For any real number a, b, and, c. For any real number a, b, and, c. Examples. Solve.

Transcription

1 Algebra 1 CCSS- 1 Standards: A.CED.1 Students will learn to solve equations, create linear equations in one variable, and use them to solve problems. Section: HW Side notes: Essential Question: What properties are used to solve equations? How do I solve one step equations? Essential Question: To solve equations we must the variable by using the properties of equality. You can do this by performing. Those are operations that each other. Adding and are inverse operations. Multiplying and are also inverse operations. Def--- Addition Property of Equality-- Adding the number to sides of an equation produces an equivalent equation. Algebraic Example For any real number a, b, and, c. Numeric Example Def--- Subtraction Property of Equality-- Subtracting the number to sides of an equation produces an equivalent equation. Algebra Example For any real number a, b, and, c. Numeric Example Examples. Solve.

2 Def--- Multiplication Property of Equality-- Multiplying sides of an equation by the number produces an equivalent equation. Algebra Example Numeric Example For any real number a, b, and, c. Def--- Division Property of Equality-- Dividing sides of an equation by the number produces an equivalent equation. Algebra Example Numeric Example For any real number a, b, and, c, such that c = 0. Examples. Solve

3 Define a variable and write an equation for the situation. Then solve. DOK 2 You have a shoe rack that can hold 25 pairs of shoes. You can still fit 8 more pairs of shoes on the rack before it is full. How many shoes are on the shoe rack? A wildlife expert estimates that in a certain year the number of male fawns born will be about the number of adult female deer. Suppose 1131 male fawns are born. About how many female deer are there? To solve an equation you must the variable using the and performing operations that each other. The addition property of equality says that the same number to both sides produces an equation. The subtraction property of equality says that the same number on both sides produces an equation. The multiplication property of equality says that the same number on both sides produces an equation. The division property of equality says that the same number on both sides produces an equation.

4 Algebra 1 Standards: Algebra 1 CCSS- A.REI.3, A.CED.1, A.REI.1 Students will learn to solve equations, create linear equations in one variable, and use them to solve problems. Section: HW Essential Question: How do I solve Two-Step Equations? Essential Question: To solve two-step equations we must still the variable. We must identify each of the operations and undo them by performing. Side notes: Examples. Solve each equation. DOK 2 Solve each equation. Justify each step.

5 Define the variable, write an equation and solve. DOK 2 Suppose you are helping to prepare a large meal. You can peel 4 potatoes per minute. You need a total of 80 potatoes. How long will it take you to finish if you have already peeled 16 potatoes? Bowling at Tustin Lanes cost Danny and Maria $12. This include both their shoe rentals at $1 each. How much did each game cast if they bowled a total 5 games? To solve two- step equations we must still (get it by itself). However, now we must identify the operation and undo them by performing to do so. To define a variable in a word problem at what they are. That is what you define the variable as.

6 Algebra 1 Standards: Algebra 1 CCSS- A.REI.3, A.REI.1 Students will learn to solve multi-equations, create linear equations in one variable, and use them to solve problems. Section: HW Essential Question: How do I solve Multi-Step Equations? Essential Question: Before you the variable you must and. Side notes: Examples. Solve each equation.

7 Define the variable, write an equation and then solve. DOK 2 A gardener is planning a rectangular garden area. His garden will be next to an existing 12 ft. fence. He has 44 feet of fence to build the other 3 sides. How long will the garden be if the width is 12 ft.?

8 Algebra 1 CCSS- 1 Standards: A.REI.3, A.CED.1, A.REI.1 Students will learn to solve equations with variables on both sides, create linear equations in one variable, and use them to solve problems. Section: HW Essential Question: How do I solve equations with variables on both sides? Essential Question: To solve equations with variables on both sides we must first of the equation, if possible. Then move the variable to only and solve like before. Examples. Solve. Side notes:

9 Define the variable, write an equation, then solve. DOK 2 A computer company, company A, charges $10 per month plus $7 per minute for access to its information. Company B charges $20 per month plus $5 per minute. For what number of minutes will the charges be the same if you use Company A or Company B?

