Ray's New Higher Arithmetic · Arts. 40–47 · Unit 2: Numeration and Notation
4. Orders and periods
Goal: Your student names the place of each figure in a number of up to fifteen figures and groups figures into periods of three.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Numeration and notation defined, the nine figures and the cipher, orders (units, tens, hundreds...), a table of the first fifteen orders, and periods of three orders each.
The lesson, step by step
Warm-up
Write 3,333 and ask what each 3 is worth. (3 thousands, 3 hundreds, 3 tens, 3 units.)
The idea
Read:
Numeration is the method of reading numbers.
Notation is the method of writing numbers.
The Order of a figure is the place it occupies in a number.
SayThe same figure is worth ten times more for each place it moves to the left.
The table of orders
Open the book to the table of fifteen orders. Read the names together from units up to hundreds of trillions.
Periods
Read:
orders are divided into groups of three each, and each group is called a period.
Each period has its own units, tens and hundreds: units, thousands, millions, billions, trillions.
Guided practice
Write 407,019,300,056 on the slate. Your student marks off the periods, names each period, then reads the whole number aloud.
Independent practice
Your student writes three numbers of 10 to 12 figures, marks the periods, and reads them to you. Then you read two long numbers aloud and your student writes them.
Wrap-up
Ask: In 5,000,000,000, which order holds the 5? (Units of billions, the tenth order.)