game is shown – maybe 2 minutes)

A couple notes: I left the START space empty and am thinking I will move the find a job activity to that space. As of this posting I did not have students find a job yet and simply opened a link to a Target store site for employment and showed them a job ad. I think I will start the game with each player finding a job and rolling the die to earn money at the start.

Below are the steps I use to create and revise the game. If you have any suggestions, please post in the comment section.

Here is a link to a master copy of the game on a Google Doc. It can be copied and then revised. I store my game pieces on here as well.

Here is a link to a master copy of a WORD document I use to position the board with a cashier to create the image shown on the Jamboard.

The image created can be uploaded to Jamboard using the Set background function.

Here is a link to the dice rolling site I use. Each player can open it or I will roll for everyone.

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 on unit costs, where is what I do. I start with a pack of items (photo below) and ask the student to compute the cost for 1 item, in this case, “what is the price for the pack of chew sticks, how many in a pack, how much for 1 chewstick?” Then I prompt the student to compute the total if he buys 3 packs. This allows the student to differentiate between the two tasks.

The cost per items is easier to grasp and then is followed with the same prompts for a jar of sauce (below). I have the student compare unit costs for the large vs the small jars and ask, “do you want to pay $4.99 per ounce or $5.99 per ounce.” This language is more accessible than “which is a better deal?” You can work towards that language eventually.

These tasks can be previewed at school with a mock grocery store. The price labels can be created on the computer.

Counting Money – Jamboard

If you have a student who is learning to count money, here is a virtual set up to do so. I suggest having the student do a test run by moving coins into a box and bills into a box. It is easy to duplicate each item by clicking on the item to duplicate it.

If it works, you can insert images of items to purchase. Note, I start with just pennies or just $1 bills and incrementally add additional currency. This is useful for developing number sense.

I also present items to purchase that are of interest to the student – the image below was used with a student who loves Minecraft.

Counting Money at the Store

The way a student counts money in school on a school desk or table (top photo) is the way he or she will attempt count at the register as seen in the 2nd photo in which the student pulled all bills from his wallet then counted, with some bills folded. (Bonus if you can identify the woman in the photo!!!)

In the top photo (below) I had the student pull bills out from his wallet, with the bills unfolded and in order in his wallet (you can see he pulled a $20 bill first). In the next photo you can see that he is counting out the bills from the wallet as he did in practice.

Reading Scatterplots with Ford Mustangs

One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. Students who do not understand the meaning of the points, including the position, will struggle to interpret the graph. This post outlines a Jamboard activity to support interpretation of the points.

Overview

I present the scatterplot of used Ford Mustangs on a Jamboard (image above) with ads for two used Mustangs along with a cutout of each car. The cutouts are used to help the students understand the reasoning behind the position of each point. Here is a FB Reel and a YouTube video showing how the Jamboard can be used. To access the Jamboard, you must make a copy. See image at bottom of post.

Steps

First, I take the cutout of the first car and “drive it” along the x-axis (top 3 photos in gallery below). This helps them understand the horizontal axis placement. Then I move the car up to the appropriate price (bottom row left). Finally, I replace the car cutout with the bigger blue dot that was placed by the ad with the car. We then discuss that a dot can be used to represent that car and the location on the scatterplot is based on the two values in the ordered pair (which can be typed into the ( , ) in the Jamboard next to each car.

The same steps are used for the other Mustang (see it “driving” along the x-axis below).

The next step would be to identify additional points on the scatterplot. I then revisit driving the cars and show that driving the car more miles results in a lower price and driving the car less miles results in a higher price.

Finally, we discuss that this is a general trend but that it is not always true for each car. I highlight a couple points where one of the cars has more miles and a higher price (below). This leads into a discussion about additional factors influencing price.

Complementary Activity

An related I have used is having students create their own scatterplot for mileage and price of used cars. They shop on Carmax.com. This allows them experience the scatterplot from a data and context point of view.

Make a copy to access Jamboard.

Intro to Systems of Equations: Camry vs Mustang Depreciation

The scatterplot above is an approach I use to introduce systems of equations. Here is the process I use. (Note: I have found that students like math associated with buying a car – relevant, real life application for them.)

  • In my class, students would have seen a scatterplot with mileage and price for a single car. I explain that we will now compare two cars.
  • To review, in a do now or initiation at the start of class I would have one group generate a scatterplot for the Toyota Camry data and the other groups, Mustang (Excel sheet for all of this note: this data is old). Then they would share with each other
  • We would revisit the relationship shown and revisit the idea of depreciation.
  • I show a Camry and Mustang and ask two questions: Which car do you think costs more brand new? Which do you think depreciates faster and why?
  • Then I show them the scatterplot above and ask which car has higher dots at the far left? Explain what this means (Mustangs start off with a higher price). Then I ask about the dots at the far right.
  • The students are then asked to estimate when the cars have approximately the same value.
  • Then I present scatterplot below, with lines of best fit (trend lines) and they are asked the same question. We estimate the specific mileage and price and write as an ordered pair.
  • Finally, I explain that this is known as a system of equations and the ordered pair is the THE solution. The entire unit will focus on finding an ordered pair as a solution.

