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Welcome to Math 112 Class #2 – 16-17 • Pick a puzzle piece and find the table where your piece matches the description. This is your new group for the next few classes. • Introduce yourself to your new teammates! • Please turn in HW #1 – make sure your NAME is printed neatly on the first page and put it in a neat pile! • Then do the warm up (bar graph questions) What does your quote have to do with this class? Warmup For those of you who received add cards last week: You must officially enroll and pay for the course by Monday, 2/20, or you will be dropped from the class. Time for Multiplication practice! Tonight’s Agenda 1. Turn in HW #1 and do warmup 2. Multiplication practice 3. Class norms 4. Review order of operations 5. Fractions 1. 2. 3. 4. 5. Fraction vocabulary Finding equivalent fractions Simplifying fractions Adding and subtracting fractions Area of a rectangle 6. The Apartment Problem 7. Quiz #1 Tonight’s positive quote! Tonight’s focus: Math practice #1 Make sense of problems and persevere in solving them. Persevere - Continue in a course of action even in the face of difficulty or with little or no prospect of success Class norms When students shout out answers in math class, the teacher should ___________________________________ When a student walks in late, the teacher should ________________________________ When several students have conversations during class, the teacher should _________________________________________ When working in groups, team members should __________________________________________ What I think about texting or using a cell phone to surf the internet during class is _____________________________________________ Class norms Be respectful Listen when others are speaking Use cell phones outside Clean up after yourself Reminders! Complete Student Survey & turn in tonight (if you didn’t do this last week) Test #1 is next week! It will be similar to tonight’s team quiz. If you do not take the first test you will be dropped from the course! Persevere Continue in a course of action even in the face of difficulty or with little or no prospect of success More Order of Operations Order of Operations review Ex. 1 6 + 16 ÷ 2 ∙4 - 8 Ex. 2 Place parentheses in the expression so that the multiplication is done first. Simplify your new expression. 6 + 16 ÷ 2 ∙4 - 8 Ex. 3 Place parentheses in the expression so that the addition is done first. Simplify your new expression. 6 + 16 ÷ 2 ∙4 - 8 Ex. 4 Find the error and circle it. Then copy over and simplify it correctly. [6 + 2(8 ÷ 4 ∙2)] - 8 [6 + 2(2∙2)] - 8 [6 + 2(4)] - 8 [8(4)] - 8 32- 8 = 24 Intro to Fractions Fractions Essential question: What is the vocabulary used for fractions? Foldable Example: 2/3 Numerator is 2 Bar means divide Denominator is 3 This means 2 3 1/3 The numerator is 1 The denominator is 3 Proper Fraction A fraction that is less than one, with the numerator less than the denominator. Example: 2/3 Improper Fraction A fraction that is greater than one or equal to one, with the numerator larger than (or equal to) the denominator. Example: 7/4 or 7/7 Mixed Number A whole number plus a fraction Example: 1 ½ or 1 ¾ Equivalent Fractions Fractions that have the same value Example: ½ = 2/4 = 4/8 Equivalent Fractions How can we find equivalent fractions using an area model? Is there another way to represent 1/3? 1 ? = 3 ? Equivalent Fractions How can we find equivalent fractions using an area model? Make 2 rows 1 ? = 3 ? Equivalent Fractions How can we find equivalent fractions using an area model? Make 3 rows 1 ? = 3 ? Equivalent Fractions How can we find equivalent fractions using an area model? Make 4 rows 1 ? = 3 ? Equivalent Fractions How can we find equivalent fractions using the Giant 1? Multiplying by 1 does not change the value of a number A fraction with the same numerator and denominator has a value of 1. The Giant One: Equivalent Fractions How can we find equivalent fractions using the giant 1? Find 3 equivalent fractions for 1/3 multiplying by the giant 1: ⅓× ⅓× ⅓× Reducing Fractions to Lowest Terms How do I simplify fractions to lowest terms? Ex. 1 Simplify 48/64 What is the largest factor that is common to 48 and 64? This is called the Greatest Common Factor (GCF). Use a factor tree to find the GCF. Next rewrite the fraction 48/64 using the GCF Find the giant 1. The remaining fraction is the simplified fraction. Ex. 2 Simplify 16/24 What is the largest factor that is common to 16 and 24? This is called the Greatest Common Factor (GCF). Use a factor tree to find the GCF. Next rewrite the fraction 16/24 using the GCF Find the giant 1. The remaining fraction is the simplified fraction. Ex. 2 Simplify 18/54 What is the largest factor that is common to 18 and 54? This is called the Greatest Common Factor (GCF). Use a factor tree to find the GCF. Next rewrite the fraction 18/54 using the GCF Find the giant 1. The remaining fraction is the simplified fraction. Ex. 3 Simplify 30/12 What is the largest factor that is common to 30 and 12? This is called the Greatest Common Factor (GCF). Use a factor tree to find the GCF. Next rewrite the fraction 30/12 using the GCF Find the giant 1. The remaining fraction is the simplified fraction. Always reduce fractions to lowest terms You do not need to change improper fractions to mixed expressions. (In other words, 4/3 is an acceptable answer – you do not need to change it to 1 ⅓)! Adding and Subtracting Fractions How can we use an area model to + and – fractions? Adding and Subtracting Fractions Before fractions can be added or subtracted, the fractions must have the same denominator. This is also called a common denominator. Make equivalent fractions Adding and Subtracting Fractions How can we use the giant 1 to + and – fractions? Example 1: ¼ + ⅓ First list the multiples of 4 and 3. Circle the first multiple they have in common. This is the COMMON DENOMINATOR. Multiply ¼ by a giant 1 to get a new fraction with the common denominator. Multiply ⅓ by a giant 1 to get a new fraction with the common denominator. Add the fractions (add numerators, keep the common denominator) and simplify, if necessary. Area of a Rectangle Apartment Problem P. 22 (1-40) Problem 1-40 The Apartment Your task: Find the possible dimensions for every room in the apartment. Section 1.2.1 (P. 22) How can I solve it? Solving Problems with Guess and Check Objectives: To solve a complex problem and develop a new problemsolving strategy called “Guess and Check” How can we organize our work for the apartment problem using a table? Here’s an example: Team Quiz #1 Everyone gets a copy of the quiz. Show all work on your own paper and consult with your team! All papers will be collected. Homework #2 Handout Test #1 will be at the beginning of class next week. If you arrive late you will not be given extra time, so plan accordingly!