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Added May 12, 2022 •

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Introduction to math problem solving

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all right you guys will come back sooner math Bridge lesson so today we are in the final lesson of our current unit which was about cost of living I'm so this is called introduction to math problems so we have three objectives that I'm person is going to be to ask the questions necessary to solve math problems requiring more than one math skill determine if an answer is reasonable use general math skills the world application apply across the board regardless of what lesson were in the the second one you know determine if the answer is reasonable and not apply in every case right so take a look at the overview says there are many different strategies you can use to solve math problems but not all strategies work well for all problem so that being said in others usually more than one way to solve a problem and I you know when I say oh there's a better way when I mean by better is it is it the order is a required less steps is it simple. That's why I referred to as a better method in this lesson will study different kind of real-world problems and discuss some ways in which they can be saw so it's going to be in a word word problem for men and will also consider whether or not the answers you find a reasonable all right so again that applies to every every problem solving a word problem and they're asking you something about distance was asking you about something about time and you get a negative answer right that's not reasonable right there's no such thing as as negative time or negative weights right you never you never watch time go backwards right are you never stepped on a scale and say oh you're negative whatever many pounds are in a doesn't exist in the physical world with any problem obviously the first step is to read it to understand it right once it is that usually you know if it's many sentences usually the law sentence is the question itself sometimes you know they said oh Sally and Harry work at a company where they make pencils even working there for 5 years Sally work 8 hours Harry work 5 how much is it work together on The Last Ship right all this contacts right which really isn't always necessary in order to answer the question the question is going to be in that last stand more than one so this is weird, right you know find out where the question is some sentences are going to have it relevant information they work at this company that's what they do fine right really matter what their name is what the company is in in the case for the example I gave her give me from asking the wrong question I always want to make sure you know what they're asking you you know even yesterday we are working on a discounts and 418 out of the 20 slides of the lesson we were figuring out the discounted price and then the last two slides they wanted to figure out the discount right which is different discounted prices how much you're paying discount is how much you're saving right so we're in the role of just find the final price final price I was about to submit an answer and I was like oh hold on they just want a discount write some sometimes easy to make a mistake like that it's all the problems are one you know you just keep stopping in and then they throw in one where they change the format to ask you for something different I'm allow you to see what information you are given right you need to see what information is already lighted so you can figure out what it is that you need to buy the question says what is it Mario asking you to find alright so let's first read the whole the whole problem but again usually the last sentence that's where the question is UCF what's Janice must walk 10 and a half miles this week in order to meet her goal of 60 mile walk this month how many miles must you walk each day if she plans to divide the remaining distance of evenly between so the question is asking what is the scenario asking you to find out so the question is what is the question also to the options the distance must travel in the last week of the month no number of days left to meet her goal know the number of miles per day walk to meet her goal yes how many miles she walk each day if she plans to divide the remaining distance up between six days so this is number of miles per day she needs to walk in order to meet the remainder of her 50 gold president for the end of the month all right so after we the problem we have an idea what they're asking us I want to write down the information we already know Sir Charles you know the 10 and a half miles six days you know in this case none of the numbers were really necessary for answering the and write we didn't do any mathematical calculations to answer the question right this question was a question about context they just wanted to know if we could identify properly identify a part of the problem okay so now we're to the same question so they want us to fill out these drop-down boxes do something formation we already have on the hiset we're not going to have this style of answering we have drop-down fill in the blank short answer however on the GED you do have the stuff out of the other answers for the goal distance that's in the first sentence meet her 50 miles so that's going to be 50 distance left to walk this month what's 110 / by Mi this week number of days she plans to walk 6 days miles remaining to walk each day miles to walk each of remaining dates equals blank miles per day so in this case they don't give us that information right obviously you be somewhere around you know somewhere between 1 to 2 mi right if she walked mile everyday for 6 days that's 6 miles right if she did to that be a little too much I'd be 12 miles by the end of the six days so it's going to be some number between one and two right but even though we can estimate what that number is probably going look like you know that's not provided to us here so out of all of these options that we have we also have a variable X so we're going to use this variable because they're asking us about him given in the problems so because that number is not given to us we can substitute it with a variable we also want to look out for keywords those are also known as mathematical operation words and here are some examples of it so these mathematical operation words indicate what operation