I love how you break down this problem! Sometimes in these types of problems, I find myself trying out random numbers, so this video was very helpful in showing me how to solve problems like this more efficiently.
The step by step process is really helping me with these problems. I never knew where to start and this technique makes the problems less intimidating.
I really enjoyed how upon first reading this problem, you went directly to explaining what an integer is...because if you don't know what a problem is asking then your chances of being able to solve it go down! First identifying what integers are then going back and using an example of a positive integer and testing it out to see which solution yields another positive integer was a great way to solve this problem correctly.
Understanding the vocabulary for this problem is essential for understanding how to solve the problem. An integer is a positive or negative number that is divisible by 1 with no remainder. Knowing this vocabulary will help me on my test. I really like the idea of plugging in a number to see what fits. That is a very smart move!
I really loved that you went through each answer and showed different examples for each of why they don't work. It shows how important it is to look for the key words in the question.
Thank you so much for throughly explaining what an integer is and providing examples. That really helped. It also helped when you explained why something was not an integer.
I really liked how you highlighted the key words, and then applied positive integers into every option to detect which one checked out. Great explanation!
I like how you go through each multiple choice option and explain the reasoning why something is correct/incorrect. This was a good refresher about integers as I hadn't reviewed it in a few weeks.
I liked how you explained to first look at the word integer. Sometimes I get caught up in that an integer actually is rather than just a number divisible by 1 with no remainder. Looking at the problem this way really helped me to focus on the task.
I had a hard time the first time i saw it on the test, but once i reviewed it again and seeing the video going through each one of the examples step by step; it made things a lot clearer.
Great! So helpful because you review what an integer is (as well as some other number terms). I also liked that you go step by step through each possible answer choice.
Learning about key terminology that has been lost from my mind for years is helpful. Without understanding what an integer really is you can't solve for P appropriately. Its is also helpful to see you work through problems and discuss the how and why of why they may be correct or incorrect.
Defining specific keywords in the problem is extremely helpful. Definitely makes process of elimination easier and solving the problem more efficiently.
This explanation of Integers really helped me. I tend to get confused with all of the vocabulary, so starting the video by defining the word was extremely helpful!
This video helped to refresh my memory on integers as well as different math symbols such as a radical. Showing the step by step process of plugging in a positive integer into each answer choice was also very helpful.
Again, I enjoyed that you broke the problem up, first showing all integers- then showing only positive integers. This really helped me to visualize what the problem was asking.
I really liked this video because I had no idea what an integer was and Chris explained it very well and I was able to understand it by having him write out each problem and explain why they weren't correct. It makes me want to focus more on mastering the vocabulary on this test.
Glad we're brushing up on integers/natural numbers...it's been a while. I'm not positive i wouldve known what either were before this video. I like how you went thru and plugged in more than one positive integer with the answers.
I appreciate you breaking that problem down, I didn't read the problem well enough and thought A was the right answer until you reiterated that we were looking for a positive integer.
Thank you for your comment Natasha! Keep making connections with the math (visual, key works, strategies...the more exposure you get will make a big difference at the workshop.). Keep up the good workshop. We will do more at the workshop. Chris Abraham ~ GOHmath.com
This problem was deceptively simple to me, but after going through the video and always going back to the definition of an integer "divisible by 1 with no remainder" and then considering the "positive" key word, helped me figure it out. I liked the way he showed me how to rule out all of the other choices.
This was a good reminder on what makes an integer an integer and natural numbers. I thought the explanations behind each possible answer were extremely helpful as it provided examples on what is and what is not an integer. This really cleared things up for me.
I struggled with this exact question before, and now that I understand what an integer is, it seems so easy. I have to remember to study my vocabulary more for this test.
I liked how you reminded us to test each answer with 2 different numbers because it showed me that one of the answers that seemed right wasn't right after I tried another number, which emphasizes the importance of using different numbers to double check before choosing an answer.
