The Curriculum of the Steiner School - Class 6

Notes and Lesson Plans

Business Mathematics: Percents, Formulas, Graphing
updated May 16, 2017

This page has helpful links and LOADS of free resources to help you plan your sixth grade year. Enjoy!

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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

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.

    dressmaker or tailor
    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

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.

My blog posts from teaching this topic:

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