1. Grade 6 Math Test Review
Representing Numbers, Place Value, Decomposing Numbers, Comparing Numbers, Rounding Numbers, Multiplying 3-Digits by 2-Digits, Exponential Notation

2. Hundred Thousand (HTh)
Representing Numbers
Millions
Thousands
Units
Position
Million (M)
Hundred Thousand (HTh)
Ten Thousand (TTh)
Thousand
(Th)
Hundred
(H)
Ten
(T)
Unit
(U)
Value
10 000
1 000
100 10 1
Numbers can be expressed in 3 different forms:
Standard form:
Word form: thirty-eight thousand nine hundred seventy two
Expanded form:
Numbers can be represented using a place value chart (above), symbols, money, etc.

3. Place Value
If you are asked how many HTh, TTh, Th, H, T, or U there are, you:
Find the digit in that place
Take that digit and all the other digits to the left of it
3 204 hundreds

4. Place Value
If you are asked to the find the value of a specific digit:
Find the digit in the number and what place it’s in
Determine the value of the digit
The 4 is in the hundreds spot: 4 x 100 = 400

5. Decomposing a Number What does it mean to decompose something?
Break something down
Take something apart
To successfully decompose a number, it is important that it is represented in an equivalent form.

6. How Can We Decompose a Number?
Expanded Form
8 512 =
8 512 =
8 512 =
Using Place Value Symbols
8 512 = 8Th + 5H + 1T + 2U
Using Order of Operations
8 512 = (8 x 1 000) + (5 x 100) + (1 x 10) + (2 x 1)

7. Decomposing a Number Using a Place Value Table
POSITION
Thousands (Th)
Hundreds (H)
Tens (T)
Units (U)
VALUE
1 000
100 10 1
NUMBER 8 5 2
8 512 = (8 x 1 000) + (5 x 100) + (1 x 10) + (2 x 1)

8. Decomposing Also Makes Multiplication Easier!
8 512 x 7 (8 000 x 7) + (500 x 7) + (10 x 7) + (2 x 7) Remember: when multiplying numbers by a multiple of 10, 100, etc., multiply the first factor without any zeroes, then add the zeroes to the end result. For example: In x 7, first multiply 8 x 7 = 56, then add the zeroes:

9. Why Compare Numbers? Two tools to help us compare numbers:
Place value chart
Number line

10. Comparing Numbers Using a Place Value Chart
HTh
TTh Th H T U 1 3 5 6 9 7 M
HTh
TTh Th H T U 1 3 7 9
Start by comparing the digit with the highest value. If they are equal, compare the digits in the next position to the right.

11. Comparing Numbers Using a Number Line
A number line is made up of evenly spaces points
The space between points is called an interval
Intervals are constant. They have the same difference
Number lines help arrange numbers in increasing or decreasing order

12. Rounding Natural Numbers
When you round a number, you replace it with one of approximate value
Rounding numbers helps you estimate operations and makes mental calculation easier

13. Rounding 542 329 to the Nearest Thousand
Step
Example
1. Circle the digit in the position to which the number will be rounded.
2. Look at the digit to the right of the circled digit.
-If less than 5, the digit to be rounded
does not change
-If greater than or equal to 5, the digit
is rounded by 1
3. Replace all the digits to the right of the circled digit with 0
is closer to than to

14. Multiplying 3-Digit Numbers by 2-Digit Numbers
Understanding a multiplication question:
829 x 74 =
1st Factor multiplied by 2nd Factor equals the Product

15. Multiplying 3-Digit Numbers by 2-Digit Numbers
Multiply each digit in the number 829 by 4 (units). Don’t forget to carry! 1 3 Th H T U 8 2 9 7 4 6 x

16. Multiplying 3-Digit Numbers by 2-Digit Numbers
Place a 0 in the units column.
Multiply each digit in the number 829 by 7 (tens). 2 6
TTh Th H T U 8 9 7 4 3 1 5 x

17. Multiplying 3-Digit Numbers by 2-Digit Numbers
Add the 2 products to find the final product of the multiplication 2 6
TTh Th H T U 8 9 7 4 3 1 5 x +

18. What Does Exponential Notation Look Like?25
Remember: the exponent means you are multiplying the base by itself a certain number of times
The power is calculated by making a repeated multiplication
“Two to the power of five”
Exponent
Base

19. Some Rules to Remember The exponent 2 represents a square number
The exponent 3 represents a cubed number
A base raised to the power of 0 always equals 1
80 = 1
100 = 1
A based raised to the power of 1 always equals itself
81 = 8
101 = 10

20. Powers of Base 10 Represent Place Values
Position M
HTh
TTh Th H T U
Value
10 000
1 000
100 10 1
Power of 10
106
105
104
103
102
101
A base 10 exponent refers to the number of zeroes