Properties covered so far:
- Commutative
- Associative
- Reflexive
- Symmetric
- Closure
- Transitive
- Distributive
- Identity
- Property of Opposites
- Property of Opposite of a Sum
Make a real-life example not shown in the videos you've seen for each property above. You will receive one point for each appropriate example. Make sure to include both of your names. Good luck, and be creative!
Commutative of Addition - Two people walk along the street, one goes first, and the other waits for the next signal. Tomorrow, the two people went to the same place. The person that waited yesterday went first and the person who walked first waited. They both got to the same destination anyway both days.
ReplyDeleteAssociative of Addition - there are two bikes (one with 2 seats. the other with just 1 seat)
a & b first ride the bike with 2 seats, and C rides the bike with 1 seat. Then, b & C ride on the bike with 2 seats, and a rides the bike with 1 seat.
Reflexive - A sheet of paper is still a sheet of paper even if you cut it in half.
Symmetric - Parents are related to children and children are related to parents.
Closure - Mushrooms and cream are unique, and they combine to get mushroom cream soup, which is also unique.
Transitive - Hee Sun and Brandon are friends, and Brandon and Andrew are friends. So, Hee Sun and Andrew are friends.
Distributive - you first drank mango juice then apple juice yesterday, and you drank both at once today, but it’s still the same thing.
Identity of Addition - If you add nothing to a cup of orange juice, then the cup of
orange juice is still a cup of orange juice.
Property of Opposites - Heaven and Hell are opposites. If they combine, nothing remains.
Property of Opposites in a Sum - One person’s house caught on fire. Another person’s house caught on fire. Then, those people moved into an apartment together. Then, the apartment caught on fire.
"Related" does not mean "equal to."
DeleteTransitive property does not work, because that is not necessarily true.
I like your Property of Opposites!
- Commutative
ReplyDeleteI eat pizza for lunch and rice for dinner. The next day, I eat rice for lunch and pizza for dinner. I ate the same food for both days!
- Associative
A boy and a girl have cleaned their desks. The boy puts his pencil and pen together, but puts his eraser in a different section. The girl puts her pencil and eraser together, but puts her pen in a different section. However, both of them have a pencil, a pen, and an eraser!
- Reflexive
In one building, the Hubba Bubba Candy Store sells one Bubba candy for $5. In another building, the Hubba Bubba Candy Store sells one Bubba candy for $5. The two Hubba Bubba Candy stores are the same stores!
- Symmetric
Lina is friends with Lola, so Lola is friends with Lina.
- Closure
A bread and a sausage makes a unique hotdog! a+b equals a unique real number!
-Transitive
Amina likes the same candy as Bell and Bell likes the same candy as Carol. I can conclude that Amina likes the same candy as Carol.
- Distributive
In France, people greet my giving “bises”, or kisses. Holly went to France and had to give 2 kisses to each of her two friends. k is the number of kisses Holly gave and b and c are her two friends. So, k(b+c) = 2(b+c)
- Identity
Sean had a box full of snowballs and another box filled with no snowballs. They are added together because he thought he would get more snowballs. However, there were only the number of snowballs in the box full of snowballs.
a+0=a
- Property of Opposites
There was a wizard who was fighting an evil wizard. They both attacked each other with their spells and they disappeared. a+(-a)=0
- Property of Opposite of a Sum
There were Sean and Will. They were both happy about their test results. Then, they fought saying that they were better than each other. So they both got mad and never talked to each other again, but they still had to be partners at school. -(a+b)=(-a)+(-b)
Symmetric: "Being friends" is not the same as "being equal."
DeleteDistributive: This does not show the distributive property.
Nice property of opposites!
Commutative - (Addition) You have math homework and a science homework and you have to finish them. You could finish math homework first that day or you could finish science homework first. Although the order changed, you get to finish all of your homework.
ReplyDeleteAssociative - (Addition) When you are eating salad, doesn’t matter whether you eat the tomato and the lettuce together and then eat the chicken. Or you eat the tomato first and then eat the lettuce and the chicken together.
Reflexive - Edward equals the reflection of Edward in the mirror. Edward is the same person.
Symmetric - If Edward’s math class partner is Grace, Grace’s math class partner is Edward.
Closure - Sausage and bread equals to HOTDOG!
Transitive - If hello and nihao (Chinese) means the same thing, nihao (Chinese) and bonjour (French) means the same thing, then hello and bonjour (French) means the same thing.
Distributive - If the test is given to Ken and Tim at the same time, they both eventually take the test. Also, if the Test is given to Ken and Tim at different times, they will still both take the test.
Identity - If someone had $100 and they were sick (they didn’t go to work), he didn’t earn any money that day. And he will still have 100$ that day.
