Transcript Math Test Review

Grade 6 Math Test Review
Representing Numbers, Place Value,
Decomposing Numbers, Comparing
Numbers, Rounding Numbers, Multiplying 3Digits by 2-Digits, Exponential Notation
Representing Numbers
Millions
Units
Million (M)
Hundred
Thousand
(HTh)
Ten
Thousand
(TTh)
Thousand
(Th)
Hundred
(H)
Ten
(T)
Unit
(U)
1 000 000
100 000
10 000
1 000
100
10
1
Position
Value
Thousands
Numbers can be expressed in 3 different forms:
1) Standard form: 38 972
2) Word form: thirty-eight thousand nine hundred seventy two
3) Expanded form: 30 000 + 8 000 + 900 + 70 + 2
Numbers can be represented using a place value chart (above),
symbols, money, etc.
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
320 451
3 204 hundreds
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
320 450
– The 4 is in the hundreds spot: 4 x 100 = 400
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.
How Can We Decompose a Number?
• Expanded Form
8 512 = 8 000 + 500 + 10 + 2
8 512 = 8 500 + 10 + 2
8 512 = 8 500 + 12
• 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)
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
1
2
8 512 = (8 x 1 000) + (5 x 100) + (1 x 10) + (2 x 1)
8 000 + 500 + 10 + 2
Decomposing Also Makes
Multiplication Easier!
8 512 x 7
(8 000 x 7) + (500 x 7) + (10 x 7) + (2 x 7)
56 000 + 3 500 + 70 + 14
59 584
Remember: when multiplying numbers by a
multiple of 10, 100, 1 000 etc., multiply the first
factor without any zeroes, then add the zeroes to
the end result. For example: In 8 000 x 7, first
multiply 8 x 7 = 56, then add the zeroes: 56 000
Why Compare Numbers?
• Two tools to help us
compare numbers:
– Place value chart
– Number line
Comparing Numbers Using a Place Value Chart
M
M
HTh
TTh
Th
H
T
U
1
3
5
6
9
7
HTh
TTh
Th
H
T
U
1
3
3
7
9
7
Start by comparing the digit with the highest value.
If they are equal, compare the digits in the next
position to the right.
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
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
Rounding 542 329 to the Nearest Thousand
Step
Example
1. Circle the digit in the position to which
the number will be rounded.
542 329
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
542 329
542 000
542 329 is closer to 542 000 than to 543 000
Multiplying 3-Digit Numbers by 2-Digit Numbers
• Understanding a multiplication question:
829 x 74 = 61 346
1st Factor multiplied by 2nd Factor equals the Product
Multiplying 3-Digit Numbers by 2-Digit Numbers
• Multiply each digit in the number 829 by 4
(units). Don’t forget to carry!
Th
1
3
H
T
U
8
2
9
7
4
1
6
x
3
3
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).
TTh
Th
x
5
2
6
H
T
U
8
2
9
7
4
3
3
1
6
8
0
3
0
Multiplying 3-Digit Numbers by 2-Digit Numbers
• Add the 2 products to find the final product of
the multiplication
TTh
Th
2
6
H
T
U
8
2
9
7
4
x
+
3
3
1
6
5
8
0
3
0
6
1
3
4
6
What Does Exponential Notation Look Like?
Base
5
2
Exponent
• 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”
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
Powers of Base 10 Represent Place Values
Position
M
HTh
TTh
Th
H
T
U
Value
1 000 000
100 000
10 000
1 000
100
10
1
Power of 10
106
105
104
103
102
101
100
•A base 10 exponent refers to the number of zeroes