Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math Properties Warm - up Just-In Power point Just the Facts Guided Practice Developing Story Independent Practice Questions and Answers Just In (warm up) Which problem situation matches the equation below? (80 + 95+86+100+x) = 90 5 A) The weights of four packages are 80 ounces, 95 ounces, 86 ounces, and 100 ounces. Find x, the sum of the weights of the four packages. B) Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on his cell phone. Find x, the average time Juan talked on his phone. C) Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the grade Courtney needs on her fifth quiz to have an average of 90. D) The heights of four trees in a park are 80 feet, 95 feet, 86 feet, and 100 feet. Find x, the average height of the trees. Just In (warm up key) Which problem situation matches the equation below? (80 + 95 + 86 + 100 + x) = 90 5 A The weights of four packages are 80 ounces, 95 ounces, 86 ounces, and 100 ounces. Find x, the sum of the weights of the four packages. False, x is the missing weight of the package B Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on his cell phone. Find x, the average time Juan talked on his phone. False, the average time have already been identified as 90 C Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the grade Courtney needs on her fifth quiz to have an average of 90. True, in order to calculate the average, base on five items one number is missing D The heights of four trees in a park are 80 feet, 95 feet, 86 feet, and 100 feet. Find x, the average height of the trees. False, x is the missing value that related o the others numbers not a combine amount of what is already given. Developing Story Just the Facts • Hello Everyone, classrooms across the district are learning about the properties of math. • Properties are statements that are true for all numbers. • During today’s math lesson, we will explore the characteristics for each property and create a model of its function in order to demonstrate the purpose and action of each. Who can name and elaborate on the math properties? Commutative Distributive Property Math Properties When I is multiplied to a factor, it does not affect the product. •to spread The order in which two numbers are added or out Identity Property multiplied does not change the sum or product . Commutative Property Travel back and forth Associative Property To connect or combine When zero is added to a number, it does not change its sum. Identity Property • The identity property of zero. states the number 0 can be added to any real number without changing its value. a+0=a • Workmat Examples: (positive integers) (algebraic notation) 8+0=8 a+0=a (negative integers) -4 + 0 = -4 (fractions) 3/4 + 0 = 3/4 (decimals) 2.2 + 0 = 2.2 Identity Property • The multiplicative identity for the set of all real numbers is 1 (one). Any real number can be multiplied by the number 1 without changing its value. Workmat (positive integers) 8*1=8 (algebraic notation) a*1=a • (negative integers) (decimals) -8 * 1 = -8 (fractions) 2/5 * 1 = 2/5 2.2 * 1 = 2.2 Commutative Property of Addition • No matter he order in which you add two numbers, the sum is always the same. • Workmat model order a different way a + b b 6+3 3+6 a+b=b+a + Let’s create a model this property. =9 + a + = 9 Commutative Property of Addition model 8 + 5 • a+b 8+5 workmat • Different _o _r d_ _e _r • b+a 5+8 workmat + + = 13 = 13 Commutative Property of Multiplication • The order in which two numbers are multiplied does not change its product. a*b = b*a Let’s use our algebra tiles to model this property. • workmat Order different way Factors will vary ( Associative) Property of Addition (a + b) + c = a + (b + c) (a * b) * c = c = (b * c) • The way in which three numbers are grouped when added or multiplied does not change the sum or product. (a + b) + c = a + (b + c) (6 + 3) + 4 = 6 + (3 + 4) Associative of Addition Property When you add three numbers together, the sum will be the same no matter how the numbers are grouped. (a*b) * c = c = (b * a) (5*3) * 6 = 6 = (3 *5) Associative of Multiplication Property No matter how you group the numbers when you multiply, the answer will always be the same product. ( Associative) Property of Addition Which expression can be written as (1 + r) + s Justify your response A 1*+(r +s) B 1 *(r *s) C 1 +(r *s) D 1 +(r +s) (Associate ) Property of Multiplication • A change in the way multiplied numbers are grouped does not affect the product. a x (b x c) • b x (a x c) Associate- connect or combine. workmat a* (b* c) Show a different group 2* (6* 9) (b*c) * a (9*2) * 6 Distributive Property • The Distributive Property allows the choice of multiplication followed by addition or addition followed by multiplication. a (b + c) = ab + ac 3 (x+1) and 3x + 3 are equivalent x x x x Distributive Property A(B+C) = AB + AC • Write an equivalent expression for 3(x+2) Picture Model using tiles X X X 3*x + 3*2 Equivalent Representation 3x + 6 Distributive Property Try this using your algebra tiles x 3(X - 2) x - - x - - Describe in your own words, the distributive property. Support your description with examples, and draw a model to illustrate the property. - - Distributive Property • Model using algebra tiles • (2+5)3 7*3 7 7 7 Can you apply your new info and solve this problem ? Let’s try • Jared deposited $5 into his saving account. Six months later, his account balance had doubled. If his balance was b dollars, which of the following would be equivalent to his new balance of 2(b+5) dollars? • F 2b + 5 H b + 10 • G 2b + 7 J 2b + 10 Developing Story (Guided practice) 1. Which is an example of the Associative Property? A 8+0=8 C 6+8=8+6 B 9 + 8 + 2 = 9 + (8+2) D 5 * (12 +3) = 5 *12 + 5 * 3 2. Which property of 3(4+8) = (3*4) + (3*8) an example of? A Associative B Commutative C D Distributive Identity 3. Define in your own words and write an example of each property A Commutative B Identity C Distributive D Associative Developing Story (Guided practice key) 1. Which is an example of the Associative Property? A 8+0=8 C 6+8=8+6 B 9 + 8 + 2= 9 + (8+2) D 5 * (12 +3) = 5 *12 + 5 * 3 2. Which property of 3 * (4+8) = (3*4) + (3*8) an example of? A Associative C Distributive B Commutative D Identity 3. Define in your own words and write an example of each property: Answers will vary A Commutative- When you add numbers, regardless of the order, the sum is the same. 4 + 8 = 12 8 + 4 = 12 B Identity - The sum of 0 and any number is the number. The product of 1 and any number is the number. 6+0=6 a+0=a 6*1=6 a*1=a C Distributive- To multiply the sum of two numbers, you can first add, then multiply. Or you can first do each multiplication, then add. 4 x (5+2) or 4 x 5 + 4 x 2 4x7 D Associative – multiply numbers, regardless of how they are grouped. Example (4 x36)x19 = 4 x(36 x 19)