1. Multiplication Properties
2-1 6th grade math
Multiplication Properties

2. Objective
To use multiplication properties and mental math strategies to compute mentally.
Why? To help you solve multiplication problems faster w/o using a paper and pencil and/or to get an estimated answer in your head before you actually solve the problem

3. California State Standards
AF 1.3: Apply … the commutative, associative, and distributive properties …; and justify each step in the process MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations

4. Vocabulary Commutative Property Associative Property Identity Property
The order in which numbers are multiplied does NOT affect the product
(switch the order)
5 x 20 = 20 x 5
Associative Property
The way in which factors are grouped does NOT affect the product
(all must be x and keep the same order, just flip the () around)
3 x (2 x 5) = (3 x 2) x 5
Identity Property
The product of 1 and any other number is that number
45 x 1 = 45
Property of Zero
The product of 0 and any number is zero
9,999 x 0 = 0
Distributive Property
Multiplying a factor by a group of addends yields the same result as multiplying that factor by each addend and then adding the products
(a number is x to a group of numbers being +) (distribute = pass/give out)
6 x (5 + 4) = (6 x 5) + (6 x 4) or 6(5 + 4) = (6 x 5) + (6 x 4)

5. How to Use Mental Math in Solving Multiplication Problems- Break Apart Method
Used with distributive property 1) Recognize how numbers can be broken apart in order to compute quickly 2) ‘Break apart’ a number to give you easier numbers with which to work 3) Use the distributive property to multiply
3 x 17 = 17 = = (3 x 10) + (3 x 7) = = 51

6. How to Use Mental Math in Solving Multiplication Problems- Compatible Numbers
Used with commutative and associative properties 1) Look for two numbers that may be ‘rearranged’ to be computed in your head = commutative prop 2) Multiply using the associative prop 3) Check your work
2 x (386 x 5)= 2 x 5 are compatible (2 x 5) x 386= = 10 x 386 =3,860

7. How to Use Mental Math in Solving Multiplication Problems- Compensation
Used with distributive property and when one of the factors is close to be rounded 1) Look for a number that may be ‘rounded’ to the nearest whole number and can be solved in our head 2) Use distributive prop to multiply the ‘added’ number to the factor, 3) And then multiply the ‘subtract’ amount from the factor 4) Multiply
4 x 598=
598 is close to 600 (by 2 counts)
4 x 600
= 4 x (600 – 2)
=(4 x 600) – (4 x 2)
= 2400 – 8
= 2,392

8. Try It! 4 x 253 Use the break apart =(4 x 250) + (4 x 3) = (1000) + 12
= 1012
2) 13 x 5
= (10 x 5) + (3 x 5) =
= 65
Use multiplication properties and mental math to simplify each expression.
4 x 253
13 x 5

9. 3) 6 x 393 Use the compensation = 6 x (400 – 7) = (6 x 400) – (6 x 7) = 2400 – 42 = 2,358 4) 4 x (7 x 25) Use the compatible numbers = (4 x 25) x 7 = 100 x 7 = 700
Try Some More!
3) 6 x 393
4) 4 x (7 x 25)

10. 5) (5 x 188) x 2
5) (5 x 188) x 2 Use compatible numbers = (5 x 2) x 188 = 10 x 188 = 1880

11. Objective Review
To use multiplication properties and mental math strategies to compute mentally.
Why? You can now solve multiplication problems faster w/o using a paper and pencil and/or to get an estimated answer in your head before you actually solve the problem.

12. Independent Practice Complete problems 7-17
Copy original problem first.
Show all work!
If time, complete Mixed Review: 18-23
If still more time, work on Accelerated Math.