NUMBERS - EXPONENTS (Part 2)

FOCUS QUESTION

How do I write numbers in the different number system?

SPECIFIC OBJ.

1.  Read, write and use numbers, using the principle of place value, in the Hindu-Arabic system of numeration.

2. Write numbers in exponential form  

3.  Write composite numbers as a product of primes in exponential form

CONTENT SUMMARY

Each place on the place value chart represents a power of ten. As we move left of the decimal place, the numbers increase in value. The opposite happens when we move right of the decimal point. All digit to the left of the decimal point are whole numbers. Digits to the right of the decimal point are fractional numbers. Every digit has three values: the place, the face and the actual or true value. The place times the place gives the actual value.

The factors of a number are all the numbers that are able to completely divide a given number without leaving a remainder. One (1) is a universal factor.

Prime factors are factors that are prime numbers.

ENGAGE

Review what is meant by prime factorization, standard form, expanded form and exponent from. We are all going to play a quick game. You will all take a strip of paper from my basket. They all represent numbers written in expanded, standard, worded and exponential form. As soon as you have selected your paper, walk around and find your number family and stand beside them. (3ft apart) Afterwards we will decide if you are family or not. 

EXPLORE

Let's just quickly use the place value mats to represent the number 4589  in expanded form.

Place each digit under their correct place.  (4000 + 500 + 80 + 9 )

4000 = 4 x 1000 

500 = 5 x 100

80 = 8 x 10

9 = 9 x 1

Today, we are going to write the expanded form of numbers in exponential form.

Let's watch this video clip so we can gain some insights as to how this is done.

EXPLAIN

Explain the steps involved in changing from expanded form to exponent form. Eg.

213   =  2 x 100   +      1 x 10       +     3 x 1

         = 2 x 10²     +      1 x 10 ¹   +     3 x 10 ⁰

EXTEND/ELABORATE

Complete the activity sheet below.

EVALUATE

1. State if each statement is true or false. They will justify their answers as they go along.

(a) 10 ⁰ = 10

(b)  In 648, 8 has the greatest value.

(c)  3 ² = 2 x 3

(d)  5 ² = 25

(e) 200 + 30 + 7 is referred to as exponential form

(f) The exponent tells how many times the base must be multiplied.

2. Complete the table below.

STANDARD     FORM	EXPANDED FORM	WORDS	EXPONENTIAL          FORM
	30 + 6		2 2    x     3 2
81		Eighty one
			5 2
100
162
	200 +40+ 5
		One thousand

3. Expand the following, then write in exponential form.

(a) 27,941

(b) 45, 798

(c) 879,416

4. 

5.