2-1 6 th grade math

1. 2-16th 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 • 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 = 10 + 7 = (3 x 10) + (3 x 7) = 30 + 21 = 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! Use multiplication properties and mental math to simplify each expression. • 4 x 253 • 13 x 5 • 4 x 253 Use the break apart =(4 x 250) + (4 x 3) = (1000) + 12 = 1012 2) 13 x 5 Use the break apart = (10 x 5) + (3 x 5) = 50 + 15 = 65

9. Try Some More! 3) 6 x 393 4) 4 x (7 x 25) 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

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.