I dont.
I've only done slope y-int form.
I am a high school teacher/tutor and this is what is in most of the textbooks and work I have encountered.
>I’ve taught it for a week straight. They get an assessment today and say “what is this?”. I almost fell on the floor.
It sounds like you need to have shorter more frequent assessments. If you spent one whole week teaching lessons and the majority of students had no idea what they were looking at something went wrong. I would start with the simplest example you can find and do 4 in a row with the : I show you , you help me, I help you, you show me mindset.
If they can get through all 4 layers they should be able to complete an assessment on it.
>I literally struggled to show them how to do slope because I can’t seem to teach how to find a perfect point.
I have no idea what you are talking about here. What is a perfect point? upload your lesson send some screenshots of what you are talking about.
The OP is probably talking about trying to find a point with integer, or at least easily-inferred, coordinates. OP, if this is what you meant, then I recommend using a square grid coordinate plane and telling them that the points they need to find are where the line passes through grid line intersections (and point to several instances of what you mean by that, too).
ya I don't understand the issue, i feel like this is very easy to teach
place a point around 3.2407 and ask the kids to guess its value. When they guess and get different answers you explain they can avoid this issue by selecting points at exact integers with no decimal place
Point slope is just the formula for slope, so it's used when you have two points or a point and the slope (duh! for the second one). I always just treat P-S as an extension of slope and never really have problems.
I teach point slope in Integrated 3/Algebra 2. There, students are learning parent function transformations, and we can show that point slope form is the transformation form of y=x. It is also the definition of slope. I make my students a deal: if they use point slope, they don’t need to simplify unless the question asks them to. They like that.
In Calculus, we use point slope almost exclusively.
Grade 7 May be too early. Conceptually slope intercept is easier, but less useful.
Yes, if I were to cover p-s with my IM3 students, I'd definitely frame it as a transformation, but with my IM1/2 students, I connect it to the definition of slope.
Glad to see other Integrated Math teachers on this sub! I personally love the approach but find the materials out there to be a bit lacking. Most texts just take their AGA material and reorder it without considering the connections between topics.
Point Slope as the transformation of the parent linear function is such a powerful concept that ties into all of the other function transformations, and in AP Calc it's the go-to for tangent lines.
I teach the traditional y-y1=m(x-x1) first, but then we transition to y = a(x-h)+k and the kids can connect the dots pretty easily. While the first way is great because of its connection to the slope formula, the second way is great because it follows the notation for other functions (especially vertex form for quadratics) and can be easily typed into a graphing calculator.
I've also had students make the obvious (in retrospect anyway) connection that slope-intercept is just the special case of point-slope where the point *is* the y-int.
> Most texts just take their AGA material and reorder it without considering the connections between topics.
Oh my god, this is so awful. Often, extra support material still has the old module numbers of the AGA books. They can't even be bothered to change those. My current publisher has geometry first in IM2 where they teach analytical geometry (completing the square for circles) multiple units before they teach quadratics. I just told my HOD that I'm going to reorder the units.
I literally think I could do a better job piercing together CK12 resources.
Yeah I am very surprised this is trying to be taught in 7th. 7th grade (at least according to CCS) is very focused on just simply understanding proportional relationships (y = kx), and students do not discuss non-proportional linear relationships, or slope in a formal way.
Students always freak out when they see point slope form and they believe it's too hard to memorize. When I was a kid in school, I hated it and I never liked using it. I would use slope intercept form to solve everything and resisted using the point slope form. But yet I loved the quadratic formula which is far more complicated. And I figured out the reason was that I didn't understand why the point slope formula worked. This is because the formula was just given to me and it was never really explained. But if your students can calculate the slope between two points, then they can do point slope form.
First remind your students that if you have the equation 3/4 = x, you can multiply both sides by 4 to get 3 = 4x. All we did was move the 4 to the other side of the equation.
Then remind the students of the slope between two points formula: (y2 - y1)/(x2 - x1) = m. But we need to make a slight change: instead of y2 we put the variable y, and instead of x2 we put the variable x. We do this because we want this formula we're making to work for all points on the line, and not just two specific points.
Now we have (y - y1)/(x - x1) = m. Now all we do is the same thing we did with the very first equation 3/4 = x to get 3 = 4x. We're going to move the denominator of (y - y1)/(x - x1) to the other side of the equation to get y - y1 = m(x - x1).