Monthly Budget Project

The images shown are excerpts from the latest iteration of a budget project I have used for years. The content addressed in this project can be used as stand alone activities and are relevant real life examples for our students. Even the younger students could benefit, e.g., learning addition by shopping for items online and recording the prices (for older students throw in computing tax). These topics are especially useful for multiplication word problems, rate, single variable equations, and linear functions (slope being rate of change such as car payment per month).

Here is an overview. You graduate from high school and are living on your own. You have a job, but your car is getting old. You need to figure out how to save for a down payment in your budget and for when you must pay a car payment and insurance. (You will have to get your OWN insurance.)

The image below shows the table for all monthly expenses.

The students have imbedded activities such as

  • estimating monthly food costs by estimating cost for meals for a single day
  • shopping for disposable household items
  • shopping for car insurance based on the car they shop for (more on that at the end) NOTE: they do not share personal information other than a school email address (or my email address) to receive the quote
  • searching for a job with a hourly pay and estimate after tax income

They shop for a car last as the idea is they need to save up for a down payment. The amount they can save is based on how much money is left over after paying all other bills. How much they save will be converted to how much they can spend on a car payment and monthly insurance payment.

Multiplication with Integers: a Meaning Making Approach

I previously tackled the difference between the ” – ” symbol used to represent a negative and a subtraction problem. This post gets into multliplication through the context of buying a Wendy’s frosty.

One comment to preface what is presented here. Negative numbers are abstract and challenging for many students. Multiplying by negatives is even more so. The approach presented here for multiplying gets a little complex, which is inherent to the topic. In other words, this is an involved process as “there is no royal road to geometry.” What I present here is a path I develop over time, as seen in the sequence below.

First, review of a couple building blocks. Multiplication can be represented at groups of items. 2 x 3 can be represented as 2 groups of 3 $1bills, e.g., you bought 2 Frosties for $3 each.

Negative in terms of money can mean you owe money. Hence, -3 means you owe $3, e.g., you order a frosty and owe $3.

If you change your mind and cancel the frosty, the $3 you owe is cancelled and you get your money back. +$3.

If you order 2 frosties, you owe $3 and another $3, which is -3 + -3. (You owe $6 or -6.)

Cancel those two frosties and you get your money back. -(-6) is now +6

2 x -3 means you means you have 2 negative 3s – repeated addition, or -3 + -3.

If you ordered the 2 frosties and owe $6 then cancel, you get your $6 back or +6.

In mathy terms, cancelling the 2 x -3 is written as -(2 x -3) or -2 x -3.

The – for the -2 can be held out front to focus on 2 orders of frosties or 2 x -3. That was covered previously. Then the extra negative cancels that order so you get your money back. And so you have multiplying two negatives!

All images were generated on this jamboard.

Scientific Notation – an Introduction

In a previous post I asked readers to identify a math topic that they wanted help unpacking. Scientific Notation was cited. Here is my approach to unpacking this topic.

My first step in presenting a new topic is meaning making. For scientific notation, the underlying idea is NOTATION – “the act, process, method, or an instance of representing by a system or set of marks, signs, figures, or characters.” We can represent numbers in different ways, one of which is scientific notation. This is useful to represent very large or very small numbers (as happens in science). It is useful because in lieu of writing out a bunch digits, the power of 10 can be used as a shortcut. In the image above you see that 4.5 x 104 has two parts, the decimal and the 10s.

Before I get into these big or small numbers, I address the concept of notation because that word is in the topic. To introduce a concept, I typically start with a related topic that is relevant for students. In this case it is money. To mirror the two parts of scientific notation, I list the bills and how many of each. In the left image below, I show both parts and pair combinations that are the same value (a single $10 bill and ten $1 bills). I then show how I can convert a single $10 bill by dividing by 10 and then multiplying the number of bills by 10 (middle image). This previews the steps used in scientific notation. Then (right image) I show the same approach for dollars and cents (which previews decimals). Note: to help flesh out the dollars and cents I would first use the linked Jamboard.

The image below left keeps the concept of money, but the images are faded. The students are still working with money and how many but now with numbers only. The middle image introduces decimals, but the same steps are used (divide by 10 and multiply by 10).

Finally, the matched pairs shown in the previous handout pages (images above) are presented with an explanation of the parts of scientific notation (below left). I explain the idea of scientific notation as a special way to write numbers, list the two parts, and then I show examples by circling the ones in each pair (bottom left) that fit the criteria. Then they identify numbers that are written in scientific notation (below right).

Following this introduction lesson, I would explain the applications (linked above) and go into more detail on how to rewrite the number in scientific notation.

Counting Out Value of Coins

Counting out the total value of a set of coins can be challenging for some students. A strategy to address this is a modified 100s chart with images of coins and decimal values.

Versions of handouts

There are 4 versions, listed in the order I used them with my students. I suggest you start with just pennies (less than 10) to acclimate them to the chart. Here is a video showing how to use chart.

  • dimes and pennies
  • nickels, pennies
  • dimes, nickels and pennies
  • quarters and pennies
FB Reel showing how it works or Youtube video

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UK Version

A request was made for a UK version. Below is the first iteration and may subsequently be revised. There are two versions: 1p 10p and 1p 5p 10p, both with 1 pound at the bottom for 100.

Jamboard

There is also a Jamboard version to allow you to work on this online. You have to make a copy of the Jamboard (see bottom image). (UK version – beta)

Make a copy to use the Jamboards.