It was nice to get a better description of what an integer is. I always have trouble with these types of problems but the way you went through each of the answers helped me understand it better.
This was a helpful review on integers, and it reinforces just how important vocabulary is for these exams. I also found Chris' approach to this problem very useful and it didn't take much time at all to confirm the correct answer by using his method.
It was helpful that you went through this on a computer like the exam, and talking through it like I might do on the test day. It also shows that you need to understand all math vocab.
I appreciated that you briefly covered what an integer was (positive and negative). I am looking forward to reviewing all different types of numbers (natural, irrational, integers, etc.). Thanks.
I liked how you continued to work through each of the possible answers instead of stopping at what might seem to be the answer. It is always best to work on the problem all the way through.
Very helpful to review what the words in the question mean. Also helpful when you explain each answer and why it is wrong,then leading us to the correct one.
This is a great example! I have seen a similar problem on the MTEL the last time I took it and I am very glad that you laid out your thought process when solving!
Hi Chris, this video was helpful in defining what an integer is an is not. This was a good review of good test-tasking strategies such as eliminating incorrect answers and testing problems with the numbers 1,2, and 3 to quickly apply the principle featured in each question. Thanks!
Defining the key word "integer" right off the bat is extremely important in understanding the problem and coming up with the correct answer. Having not known the definition of an integer before watching the video, I learned what it means and how to find the right answer.
Chris, I find it very helpful to plug in a number, particularly for problems like this one. Great review of vocabulary, it was appreciated. This was great, thank you!
It was very helpful going through each possible answer by filling it in with possible numbers for P. Also by having you explain what an integer was made the problem easier to understand.
I initially got this question incorrect when practicing before the video. The video demonstrated how important it is to understand the mathematics terminology and how each problem did or did not answer the question. Thank You!
This video was a helpful reminder that knowing the vocabulary can sometimes be half the battle in approaching these questions. Without it I could be grasping at straws.
I like how you took the concept of positive integer and went through each possible answer and used your knowledge of what a positive integer was to find the correct solution. I also like how you tried multiple numbers which answers b-d to show that even if one example works as it did in b, that doesn't necessarily mean that it is the solution.
The explanation on what an integer was helped me to fully understand the question. Also the trial and error of placing numbers in the problems helped to find the right answer.
I like how easy it is to once the problem was broken down.Talking about what is an integer is and is not. Good reminder to try more than 1 to make sure of your answer.
I was able to apply the knowledge that any positive multiplied by another positive equals a positive to help me see that it must be option D. The definitions of an integer and connecting that to natural numbers was very helpful for me. Thanks!!
It was very helpful to review what an integer is and understand the vocabulary behind the problem. I like how you went through each of the possible answer choices to find the correct one. It was a helpful visual to see why A, B, and C would not work.
I found it helpful that it broke down the difference between what is a positive vs. negative integer and what is a natural number. The review of rational/irrational numbers was helpful too.I also think the strategy of plugging in with more than one example is something I need to remember.
Good refresher on integers. I also questioned whether zero was positive or negative when I tried the problem on my own before I watched. When I first opened the video I was intimidated but then realized how easy it was.
I'm really glad chris defined the word integer. I have a much better understanding of how to walk through a problem involving vocab words like integer, natural number, rational number, etc.
The explanation of the different types of numbers throughout the problem was helpful! Also, the reminder to try each answer twice is helpful. I always forget to do that because I get overwhelmed.
knowing the vocab for this problem such as integer is the most helpful part. being able to eliminate all negative numbers and focus on just positive numbers-
It really is so helpful having a video like this to refresh my memory on the ground rules of integers. Just by knowing the rules, I am able to solve this problem.
This video was a great review. It was easy to cross out B and C as the answer. At first, I thought A was the answer because I overlooked the POSITIVE integer in the question. Shows how easy it is to get the wrong answer if you don't read question carefully.
When I begin to study for this test I think I know the vocabulary but I always get things confused. I find it very helpful that you go into great detail with the vocabulary to enhance my learning of it.