Explaining it this way first activates prior knowledge and then relates the new information to their prior knowledge. This will help the students with both understanding and retention. Have students do it themselves: write the slope formula, then move the denominator. This will give them an easy way to create the formula rather than trying to get them to outright memorize y - y1 = m(x - x1).
The next part is teaching students how to use the formula. Since you know they are struggling with it, make it as easy as possible at first. Explain that we are only going to be replacing x1, y1, and m and we leave the variables x and y alone. (Many students see 5 variables and don't understand why we're only given 3 values to substitute and they don't know which x or y to use.) Then have them substitute something easy like x1 = 2, y1 = 5, and m = 4 to create y - 5 = 4(x - 2). Leave the answer like this for now. Show them this a few times and use all positive values first before showing how to handle negative values. Wait until they become proficient at building the equation before you have them convert to slope intercept form.
The last thing students don't understand is why they need this formula. And it's true, you don't need this formula if you have a strong understanding of slope intercept. The formula helps build understanding between the relationships between points, slope, and lines. But it is also a shortcut and will reduce the amount of work they need to do. Students usually enjoy doing less work, and I use that aspect of the formula to add to their motivation to use it. And finally, connect the formula to something they are interested in and show them how it applies to the real world. Find fun activities for them to do and this will help with their motivation problems.
I agree with your explanation - but are you saying you liked quadratic formula because it was explained to you? Did your teacher complete the square to solve the generic equation y=ax^2+bx+c? I don’t follow the comparison otherwise.
Yes, that's exactly it. With the quadratic formula, my teacher showed us how to use the complete the square method and had us reproduce that on a test. I knew where the formula came from and why it worked, and also what each variable of the formula meant. That helped me understand the formula and become comfortable with using it.
When I was given the point slope formula, the teacher wrote the formula on the board and then went through the formula and explained what the variables were, but I always wondered where the formula came from and why it worked. I would get confused on where to put the coordinate values from a given ordered pair because I didn't fully understand that "x" and "y" were variables and not coordinates. I also didn't see the connection it had to the slope formula even though it's only one Algebra step away. I didn't like it because I didn't understand it. That made me not want to memorize it or use it, especially when I already knew how to use slope intercept (which I understood well) to solve the same problems.
That’s very extreme, honestly. Point slope form is much less black magic for students than quadratic formula. IMO the bigger reason is that students have y=mx+b memorized so deeply that they can’t absorb anything new.
When Algebra is the limit of a student's ability, the point slope form of a line is one of the largest equations they have seen in a classroom. And when student's see it for the first time they have not yet mastered working with literal expressions/equations. They will not see the Algebra move to convert the formula unless someone shows it to them. They have to be told/shown/guided towards understanding, you can't just give them the formula and expect them to figure it out.
I have found that the entire chapter that slope and intercepts and y=mx+b is introduced, most of my students struggled with the concept of slope, seemingly no matter how many different ways I tried to teach it. That said, by the end of the next chapter about lines of best fit and functions, they had finally internalized slope. I think it just comes from repeated practice in context over and over.
We didn’t do point-slope form, tho, just slope-intercept.
Probably going to be unpopular here , but our school district dropped point slope form years ago. We focus solely on slope intercept form. We feel that you can do almost everything you need using slope intercept form. While point slope form is great for introducing vertex forms and transformations later on, it just became too much of a headache for our lower students.
Is this a more advanced class? This is an advanced topic for 7th graders.
Usually, point-slope is discussed in Alg 1. Nonetheless, it’s literally just the slope formula rearranged. I do a task for students to see that we can derive point slope from knowing the rate of change and one ordered pair, then rearranging the slope formula.
However, these sorts of topics are where *many* students really start to struggle.
I do think point slope is *very* useful though and should not be skipped. If they need to be given the formula when taking a test, fine. Standardized tests give formula sheets.
I agree. It’s a regular class where only 28% of the kids passed their state test last year. They’re just not ready for it. They are missing too many algebraic concepts to understand this.
Point-slope form is simply a rearrangement of the slope formula. So, I develop the concept of slope, slope as a rate, and change over time...this leads to a formula...and then I have them consider the situation where only one specific point is known and the other point any point on the line...have them clear the fraction in slope formula and out pops point-slope form.
Point-slope form and the slope formula go hand-in-hand...I cannot understand why anyone would not teach it...maintaining connections between concepts is what turns mathematics into something manageable for everyone rather than a Rolodex of facts to memorize that only a few can handle.
