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Functions are of central importance in algebra, and problems based on functions form a major subset of questions appearing on the SAT/ACT. Wouldn’t it be awesome if you had a easy, reliable way to navigate straight to the answer to any question involving functions?  "GPS" will do it for you.  The acronym outlines three options that will help solve any function-related question on the SAT/ACT.  “G” stands for “graph.” (Would a graph be helpful?) “P” stands for “points.” (Could you use coordinates of specific points?) “S” stands for “substitute.” (Does a simple substitution solve the problem?) Looking at virtually any function question on the SAT/ACT through these lenses will quickly and easily reveal the path to the answer. Many times solutions can be found through simple visualization or basic pencil and paper techniques.  Otherwise, Desmos can be used to carry out graphing, locating points, or doing substitution. - For practice, search Google for worksheets coverin...

Functions are of central importance in algebra, and problems based on functions form a major subset of questions appearing on the SAT/ACT. Wouldn’t it be awesome if you had a easy, reliable way to navigate straight to the answer to any question involving functions?  "GPS" will do it for you.  The acronym outlines three options that will help solve any function-related question on the SAT/ACT.  “G” stands for “graph.” (Would a graph be helpful?) “P” stands for “points.” (Could you use coordinates of specific points?) “S” stands for “substitute.” (Does a simple substitution solve the problem?) Looking at virtually any function question on the SAT/ACT through these lenses will quickly and easily reveal the path to the answer. Many times solutions can be found through simple visualization or basic pencil and paper techniques.  Otherwise, Desmos can be used to carry out graphing, locating points, or doing substitution. - For practice, search Google for worksheets coverin...

Functions are of central importance in algebra, and problems based on functions form a major subset of questions appearing on the SAT/ACT. Wouldn’t it be awesome if you had a easy, reliable way to navigate straight to the answer to any question involving functions?  "GPS" will do it for you.  The acronym outlines three options that will help solve any function-related question on the SAT/ACT.  “G” stands for “graph.” (Would a graph be helpful?) “P” stands for “points.” (Could you use coordinates of specific points?) “S” stands for “substitute.” (Does a simple substitution solve the problem?) Looking at virtually any function question on the SAT/ACT through these lenses will quickly and easily reveal the path to the answer. Many times solutions can be found through simple visualization or basic pencil and paper techniques.  Otherwise, Desmos can be used to carry out graphing, locating points, or doing substitution. - For practice, search Google for worksheets coverin...

It seems our schools are always in trouble for this reason or that one.  This was not at all the case when I was a boy in the 1960’s. California public schools, K-College, were unquestionably the best in the world, and all were levels were free or very low cost. So it’s especially hard for boomers like myself to see the kite hit the ground like this. As a private academic coach for more that 45 years, I’ve tried to figure out what went wrong. I still don’t know, after all these years. And now, a sobering new trend is emerging. Teachers are leaving K-12 schools in droves. The reasons are many and various. But what I hear over and over again is that they boil down to several core issues: low salary, poor mental health, toxic work cultures, unsupportive administrations, lack of respect inside and outside school, lack of authority in the classroom, and out of control students and parents. I have no answer, but I do have suggestions. At a minimum: Pay teachers like doctors, require the...

It seems our schools are always in trouble for this reason or that one.  This was not at all the case when I was a boy in the 1960’s. California public schools, K-College, were unquestionably the best in the world, and all were levels were free or very low cost. So it’s especially hard for boomers like myself to see the kite hit the ground like this. As a private academic coach for more that 45 years, I’ve tried to figure out what went wrong. I still don’t know, after all these years. And now, a sobering new trend is emerging. Teachers are leaving K-12 schools in droves. The reasons are many and various. But what I hear over and over again is that they boil down to several core issues: low salary, poor mental health, toxic work cultures, unsupportive administrations, lack of respect inside and outside school, lack of authority in the classroom, and out of control students and parents. I have no answer, but I do have suggestions. At a minimum: Pay teachers like doctors, require the...

It seems our schools are always in trouble for this reason or that one.  This was not at all the case when I was a boy in the 1960’s. California public schools, K-College, were unquestionably the best in the world, and all were levels were free or very low cost. So it’s especially hard for boomers like myself to see the kite hit the ground like this. As a private academic coach for more that 45 years, I’ve tried to figure out what went wrong. I still don’t know, after all these years. And now, a sobering new trend is emerging. Teachers are leaving K-12 schools in droves. The reasons are many and various. But what I hear over and over again is that they boil down to several core issues: low salary, poor mental health, toxic work cultures, unsupportive administrations, lack of respect inside and outside school, lack of authority in the classroom, and out of control students and parents. I have no answer, but I do have suggestions. At a minimum: Pay teachers like doctors, require the...