I liked how you broke down the problem and identifying key words with the problem. I thought considering dividing by ten is a way I did not think about instead of just crossing out zeroes.
This video made me realize/remember what an integer is. Integers are positive or negative and divisible by 1 with no remainder. Looking forward to hearing more about irrational numbers and hoping for more help with the radical sign.
I realized that knowing the vocabulary is essential for understanding how to solve the problem. This was a good review. Also, plugging in multiple numbers was a good strategy.
This was helpful in refreshing my memory about positive integers. I also realized that it's important to try at least two ways to make sure that it's okay to eliminate an answer. No remainders and divisibility rules were also helpful reminders.
Understanding the vocabulary terms helps to understand what the problem is actually asking. It was helpful that you went over vocabulary terms such as. Integer, natural number, and irrational number. I've heard these terms before but didn't fully understand them.
I love how you break down this problem! Sometimes in these types of problems, I find myself trying out random numbers, so this video was very helpful in showing me how to solve problems like this more efficiently.
I love that you plug in numbers to every answer to help us see why we chose the one we do.
The step by step process is really helping me with these problems. I never knew where to start and this technique makes the problems less intimidating.
I really enjoyed how upon first reading this problem, you went directly to explaining what an integer is...because if you don't know what a problem is asking then your chances of being able to solve it go down! First identifying what integers are then going back and using an example of a positive integer and testing it out to see which solution yields another positive integer was a great way to solve this problem correctly.
It was very helpful to see how you broke down each answer and plugged the numbers.
Understanding the vocabulary for this problem is essential for understanding how to solve the problem. An integer is a positive or negative number that is divisible by 1 with no remainder. Knowing this vocabulary will help me on my test. I really like the idea of plugging in a number to see what fits. That is a very smart move!
I really loved that you went through each answer and showed different examples for each of why they don't work. It shows how important it is to look for the key words in the question.
Thank you so much for throughly explaining what an integer is and providing examples. That really helped. It also helped when you explained why something was not an integer.
I really liked how you highlighted the key words, and then applied positive integers into every option to detect which one checked out. Great explanation!
I like how you go through each multiple choice option and explain the reasoning why something is correct/incorrect. This was a good refresher about integers as I hadn't reviewed it in a few weeks.
I like that you test out each problem twice, great strategy
I liked how you explained to first look at the word integer. Sometimes I get caught up in that an integer actually is rather than just a number divisible by 1 with no remainder. Looking at the problem this way really helped me to focus on the task.
I like how you highlighted the key words, It was very helpful. Integers can be confusing, but its important to break down each problem.
I had a hard time the first time i saw it on the test, but once i reviewed it again and seeing the video going through each one of the examples step by step; it made things a lot clearer.
I like how you worked through each example of showing how a fraction or square root was not an integer.
Great! So helpful because you review what an integer is (as well as some other number terms). I also liked that you go step by step through each possible answer choice.
Learning about key terminology that has been lost from my mind for years is helpful. Without understanding what an integer really is you can't solve for P appropriately. Its is also helpful to see you work through problems and discuss the how and why of why they may be correct or incorrect.
Defining specific keywords in the problem is extremely helpful. Definitely makes process of elimination easier and solving the problem more efficiently.
loved how this video broke down each answer and explained why they were wrong! extremely helpful!
The video clearly breaks down the definition to help answer the question. So good!
This explanation of Integers really helped me. I tend to get confused with all of the vocabulary, so starting the video by defining the word was extremely helpful!
I like how you explained what an integer is and how it must be divisible by one with no remainder. That was very helpful to help answer this question.
I have seen this questions so many times before. I like that you broke it down into the vocab and then tested each choice.
This video helped to refresh my memory on integers as well as different math symbols such as a radical. Showing the step by step process of plugging in a positive integer into each answer choice was also very helpful.
I loved how you kept going if one worked just to see if other numbers worked as well.