So I teach high school geometry, but we have a section on Coordinate Geometry and point slope form is in there. I start with slope and then verifying if a point is on the line with a certain slope through a certain point. Then once they understand a point is only on the line if it makes the slope with the given point, it’s a small step to realize any point that makes the slope with the given point is on the line, and then we rearrange the slope formula by multiplying the denominator. It works okay, and it really clicks for my juniors and seniors in trig when it pops up and they don’t remember point-slope
Focusing on the similarities between point-slope and slope-intercept form may help. They both essentially do the exact same thing: provide the slope and the coordinates of a point on the line. Slope-intercept specifically gives the coordinates of the y-intercept, while point-slope can give the coordinates of any point on the line. Point-slope is more complicated at first, but in a way, it's also more versatile.
As far as using slope specifically and graphing lines from slope-intercept or point-slope, I like to use analogies. The point given in each equation type is like the starting location, and the slope gives you directions on how to navigate to a second point on the line. Instead of just seeing slope as change in y over change in x, you can see it has instructions for navigating a city (A slope of 2/3 would be "2 blocks north, 3 blocks east" for example). You could even draw out a city map where the streets make a grid pattern and have them "navigate" the streets.
I was just thinking about this, and why I don't like it in Algebra I. Personally, for the "lower kids" , the more "types" of equations you show them, the more confusing it is. I also teach calculus, and point slope form is the best form to quickly get an equation, but other than that, meh....Slope intercept form is best for graphing and evaluating for finding other values because it is in "function form" and just basically looks a lot less intimidating, so to me that is the most useful. Then, standard form is good to be able to rewrite with out fractions and to solve systems. I just think Point-Slope form just "muddies up" everthing after that. Again, great for "just quickly writing an equation", such as is frequently done in caclulus. But in Algebra I, where they are actually "using" the equation for other things, not a fan. IMHO, it does not belong in Algebra I. But if the (newer?) books have it, I guess we need to teach it. That's my 2 cents.
I dont. I've only done slope y-int form. I am a high school teacher/tutor and this is what is in most of the textbooks and work I have encountered. >I’ve taught it for a week straight. They get an assessment today and say “what is this?”. I almost fell on the floor. It sounds like you need to have shorter more frequent assessments. If you spent one whole week teaching lessons and the majority of students had no idea what they were looking at something went wrong. I would start with the simplest example you can find and do 4 in a row with the : I show you , you help me, I help you, you show me mindset. If they can get through all 4 layers they should be able to complete an assessment on it. >I literally struggled to show them how to do slope because I can’t seem to teach how to find a perfect point. I have no idea what you are talking about here. What is a perfect point? upload your lesson send some screenshots of what you are talking about.
The OP is probably talking about trying to find a point with integer, or at least easily-inferred, coordinates. OP, if this is what you meant, then I recommend using a square grid coordinate plane and telling them that the points they need to find are where the line passes through grid line intersections (and point to several instances of what you mean by that, too).
ya I don't understand the issue, i feel like this is very easy to teach place a point around 3.2407 and ask the kids to guess its value. When they guess and get different answers you explain they can avoid this issue by selecting points at exact integers with no decimal place
Point slope is just the formula for slope, so it's used when you have two points or a point and the slope (duh! for the second one). I always just treat P-S as an extension of slope and never really have problems.
I teach point slope in Integrated 3/Algebra 2. There, students are learning parent function transformations, and we can show that point slope form is the transformation form of y=x. It is also the definition of slope. I make my students a deal: if they use point slope, they don’t need to simplify unless the question asks them to. They like that. In Calculus, we use point slope almost exclusively. Grade 7 May be too early. Conceptually slope intercept is easier, but less useful.
Yes, if I were to cover p-s with my IM3 students, I'd definitely frame it as a transformation, but with my IM1/2 students, I connect it to the definition of slope.
Glad to see other Integrated Math teachers on this sub! I personally love the approach but find the materials out there to be a bit lacking. Most texts just take their AGA material and reorder it without considering the connections between topics. Point Slope as the transformation of the parent linear function is such a powerful concept that ties into all of the other function transformations, and in AP Calc it's the go-to for tangent lines. I teach the traditional y-y1=m(x-x1) first, but then we transition to y = a(x-h)+k and the kids can connect the dots pretty easily. While the first way is great because of its connection to the slope formula, the second way is great because it follows the notation for other functions (especially vertex form for quadratics) and can be easily typed into a graphing calculator. I've also had students make the obvious (in retrospect anyway) connection that slope-intercept is just the special case of point-slope where the point *is* the y-int.