Property of Opposites - Someone is playing on her drums. Drummers always have 2 sticks (1 in each hand). But during a concert the person who is playing the drum drops one stick in his right hand. (dropping a drum stick = negative) (left hand still has the stick = positive). With only one stick, you can’t in the concert. So no concert.
Property of Opposite of a Sum - You were riding in a car with your friend but a Mercedes Benz GLK SUV crashed with your car. You and your friend’s arm breaks. (This equals to...) You were riding in your car by yourself, you have a car crash with a Range Rover, you break your arm. And also your friend was riding in there own car, their car gets crashed by MY car and the Range Rover, which will break their arm too.
Reflexive property is the same as the videos we watched.
DeleteI like your transitive property!
Commutative: It does not matter if you eat a donut first than a cup of coffee or if you drink a cup of coffee than eat a donut second because in the end you have ate/drank both of them.
ReplyDeleteAssociative: If Ho Hsuan buys Apple and Pie in Store A, and bought baking soda in store B, and Jay buys apple in store A , pie and baking soda in store B, they will have the same things in the end
Reflexive: Ho Hsuan is Ho Hsuan always, because he is himself.
Symmetric: If you say that Ho Hsuan's textbook is the same brand as Jay's textbook, then you can say Jay's textbook is the same brand as Ho Hsuan's textbook.
Closure: For every parent it will produce an unique offspring, that is different from any other offsprings.
Transitive: If Hee Sun's pen is the same as Brandon's pen, and Brandon's pen is the same as Jay's pen, then Hee Sun and Jay's pen are the same.
Distributive: Mr. Jobe’s A block has X amount of people, and his B block has Z amount of people, if he wants to give 2 candies to everyone, he will need 2X+2Z candies.
Identity: Ho Hsuan scored X on his game, he played the game once, so he received a score of X.
Property of Opposites: If Jae pushes a chair with 20 KG of strength, and Ho Hsuan pushed it back with 20 KG of strength, the chair would be back in the same spot.
Property of Opposites of a Sum: Jay had 3 erasers, and Ho Hsuan had 5 erasers. They decided to store the erasers in one container altogether. Unluckily, they lost the containers, losing all the 8 erasers. Jay and Ho Hsuan individually bought 3 and 5 erasers each and stored them separately. Still, they lost all the erasers in the end.
Your distributive property example does not demonstrate the distributive property completely.
DeleteI like your property of opposites example!
Commutative:
ReplyDeleteEric put on the left shoe first and the right shoe second, yesterday, he wore the right shoes first and left shoes second. No matter the order, Eric still wore both shoes.
Associative:
Eric ordered a 3x3x3 Rubik's cube which was $23, a 4x4x4 cube which costs $30 and a 5x5x5 cube which costs $37. No matter how he adds the prices, he still needs to pay the same amount of money.
Reflexive:
Christina is sick today. However, a day before yesterday, Christina was spirited and healthy. Even though, Christina was sick or not. No matter what I do or what I’m being. I’m still the same person. I’m Christina! Sick Christina and Not sick Christina equals the same person which is Christina!
Symmetric:
If D# is E flat than E flat is D sharp.
Closure:
Eric’s mom wants coffee. Therefore, Eric made it for her. Eric mixed hot water with coffee mix and got a coffee not a lemonade.
Transitive:
1. Brownie Leaf and Choco Leaf came from same tree. If Choco Leaf and Barnie Leaf came from the same tree too. Then, Brownie Leaf and Barnie leaf came from the same tree too.
2. If group "Christina" defeats group "Eric,” and group "Eric" defeats group "Sebin" then group "Christina" will have to defeat group "Sebin."
Distributive:
Christina wanted to eat beef so she went to eat beef. Eric wanted to eat beef so he went to eat beef. Christina and Eric both wanted to eat beef so they went to eat beef together. Together and separately they both eat same amount of beef.
Identity property (multiplication):
Christina’s mom gives Christina $50 per week. How much money Christina gets per week? $50*1=$50
Property of Opposites:
Let soda equals positive. Let vinegar equal negative. There was some soda in beaker and as Christina pour the vinegar to soda. It explodes which equals 0 meaning that no one wants to drink.
Property of Opposite of a Sum:
Christina and Eric ate hamburger together. Hamburger bread was in spoil so they both have a stomach ache. Christina ate hamburger bread which was stale so she had a stomach ache. Erica ate hamburger bread which was stale too. Therefore, he had a stomach ache. Even though Eric and Christina ate together or separately, they both have a stomach ache.
I LOVE your symmetric example!!!
DeleteYour associative property example is not specific enough.
