From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

Classroom Activity

Activity 1 One Step Equation: Focus on Multiplication Property of Equality

1. Your friend tells you she bought 12 bananas. On this particular day, every bunch had the same number of bananas so she bought 2 bunches. She says to you “How many bananas do you think were on each bunch?”
2. Your teacher and your mom are talking at the registration when your teacher suddenly turns to you and asks your grandmother’s age. You forgot how old your grandmother is but you remember that your youngest aunt Kristie is 30 years old and half the age of your grandmother. How old is your grandmother?
3. Your little brother is having a big birthday party. Your mom invited all 24 students in his class and they all came, how unusual. Your brother wants to form groups with 4 kids to play in a game at his party. He wants to know how many groups he would have so the right amount of the material is prepared for the game.
4. You are playing a guessing game with your friend Mary. She says that she has $25 in her bank account. This is ¼ the amount her sister Emily has in her bank account. Mary asks you how much Emily has in her bank account
5. Solve the following one-step equations and justify each step.
   1. 8y = 16
   2. x/8=16,
   3. a/5=10
   4. 10 = 5a
   5. 10 = z + 7
6. Write a word problem that can be modeled by 3x = 18. Use at least 3 complete sentences to describe the situation with detail. Solve the problem using arithmetic and algebraic approach.
7. Write a situation in which the unknown value is 2/3. In other words when you solve your algebraic equation the solution would have a value of 2/3. Use at least 3 complete sentences to describe the situation. You may use any of the four operational symbols (+, -, /, x).

Activity 2 Two-Step Equations: Focus on Addition Property of Equality & Multiplication Property of Equality

1. There are 31 desks in your math class. Because the classroom is not a prefect rectangle, some desks are arranged in rows and other desks are arranged in a group of 6 desks. You are sitting in a group of 4 desks. As you look around you realize there are 5 rows. You started to wonder how many desks are in a row.
2. Your grandmother is telling you a story of why she only has 6 hats even though she used to have a lot them. On her 40th birthday, there was a fire because not all the birthday candles were put out. She was able to salvage only one-third of her hats. Then she lost 2 more hats most recently. How many hats did she have before the fire?
3. Your friend tells you that she is grounded for next four weeks. She will not receive any allowances. Fortunately, she had $100 dollars saved up babysitting for $5 an hour. If she spends the same amount each week and has $60 left at the end of 4 weeks, how much did she spend each week?
4. A martial arts school is offering a special where students can enroll for two-fifths of the regular price, after a $3 application fee. Find the regular price of the enrollment if you paid $32.50.
5. Write a situation in which the unknown value is 1 2/3. In other words when you solve your two-step algebraic equation the solution would have a value of 1 2/3.  Use at least 3 complete sentences to describe the situation with detail. You may use any of the four operational symbols (+, -, /, x). Solve the problem.
6. Solve following two-step equations using Properties of Equality. Verify your solution.
   1. 7 = 8x + 31
   2. x/8 -4=16
   3. 103 = −9x – 13
   4. 8 + b/-4 = 5
   5. (4/5)x+2= 2x

Classroom Activity 3 Multi – Step Equations Problem Sets

Combine like terms

1. Jacqueline bought four cases of vitamin water drinks for an upcoming meet. She bought three more cases and, in addition spent $6.95 on snacks. If she spent $134.35, how much did she pay for each case of vitamin drinks?
2. Mary’s sister is three years younger than twice Mary’s age. The sum of their age is 33. How old is Mary?
3. Solve
   1. 2a + 3 + 3a = 18
   2. 24 = 5x – 2x + 3
   3. 9x – 5 – 6x – 1.3 = 2.1
   4. 5v – 0.9v + 2.1 = 4.5

Distributive Property

1. Jack and Jim collect Pokemon cards. Jim has 12 more than Jack has, and together they want to triple their collection for a total of 66 Pokemon cards. How many Pokémon cards does Jack currently own?
2. Maria is selling tickets to her school’s talent show. Adult tickets cost $5 and children’s tickets cost $3. Maris sells a total of 50 for $214. How many adult tickets and children’s tickets did she sell?
3. Jeremy bought post cards on a trip. He sent 15 cards to his friends. He sent two-third of the remaining cards to his family. Then he sent one of the remaining cards to his teacher. He was left with 3 cards. How many post cards had Jeremy bought?
4. Solve
   1. 32 = 8(x + 2)
   2. 5(1 – 2w) + 8w = 15
   3. 3 = 3(x – 2) – 5(2x + 1)
   4. (-3+y)/4=103

Variables on both sides

1.  Four times Nia’s age, decreased by three is equal to three times Nia’s age, increased by seven. How old is Nia?
2. Find three consecutive integers such that twice the greatest integer is two less than three times the least integer.
3. Mike shared a package of lined paper with three of his classmates. He gave 1/4 of the pack to Aaron, 1/3 of what was left was given to Emily. Then Kyle took 1/6 of what was left in the package. Mike kept the remaining 30 sheets. How many sheets of paper were in the original package?
4. Solve
   1. 7a – 17 = 4a + 1
   2. 3m – 10 = 2(4m – 5)
   3. 5 + 2(n – 4) = 1 – 3(n + 2)
   4. 1/3(x+1)=(2/9)x+ 7/9