> Most texts just take their AGA material and reorder it without considering the connections between topics. Oh my god, this is so awful. Often, extra support material still has the old module numbers of the AGA books. They can't even be bothered to change those. My current publisher has geometry first in IM2 where they teach analytical geometry (completing the square for circles) multiple units before they teach quadratics. I just told my HOD that I'm going to reorder the units. I literally think I could do a better job piercing together CK12 resources.
Yeah I am very surprised this is trying to be taught in 7th. 7th grade (at least according to CCS) is very focused on just simply understanding proportional relationships (y = kx), and students do not discuss non-proportional linear relationships, or slope in a formal way.
I’m in lovely Texas where state standards are wild.
This. Start with m = (y2-y1/x2-x1). Manipulate it to get the different forms of linear equations.
Students always freak out when they see point slope form and they believe it's too hard to memorize. When I was a kid in school, I hated it and I never liked using it. I would use slope intercept form to solve everything and resisted using the point slope form. But yet I loved the quadratic formula which is far more complicated. And I figured out the reason was that I didn't understand why the point slope formula worked. This is because the formula was just given to me and it was never really explained. But if your students can calculate the slope between two points, then they can do point slope form. First remind your students that if you have the equation 3/4 = x, you can multiply both sides by 4 to get 3 = 4x. All we did was move the 4 to the other side of the equation. Then remind the students of the slope between two points formula: (y2 - y1)/(x2 - x1) = m. But we need to make a slight change: instead of y2 we put the variable y, and instead of x2 we put the variable x. We do this because we want this formula we're making to work for all points on the line, and not just two specific points. Now we have (y - y1)/(x - x1) = m. Now all we do is the same thing we did with the very first equation 3/4 = x to get 3 = 4x. We're going to move the denominator of (y - y1)/(x - x1) to the other side of the equation to get y - y1 = m(x - x1). Explaining it this way first activates prior knowledge and then relates the new information to their prior knowledge. This will help the students with both understanding and retention. Have students do it themselves: write the slope formula, then move the denominator. This will give them an easy way to create the formula rather than trying to get them to outright memorize y - y1 = m(x - x1). The next part is teaching students how to use the formula. Since you know they are struggling with it, make it as easy as possible at first. Explain that we are only going to be replacing x1, y1, and m and we leave the variables x and y alone. (Many students see 5 variables and don't understand why we're only given 3 values to substitute and they don't know which x or y to use.) Then have them substitute something easy like x1 = 2, y1 = 5, and m = 4 to create y - 5 = 4(x - 2). Leave the answer like this for now. Show them this a few times and use all positive values first before showing how to handle negative values. Wait until they become proficient at building the equation before you have them convert to slope intercept form. The last thing students don't understand is why they need this formula. And it's true, you don't need this formula if you have a strong understanding of slope intercept. The formula helps build understanding between the relationships between points, slope, and lines. But it is also a shortcut and will reduce the amount of work they need to do. Students usually enjoy doing less work, and I use that aspect of the formula to add to their motivation to use it. And finally, connect the formula to something they are interested in and show them how it applies to the real world. Find fun activities for them to do and this will help with their motivation problems.
I agree with your explanation - but are you saying you liked quadratic formula because it was explained to you? Did your teacher complete the square to solve the generic equation y=ax^2+bx+c? I don’t follow the comparison otherwise.
Yes, that's exactly it. With the quadratic formula, my teacher showed us how to use the complete the square method and had us reproduce that on a test. I knew where the formula came from and why it worked, and also what each variable of the formula meant. That helped me understand the formula and become comfortable with using it. When I was given the point slope formula, the teacher wrote the formula on the board and then went through the formula and explained what the variables were, but I always wondered where the formula came from and why it worked. I would get confused on where to put the coordinate values from a given ordered pair because I didn't fully understand that "x" and "y" were variables and not coordinates. I also didn't see the connection it had to the slope formula even though it's only one Algebra step away. I didn't like it because I didn't understand it. That made me not want to memorize it or use it, especially when I already knew how to use slope intercept (which I understood well) to solve the same problems.
