Welcome to Week 6: School 2019 and Mathematical Inquiry

February 13-14, 2019 Order of Magnitude Task Math Inquiry

Class Norms

Classroom Norms 1. Start and end on time 2. Be fully present and respectful 3. Take notes on any new information 4. Adhere to CHAMPS expectations 5. Maintain a growth mindset

Warm-up – Do Now Review over SEL Objective Learning Objective Class/Group Norms Previous learning - ASE…Assess/Setup/Evaluate Number Talk Engage in Today’s Math Task AGENDA:

8 Mathematical Teaching Practices MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning.

Objective & Learning Target CCSS 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. Learning Target: We will learn how to express really big numbers and really small numbers.

Concept Development Magnitude Using exponential notation to describe measurements that are either very large or very small. This is expressed in integer powers of 10. The biggest six digit number is still smaller than the smallest 7 digit number.

There are not “a lot” of real world connections… but this skill involves… Laws/rules of operations with exponents Four functions (+/-/x/÷) Cross canceling Properties of multiplication/division

Vocabulary Base: the number that is going to be raised to a power Power: product of multiplying a number by itself or numbers using an exponent and a base or numbers using the exponent and a base Exponent: a small number written above and to the right of the base number, it tells how many times the base number is being multiplied or the number of times the base is used as a factor Rational Number: a number that can be made into a ratio/fraction Exponential Notation: a simplified way to write large numbers

Key Vocabulary: Part 2 Like Terms: Terms that have the same combination of variables and exponents are called like terms. A terms with a coefficient of EX1. A term that does not show a coefficient, such as x or xy2 technically has one as its coefficient. So, x and 1x are equal as are xy2 and 1xy2. Coefficient

Key Vocabulary: Part 2 Monomials: is some number expressions in order to multiply a number and one or more variables. EX. 1 You can simplify monomials by using the law of exponents. 3 2 x 3 4 =(3x3) (3x3x3x3) which are 6 factors 3 6 The sum of the original exponent is the exponent in the final product.

Key Vocabulary Continue Scientific Notation is when a number is written as the product of a factor and an integer power of 10. The factor must be greater than or equal to 1 and less than 10. Symbols: a x 10 n, where 1 less than or equal to a less than or equal to 10 and n is an integer Example: 425,000,000 = 4.25 x 10 8 Power of 10: Multiplying a factor by a positive power of 10 moves the decimal point – right; multiplying a factor by a negative power of 10 moves the decimal point left.

Key Vocabulary Continue We use these rules to express a number in scientific notation. -If the number is greater than or equal to 1, the power of 10 is positive. -If the number is between 0 and 1, the power of 10 is negative.

Discussion Students will Think/Pair/Share Using Stick notes

What rule can you identify from the following examples? = = = 2 14 Rule: n a n b = n a+b Product of Powers When you multiply two powers that have the same base, add the exponents and keep the base Exponent patterns

What rule can you identify from the following examples?  5 1 =  8 2 = Rule: n a  n b = n a-b =6 4 Quotient of Powers When you divide two powers that have the same base, subtract the exponents and keep the base

Exponent patterns What rule can you identify from the following examples? 1.(5 4 ) 1 = (8 9 ) 2 = (3 2 ) 5 = 3 10 Rule: (n a ) b = n a*b Power of a Power When you take the power of a power, multiply the exponents and keep the base

#7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha! If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!

#8: Zero Law of Exponents: Any base powered by zero exponent equals one. So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.1.

Warm up Feb Find the slope of the following lines: 2. Put the following in order from least to greatest:  6, 2.35, 2¼, Find the slope of the line between the points (3, 1) and (9, 2)

Warmup Feb Find the slope of the line: 2. Graph the line y = -2x Solve for x : 5x – 7 = -2(x – 3) 4. Find the slope of the line through the points (4, -10) and (8, 2)

Number Talk & Launch The following statements are all INCORRECT. 1. Identify the mistake(s). 2. Correct. 3. Justify (show) your reasoning.

Order of Magnitude Task

SOLUTIONS