# Math unit 2 gr 6 whole numbers

```Unit 2 Whole Numbers – grade 6,
Learning Goals
1. Read and write whole numbers in standard form, expanded form, and
written form
2. Use place value to represent and read whole numbers
3. Compare and order whole numbers
4. Identify and describe multiples and factors to 100
5. Identify and describe composite and prime numbers to 100
6. Use order of operations
7. Estimate sums, differences, products and quotients
8. Use mental math to add, subtract, multiply and divide
9. Add four 3-digit numbers and subtract from a 5-digit number
10. Multiply and divide by a 2-digit number
11. Pose and solve multistep problems
p.30
Whole Numbers Key Words
(6TB31)
 Million = one thousand thousand
 Period = in a large whole number, each group of 3 place values from right to left
 Billion = one thousand million
 Trillion = one thousand billion, or one million million
 Common multiples = a number that is a multiple of two or more numbers; 6 is a common
multiple of 2 and 3
 Prime number = a whole number with exactly two factors, itself and 1; 7, 13, 19, and 23 are
prime numbers
 Factors = numbers that are multiplied to get a product
 24 has 8 factors: 1, 2, 3, 4, 6, 8, 12, and 24. The prime factors of 24 are 2 and 3. A number
with more than 2 factors is a composite number.
 Composite number = a number with three or more factors; 8 is a composite number because
its factors are 1, 2, 4, and 8
 Expressions = a mathematical statement with numbers and operations.
Lesson 1 – Exploring One Million
One million = 1000 thousands
1 000 000 = 1000 thousand cubes
1 000 000 mm = 1 km
1 000 000 pennies = \$10 000
\$1 000 000 = ten thousand \$100 dollar bills
1 000 000 min is about 2 years
Note: We leave a space between the periods when we write a number with 5 or more digits!
When we read large numbers, we say the period name after each period except the units period!
Lesson 2 – Understanding Large Numbers (6TB35)
Strategy: How to read and write large whole numbers? e.g. 3 159 119
Millions period
hundreds
tens
Thousands period
Units period
ones
hundreds
tens
ones
hundreds
tens
ones
3
1
5
9
1
1
9
3 000 000 100 000 50 000 9000
100
10
We can read this number as:
three million one hundred fifty-nine thousand one hundred nineteen
We can write this number in:
- Standard form  3 159 119
- Expanded form  3 000 000 + 100 000 + 50 000 + 9000 +100 + 10 + 9
- Number-word form  3 million 159 thousand 119
Note: One thousand million is one billion.
One thousand billion is one trillion.
trillions
billions
millions
thousands
units
9
Lesson 3 – Comparing and
Ordering Numbers
(6TB39)
 You can use a place-value chart to order numbers from greatest to least.
Lesson 4 – Exploring Multiples
(6TB43)
Recall that to find the multiples of a number, start at
that number and count on by the number. You can use a
hundred chart to find the multiples of a number.
The multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
The multiples of 6 are:
6, 12, 18, 24, 32, 36, …
12, 24, and 36 appear in both lists. They are multiples of 4 and of 6. They are common multiples of
4 and 6. Each common multiple of 4 and 6 is divisible by 4 and by 6.
Lesson 5 –Prime and Composite
Numbers (6TB45)
Numbers multiplied to form a product are factors of the product.
2
factor
x
8
=
factor
16
product
A prime number is a number greater than 1 that is divisible only by 1 and itself.
23 has 2 factors: 1 and 23. A number with exactly 2 factors, 1 and itself, is a prime number. 23 is a prime
number.
A composite number can be written as a product of prime factors: 24 = 2 x 2 x 2 x 3.
24 has 8 factors: 1, 2, 3, 4, 6, 8, 12, and 24. The prime factors of 24 are 2 and 3. A number
with more than 2 factors is a composite number.
Lesson 6 – Strategies Toolkit
Strategies
 Make a table
 Use a model
 Draw a diagram
 Solve a simpler problem
 Work backward
 Guess and check
 Make an organized list
 Use a pattern
 Draw a graph
 Use logical reasoning
(6TB48)
Lesson 7 – Using Mental Math
(6TB50)
Use mental math to add. Rearrange and use compatible numbers.
Compatible numbers are pairs of numbers that are easy to
computer.
60 + 35 + 40 = (60 + 40) + 35 = 100 + 35 = 135
Note: Changing the order of the numbers being added or multiplied does not
change the sum or product.
Use mental math to subtract. When no regrouping is needed, start
subtracting from the left.
E.g. 687 – 464 = 223. Think: 600 – 400 = 200
80 – 60 = 20
7–4 =3
 Use mental math to multiply. Rearrange and use compatible numbers.
Compatible numbers are pairs of numbers that are easy to computer.
4 x 19 x 25 = 19 x (4 x 25) = 19 x 100 = 1900
Note: 25 and 4 are compatible numbers. Their product, 100, is easy to multiply with
any other factor.
 Use mental math to multiply. Break one of the numbers apart to make
numbers that are simple to work with.
E.g. 6 x 27 = 6 x (20 + 7) = (6 x 20) + (6 x 7)
= 120 + 42
= 162
Note: Twenty-seven breaks apart to 20 + 7. It’s easy to multiply 20 by 6 and 7 by 6.
Lesson 8 – Order of Operations
(6TB54)
An expression is a mathematical statement with numbers and
operations. When we calculate the answer, we solve the expression.
The order of operations is:
Brackets
Multiply and Divide (in order, from left to right)
Add and Subtract (in order, from left to right)
Subtracting Whole Numbers (6TB60)


Keep adding the next number to the previous sum

Use place value to subtract
Note: Recall that adding to check a subtraction is using the inverse
operation. Addition is the inverse of subtraction.
Consecutive numbers are numbers such as 100, 101, 102, 103.
Lesson 10 – Multiplying Whole
Numbers (6TB64)
Do you remember?
Multiplication and division are inverse operations. You can use one to check the
other.
 You can use an area model to multiply. Sketch a rectangle and label the length and the width.
Then divide the rectangle to show hundreds, tens, and ones. Label the dimensions of the
 You can break the numbers apart to multiply 197 = 100 + 90 + 7
 You can use a short way to multiply  197 x 68 = (197 x 8) + (197 x 60)
 You can check by dividing
Lesson 11 – Dividing by a 2Digit Number (6TB68)
Remember the definitions of divisor, dividend, and quotient?
77 divided by11= 7
The divisor is 11. The dividend is 77. The quotient is 7.

You can use Base Ten Blocks and place value
Lesson 12 – Another Method for
Dividing (6TB72)

Estimate. You can also estimate by thinking multiplication. 60 x 80 =
4800. So 4840 divided by 58 is about 80.

Use place value to divide.

Remember to use remainders were appropriate.
Unit 2 – Show what you know! 6TB77
Unit Problem – At the Apiary (6TB78)
Check List: