Converting Between Decimals, Fractions, and Percents

Some FREE resources from Teachers Pay Teachers which I've found useful, and a few notes from our tutoring sessions.

In Waldorf, percents are done in 6th grade as part of Business Math.

Mathematics Lessons for the Sixth Grade
by Ernst Schuberth

Note: this book is also available for FREE as a downloadable PDF from the Online Waldorf Library here.

Session One

Parts of a Whole Quick Quiz: Decimals, Fractions, and Percents!
as a pretest

solve using the Decimal Checker Board and look for patterns:
37 x 0.1
4.26 x 100
9.3 x 10
2.715 x 10
6.0 x 10

fill in Converting Fractions, Decimals, and Percents Math Wheel
for the following:
decimal ---> fraction
percent ---> fraction

factor 100
(1, 2, 4, 5, 10, 20, 25, 50, 100)

assign Fraction Flowers: Percent, Decimal, and Fraction Conversions
as independent follow up work

Session Two

review Fraction Flower, explain that the reason that equivalent fractions can be made by multiplying the numerator and denominator by the same number (for example, 4) is that it is the same as multiplying by the fraction 4/4, which is the same as multiplying by 1!

fill in Converting Fractions, Decimals, and Percents Math Wheel
for the following:
decimal ---> percent
percent ---> decimal
fraction ---> decimal
fraction ---> percent

do #1, 2, 3 of "Percent on a Hundred Chart" from Percent of a Number Freebie Sampler

assign "Percent of a Number: Odd Man Out" from Percent of a Number Freebie Sampler as independent follow up work
(solve by converting the percent to a fraction and using mental math)

Session Three

review Odd Man Out

retake pretest #1 - 12 and compare
Parts of a Whole Quick Quiz: Decimals, Fractions, and Percents!

begin Using Multiples to Introduce Percents
(print pages 1 to 20 of student packet, ie. pages 38 to 57 of PDF)
page 1
page 2 (multiples of 4 & 7)

do #4, 5, 6 of "Percent on a Hundred Chart" from Percent of a Number Freebie Sampler

assign rest of page 2 (multiples of 9) as independent follow up work

Session Four

review page 2 of Using Multiples to Introduce Percents

do "Review of Multiples" pages 3, 4, and 5

do "Multiples and Percents" pages 6 and 7

assign page 8 as independent follow up work

Session Five

review page 8 of Using Multiples to Introduce Percents

do "Multiples and Percents" page 9, review that you can simply remove and replace zeroes when working with multiples of 10, think of skip counting as kangaroo jumps along the number line and explain that the second row of the table is going past the whole and continuing to jump, review that 150% means the whole plus half and practice calculating 150% of various numbers

do page 10, review checking for reasonableness and/or a faster way to do mental math by taking apart the number by which you are skip counting, get out 7 blank tiles and go through the second row of the table by taking the 7 apart (how much to get to the next 10, how much remains?)

do page 11 (complete table); get out colored bead bars and build 3², 5², 7²; explain that 3² can be thought of as "3 three times" OR "three skip counts of 3"; find 15² by counting fifteen skip counts of 15

assign rest of page 11 (questions) as independent follow up work

Session Six

review page 11 of Using Multiples to Introduce Percents

begin to fill in 15 x 15 table from Multiplication Chart Magic for Simplifying Fractions (page 3)

read Fractions in Disguise: A Math Adventure by Edward Einhorn



practice using multiplication chart to simplify fractions (page 5)

do page 12 of Using Multiples to Introduce Percents

assign the completion of 15 x 15 table as independent follow up work

Session Seven

review 15 x 15 table

use 15 x 15 table to solve practice problems from Multiplication Chart Magic for Simplifying Fractions (page 6)

note that factoring the numbers will help narrow down which columns to look in on the chart

practice factoring numbers: eg. 24
(1, 2, 3, 4, 6, 8, 12, 24)

without using the chart -- and instead factoring each numerator and denominator -- begin Simplifying Fractions Coloring Worksheet

Session Eight

continue to work with Using Multiples to Introduce Percents

do "Percents and Multiples" pages 13 and 14

do "Multiples and Percents" pages 15, 16, 17, and 18

begin "Percent Practice and Review" page 19

assign the completion of Simplifying Fractions Coloring Worksheet as independent follow up work

Session Nine

review coloring worksheet

complete pages 19 and 20 of Using Multiples to Introduce Percents

do Percent of a Number Guided Practice, using the Decimal Checker Board as needed

do "Percent of a Number Sorting Activity" from Percent of a Number Freebie Sampler, using the Decimal Checker Board as needed

assign practice problems around Converting Fractions, Decimals, and Percents Math Wheel as independent follow up work

Session Ten

review math wheel practice problems

finish "Percent of a Number Sorting Activity" from Percent of a Number Freebie Sampler, working problems without the Decimal Checker Board

do Percent of Change Lesson Guided Notes (page 2)

begin Practice Problems (page 4)

assign the remaining problems as independent follow up work

Session Eleven

begin Percent of Change Fall Coloring Activity

assign the remaining problems as independent follow up work

Session Twelve

review percent of change practice problems and fall coloring activity

do Percent of Change Lesson Error Analysis (page 3)

take Percents, Proportions, Scale Drawings Test

assign Percent Shopping Spree as independent follow up work

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Recommended resources for percent of change (these are NOT all free):

• Percent of Change Lesson ($3.00)
  Guided Notes
  Practice Problems
  Error Analysis
• Percent of Change Coloring Activity ($1.75)
  All Seasons: Outer Space
  Seasonal: Fall
• Percents, Proportions, Scale Drawings Test
  final assessment

  this is a Word document so it is editable; I am keeping 7 problems
  #1 (Kyle's map)
  #3 (Oldwick High School)
  #4 (Adams Middle School)
  #8 (percent of change)
  #9 (hamburger meat)
  #11 (Julianne's dress)
  #12 (Jenny's backpack)

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