10 Algebra 1 CCSS- 1 Standards: A.REI.3, A.REI.1 Students will learn to solve multi-equations, create linear equations in one variable, and use them to solve problems. Section: HW Side notes: Essential Question: How do we solve equations by clearing fractions and decimals from them? Essential Question: To solve equations by clearing fractions you must find the. Then multiply the to, and solve by the variable. Examples. Solve.

11 To clear decimals from an equation you must find the number of after the decimal point of all the terms across the equation. If the greatest number of decimal places is 1, multiply sides of the eq. by If the greatest number of decimal places is 2, multiply sides of the eq. by If the greatest number of decimal places is 3, multiply sides of the eq. by And so on. DOK 2 Define the variable, write an equation, then solve Your dad rented a moving truck for $59.95 plus $.25 per mile. Before returning the truck he filled up the gas tank, which cost $ The total cost of the truck was $ Find the number of miles the truck was driven.

12 Algebra 1 Standards: Algebra 1 CCSS- A.CED.4, 1 Students will learn to rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Section: HW Side notes: Essential Question: How do we rearrange formulas and equations and solve them for a specific variable? Essential Question: Def--- A literal equation is an equation that involves variables. To solve for specific variable in a literal equation you use the methods we have been using to solve equations. You must still the variable being asked to solve for. Examples. Solve each equation for y. Then find the value of y for each value of x.

13 Def--- A formula is an that states a among quantities. Examples of commonly used formulas Area of a triangle Circumference of a circle Area of a circle Distance traveled To solve for specific variable in a formula you use the methods we have been using to solve equations. You must still the variable being asked to solve for. Examples. Solve each equation for x. Examples. Solve for the indicated variable.

14 DOK 2 Construction bricklayers use the formula n = to estimate the number n of bricks needed to build a wall of length and height h, where and h are in feet. Solve the formula for h. Estimate the height of a wall 14 feet long that requires 784 bricks to build.

15 Algebra 1 CCSS- 1 Standards: N.Q.1 Students will learn to write ratios and find unit rates to compare quantities. They will also learn to convert units and rates to solve problems. Section: HW Essential Question: What is a ratio? What is a rate? What is a unit rate? How do I convert one unit to another? Essential Question: Def--- A ratio two numbers using division. The ratio of two numbers and can be written in three ways: Side notes: Where b = 0!! What this means is that for of one quantity you have of another quantity. Def--- A rate is a that compares two quantities measured in different units. Def--- A unit rate is a rate that has a denominator of. Examples. 1) You are shopping for T- shirts. Which store offers the best deal? Store A: $25 for 2 shirts. Store B: $45 for 4 shirts. Store C: $30 for 3 shirts To convert from one unit to another, such as feet to inches, you the original unit by a. Def--- A Conversion Factor is a of two measures in different units. For example...

16 Examples. Convert the given amount to the given unit 1) 330 min ; hours 2) 200 cm ; meters 3) 5 ft. 3 in. ; inches Complete each statement. 4) 2.2 kg = lb 5) 50 cents/ hour = dollars/ day 6) 60 mi/ h = feet/ sec DOK 2 The maintenance worker discovers a leak in the water fountain. He found that it was leaking at a rate of 16 fluid ounces per minute. How fast was the fountain leaking in gallons per hour?

17 Algebra 1 CCSS- 1 Standards: N.Q.1 Students will learn to how to solve proportions and how to apply them. Section: HW Essential Question: What is a proportion? How do you solve proportions? Essential Question: A proportion is an equation that states two are equal. Side notes: To solve proportions you can use one of two methods: 1) Using the Multiplication Property of Equality 2) Using the Cross Products Property of a Proportion Examples.

18 DOK 2 A florist is making flower bouquets. He uses 4 dozen tulips for every 8 bouquets. How many dozens of tulips does he need to use to make 32 bouquets?