we're going to be using so let me go through this list so some refers to addition in all Edition x is also Edition Kris is usually a addition however in some rare cases that could be multiplication for example what is 2 increased by three times its original size right also include 3 * 2 you could technically also applied multiplication most of time it's going to have to do it decrease is subtraction exceed that's going to also be subtraction is going to be a difference right so let's say if I have a word problem the speed limit is 50 miles per hour Tom was driving 65 how many miles per hour did he exceed the speed limit so it's going to be subtraction problem where you take his feet and protected from the speed limit to find out how many he was speeding or exceeding the speed limit if they wanted to find the area that's going to involve multiplication right at least if it's a you know if you're finding the area of a Square rectangle it'll just be multiplication if you need area of a triangle when you have to multiply first and then divide so you know what each of those cases does involve multiplication you know you can calculate perimeter through addition or you can use multiplication in some instances such as let's see if you have an equilateral triangle that means all the sides are equal then you could just take one side x x 3 and find your perimeter or ask where you could take one side x to find the perimeter but in any case you can always add all the sides together how many more that's also like a subtraction problem because that's similar to exceed so I can say for example team one Had Each player's team to only have four how many more players that someone had them team too so that's a subtraction problem 8 - 4 equals 4 or more players all right so back to the original problem you notice we're just using different aspects of interpreting math problems with that same problem okay so take a look at these phrases we have here right there asking us what key words from the scenario will help you determine the operation you must use to solve the problem rephrasing discussion is which one of the following phrases contains a math operation term right so here we have meet her goal divided evenly how many miles must walk so only one of these phrases a math operation term divided evenly that's the that's the operation word right key word right there so we know where none of these other phrases contain any math operation words okay we can also draw a picture or write an equation the picture sometimes helps to understand the problems right sometimes if you have a lengthy word problem a common one is you know talking about a person who's traveling around the city running errands right person Bob goes from his house to the pharmacy and then from the pharmacy to the grocery store which is on the same street and then go see for example Pharmacy is 10 blocks from his house the grocery store is 15 blocks East from the pharmacy and then he walks back to his house how many blocks if you walk in total so for a problem like that where you have components could be easier to just have a picture the house the pharmacy the grocery store draw how many how many blocks he walks to his first destination how many blocks the second blocks back home and they cancel it up so sometimes it's easier to have a visual representation write an equation I'll be even more, right specially when working with algebra you know here's a common problem you may have right person person a makes twice as much money as a person be in total there combined is $100,000 how much does a person a and a person be make sure you'd have to set up an algebraic equation you don't know how much person B makes so use a variable X you also don't know how much percent he makes so you know whatever they're the amount that they make is double the amount that person be makes to a person be makes x amount of dollars for a year then person a makes 2x twice as much so you to set up your equations with two X Plus x equals 100000 you combine like terms you have 3 x equals 100000 100,000 / 3 what ever you get as your answer that's how much person be makes you double that and then that's how much person a makes a year so that's just one common example of where you would need to set up an equation to to solve Ross in Wynnewood systems of system of equation frame that's what you some examples of a half price alright then maybe on the next page okay Jackson needs to hang a curtain over a 30 inch window the curtain is 36.8 inches wide is Jackson Center how much is a curtain will hang beyond the window Edge on each side okay you know they say you can draw it to help to help understand it a little bit better right you know on the task you have access to a wipe or like if you have a whiteboard you can use it so that may help but also it helps to to visualize a lot of the problem maybe you don't have time to sit there and you know drop multiple problems out if you have a lot of problems we're drawing does help but you can also do you know visualizer you know you see a window it doesn't matter what 30 in looks like just picture window and then picture turned in that is wider than the window so it goes past the window right Century here you have a 6.8 in not exceed the width of the window right so you have 618 in remaining and so if they were to center it then is that is 6.8 in would be split on both sides have 3.4 in on one side 3.4 on the other side let's see if they show us a drawing here next page so there it is the window seating at yeah this is a way to solve it right you can do it in half and then figure out how much I think the easier way is just take your total width of the shade subtracted from the window and divide your answer by two they somehow managed to to turn this into an algebraic problem which again not necessary right we talked about it the better way of solving it the better way is the easiest way me and my c e z u least amount of steps quickest if it doesn't have to be hard to break, it's just a subtraction and Division okay so acts over no problem she must walk two and a half miles and she has six days to do it so which one of these one of these letters has equation set up so that we would find her answer which one shows 10 and a half miles is being divided into 6 days perfect all right and then we finally solved the problem right so you know even though we were abused by jiffy it's not always going to be the case that you're going through five steps just to get an