Place between 35 and $40, and he charges eight cars, it looks like he's charging $60. It looks like he's charging, well it looks like some The points on theįollowing coordinate plane show how much Drew chargesįor two, five, and eight cars. Drew charges a set rateįor each car he washes. Here we're told DrewĮarns money washing cars for his neighbors on the weekends. Every time we add anotherīatch, we're gonna have eight more cups of flour,Įvery time we add a batch, eight more cups of flour. Every time we move one to the right, we're gonna move eight up. You could connect them all with one straight lineīecause we have a fixed ratio. Of flour are constant, that all of these points, And what you'll see,īecause the ratio between our batches and our cups Going to have to bring that to 24 which is right here and I can see the 25 right above that. We are going to need 24 cups of flour, and thatĪctually goes slightly off of our screen here, let We're going to need 16 cups of flour so that puts us right over there, that's 16. So one batch, this isĮight right over here, five, six, seven, eight, and then for two batches, On the horizontal axis that is our batches, and So we wanna graph one batch, eight cups, two batches, 16 cups, Plot the ordered pairs x comma y from the table So instead of eight, it wouldīe eight times three, or 24. The number of batches, it would be three times the Well if he has twice as manyīatches, he's gonna have twice the number of cups of flour. So if you have two batches how many cups of flour would that be? Pause the video and try to figure it out. So they're saying that for every batch, he needs eight cups of flour or he needs eight cups Make one batch of muffins for his bakery. Thus, 5th grade ends with additional cluster content, but that designation should not diminish its importance this year and for years to come.- We are told that a baker uses eight cups of flour to This then deeply informs students’ work in all high school courses. This work is an important part of “the progression that leads toward middle-school algebra” (6-7.RP, 6-8.EE, 8.F) ( K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, p. This visual representation allows for a rich interpretation of these contexts (MP.2, MP.4). Then, after students have grown comfortable with the coordinate plane as a way to represent two-dimensional space, they represent real-world and mathematical situations, as well as two numerical patterns, by graphing their coordinates. After a lot of practice identifying the coordinates of points as well as plotting points given their coordinates with coordinate grids of various intervals and scales, students begin to draw lines and figures on a coordinate grid, noticing simple patterns in their coordinates. Thus, students start the unit thinking about the number line as a way to represent distance in one dimension and then see the usefulness of a perpendicular line segment to define distance in a second dimension, allowing any point in two-dimensional space to be located easily and precisely (MP.6). Students’ preparation for this unit is also connected to their extensive pattern work, beginning in Kindergarten with patterns in counting sequences (K.CC.4c) and extending through 4th grade work with generating and analyzing a number or shape pattern given its rule (4.OA.3). Then, in 4th Grade Math, students learned to add, subtract, and multiply fractions in simple cases using the number line as a representation, and they extended it to all cases, including in simple cases involving fraction division, throughout 5th grade (5.NF.1-7). For example, two fractions that were at the same point on a number line were equivalent, while a fraction that was further from 0 than another was greater. Then in 3rd Grade Math, students made number lines with fractional intervals, using them to understand the idea of equivalence and comparison of fractions, again connecting this to the idea of distance (3.NF.2). Students were introduced to number lines with whole-number intervals in 2nd grade and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5-6). Students have coordinated numbers and distance before, namely with number lines. In Unit 7, the final unit of the 5th grade course, students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations.
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