Business Mathematics: Percents, Formulas, Graphing
updated October 27, 2024
Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!
This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorf-y than others. Please feel free to take what you like and leave the rest.
This page has helpful links and LOADS of free resources to help you plan your sixth grade year. Enjoy!
Mission Statement - Consulting Services - Lending Library
Business Math
for Class 6
Pinterest - Renee Schwartz
My curated collection of visuals! Browse sample main lesson book pages, watercolor paintings, chalkboard drawings, etc. for
Business Math.
FREE eBooks at the Online Waldorf Library
Excellent resource! Published Waldorf curriculum books provided here in PDF format for you to download, keep, and read... for free!
Sample Lessons and Free Curriculum
Other Helpful Links
BLACKBOARD SKETCHING book
by
FREDERICK WHITNEY (1908)
available online for free - with step by step directions and illustrations
For percents, look at coconut flour! "You can replace up to 20% of the flour called for in a recipe with coconut flour, adding an equivalent
amount of additional liquid."
Why Paper Checks Refuse to Die
The New York Times - Jul 24, 2024
Of course, there is an endless number of movies you could watch if you wanted to talk about inflation... watching
something and trying to figure out how much that would be in today's dollars (like in
His Girl Friday when Hildy says, "Hey! I paid twelve bucks for that hat.)... but a
sweet picture book I want to remember about is Night of the Moonjellies by Mark Shasha.
 
Books to Buy
Ernst Schuberth's book (link to download as a FREE PDF is above; link to purchase the book is below) is the authority on this block.
Note: Jamie York recommends this book and lists the contents of this main
lesson in bullet points in his middle school math book (pp.22-26), also nothing that "what is listed here is too much to cover in one main lesson, and therefore much of the material on percents will need to be continued
in the track class." By this he means an afternoon math class which meets a few days a week through the school year to continue practicing the content of the main lessons in math. He also suggests nightly math homework; I
have some notes about this on my Middle School Mathematics page.
Mathematics Lessons for the Sixth Grade
by Ernst Schuberth
 