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ReplyDeleteHee Sun Kim & Brandon Park
ReplyDeleteCommutative: a+b=b+a
ex) They are still the same whether you do science homework first and math homework or if you do math homework first and you do science homework.
-math and social studies homework are both due next day
Associative: (a+b)+c = a+(b+c) a: coffee b: milk c: sugar
ex) They are still the same whether you pour coffee and milk together and add sugar or you prepare coffee and you add the mixture of milk and sugar into it.
Reflexive:
ex) This Brandon is Brandon because he is himself.
Symmetric: if a=b, then b=a
ex) If Brandon’s Korean name is H.Y then H.Y is Brandon
Closure: There is only ONE and ONLY ONE possible answer when you add or multiply two real numbers
ex) Tons of Homework due next day means less sleep.
Transitive Property:
ex) If Lina is my friend and Sebin is also my friend, Lina and Sebin are friends, too.
friends: same age.
Distributive:
ex) If there are two cages of monkeys in the zoo, one is called cage a and another one is called cage b. Zookeeper wants to give 6 bananas each.
Identity: a * 1= a
ex) If you give a candy to a kid, the kid will still be same the kid.
Property of Opposites
ex) If you had $5 in your bank account and you used $5, you have no money in your account.
Property of Opposite of a Sum
ex) Student A had 3 phones and student B had 2 phones, but they got caught by the teacher so now in total student lost 5 phones by the teacher.
-(3+2)= -5
I like your associative property example!
DeleteTransitive: This is not always true.
Distributive: This does not represent distributive property yet. Keep explaining.
Identity: How is this multiplying by one?
Opposite of a sum: This does not represent the property.
Commutative- When your making a salad, the order in which you cut the vegetables do not matter.
ReplyDeleteAssociative- When you are riding a sled if you sit in the front and your mom sits behind on the same sled, and your dad sits by himself in the back, it is the same as you riding in front on one sled, and your mom first and your dad in one sled.
Reflexive- If there is a chocolate and it melts it’s still a chocolate.
Symmetric- If your mom had a car accident with a Taxi driver, the Taxi driver had a car accident with your mom.
Closure- If you add heat to a cracked egg, it will always equal a fried egg.
Transitive- There are three puzzles: Puzzle A, Puzzle B, and Puzzle C. Puzzle A Fits well with Puzzle B. Puzzle B first well with Puzzle C. Therefore, Puzzle A also fits well with Puzzle C.
Distributive- House A was flooded and House B was flooded too, then House B and A are both flooded.
Identity - There is a cup of water. You pour the water into a different cup. It is still a cup of water.
Property of Opposites - If there is a healthy person, and someone with diseases affect them, then the healthy person will turn sick, being the opposite of healthy.
Property of Opposite of a Sum - A mean person talks to two kind people at the same time, and turn them into mean people. This is the same as the mean person talking to each of the kind person separately.
Symmetric: But are these equal?
DeleteProp of Opposites: This does not represent the property of opposites.
I like your closure property example!
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ReplyDelete* SARAH & JUN 8A*
ReplyDeleteCOMMUTATIVE
a+b = b+a
A girl played and then did her homework, the other day, she did her homework and played. Her order of her schedule is different, but things accomplished was the same.
ASSOCIATIVE
a+(b+c) = (a+b)+c
An orange was put in the blender, then sugar ice was later put in. The next day, orange and sugar were blended together, then ice was later put in. The procedures differed, but they both made orange juice!
REFLEXIVE
a=a
A pen produces a red ink, and another pen produces red ink, so they are both red pens!
SYMMETRIC
a=b, b=a
If orange, sugar, and ice is mixed, it produces orange juice! Then, orange juice is made out of orange, sugar, ice.
CLOSURE
a+b=c
Blue paint and yellow pain is mixed, then it will make green paint, not a white paint!
TRANSITIVE
a=b, b=c, a=c
Mr. Myer is a math teacher, so is Mr. Forrestal. Mr. Forrestal is a math teacher, and so is Mr. Jobe! That means that Mr. Myer and Mr. Jobe are both math teachers.
DISTRIBUTIVE
a(b+c)=ab+ac
A commercial paper was given each to person B and C. Now, they both have a commercial paper each!
IDENTITY
a+0=a
Today was Jun’s birthday. Sarah gave Jun two big presents, but no one gave him anything else. He got two presents in total.
PROPERTY OF OPPOSITES
a+(-a)=0
A cat and a dog fought, and they both died. They are now, nothing.
PROPERTY OF OPPOSITES OF SUM
-(a+b)=(-a)+(-b)
Sarah and Jun borrowed money from the bank, separately. It is the same as them borrowing the same amount of money together.
I like your symmetric and closure properties!
DeleteDistributive: Does not represent the property.
