Hierarchy of Hands on Equations
1. Understand the definition of a constant
2. Understand the definition of a variable
3. Rules for balancing an equation
4. Balance an equation with constants and variables
5. Balance equations with constants and variables on both sides addition
6. Balance an equation using subtraction of constants and variables
7. Balance an equation using multiplication of constants and variables
8. Balance an equation with constants, variables and opposite variables
9. Introduce opposite constants
CAMMP 2014 - Module 1
College of Education
Reading and Elementary Education
Names: Floyd, Michael and Pompée, Crystal
Integrated, Thematic Problem Solving Unit: X-Men: Days of Future Math
Grade Level: 6th
Arithmetic Topic (operation): Algebraic equations
HIERARCHY STEP #
#1: Understand the definition of a constant
#2: Understand the definition of a variable
#3: Rules for balancing an equation
#4: Balance an equation with constants and variables
THEME PROBLEM #1
Professor X has 3 new mutants in his school. When joined with the other mutants who were already there, he has a total of 6 mutants. How many mutants were already in Professor X’s
school?
THEME PROBLEM #2
Wolverine and Magneto have 2 days to defeat 8 Sentinels.Since they want to defeat the same number of Sentinels each day, how many sentinels should they defeat each day?
Summary Table
Action Language: x joined with 3 equals 6
2 sets of x equals 8
Open Number Sentence: x + 3 = 6
2x = 8
Manipulative: Hands on equations
Quantitative Solution: 3
4
Referential Meaning: mutants
sentinels
CONCRETE MANIPULATIVE:
REPRESENTATIONAL MANIPULATIVE: Hands on equations
TRANSITIONAL ACTIVITIES: Computer Activities
Memory matching game using equations (constants only, no variables)
http://www.math-play.com/Equation/Equation-Game-Online.html
Multiplication game where students solve equations in order to steer their rocket ship:
http://www.mathplayground.com/spaceracer_multiplication.html
STUDENT PROBLEMS:
1. Mystique just changed into 2 people today. When joined with the other people she changed into yesterday, that makes 9 people she has changed into. How many people did Mystique change into yesterday? (Hands on equations)
2. Gambit and Storm each purchased a new X-Men costume. Together, their costumes cost $16. Gambit’s costume was $7. How much was Storm’s costume? (Hands on equations)
3. Magneto is showing off his juggling skills. He starts off by juggling 8 quarters without using any hands. By the time he’s done adding coins, he is juggling 16 quarters in all. How many more quarters did he add to his impressive juggling set? (Hands on equations)
4. Beast had 10 bananas in his lunch box. He found 4 more in his jacket pocket. He ate some of the bananas and still had 9 left. How many bananas did Beast eat? (Hands on equations)
5. Colonel William Stryker is measuring the weight of an unknown chemical. He puts the unknown chemical and an 8-ounce weight on one side of a scale. He put a 10-ounce and a 4-ounce weight on the other side. If both sides weighed the same, how much did the unknown chemical weigh? (Hands on equations)
6. Rogue went to the store and spent $12. She bought 3 equally priced gloves. How much did each one cost? (Hands on equations)
7. Beast is buying gas for the X-plane. He had $9, but lost $1. He used his remaining money to buy four gallons of gas, each costing the same amount. How much did each gallon of gas cost? (Hands on equations)
8. There are 2 teams of Sentinels on patrol tonight searching for mutants. They are joined by 3 more sentinels, which makes seven Sentinels altogether. How many Sentinels were in each team? (Hands on equations)
9. One the first day of class, the new mutant students are put into 3 groups. On the second day of class 2 new students join the class. Now there are 14 students in the class. How many mutants were in each group? (Hands on equations)
10. One Sentinel caught twice as many mutants as the other Sentinel. This gave Dr. Trask just enough to release 9 and keep 9. How many mutants did each Sentinel catch? (Hands on equations)
STUDENT ANSWER KEY:
1. Quantitative Meaning: 7
Referential Meaning: people
2. Quantitative Meaning: 9
Referential Meaning: dollars
3. Quantitative Meaning: 6
Referential Meaning: quarters
4. Quantitative Meaning: 5
Referential Meaning: bananas
5. Quantitative Meaning: 6
Referential Meaning: ounces
6. Quantitative Meaning: 4
Referential Meaning: dollars
7. Quantitative Meaning: 2
Referential Meaning: dollars
8. Quantitative Meaning: 2
Referential Meaning: sentinels
9. Quantitative Meaning: 4
Referential Meaning: mutants
10. Quantitative Meaning: 6
Referential Meaning: mutants
CAMMP 2014 – Module 2
College of Education
Reading and Elementary Education
Names: Floyd, Michael and Pompée, Crystal
Integrated, Thematic Problem Solving Unit: X-Men: Days of Future Math
Grade Level: 6th
Arithmetic Topic (operation): Algebraic equations
HIERARCHY STEP #5
Balance equations with constants and variables on both sides addition
THEME PROBLEM #1
Wolverine and Cyclops spent the same amount at the store on supplies. Wolverine knew that his new boots cost $4, but forgot how much his 2 equally priced t-shirts cost. Cyclops bought 3 of the same t-shirts and a new pair of $1 glasses. How much was each t-shirt?
