Reflection Today Long Division Practice Every house is built by - - PDF document

Reflection

Every house is built by someone, but God is the builder of everything. Hebrews 3:4

Today

 Long Division Practice  The Sieve  Number Theory

» Terminology and notation » Primes and composites

 Divisibility tricks

Don’t Forget

 Pick up today

» Graded stuff » RQ 5.1-5.2 » Sieve

 Turn in today

»   Exam 2 November 10th

Long Division is not optional 23 2 5 6 3 2

2 3 4 2

      x x x x x x Number Theory

 Counting Number properties and

relationships

 Fundamentals needed for fraction

arithmetic

 Teacher knowledge required

beyond student tasks

Definition

(Assume we are talking about counting numbers until further notice.) If ka=b, then a divides b, written a|b.

Equivalent Statements

3|21 means

 3 divides 21  3 is a factor of 21  3 is a divisor of 21  21 is a multiple of 3

Test Questions

Which of the following means the same as n|m?

• a. nm has remainder 0.
• b. n=km for some counting number k.
• c. m=kn for some counting number k.

Notation

8 5 3   5 7 2   N  13 N  13 30 6

Sieve Number Theory

 In chemistry, all compounds are

made up of elements.

 In number theory, all counting

numbers are products of prime numbers.

Reflection

‘Not by might nor by power, but by my Spirit,’ says the Lord Almighty Zechariah 4:6b

Today

 Stumpers  Divisibility

» Tests for 2, 3, 4, 5, 8, 9, 10, 11, &

• thers

» Some properties of divisibility

 Quiz

Today’s Objective

137,598,264

Don’t Forget

 Pick up today

» Graded stuff » Practice 5.2 » Study Questions » Primary 4A p. 25

 Turn in today

» Long Division HW » RQ 5.1 & 5.2

 Exam 2 November 9th

Stumpers Divisibility Properties

• 1. If a divides b and a divides c, then…
• 2. If a divides b but does not divide c,

then…

• 3. If a divides b, then…
• 4. If a divides b and b divides c, then…

From your reading

Algebraic proof bottom of page 111.

Testing for Divisibility

 Multiples of 2…  Multiples of 4…  Multiples of 8…  Multiples of 5…  Multiples of 3…  Multiples of 9…  Multiples of 10…  Multiples of 11…

Casting out 9’s

Is 9 a factor of 423? What about 426? 236,059,725 Make this a multiple of 9: 473,02__

Divisible by 11?

• 1. 187
• 2. 145
• 3. 3091
• 4. 9,372,308
• 5. 6,987,308

Today’s Objective

137,598,264

Practice #1

The End of Section 5.2

Finish homework from section 5.2 for next time.

Why does the 9 test work?