TURNING FIFTEEN


In this 1-hour lesson, we will TURN 15 into many different UNITS, and will describe 15 in relation to YEARS, DECADES, CENTURIES, MILLENNIA, TENTHS, and HUNDREDTHS.


We will talk about those relationships with money models, spoken words, written words, and finally, with equations using math symbols.


PANIC NOTE:

Seeing all of this in writing is OVERWHELMING, to be sure!


*Connecting ideas to real money and seeing numbers on the place value chart,

takes away distressing BRAIN STATIC.


METHODOLOGY

  1. MODEL MATH IDEAS WITH MONEY.

  2. Record the TOTAL on the Place Value Chart.

  3. DESCRIBE WITH YOUR WORDS, ALOUD.

  4. WRITE IN COMPLETE SENTENCES in NOTEBOOK (color-code and illustrate).

  5. Express the words as EQUATIONS, using math symbols.

  6. READ the equations aloud (convert the symbols back into WORDS).

  7. TEACH someone else how it works!


REVIEW: We use the decimal place value chart to encode (write) numbers and to easily perform UNIT CONVERSIONS.


A. Model the number with money by counting bills into patterns.


B. Say what you did: "I put a $1 down ten times and I have ten dollars altogether."


C. Write the equations that symbolically represent what you did:

1 x 10 = 10 I put a 1 down ten times.

10 x 1 = 10 Ten times, I counted a one-dollar bill.


D. 10 ones can be traded for a $10.

1 x $10 = $10

$10 x 1 = $10


E. Act out the numbers and write EQUATIONS for what you do in a notebook. COLOR-CODE and ILLUSTRATE your notes, as shown below. Date your notes. Take pictures of your money patterns and notes.


FLUENCY: Each idea can be expressed in many ways. The more ways you can express an idea, the more fluent you are in the language.


A UNIT is the one thing we're talking about- the subject.


HAPPY FIFTEENTH BIRTHDAY!


  • YEAR is the UNIT.


If you had a dollar for every year, you'd have 15 dollars.

Many ways to describe this:

  • $1 x 15 years = $15

  • $1 per annum x 15 years = $15

  • $1 for each year x 15 = $15

  • 1 x 15 = 15


$15 dollars can be expressed as

  • 15 ones

  • $1 x 15 = $15

  • 10 ones and a $5 bill (5 ones)

  • (1 x $10) + ($5 x 1) = $15

  • $10 + $5 = $15

  • (1 x 10) + (5 x 1) = 15

  • 10 + 5 = 15


Let's CONVERT UNITS!

  • Evy is 15 years old. Years is the UNIT.

  • Evy is 1.5 decades old. Decade is the UNIT. (set of 10 years)

  • Evy is 0.15 centuries old. Century is the UNIT. (set of 100 years)

  • Evy is 0.015 millennia old. Millennium is the UNIT. (set of 1000 years)

15 years = 15 ones


How many decades is 15 years?

Many ways to describe this:

  • A decade is ten years.

  • 15 years is 1 and a half decades.

  • 15 years is 1 decade + 5 more years.

  • 15 years is 1 set of 10 and 5 ones.

(5 + 5) + 5 more years.

5/(5 + 5) = 1 five of 2 fives that make ten = 1/2 = half


15 years is how many centuries?

Many ways to describe this:

  • 15 years in NO centuries because 15 is less than 100 years.

  • 15 years is 0 centuries, 1 decade, and 5 years.

  • 15 years is 15 out of 100 years in a century.

  • 15/100 in a century.

  • fifteen-hundredths century

  • 0.15 century

0 hundred

1 ten

5 ones


15 years is how many millennia (1000 years)?

Many ways to describe this:

  • 15 years in NO millennia because 15 is less than 1000 years.

  • 15 years is 0 millennia, 1 decade, and 5 years.

  • 15 years is 15 out of 1000 years in a millennium: 15/1000

  • 15/1000 millennium.

  • fifteen-thousandths millennium

  • 0.015 millennium

  • 0 thousand

0 hundred

1 ten

5 ones


I have a jar full of change (coins), and want to trade some dimes for your 15 dollars.


How many dimes (ten cents or tenths) do I need to trade for $1?

Many ways to describe this:

  • A dime is 1 of 10 needed to trade for $1.

  • A dime is 1/10 of a dollar.

  • A dime is one-tenth of a dollar.

  • A dime is 0. whole dollars

and 1 tenth of a dollar.

0.1

0 pennies

0.10 is the decimal expression of a dime or a tenth.

10¢ is ten cents or 10 pennies = 1 dime

          • Ten dimes = $1.

          • 0.10 x 10 = $1.

          • 1/10 x 10 = $1.

          • Ten-tenths is one dollar.

          • 10/10 = 1


$15.00 is how many dimes?

Many ways to describe this:

  • $15 DIVIDED BY dimes.

  • 15 dollars converted into dimes.

  • 15 dollars converted to tenths.

  • The Dollar unit is CONVERTED into the tenth unit.

  • Each dollar is TRADED for tenths.

  • Each dollar is EXCHANGED for tenths or dimes.

  • 15 ÷ dime

  • 15 ÷ 0.10

  • 15 ÷ 1/10

  • 15 ÷ one-tenth

  • 15 ÷ 10¢

  • 15.0

  • 15.0

  • 150 dimes = $15

  • 150 tenths = $15

  • 0.10 x 150 = $15

  • 1/10 x 150 = $15

  • 10¢ x 150 = $15


$15.00 is how many pennies?


Many ways to describe this:

  • $15 DIVIDED BY pennies.

  • 15 dollars CONVERTED TO pennies.

  • 15 dollars TRADED FOR hundredths.

  • The Dollar unit is CONVERTED INTO the hundredth unit.

  • Each dollar is TRADED FOR hundredths.

  • Each dollar is EXCHANGED for hundredths or pennies.

  • Since $1 = 100 pennies:

  • Each penny is 1 of 100 pennies needed to = $1.

  • Each penny is 1/100

  • Each penny is one-hundredth of a dollar.

  • 15 ÷ 1 penny

  • 15 ÷ 0.01

  • 15 ÷ 1/100

  • 15 ÷ one-hundredth

  • 15 ÷ 1¢

  • 15.00

  • 15.00

  • 1,500 pennies = $15

  • 1,500 hundredths = $15

  • 0.01 x 1,500 = $15

  • 1/100 x 1,500 = $15

  • x 1,500 = $15

  • x fifteen hundred = $15

  • x one thousand five hundred = $15

  • fifteen hundred pennies is fifteen dollars


This exercise is sure to exhaust a mathematician!


Who knew there was so much to TURNING 15?


MONEY TIP: Store and organize the money in a 3' x 5" index card box (see images attached) and label tabs to divide each of the 20 denominations or 9 periods (ex. millions) of bills. Example TABS: ONE, $1., UNIT; TEN, $10, da; HUNDRED, $100, h; THOUSAND, $1,000, k; TEN THOUSAND, $10 k; HUNDRED THOUSAND, $100 k; MILLION, M, $1 M; TEN MILLION, $10 M; HUNDRED MILLION, $100 M; BILLION.... [You can label your section with the number, the word, or the word and the symbol. All options will not fit on the tab.]