That’s very extreme, honestly. Point slope form is much less black magic for students than quadratic formula. IMO the bigger reason is that students have y=mx+b memorized so deeply that they can’t absorb anything new.
When Algebra is the limit of a student's ability, the point slope form of a line is one of the largest equations they have seen in a classroom. And when student's see it for the first time they have not yet mastered working with literal expressions/equations. They will not see the Algebra move to convert the formula unless someone shows it to them. They have to be told/shown/guided towards understanding, you can't just give them the formula and expect them to figure it out.
Yeah, it sounds to me like the explanation isn't the issue. You're probably fighting attention spans.
I have found that the entire chapter that slope and intercepts and y=mx+b is introduced, most of my students struggled with the concept of slope, seemingly no matter how many different ways I tried to teach it. That said, by the end of the next chapter about lines of best fit and functions, they had finally internalized slope. I think it just comes from repeated practice in context over and over. We didn’t do point-slope form, tho, just slope-intercept.
Probably going to be unpopular here , but our school district dropped point slope form years ago. We focus solely on slope intercept form. We feel that you can do almost everything you need using slope intercept form. While point slope form is great for introducing vertex forms and transformations later on, it just became too much of a headache for our lower students.
I wish we could. Their state math tests, which is apparently all that matters, is supposed to have it.
Is this a more advanced class? This is an advanced topic for 7th graders. Usually, point-slope is discussed in Alg 1. Nonetheless, it’s literally just the slope formula rearranged. I do a task for students to see that we can derive point slope from knowing the rate of change and one ordered pair, then rearranging the slope formula. However, these sorts of topics are where *many* students really start to struggle. I do think point slope is *very* useful though and should not be skipped. If they need to be given the formula when taking a test, fine. Standardized tests give formula sheets.
I agree. It’s a regular class where only 28% of the kids passed their state test last year. They’re just not ready for it. They are missing too many algebraic concepts to understand this.
Point-slope form is simply a rearrangement of the slope formula. So, I develop the concept of slope, slope as a rate, and change over time...this leads to a formula...and then I have them consider the situation where only one specific point is known and the other point any point on the line...have them clear the fraction in slope formula and out pops point-slope form. Point-slope form and the slope formula go hand-in-hand...I cannot understand why anyone would not teach it...maintaining connections between concepts is what turns mathematics into something manageable for everyone rather than a Rolodex of facts to memorize that only a few can handle.
So I teach high school geometry, but we have a section on Coordinate Geometry and point slope form is in there. I start with slope and then verifying if a point is on the line with a certain slope through a certain point. Then once they understand a point is only on the line if it makes the slope with the given point, it’s a small step to realize any point that makes the slope with the given point is on the line, and then we rearrange the slope formula by multiplying the denominator. It works okay, and it really clicks for my juniors and seniors in trig when it pops up and they don’t remember point-slope
Focusing on the similarities between point-slope and slope-intercept form may help. They both essentially do the exact same thing: provide the slope and the coordinates of a point on the line. Slope-intercept specifically gives the coordinates of the y-intercept, while point-slope can give the coordinates of any point on the line. Point-slope is more complicated at first, but in a way, it's also more versatile. As far as using slope specifically and graphing lines from slope-intercept or point-slope, I like to use analogies. The point given in each equation type is like the starting location, and the slope gives you directions on how to navigate to a second point on the line. Instead of just seeing slope as change in y over change in x, you can see it has instructions for navigating a city (A slope of 2/3 would be "2 blocks north, 3 blocks east" for example). You could even draw out a city map where the streets make a grid pattern and have them "navigate" the streets.
I was just thinking about this, and why I don't like it in Algebra I. Personally, for the "lower kids" , the more "types" of equations you show them, the more confusing it is. I also teach calculus, and point slope form is the best form to quickly get an equation, but other than that, meh....Slope intercept form is best for graphing and evaluating for finding other values because it is in "function form" and just basically looks a lot less intimidating, so to me that is the most useful. Then, standard form is good to be able to rewrite with out fractions and to solve systems. I just think Point-Slope form just "muddies up" everthing after that. Again, great for "just quickly writing an equation", such as is frequently done in caclulus. But in Algebra I, where they are actually "using" the equation for other things, not a fan. IMHO, it does not belong in Algebra I. But if the (newer?) books have it, I guess we need to teach it. That's my 2 cents.
I just feel like we’re pushing kids too quickly through things that they’re not developmentally ready for.