Introduction to Algebra

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Information about Introduction to Algebra

Published on July 14, 2009

Author: mrferrell


Algebra : Algebra What do you already know about this topic? Slide 2: Objective : Write and solve one-step equations for real-world situations. Objective Algebra Vocabulary : Constant A number that cannot change. Variable A letter or symbol that represents a number. Equation A mathematical sentence that uses the symbol = between two expressions to show that they have the same value. Algebra Vocabulary REVIEW Vocabulary : Difference Product Sum Quotient REVIEW Vocabulary What is this? : How do you think this could be connected to solving equations? What is this? Slide 7: v + 2.43 = 34.12 How do we find the value for v? Why do you subtract when the addition operation is shown? Slide 8: W – ½ = 12 ¼ How do we find the value for W? Why do you add when the subtraction operation is shown? Slide 9: 12y = 144 How do we find the value for y? Why do you divide when the multiplication operation is shown? Slide 10: Q ÷ 30 = 900 How do we find the value for Q? Why do you multiply when the division operation is shown? Example Question : Jim has 18 CDs. He bought x more. Then he had 21 CDs. Write and solve the equation for x. 18 + x = 21 x = 3 Example Question Example Question : Rhonda had u CDs, and each of her CDs had 10 songs. Her collection had 120 songs total. Write an expression and solve for u. 10u = 120 u = 12 Example Question Practice Question #1 : The area of Tiffani's bedroom (b) is 2 times the area of her bathroom. Her bathroom is 10 square feet. Which equation best describes this situation? 10 = 2/b b = 2 + 10 10 = 2b b = 2 x 10 Practice Question #1 Practice Question #2 : Each day an adult bear eats 3.5 times the amount of food it ate each day when it was a cub. As a cub, it ate 4 pounds of food each day. Which equation could be used to determine the amount of food the adult bear eats each day (b)? b = 4 + 3.5 b = 4 x 3.5 4 = 3.5b 4 = b + 3.5 Practice Question #2 Practice Question #3 : Jared ran 2 miles in 8.5 minutes. Which equation could be used to determine the average number of minutes it took Jared to run each mile (k)? k - 2 = 8.5 k + 2 = 8.5 k/2 = 8.5 2k = 8.5 Practice Question #3 Practice Question #4 : The sum of Keira's math test scores during the first semester was 480 points. Her average test score was 96 points. Use the equation below to find the number of tests Keira took during the first semester (x). 480/x = 96 4 tests 5 tests 6 tests 7 tests Practice Question #4 Practice Question #5 : It took Jacob 1.2 more minutes to run a race than Colton. It took Colton 8.2 minutes to run the race. Which equation could be used to determine the number of minutes it took Jacob to run the race (m)? m = 8.2 - 1.2 m = 8.2 / 1.2 m = 8.2 + 1.2 m = 8.2 x 1.2 Practice Question #5 Practice Question #6 : Students at PRMS plan to raise X dollars for an end-of-year celebration. They have raised $89.45. The students still have $176 left to raise. What is the total amount of money the students plan to raise? X - $57.55 = $382 $219.84 $265.45 $239.55 $263.77 Practice Question #6 Practice Question #7 : Mom’s antique clock is 189 years old, which is 9 times as old as Dad's clock. The equation below can be used to determine the age of Dad's clock (r). How many years old is Dad's clock? 189 = 9r 31 years old 21 years old 11 years old 17 years old Practice Question #7 Practice Question #8 : A city's usual population (p) increases by 35,000 tourists during the summer. The city's total summer population, including tourists, is 69,250 people. What is the usual population of the city without the tourists? 69,250 = p + 35,000 22,600 70,000 104,250 34,250 Practice Question #8 Practice Question #9 : Worth's Construction Company hired y workers in January. In February, the company hired 7 extra workers. They now have a total of 37 workers. Which equation could be used to determine the exact number of workers hired in January (y)? 37 = 7y y = 37 – 7 37 = y – 7 y = 37 x 7 Practice Question #9 Practice Question #10 : Tanner signs a contract to earn $21.9 million for the next three years playing football. Use the equation to determine the average amount of money, in millions of dollars, that the Tanner will earn each year (x). 3x = 21.9 $11.76 million $17.76 million $ 7.5 million $ 7.3 million Practice Question #10 Practice Question #11 : Morgan has $72.24. She has four times the amount of money that Veronica has (g), as represented in the equation below. Exactly how much money does Veronica have? 4g = 72.24 $18.06 $2.24 $68.24 $24.96 Practice Question #11 Practice Question #12 : Savannah earns $900 per month which is $100 more than Sabrina earns per month. Which equation could be used to determine the amount of money Sabrina earns per month (r)? 900 = r – 100 900 = r + 100 900 = 100/r 900 = 100r Practice Question #12 Enrichment Question : Write a word problem that can be represented by the following equation: y ÷ 12 = 5 Be sure to include what the variable y represents in your problem description. Then solve the equation for the variable. Show all the steps in your solution and label your answer appropriately. Enrichment Question Enrichment Question : Jill grew to 120% of her height from one year ago. At that time she was 4 feet 4 inches tall. How tall is she now? Enrichment Question Slide 27: Why might someone say that algebra is weightlifting for the brain?

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