 
Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!
This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorf-y than others. Please feel free to take what you like and leave the rest.
I am currently teaching this main lesson block, February 2017.
Note: I taught a previous version of it last school year; this was before I found
Schuberth's book. Here is my blog post with pictures of all of our main lesson book pages.
Some of the links I include below are to free lesson plans in PDF form which you can download from Teachers Pay Teachers.
To make this fun, we are using extra-large 12 x 18 inch spiral bound MLBs and designing the book to look like a row
of shops along the street in a town. At each type of business there will be some math problems.
bakery
restaurant
dressmaker or tailor
bank
toy store
animal groomer
grocery store
travel agency
a variety of additional stores of your choice
Here was our structure, from Jamie York's notes:
Introduction / Using Multiples to Introduce Percents
to start this block: Using Multiples to Introduce Percents (DON'T SKIP)
(pp.1-19 of packet; answer key is given first; student pages begin on page 37)
Hands-On Mini Activity: Percent Models (we modeled 95%, 135%, 0.5%, 5%, 50%)
use with Hundreds Grid with Number Line
Percent Poetry - 100% Me!
fun and surprisingly challenging
Skill #2 - Determining a Certain Percent of a Given Number (ex: what is 20% of 400?)
practice problems: Percent of a Number Guided Practice
(for his strategy #3)
Skill #3 - Determining a Percentage (ex: 320 is what percent of 400?)
practice problems: Loopy Percents (you need 75 Fruit Loops per child/group)
my students really balked at the idea that you convert a fraction to a percent by dividing the top number by the bottom number... it seems so counter-intuitive to divide the big number into the little one... so I didn't argue and let them
solve the problem both ways and then check for reasonableness... ultimately they figured out that doing it the way I showed them got the right answer!
introduce the topic and the concept of the MLB using a book showing a line of shops on the street, such as
A Street through Time
by Anne Millard
Skill #1 - Percent to Fraction Conversions
practiced as homework with flashcards
one half = 50%
The Lion's Share
by Matthew McElligott
of course, now you must bake something and divide it up! we made delicious brownies
imagine some percent to fraction problems for a bakery
our MLB page was a display of four percent to fraction conversions with pairs of cakes drawn and colored in identically - this works best if you have a shape to trace and which divides easily - we used a rectangular block from the Grimm's Color Charts Rally
building blocks set
1/2 = 50%
1/4 = 25%
1 (whole) = 100%
1/3 = 33 1/3%
make the set of flashcards for at home practice - there are 24 (including 1 whole = 100%)
practice problems:
fun game for practice: Whack a Fraction Decimal Percent (Christmas theme)
you must print the cards in color to play this game
Skill #4 - Percent Increase and Decrease Problems
imagine some percent increase problems for going to dinner and adding a tip, inspired by
If an Armadillo Went to a Restaurant
by Ellen Fischer
in our initial lesson we did 20% (or 1/5) tax on two bills - $5.75 at a diner and $230.00 at a fancy restaurant
we invented three receipts for the MLB; his business was an Italian restaurant
(no charge for soda or french fries but you pay 50 cents for any kind of sauce)
Skill #5 - Profit, Commission, and Tax
imagine some problems for a dressmaker's business, inspired by
Halibut Jackson
by David Lucas
discussion: do you think it's a good idea for salespeople to work on commission or not?
three demonstration problems from Jamie York
we invented three story problems for the MLB; his business was "Madame Bouffant's Skirts, Shirts, and Socks"
practice problems: Scaffolding Sales Tax Percent Word Problems
Skill #6 - Interest (simple interest - compound interest should be delayed until 7th grade)
imagine some problems for banking (mortgages and savings accounts), inspired by
Leah's Pony
by Elizabeth Friedrich
discussion: the Great Depression
discussion (the next day): checking accts vs. savings accts, debit cards vs. credit cards, credit scores, mortgages and down payments
we invented three story problems for the MLB: Dewey who goes to the bank and wants an auto loan and has a good credit score, Leo who wants to buy a $500,000 house and puts 10% down and gets a 30 year mortgage with a 2% interest rate, and Peyton who wants
a credit card and has a bad credit score and gets a $250.00 line of credit at 18% interest
practice problems: Percent of a Number Sampler
(I like all the activities except the ratio tables)
Skill #7 - Discount and Loss
Skill #8 - Rate of Pay
imagine some problems for an animal grooming business, inspired by
Pete the Sheep-Sheep
by Jackie French
Skill #9 - Unit Cost
Skill #10 - Temperature Conversion Formulas (°C to °F, °F to °C)
practiced as homework as an introduction to formulas
imagine some problems for temperature (travel agency posters), inspired by
Something to Tell the Grandcows
by Eileen Spinelli
current weather forecast for South Pole, Antarctica
The highest temperature ever recorded at the Amundsen-Scott South Pole Station was
-12.3 °C (9.9 °F) on Christmas Day, 2011. The lowest was -82.8 °C (-117.0 °F) on June 23, 1982.
practice problems (all whole numbers): Temperature Conversions Round Robin Activity
I discovered that students haven't always seen examples of travel posters, so some images to share would be helpful:
Skill #11 - Business Formulas (rate of pay, simple interest, price after tax, discount price)
imagine some problems for all kinds of silly shopping, inspired by
A Boy Had a Mother Who Bought Him a Hat
by Karla Kuskin
I have the original version, illustrated by her, but it doesn't seem to be available anymore. Here are
all the things she buys him: a hat, a mouse, new shoes, new rubber boots, skis, a mask, a cello, an elephant, and another hat.
Skill #12 - Graphing (bar graph, line graph, pie chart)
practiced as homework after the block ends
Equivalent Forms - Ratios, Fractions, Decimals, Percent
Activities from Hands-On Math: Ready to Use Games and Activities for Grades 4-8
are always presented in groups of three carefully scaffolded activities, starting with "concrete action," moving to "pictorial action," and ending with "cooperative groups."
Construct Bar Graphs Where Each Cell Represents Multiple Units
"Scaling Down" on p.408
"Changing the Scale" on p.410
"Graphing with Large Numbers" on p.412
Construct Line Graphs
"Tracking Changes" on p.413
"Making a Line Graph Record" on p.415
"Bottles Up!" on p.415
Find the Mode of a Given Set of Data
 
"What's the Favorite?" on p.425
"Shapes Away!" on p.425
"Mode Detectors" on p.426
Find the Mean of a Given Set of Data
"Fair Shares" on p.427
"Drawing Fair Shares" on p.428
"Mean Fling" on p.430
Find the Median for a Given Set of Data
"Who's in the Middle?" on p.431
"Median Hunt" on p.432
"Median Spin" on p.437
Construct Circle Graphs
"Surveying with Circles" on p.443
"Hub and Spokes" on p.444
"Graphing with Angles" on p.448
Note: I am really proud of our graphing exercise the last time I taught this block
and I highly recommend coming up with your own research question and gathering the data and then conveying it visually with whatever type of graph is most appropriate.
Another option for this block is to use the series of Economics in Action books. I recommend What is Trade? by Carolyn Andrews for the 3rd grade Currency block.
The other books in the series are more complex topics. They are:
 
 
 
 
 
 
 
FUN FACT: There is a U.S. National Debt Clock at the top of Idaho Senator Mike Crapo's website.
I'm sure there are plenty of others all around the internet but this was the first one I stumbled upon. It would be interesting for students
to consider what might make up the national debt, as well as why it would be rising so quickly (without getting into political matters.)
In 8th grade when students study World Geography & Economics, they can go into all of this more deeply.
"Tax cuts, stimulus programs, increased government spending, and decreased tax revenue caused by widespread unemployment generally account for sharp rises in the national debt."
https://fiscaldata.treasury.gov
My blog posts from teaching this topic:
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