6 5 1 Grade 6 Unit 5 Lesson 1 Morgan Open Up Resources

hey this is math 6 unit 5 lesson one using decimals in shopping context okay so we're going to use what we know about decimals to make some shopping decisions here so first of all we have snacks from concession stand and it says CLA went to concession stand that sells pretzels for $325 drinks for a85 and bags of popcorn for 99 each she bought at least one of each item and spent no more than $10 okay so she got at least one of everything and spent no more than 10 so 10 is the maximum amount that she could have spent there all right let's see what the questions are asking us here we have lots of dollar amounts here we also have decimal values here we notice here since we're playing with decimals we can make couple couple notes here that 325 is kind of you kind of estimate close to three but little more than three not much that 25 cents we have ways to go for $185 it's kind of close to more like two and if was going to estimate anything with 99 I'd probably just round it up and think of it as being about dollar right 1.0 if was estimating so the first question asks us here it says could Clara purchase this is could have just wondering could she have purchased two pretzels two drinks and two bags of popcorn and explain your reasoning Okay so you don't have to add everything up to figure this out it's just one of these could she so can you estimate little bit right you certainly could add them up right we could do three pretzel two pretzels and say well it's 325 for 1 and 325 for two we can add that up we could do the drinks and we can add up a185 and $185 for two drinks and we can add the popcorn at 99 each and add it up as well okay what we're also suggesting is maybe you don't have to add that up we know that she has to have total of something less than $10 if we estimated these at being somewhere like about $3 each that's like $3 plus $3 this we estimated being about more like $2 piece so that's $2 and $2 we're already at 6 789 $10 in estimating right there that's already $10 plus we have to add the two popcorns which is another dollar and dollar + one + one so just by estimating we would say that Claire has probably spent more than $10 do we know that for sure no we don't know that for sure but just an estimation we would say it looks like she most likely spent more than $10 now you can go ahead and add those up and verify that but probably there's not huge need for that because our estimate's going to be pretty close to the real answer if you add them all up actually what you end up with just as side note here I'm not going to add them for you but you end up with $12.18 if did my math right there right so our estimate was very close to the actual so you could prove that by adding them up if you chose to so we would say no she couldn't do all those things now could she had bought one pretzel one drink and five bags of popcorn well again remember our pretzel was $3.25 or about $3 our drink was $185 or about $2 and the popcorn is sitting there somewhere about dollar piece so five of those so 5 * 1 is $5 so we're sitting there right at about $10 so could she have done that we'd probably say yeah she probably could it's maybe not sure right it's maybe if we had to kind of estimate there it's really close it's matter of well what's going to be the difference here between this pretzel and this popcorn here right this is 25 cents over and this is 15 cents there's so there's difference here between those of about 10 cents okay in terms of estimation in fact we need to add an extra 10 cents there if we're going to not estimate okay so we take that we have to add an extra 10 cents well that's going to put us over already now the 99 cents is minus 5 cents because it's going to be 5 cents less for each bag so we have an add to 10 cents subtract to 5 cents and end up being total of 5 cents over your $10 limit so let's just see what that actually looks like okay we would do $3.25 pretzel right and then we would do $185 for the drink so we're there so far we also know that we have 99 Cents we have five of those so can actually multiply that out 5 * 9 is 45 and then 5 * 9 is 45 + four more is 49 notice that have two digits behind the decimal so I'll move the decimal here two spaces to get 495 so our popcorn is costing 495 now if add all those up making sure that line up all my my my place values here my ones my decimal my and hundreds 5 + 5 + 5 is 15 carry that one right there 9 + 1 is 10 and 8 + 2 is 10 so this becomes 20 so carry the two there then have 5 6 7 8 910 there for $105 so what do we notice we notice that she went over her $10 budget $10 budget by 5 which is what we also said right there so could she we would say no she couldn't do it here so this is definite no this one's lot closer but still no right there okay let's look at activity number two activity number two is little more complicated and so if you're doing this in class your teacher might be giving you some advertisements