hey everybody we're going to be talking about fractions today and so here we're dealing with the definition of a fraction and you also need to make sure that you're reading the section so here is the definition of fraction from our textbook so the whole a whole is divided into b equal parts then the amount formed by one of those parts is 1 over B of the whole the fraction a over B of our whole is the amount formed by a part each is size one over B of the hole so we have a hole like say a whole candy bar and we're dividing it into let say our denominator is four so we're going to divide our candy bar into four each of our pieces of our candy bar is 1/4 of the whole and let's say I want three of those so three over four would be the the representation of the amount I have with a fraction 34s would be three of those fourth size pieces of the hole so activity 2A I do I work through in your u in on the video and that's something where we discuss um how to understand a fraction and how maybe the way that we learned how to understand a fraction of like if it's three fours three out of four um might be misunderstood in certain ways by students so make sure you watch the video where we talk about that activity now now some key components of a fraction We Have A over B A Parts each of size one over B of the unit amount so sometimes we focus on a parts each of size one over B okay and sometimes we focus on A over B of the unit amount so sometimes we P focus on 58 of a pizza or we focus on 58 pizzas okay so just keep that in mind that it just kind of depends on what we're talking about and what unit we're deal deal with what is our hole that is what's really key in understanding fractions so the size of the hole matters so Markus offered a choice of a third of a of a pizza or a half of a pizza because he's hungry and likes Pizza he chooses the half his friend Jan gets the third of a pizza but ends up with more than Mark how can that be so looking at this picture here right it depends on the size of your pizza you made the assumption that both pizzas were the same size but if you have a small personal size pizza versus a large pizza the half size of the personal Pizza is not going to be as big as the third size of the large pizza okay so knowing what the hole is matters activity 2f here's a video link for that okay and activity 2f you are looking at um you're looking at critiquing fraction arguments so um in this activ ity we talk about different um things that students could say and how that kind of changes um or how it it could be inaccurate or accurate depending on how you look at it activity 2H is the next activity and I have a video there for you as well in activity 2H this is fractions on a number line so that's a really good way to show students how fractions relate to each other is using a number line so make sure you're um watching that video and working that activity too now we have different ways we can model a fraction okay the first way is an area model so this is kind of what we're probably used to where you know you have a piece of or a pizza and you shade half of it that would be an area model we can use these types of manipulatives for area models so we can use circular pie pieces rectangular regions you can use a Geo board you can use Grid or dot paper you can fold paper just in general and then you can also use pattern blocks okay we also have area models but we have length models so length models we would use a ruler or folded pieces of paper or Quire rods and those are just set lengths with these certain rods so you know if I want using a ruler one and a half inches something like that I could just show that on my ruler so using uh length models is another way to represent fractions your third way to represent fractions would be with a set model so let's say you have two color counters or a set of objects um you can use fractions to represent how many of that set so for example down with the cars and the trucks right we have two3 are cars or six ns are cars or something another example would be like you know if you're in a classroom you say um a third of the people in the classroom wear glasses right so it's using fractions to repres represent a set we're not talking about area right we're not talking about length we're talking about individuals and what portion of them have some sort of characteristic now how do we interpret fractions greater than one so this is where our definition of a fraction comes in handy so proper fractions where the numerator is smaller than the denominator improper fractions is where the numerator is greater than or equal to the denominator so how does the Shaded region represent 5/3 or 56 okay so what we could do is we could view this and I need a hint hint hint this is something that's going to pop up on your exam okay but you can view this in two different ways you could view this as these two rectangles okay these two rectangles here are a hole so I have six pieces six equal pieces and I have five of the six five six shaded I also could view this as this is a hole and this is a hole so my hole was divided into three and I have five 1/3 pieces okay right now we can't say which is which because I haven't said what the whole is defined as now so if I said for example represent this picture with two different fractions 5/3 or 5 six would be valid way to represent it because you don't know what the unit is is the unit each individual one of these or is the unit the whole so equivalent fractions two fractions are equivalent if they represent the same number or if they