THEME PROBLEM #2
Magneto had 4 bags of marbles. Each bag had the same number of marbles in it. Professor X had a bag with 8 marbles and another 2 bags with the same amount as each of Magneto’s bags. If both men had the same number of marbles, how many were in each bag?
Summary Table
Action Language: 2 sets of x joined with 4 equals 3 sets of x joined with 1
4 sets of x equals 8 joined with 2 sets of x
Open Number Sentence: 2x + 4 = 3x + 1
4x = 8 + 2x
Manipulative: Hands on equations
Quantitative Solution: 3
4
Referential Meaning: dollars
4 marbles
CONCRETE MANIPULATIVE:
REPRESENTATIONAL MANIPULATIVE: Hands on equations
TRANSITIONAL ACTIVITIES: Computer Activities
Computerized hands on equation scale. When the equation is unbalanced, the scale tips
www.mathplayground.com/algebraequations.htm
Solve for X, click the balls in order from least to greatest
http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm
STUDENT PROBLEMS:
1. Rogue bought 3 pies all at the same price and a $1 Snickers. Jubilee bought one of the same pies and spent $9 for flowers. They both spent the same amount. How much did each pie cost?
2. Colossus collects Marvel comic books. He has 4 sets of the X-Men comic books and 3 sets of Batman comic books. Quicksilver only has 1 set the same as Wolverine and 18 other comic books. The total number of comic books owned by Wolverine and Cyclops is the same. All the sets have the same number of comics. How many comic books are in each set?
3. Gambit can buy 6 deck of cards and a $1 set of dice for the same price as 3 decks of cards and ten $1 sets of dice. How much does a deck of cards cost?
4. It’s graduation day at the academy! Dr. Jean Grey can buy 6 pizzas for the pizza party for the same price as 2 pizzas and 8 one-dollar drinks. How much does each pizza cost?
5. Iceman had 4 ice marbles. His friend Pyro gave him a few others. Pyro has three times as many marbles remaining as he gave to Iceman. Together, Iceman and Pyro have 24 marbles. How many marbles did Pyro give to Iceman?
6. The X-Men are enjoying a warm summer vacation in Mexico. Beast had 13 pesos in singles and 2 coins. Storm had a one-peso bill and four of the same coins that Beast had. They both had the same amount of money. What is the value of each of the coins?
7. No one really knows how old Wolverine is, but they’d love to find out. He left a riddle in the cafeteria to help the students out. “Three times my age, increased by 5, is the same as twice my age increased by 10. Find my age.”
8. 3x = x + 4
9. x + 4 = 2x + 3
10. 2x + 3 + 3x = x + 11
STUDENT ANSWER KEY:
1. Quantitative Meaning: 4
Referential Meaning: dollars
2. Quantitative Meaning: 3
Referential Meaning: comic books
3. Quantitative Meaning: 3
Referential Meaning: dollars
4. Quantitative Meaning: 2
Referential Meaning: dollars
5. Quantitative Meaning: 5
Referential Meaning: marbles
6. Quantitative Meaning: 6
Referential Meaning: currency of the coin
7. Quantitative Meaning: 5
Referential Meaning: years old
8. Quantitative Meaning: 2
9. Quantitative Meaning: 1
10. Quantitative Meaning: 2
CAMMP 2014 – Module 3
College of Education
Reading and Elementary Education
Names: Floyd, Michael and Pompée, Crystal
Integrated, Thematic Problem Solving Unit: X-Men: Days of Future Math
Grade Level: 6th
Arithmetic Topic (operation): Algebraic equations
HIERARCHY STEP #6
Balance an equation using subtraction of constants and variables
THEME PROBLEM #1
Storm has 5 boxes of supplies and 2 more items in her shopping bag. She doesn’t have enough money for everything so she has to put back 3 boxes. For the same amount of money she could get 1 box of supplies and 5 items. Each box holds the same number of items. How many items are in each box?