Transitive: Almost, but does not completely make sense.
Opposites: Cats and dogs are opposites? Hmmmm...ok.
Commutative Property: In the lunch line there was Jack, Jill, and Mr. Jobe, in order. Jack was in line first then Jill, finally Mr.Jobe was at the end of the line. Mr. Jobe very hungry cut in line and went in front of Jack, but Jack who was very generous didn’t care a bit.
ReplyDeleteAssociative Property: There were three dogs out in the field in order , Papillon 1, Papillon 2 and a Papillon 3. The owner of these dogs wanted Papillon 1 and Papillon 2 to breed, so the owner put a fence around Papillon 1 and Papillon 2, but the owner found out that Papillon 1 and Papillon 2 were both male dogs. So, the owner put the fence around Papillon 2 and Papillon 3, and it worked out. (*Their order didn’t change.)
Reflexive Property: The fire hydrant in Mr. Jobe’s room is the same as the one down the hall so both fire hydrants are the same.
Symmetric Property: Mr.Jobe and Ms.Anderson took a math test. They decided that the person who gets the lower score to buy lunch. After they took the math test, they compared their marks but, it turned out that they both got 100%. Mr.Jobe got 100% and Ms.Anderson got 100% so, Mr.Jobe’s score equals to Ms.Anderson’s score and Ms.Anderson’s score equals to Mr.Jobe’s score.
Closure Property: Daniel was hungry and wanted to eat a peanut butter sandwich. To make one, he need peanut butter and bread, added together to create a unique sandwich, Peanut Butter sandwich.
Transitive Property: Jack sat on a pink chair, but the chair broke because he was too heavy. Then, Jack sat on a yellow chair, but again the chair broke. Lastly, he sat on a blue chair, but that one broke too. Let’s suppose that the pink chair=a, yellow chair=b, blue chair=c. a=b, because they are both broken, and b=c because they are both broken too. Hence, a=c.
Identity: There was a piece of cracker. A baby came and broke the piece of cracker to little pieces, but did not actually eat them. Though, the baby broke the cracker into little pieces, the broken pieces and the piece of the original cracker will be the same. Here, let’s suppose the piece of a cracker is a and the breaking action is 1. a*1=1
Property of opposites: Serena wanted to buy a new camera, so she went to a shop. The salesman said that the camera was $3000. Serena checked her accounts, but her whole money she possessed was $3000, but anyways she really wanted to buy it so, she bought it. Let’s put the money Serena possess as +3000 and the money she paid as -3000. Ergo, +3000+(-3000)=0.
Distributive Prop of Addition: A mother gave her son a lollipop, but since she didn’t give one to her daughter, her daughter began to cry. So, the mother went to the store to buy a lollipop. Ergo, the mother gave both her daughter and her son a lollipop, each.
Property of Opposite of a sum: Edward and Bella did a project together, but they failed the project. Edward and Bella failing the project together, is the same as Edward failing the project and Bella failing the project.
I like your associative property example!
DeleteIdentity: How can the breaking action be one? This does not represent multiplying by one.
Distributive: This does not completely represent the distributive properly, where the multiplying by a sum equals the sum of the products.
Commutative: Angry birds, it doesn’t matter whether the order of birds change, it attacks same.
ReplyDeleteAssociative: Mom simultaneously called and drove , and got out and messaged. Next day, mom called someone, then got into her car and messaged as she drove the car.
Reflexive: The pants that Spongebob wore today, and the pants that Spongebob will ware tomorrow.
Symmetric: Today, with chocolate, marshmallows and crackers, you made S’mores. The next day, a friend of you gave you a S’more, but since you ate it yesterday, you wanted to eat chocolate, marshmallows and crackers separately, so you separated it and the S’more became back to chocolate , marshmallow and crackers.
Closure: Light bulb + electricity= light!
Transitive Property：If Road Coke parallel Road Sprite. Road Sprite parallel Road Tea. Road Coke parallel Road Tea.
Distributive Property : If my mother give me 1000 yuan in the morning and 1000yuan in the afternoon and it lasts a week. It is the same as she gives me 2000yuan at night and lasts a week.
Identity Property : You had 5 leads in you sharp pencil, but you wanted to put more lead inside it. So you tried to put it in, but there was no space to put it in, so there were 5 leads in the sharp pencil.
Property of Opposites : White plus Black is grey.
Property of Opposite of a Sum I spend $a +$b(I bought 2 things) in the supermarket.
The next day I go to supermarket twice. The first time I spent $a, the second time, I spent $b.The cost of two days is the same.
I love your associative and reflexive properties, especially the SpongeBob example.
ReplyDeleteProperty of Opposite of a Sum: How is this example like distributing a negative?