CHAPTER 1 BLUE Mrs. Kane

Math in History There are two uses of the number 0 in mathematics. Zeros can be used as a place holder in a number system. For instance, the numbers 27 and 207 are different. Then Mayans used zero in this way. Zero can also be used to represent a number on the number line. The properties of 0, such as “the sum of zero and a number is that number” were described by Indian mathematicians over 3000 years ago.

What You Learned Before Converting Measures Page B1 in textbook Set up the proportion with like labels Solve Adding and Subtracting Fractions You must have a common denominator

What you Learned Before

1.1 Solving Simple Equations Expression Equation Variable Part of an equation (no equal sign) Two equal expressions (equal sign) Letter that represents a value

1.1 Solving Simple Equations Addition Property of Equality Subtraction Property of Equality Adding the same number to both sides of an equation produces an equivalent equation Subtracting the same number to both sides of an equation produces an equivalent equation

1.1 Solving Simple Equations Multiplication Property of Equality Division Property of Equality Multiplying each side of an equation by the same number produces an equivalent equation Dividing each side of an equation by the same number produces an equivalent equation

1.1 Solving Simple Equations Rule: Goal of solving equation: What you do to one side you must do to the other Isolate the variable

1.1 Solving Simple Equations

1.2 Solving Multi-Step Equations (Activity) Hand out cards Find the other people in the class that have a like term and gather in a group.

1.2 Solving Multi-Step Equations (Activity)

Look at Triangle E and Triangle F in Activity 1, why are there variable expressions for only two angles? Find the angle measures: y⁰y⁰ x⁰x⁰ x⁰x⁰ z⁰z⁰ x⁰x⁰ y⁰y⁰

1.2 Solving Multi-Step Equations Key Idea: To solve multi-step equations, use inverse operations to isolate the variables Steps to solving Multi-step equations 1. Use the Distributive Property 2. Combine like terms on each side of the equal sign 3. Combine like terms on opposite sides of the equal sign 4. Multiply or divide to solve for the variable

1.3 Solving Equations with Variables on Both Sides (activity) What balances with the cylinder? Explain.

1.3 Solving Equations with Variables on Both Sides (activity) Activity 1: How do you find the perimeter of a rectangle? How do you find the perimeter of a composite shape? How do find the area of a rectangle? How do you find the area of a composite shape? How do you label perimeter? What does that mean? How do you label area? What does that mean? Activity 2: How do you find the surface area of a rectangular prism? How do you find the volume of a rectangular prism? What are the labels?

1.3 Solving Equations with Variables on Both Sides Key Idea: To solve an equation with variables on both sides, collect the variable terms on one side and the constant terms on the other side. Steps to solving Multi-step equations 1. Use the Distributive Property 2. Combine like terms on each side of the equal sign 3. Combine like terms on opposite sides of the equal sign 4. Multiply or divide to solve for the variable

1.3b Solutions of Linear Equations Does every equation have a solution? Does every equation have just one solution? Is it possible for an equation to have two solutions?

1.3b Solutions of Linear Equations

1.4 Rewriting Equations and Formulas (Activity)

1.4 Rewriting Equations and Formulas

1.5 Converting Units of Measure (Activity) Do you know who was the tallest man ever to live (for whom there is irrefutable evidence)? Robert Pershing Wadlow, born in Alton, Illinois, on February 22, When he was last measured he was 8 feet 11.1 inches tall. He wore a size 37AA shoe (18 ½ inches long) and his hands measured 12 ¾ inches from the wrist to the top of the middle finger. Wadlow died on July 15, 1940 as a result of a septic blister on his right angle caused by a brace, which had been poorly fitted only a week earlier. How tall was Wadlow in inches? inches

1.5 Converting Units of Measure History of Customary Length: The Egyptian cubit was developed about 300 B.C. the unit was based on the length of the arm (from the elbow to the extended finger). The Romans adopted the foot from the Greek and divided it into 12 sections called the unicae, which came to be known as an inch.

1.5 Converting Units of Measure History of Metric: The word meter is from the Greek word metron, which means a measure. In 1793, the meter was defined to be one ten-millionth of the length of the earth’s meridian along a quadrant. This is the same as one ten-millionth of the distance from the North Pole to the equator, along the meridian running near Dunkirk in France. The United States is the only industrialized country that does not use the metric system as its predominant system of measurement.

1.5 Converting Units of Measure Vocabulary: Conversion Factor – rate that equals 1 1 in = 2.54 cm 1 cm ≈ 0.39 in Conversions on B1