from newspaper actually just went to target.com to look up some prices for this activity but I'll show you that in minute it says if you're planning dinner party with budget of $50 so you have $50 for party and menu that consists of one main dish two side dishes and one dessert and there will be eight guests at your party choose your menu items and decide on the quantities to buy so you stay on budget if you choose meat fish or poultry for your main dish plan to buy at least half pound per person wow okay you use the worksheet to record your choices and estimated cost then find the estimated total cost and cost of person and see the example in the first two rows so basically this is deal you're having party for eight people right and you have $50 to spend on the whole party so think of it this way if have $50 and divide that by 8 8 goes into 50 it hold six times for 48 with remainder of Two and zero bring that down so you know have little more than $6 to spend so8 goes into 20 two times and there's 16 there's four so basically have $6.25 to spend on every person's dinner right I'm making dinner party that's my budget $50 $625 is what you can spend so let's see how you can do that that by creating an actual menu now first of all the budget for our guest we just did that is right now we said that we took our eight people and we took our budget and we divided that up and we end up with $6.25 because 6 * 8 is 48 we subtract we get two put decimal there put decimal there add zero bring it down for 20 8 goes in 22 times for 16 we subtract that for four bring zero down we have 40 and 8 goes into five 4 five times so we know that our budget is about $6.25 per guess is about what we should spend or what we can spend do we have to spend that much nope we can give them some cheap food and then save the money for going to the movies by ourselves later or who knows what so here's the idea first of all you have your main dish so went ahead and said I'm going to just do simple dinner and decided was going to do some chicken decided would do just some rice would do salad and so put looked up for seesar salad here and then wanted for dessert like the just had this for Thanksgiving actually really like the razzleberry pie it's Marie calendar pie and they sell it at Target too so just went to target.com and found some prices for some things now it said that we had to have remember the for the main dish if you used meat you had to have five lb for every person now because we're doing 8 people that meant that 8 * 5 is 40 and have one digit behind the decimal there so have to move this to one space there would need 4 lb of meat so if I'm do chicken need to have 4 lbs of chicken okay is what I'm going to need to have there for the rice rice depends on how you want to buy it but was able to buy one pound of rice in baggie and Caesar salad was able to buy two kits of Caesar salad and then one whole pie here now looking at target.com the chicken in the on the Target ad said that it cost $2.99 per pound that's what found in the advertisement when went to the chicken there so let's just see here well yeah that's what found so if multiply that out my estimated first here this is going to be four of those times about three so 4 * 3 tells me that's about $112 there for the chicken okay in terms of the estimated cost per person we would take the $12 $ and we would divide that by the eight people and 12 / 8 is going to be equal to on our case here $150 and you could use it with calculator or you could do it long division here the idea is that if you use long division we would do 8 and 12 ID 8 looks like this 8 goes into 12 one time 1 * 8 is 8 we subtract 12 - 8 is 4 so I'm not done yet put decimal here and immediately put decimal up top okay and we add zero and bring the zero down and eight goes into 40 goes in there five times and it goes in evenly and we have no remainder so we can add another zero there just to have placeholder for our money and we would say 12 8 is a150 so the chicken's going to cost $150 per person got it now the rice came in like big old bag of rice one pound of rice ended up costing 75 is what it costs for one bag of rice so rice is not too expensive now as an estimate here I'm buying one of those and it's about dollar okay so we're going to spend about dollar on Rice estimated there so if take my dollar and divide that by eight that's like taking again here's your eight and we're going to have $18 goes into one zero times put our decimal up right away eight goes into 10 two times I'm sorry two times one time sorry about that goes in there one time and so we have8 and we subtract and we have 10 - 8 is 2 bring the zero down 8 goes into 20 two times and so we have 16 is it can end up right well it's ends up being 0.125 can you have 0.125 no again it's an estimate so we could say something like either 12 cents or 13 cents let's just go with 12 cents for now okay well we'll do 13 just to round up since it's money so about 13 cents there is what