answer right there just being thorough in all the potential steps up it could be they're being very meticulous in The Break-Up example in this problem they they you no man should turn into an algebraic equation fireman right you could have just taken width of the cover subtracted from the window what are we have remaining / 2 because it's going to be on either side of the window that's only the remaining with the same answer 3.4 all right and then the final step is just us looking at the is this reasonable right remember I talked about for example if you had a word problem talking about time how long is it going to take to travel but let's let's say like for example let's say we have problems that says oh from Los Angeles to San Francisco it takes 8 hours to travel by car it takes half the amount of time to go to Baja California how many hours is it going to take to I get to Baja California if you end up with a negative answer somehow right let's just somehow you and you know that that's not reasonable because of the context of the question now if the question was about a bank account balance and you got a negative answer that's reasonable bank account balances can go into the negative right you can overdraw your account you can be in that right that does exist so it always has to be reasonable in the context okay. Ask me a question about a person's height and you don't answer that's a reasonable answer safe going to compare the question to the answer can be the difference between a right and wrong it yeah I think it's just a matter of being thorough right is everything look right cuz it look okay as it should let's look over the window example to see if it's logical we do this all the time right I mean imagine like let's say you have a joint bank account with someone and they and Lycia charge what's a $500 charge I'm just grabbing a lunch in between on my lunch break and you owe $500 for lunch like that doesn't make sense that's not reasonable listen to everyday like we know what to expect what seems logical reasonable typical and we do the same thing with Matt is this look okay to raise any red flags so yeah this looks perfectly fine right the combined all of these measurements it would equal 36.8 3.4 + 30 + 33.4 and if I had this other 3.4 that's going to take it to 36.8 so reasonable make sense we checked it out with the mask all right there doing the work there verifying everything's in order alright so let's drop this lesson up here we have the six steps that we reviewed first thing of course need to read the problem right you don't really you don't know what you're looking for right down the given information you know part of that process of stuff to write down the information is also determining what information is irrelevant you know you can think of some times when you need a specific answer someone's responding they giving you all this other details or information that's kind of relevant are you may have seen it when people go to testify in front of Congress and they go they awesome or no and then and then asking a question to go thank you Congressman person for the question yes I think it's very important that you do ask God and the American people deserve an answer and you know it's it's it's something that we know we really want every want to be clear on in regards to my position and it's just like is it yes or no right. That's what we're doing here with this information is this relevant or not right separating the information look for keywords also known as look for a math operation terms oh what is the sum of this what is the total what is the difference what is the product in all how many individuals were there how many more of option A was there than option be ran all of these math operation trips for if necessary you can draw a picture to help you visualize it again I would always always first recommend try try to imagine it first and then if you know if it's kind of a lot of information to hold then just go to the picture go to draw it too understandable of course number 5 the whole reason that we do it's all the prom and then 6 to take a quick glance make sure it's logical reasonable it's in with the parameters right we were talking a little bit about that lost in yesterday about discounts right now free sample of something was 30% off and one of the options is is half the price you know that's not reasonable there's no way you could be half the price of it's only 30 okay now they want us to solve it so we're just going 10.5 divided by 6 1.75 miles per day okay Cantley was selling her stock of free radios for 1595 each there's a coupon available five off every $50 purchase I mean readers will someone have to buy advantage of the coupon all right so they need to hit $50 right that's what they need a hit in order to get $5 off so you just take the $50 threshold you divide 1595 see how many do we have to buy it right now our answer is 3.13 for whatever similar to Pi almost this how many radios you would have to buy it right but we also have to think is this answer reasonable right could someone purchase a portion of a radio I know right you can't you can purchase of course you know I wouldn't make sense he or she would have to purchase for radios right the deal now if this was again context matters you know there's some things that you can purchase a portion of right like let's say I got the grocery store and you're buying something that goes on a scale right the fruits the vegetables on a scale if you're buying beans or grains in a lot of times you have the bags can you fill it up and put on the scale and that's how much you paid so in that case if they say oh how much would you need to get $5 off of $50 purchase one that cuz you know you don't have to necessarily by let's change it to pounds instead of radios you don't have to buy four pounds You by three points and you know 1347 whatever pounds of rice or whatever your bye but in this case you know no one's going to cut a radio into a into pieces and sell it John earns 450 for every in-ground pool installation he sells 253 per month 6 pools in March how much does he earn okay so this is his fixed rate right that's his fixed rate 253 from now so he's going to that regardless of 0 or 100 now he makes Commission of 4:50 to 4:50 is his commission for cool PCL 6 at the total of 2700 on top of that we're going to hide his fixed monthly rate of 253 what's going to be a total of 53 Rodriguez

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