are equal so if they represent the same number same thing is saying they're equal okay so in general one2 two fours 3 six 48 and so on are the same are equivalent fractions okay and here you can see you can multiply the numerator denominator by two or by three or by four or by five and I talk about that in one of the activities but this is a link to a video from your textbook about equivalent fractions and I suggest you look look at that it's actually uh a video made by the author of your textbook activity 2J is where we really get into equivalent fractions and explaining how that works so make sure you watch this video um click the link and then you can go and watch the video and I explain you know how when we multiply the numerator and the denominator by the same number what that is essentially doing you're multiplying by one so that's why we have equivalent fractions and so on so like the the meaning behind that and working through a couple of problems to break it down into something that students can understand and you can understand now comparing fractions we have different methods to compare fractions number one we could use decimals okay now be careful with this because some students haven't learned decimals yet so whenever you are comparing fractions you don't always want to default the decimals because decimals aren't something that they maybe have seen yet um so other methods and you need to make you know these other ways common denominators if you have a common denominator then you compare the numerators so if I have three six and I have four six I can tell which one's bigger you can also use cross multiplication whenever you're using cross multiplication and they get into this in your textbook you need to make sure you only use cross multiplication when there's an equal sign between the fractions do not use cross multiplication when you're multiplying fractions okay so your two fractions have to have an equal sign between them that's when you can cross multiply common numerators this is a way that you can compare fractions it's not as common as common denominators and cross multiplying common numerators is a way of thinking that if the numerators are the same so let's say you have 3 fths and 38 okay the numerators are both three so then you think about the size of the partitions of the whole based on the denominator so like I said I had 3 fifths and 38 so three over five and so if five is my denominator that means I took my whole let's say candy bar and divided into five pieces 38 means I took my whole candy bar and divided into eight pieces so my candy bar divided into eight pieces those little individual partitions is smaller than the fifth partitions right because I had to take my candy bar which is the same hole and divided in eight pieces versus five pieces so if my numerators are the same both are three my 3 fifths is going to be bigger than my 38s because my eighth size pieces are very small compared to my fifth size pieces all right and we talk about more that of that in your textbook um and then using benchmarks this is where you kind of Reason in your head what fraction is closer and then if you can use those kinds of benchmarks or um landmarks or things like that those kinds of numbers and then you can compare so like let's say a a fraction you have is closer to 1/2 and then the second fraction you're comparing is more close to 34s well you'll know that the second fraction is going to be bigger because it's closer to a larger value okay percentages this means of each hundred or out of a 100 so 35% would bean 35 out of 100 so some common percentages here Express as fractions so 25% % would be about a fourth or would be a fourth 50% is a half 75% is 34s 10% is a tenth 20% is a fifth and 5% is a 20th okay those are kind of interesting but make sure you kind of understand how fra how fractions relate to percentages and I have pictures down here to kind of show you how that works okay math drawings for that we'll get more into percentages a little bit later but this is just talking about how fractions uh fractions relate to percentages now how to think about basic percent problems so we have p over 100 equals the portion the portion over the whole amount or P percent of the whole amount is the that portion or the portion is p percent of the whole amount these are all different ways to think about this it's a helpful way to organize this information is use a percent table namely a table of this for uh this form P percent equals your portion like 35% of something right uh how much of that and then 100% is the whole amount right and there's some examples in your text now this is what you need to have done by 9:15 um we have what is a fraction activity and reflection you now keep in mind for the what is a fraction activity that is a separate file from your group of activities okay for chapter 2 it's a separate file it's a from a different textbook you you will need to use Quire rods or pattern blocks now we have you can if you have access to these handson it'll be a little bit easier but I also have links for digital versions of them and I have video links for you to see how they work okay so you're going to need to use que and er odds and pattern blocks for the what is a fraction activity you also have the reflection on 2 e and then you have problem set two and you have chapter two what were they thinking okay if you have any questions please feel free to email me um and yeah uh chapter 2 again doe 9:15 or do you know whenever it's due on the on canvas you should have it in your calendar