it costs for rice for each person noticed that they sold kits of salad the Caesar salad kit all ready to go and kit cost $349 so if thought about this buying two of those would do two kits times about 350 left it at 350 because know that 350 * 2 is seven not too bad there so then if estimate 7 / 8 well 7 goes into eight how many times Well it goes in there once right seven goes into eight sorry other way eight goes into seven this way sorry about that it doesn't go into seven at all have to put our decimal point up right away and so 8 goes into 70 whole 8 times for 64 and we subtract and get six there and it goes into 67 times for 56 and again we're just estimating so we don't have to finish that out but we'd say it's about 87 cents person for the Caesar salad and the pie online it said it cost me $6.39 could buy one of those every day and just enjoy it so one times about six and left it at one Pi because usually you can cut pi into 8 slices right not the biggest slices but that'd be fine for party so 1 * 6 is 6 and again if take the $6 and divide it by8 then end up with in this case here about 75 okay so for my estimated total my estimated subtotal is all these things here that's going to be 12 + 1 + 7 + 6 so when add up 12 1 7 and six end up with about $26 is my estimated total my estimated cost per person is what happens when add up $150 and 13 and 87 and 75 and when add those up we have 0 + 3 and 7 and 5 that's going to be total of 15 there carry the 1 so 1 + 5 is 6 + 1 is 7 7 + + 8 is 15 15 + 7 is 22 so put two there in decimal carry two up there 2 + 1 is three still three still three still three so we have three so my estimated cost per person for this meal is $325 again the idea is here it says if you got did you get close to your budget if so go to next question if you do not change your things to make it closer again could change this could buy fancier rice or fancier side dish to get closer the main thing here just is because we're just using an example is didn't go over my budget did okay and that was our goal was to at least stay under and not you know have big debt for having party is this the best way to figure this out probably not you know realistically you know are you just going to serve chicken plain rice and salad and Pie probably not you probably want to put something on that chicken and make it taste little better you might want to add some of the rice to make it taste little better but anyways either way I'm staying under budget and I'm going to be okay all right the next thing says to calculate the actual cost of the two most expensive items and add them so when we do that there our two most expensive items in our case were the chicken at 2.99 pound okay and then let's just go with the and the the Caesar salad now the reason it's the most expensive is our estimate total is $12 $7 making the most so if we take our $299 pound chicken * 4 9 * 4 we have 36 so write that just like this and then 9 * 4 is 36 we add the other three for 3 9 have our decimal here still cuz we're doing money and then 4 * 2 is 8 + 1 3 more is 11 so it cost $1.96 for the chicken is what the actual cost would be and then for our our Caesar salad kits which are $349 each we're going to buy two of those so 9 * 2 is 18 4 * 2 is 8 + 1 more is 9 put our decimal here for money and 2 * 3 is 6 so 698 there then it wants us to add them together so we do $11.96 and we're going to add that to $6.98 6 * 8 or + 8 is 14 we have 9 + 9 is 18 + 1 is 19 carry the 1 and 6 + 1 + 1 is 8 and then one there so we have $1.94 for our two most expensive items so how will you know if your total cost for all menu items will or will not exceed your budget exceed means to do what exceed means to go over your budget it's going over your budget is there way to predict this without adding all the exact cost yeah we could do that for me know that I'm not going to exceed because was way under budget right was only estimated to be able to spend about $325 person that's not very expensive there and my total was total of $26 had $50 to work with so probably could have bought some nicer things and some nicer dishes maybe instead of chicken want to upgrade that to steak next time or maybe shop at super market that doesn't have low prices and so end up having to spend more so you're going to do different things depending on what you do and that's okay so summary today we often use decimals when dealing with money in these situations sometimes we round and make estimates other times we calculate the numbers more precisely so we can do estimates or we can do things precisely depends on what we're want to do with it so there are many ways we can add subtract multiply and divide decimals when we perform these computations it's helpful understand the meaning of the digits in number and the properties of operations we'll investigate the how these understandings help us work with decimals and upcoming lessons there so we're going to pause there let you work on your homework and we'll see