THEME PROBLEM #2
Some of the X-men are pooling their money together to buy new outfits. Rogue puts her money in first. Jubilee puts in twice as much as Rogue. Gambit takes away the same amount of money as Rogue put in, but puts in one dollar. The total amount of money they have is the same as the amount Rogue put in plus $9. How much did Rogue put in?
Summary Table
Action Language: 5 sets of x takeaway 3 sets of x joined with 2 equals x joined with 5
2 sets of x joined with x, takeaway x, joined with 1 equals x joined with 9
Open Number Sentence: 5x – 3x + 2 = x + 5
2x + x – x + 1 = x + 9
Manipulative: Hands on equations
Quantitative Solution: 3
8
Referential Meaning: items
dollars
CONCRETE MANIPULATIVE:
REPRESENTATIONAL MANIPULATIVE: Hands on equations
TRANSITIONAL ACTIVITIES: Computer Activities
Math Basketball: Basketball game dealing with subtraction in algebraic equations
http://www.algebra4children.com/Games/games-2/Pre-algebra-subtraction/hoopshoot-pre-algebra-subtraction.html
Make X game. Create an equation to make X a certain number using cards
http://www.sheppardsoftware.com/mathgames/makex/makeXAS2_level1.htm
STUDENT PROBLEMS:
1. Professor X is trying to figure out how to best set up the X-men teams. Last week he set up three teams of X-men, but this week he had to take one team away to go on a special mission. The number he’s left with is the same as if he only had 1 team plus 9 X-men. If each team has the same number of X-men, how many X-men are in each team?
2. Wolverine can be such a hard math teacher. He gives the students a super hard problem to figure out how old he is. He says “five plus my age plus 3 times my age, take away my age is the same as 2 times my age plus 9 minus my age. How old am I?”
3. On Monday three groups of Sentinels were spotted heading toward the Xavier school. On Tuesday one more group of Sentinels were spotted. On Wednesday Storm was able to destroy two groups of Sentinels. On Thursday 8 more Sentinels were sent out. That afternoon, Cyclops got a tip that the total number of Sentinels headed for the school was the same as one group of Sentinels plus 18 Sentinels. How many Sentinels are in each group?
4. 4x- 2x +3 = 2x+ 2x -x
5. 7x – 5x + x + 4 = 3x – x + 8
6. x – x + 4x + 6 = 2x + 26
7. 4x + 7 – x = 2x + 10
8. 4x – 2x + 4 = x + 10
9. 8 + 2x + 3 – x = 2x + 1
10. x + 2x – x + 7 = 4x – x + 2
STUDENT ANSWER KEY:
1. Quantitative Meaning: 9
Referential Meaning: X-men
2. Quantitative Meaning: 2
Referential Meaning: years old
3. Quantitative Meaning: 10
Referential Meaning: sentinels
4. Quantitative Meaning: 3
5. Quantitative Meaning: 4
6. Quantitative Meaning: 10
7. Quantitative Meaning: 3
8. Quantitative Meaning: 6
9. Quantitative Meaning: 10
10. Quantitative Meaning: 5
CAMMP 2014 – Module 4
College of Education
Reading and Elementary Education
Names: Floyd, Michael and Pompée, Crystal
Integrated, Thematic Problem Solving Unit: X-Men: Days of Future Math
Grade Level: 6th
Arithmetic Topic (operation): Algebraic equations
HIERARCHY STEP # 7
Balance an equation using multiplication of constants and variables- Hands on Equations
THEME PROBLEM #
When Professor X’s vials of serum is increased by 2, and the sum is doubled, 16 is obtained. How many vials of serum did Professor X have?
Summary Table
Action Language: 2 sets of x joined with 2 equals 16
Open Number Sentence: 2(x + 2) = 16
Manipulative: Hands on equations
Quantitative Solution: 6
Referential Meaning: vials of serum
CONCRETE MANIPULATIVE:
REPRESENTATIONAL MANIPULATIVE: Hands on Equations
TRANSITIONAL ACTIVITIES: Computer Activities
Algetiles: Create and solve equations using the blocks
http://illuminations.nctm.org/Activity.aspx?id=3482