you in minute after you do it on your own all right here we are for homework for math 6 unit 5 less than one says may had $14.50 she spent $435 the snack bar and 525 at the arcade what is the exact amount of money she has left okay so couple ways of approaching this here we can know that she has this amount and we could subtract that and then from that answer subtract that or we could combine these together for how much she spent and subtract that total from that either way you have to do couple different operations here I'm going to first of all go ahead and go Ahad and add those together to see how much she spent so she spent 525 + 435 that's what she spent 5 + 5 is 10 carry the 1 1 + 2 + 3 is 6 include my decimal 5 + 4 is 9 so know that she spent $960 she started with $14.50 and my goal is find how much she had left so to the 1450 and we're subtract 1450 we're going to subtract $960 from that one right there so 0 - 0 is 0 can't do 5 - 6 so have to borrow from here so that becomes 3 this becomes 15 15 - 6 is 9 keep the decimal there 3 - 9 can't quite do that so borrow there we have 13 - 9 which is 4 so how much money does she have left she has $4.90 again you could have done different order but you still end up with $4.90 as your solution right there number two large cheese pizza costs $7.50 Diego has $40 to spend on pizzas how many large cheese pizzas can he afford explain or show your reasoning well saying how it's just Diego he can really only afford one he shouldn't eat more than one whole pizza or else he might not feel good the next day but let's pretend that he can eat as much as he wants so if he had 750 the question is 750 times how many can get you close to $40 but really we don't want to be equal to $40 we want to make sure that we are what less than $40 okay that's what we're asking we want to make sure we don't go over our budget there so thought of it this way thought well if he was to buy two pizzas 750 * 2 would have total of decimal there $15 for two pizzas so know he can get two and thought well know that need to get the 40 so if two gets me to 15 then know that in our case here four because multiply this times two more would get me to 30 right so 15 * 2 is $30 so know that have two have four pizzas and I'm not not quite there yet can't do another two pizzas because 30 + 15 is 45 but could certainly do one more pizza for $37.50 so that's one more pizza there so in total it looks like he could order five whole pizzas now how you go about solving that that's up to you there are other ways of doing that but that's one way of looking at how you could figure that out number three tickets to show cost 550 for adults 425 students family is purchasing two adult tickets and three student tickets estimate the total cost sure all right well 550 and we have times we have about two of those people right we have two of those for 550 and the student tickets we have three of those so it's times about three of those estimating depends on what you want to do if you want to say that this is about 12 $6 each okay you could say this is about six so 6 + 6 is about $12 for the adult tickets this one here is about $4 * 3 which is another $2 so maybe about $24 is an estimate to find the exact cost we'd multiply this and 2 * 0 is 0 2 * 5 is 10 carry the 1 and 2 * 5 is 10 + 1 is 11 so the exact cost is $1 for the adult tickets plus and then we have 5 * 3 is 15 carry the 1 3 * 2 is 6 + 1 is 7 decimal place there and 3 * 4 is 12 so $12.75 when we add those up we can add them this way right here if we wanted to we end up with five 7 3 and 2 we have $23.75 is the total amount of the exact cost if the family pays $25 what is the exact amount of change they'll receive well change is found by taking how much you have and subtracting from that what you spend so we have to borrow here that becomes 10 we borrow from the 10 to make that nine and this becomes 10 so 10 - 5 is 5 9 - 7 is 2 keep our decimal place there and 4 - 3 is 1 and that's zero so the change would be a125 all right number four chicken costs $3.20 per pound beef costs 4459 per pound answer question and show your reasoning what's the exact cost of 3 pounds of chicken so here's our chicken we're going to multiply it by three 3 * 0 is 0 3 * 2 is 6 decimal point and 3 * 3 is 9 so you would say $960 how about 3 lb of beef we multiply 459 * 3 9 * 7 is 27 5 * 3 is 15 + 2 more is 17 carry the 1 17 decimals there 3 * 4 is 9 sorry 3 * 4 is 12 plus 1 more is 13 so our beef is going to be $13.77 right there how much more does 3 lbs of beef cost than chicken so we're comparing how much more something than something so we're comparing 137 7 and $960 and find out what the difference is going to be 7 - 0 is 7 7 - 6 is 1 decimal there and we do borrow 13 - 9 is 4 so the beef costs $417 more think back to our lesson today when we bought chicken in my menu thing the chicken kept the price down if had bought beef it would have cost more and my total rout increased all right number five how many 1/5 glasses can fill 1 and2 bottle of water so what we're asking is how many if have 1 FS glasses how many of those times how many of those would it take to get up to 1 and2 lers for bottle of water if have 1 of these glasses how many of those could have in order to get to that amount or as division problem this becomes what this becomes 1 and2 /5 = what I'm looking for all right that's my setup so 2 * 1 is 2 + 1 is 3 so we have 3 over 2 and instead of dividing I'm going to multiply by the reciprocal okay can reduce anything here not really so we multiply straight across 3 * 5 is 15 2 * 1 is 2 so have 15 over 2 is how many of those can use glasses can use or seven and half if want to make that mixed number all right okay question same kind of idea it's going to review from unit four how many 1 and 1/2 bottles does it take to fill 16 jug again same idea how many 1 and A2 things 1 and A2 time how many does it take to get to 16 or as division problem 16 / 1 and half equals what so this becomes 16 * the reciprocal 1 and half is the same as 3 over 2 but the reciprocal is 2 over3 all right so that's 16 over 1 multiply straight across cross 16 * 2 is 32 over 3 and 3 goes into 32 10 whole times with two left over so we would say 10 and 2/3 bottles of water to fill that jug all right number six number six all right use the grid to complete this problem now maybe because had the first edition book here not the second one it's not going to quite work out it says let the side length of each small square and each grid represent half of unit okay if do that honestly don't have quite enough squares there so made each Square for me made it represent one unit okay otherwise couldn't make it work right draw two different triangles each with base of 5 and A2 and an area of 19 1/4 all right so in order to find it to make that triangle work had to have base and the other element need to have for my area of triangle angle is height I'm going to zoom just little bit here have to have height as well and that's because remember area equals 12 of base time height and we got that because square is length time width or base times height and triangle is half of square so in this case here we have the area is 19 and4 is equal to half * base which is 5 and2 and we have no idea idea what that Height's going to be can't draw triangle until figure out what that Height's going to be so need to solve this problem first of all before can move forward so let's go ahead and do couple things here this one here we can rewrite this as it's an improper 4 * 19 is actually 76 + 1 is 77 so this becomes 77 over 4 is equal to half * and let's make this improper 2 * 5 is 10 + 1 is 11 so 11 / 2 * I'm going to gohe and combine these as my next step so have 774 = 114 * and so to get the by itself I'm going to divide both sides by 114 so put 774 / 114 = 8 and to solve that we do 774 * the reciprocal 4 over 11 and then can reduce reduce and 11 goes into 77 7 times and So my answer is seven for my height my height is going to be seven so now know have height of seven so this is where my base doesn't quite work out if this was each going to be well even my height if my Height's going to be seven if this was half how many would how many of these half things would need to get to Seven well it' be 7 * 2 which is 14 only have 1 2 3 4 5 6 6 7 8 9 10 doesn't work that's why changed it to be one unit long okay so not the end of the world just what it is so let's make triangle with base of 5 and A2 so I'm going to go out 1 2 3 4 5 and half and my height is going to be seven so we'll go up 1 2 3 4 5 6 7 and then we can connect this dot here make sure that's right angle cuz that's height so there's my 7 my 5 1/2 and my area is 19 and 1/4 so that's one triangle can make another sure can as long as want to make sure that the base is still 5 and 1 half I'll be okay so can go 1 2 3 4 5 and half and if remember as long as come down at 90° angle can make my height at any spot so can actually make it right here this is my height there and can connect DOT like this to make triangle like that and that becomes my triangle so this whole thing is 19 and 1/4 this is my height of and my base of 5 and A2 all right so why does each one have the same area well it has the same area of 1914 because it has the same base and the same height and that's just how it's found it looks different but it's the same idea and finally our last one here here find each quotient so 56 / 16 is the same as doing what it's the same as multiply by the reciprocal so that cancels that cancels and you're left with five here let's write this as improper 6 * 1 is 6 + 1 is 76 multiply by the reciprocal 12 over 1 so this reduces six goes in here one time six goes in here two times nothing else reduces so we're left with 7 * 2 is 14 and finally our last one we have 10 6 * reciprocal 24 over 1 and 6 goes in there one time six goes in here four times and 10 * 4 is 40 and that's it all right that's all for today have great one and we'll see you next time