Again, I enjoyed that you broke the problem up, first showing all integers- then showing only positive integers. This really helped me to visualize what the problem was asking.
I really liked this video because I had no idea what an integer was and Chris explained it very well and I was able to understand it by having him write out each problem and explain why they weren't correct. It makes me want to focus more on mastering the vocabulary on this test.
Glad we're brushing up on integers/natural numbers...it's been a while. I'm not positive i wouldve known what either were before this video. I like how you went thru and plugged in more than one positive integer with the answers.
I appreciate you breaking that problem down, I didn't read the problem well enough and thought A was the right answer until you reiterated that we were looking for a positive integer.
Knowing the vocabulary is important and I liked how you gave multiple examples. I also liked how you checked more then once. Good strategy to use.
Thank you for your comment Natasha! Keep making connections with the math (visual, key works, strategies...the more exposure you get will make a big difference at the workshop.). Keep up the good workshop. We will do more at the workshop. Chris Abraham ~ GOHmath.com
I like how you point out the question is asking for positive integers and how thinking about the vocabulary in the question can help you solve it
This problem was deceptively simple to me, but after going through the video and always going back to the definition of an integer "divisible by 1 with no remainder" and then considering the "positive" key word, helped me figure it out. I liked the way he showed me how to rule out all of the other choices.
This was a good reminder on what makes an integer an integer and natural numbers. I thought the explanations behind each possible answer were extremely helpful as it provided examples on what is and what is not an integer. This really cleared things up for me.
I struggled with this exact question before, and now that I understand what an integer is, it seems so easy. I have to remember to study my vocabulary more for this test.
I liked how you reminded us to test each answer with 2 different numbers because it showed me that one of the answers that seemed right wasn't right after I tried another number, which emphasizes the importance of using different numbers to double check before choosing an answer.
I like how you go through each option, and explain why it does or does not work. It really makes you think.
It was nice to get a better description of what an integer is. I always have trouble with these types of problems but the way you went through each of the answers helped me understand it better.
This was a helpful review on integers, and it reinforces just how important vocabulary is for these exams. I also found Chris' approach to this problem very useful and it didn't take much time at all to confirm the correct answer by using his method.
I like how you went through the vocabulary as you were working out the problem. It helped out a lot!
Love the review of math vocab that I haven't seen in years. It makes the problems so much easier.
You broke this down step by step and gave excellent explanations of key vocabulary terms.
I like how you went over what an integer is. I would have thought zero could be one and that would have made my answer wrong.
It was helpful that you went through this on a computer like the exam, and talking through it like I might do on the test day. It also shows that you need to understand all math vocab.
I liked the review on what EXACTLY an integer is, made the problem a lot easier!
This helps to show how much vocabulary is needed to help understand the questions on this exam.
It was really helpful to watch you plug in the numbers into each equation and show us to try it twice to make sure the answer is correct.
I appreciated that you briefly covered what an integer was (positive and negative). I am looking forward to reviewing all different types of numbers (natural, irrational, integers, etc.). Thanks.
I liked how you continued to work through each of the possible answers instead of stopping at what might seem to be the answer. It is always best to work on the problem all the way through.
Very helpful to review what the words in the question mean. Also helpful when you explain each answer and why it is wrong,then leading us to the correct one.
Watching you try out each possible answer is very helpful in understanding how you get the final answer.
This is a great example! I have seen a similar problem on the MTEL the last time I took it and I am very glad that you laid out your thought process when solving!
Hi Chris, this video was helpful in defining what an integer is an is not. This was a good review of good test-tasking strategies such as eliminating incorrect answers and testing problems with the numbers 1,2, and 3 to quickly apply the principle featured in each question. Thanks!
Defining the key word "integer" right off the bat is extremely important in understanding the problem and coming up with the correct answer. Having not known the definition of an integer before watching the video, I learned what it means and how to find the right answer.
I really liked how you explained the vocabulary and solved each of the answers.
the breakdown of the different choices was super helpful, and helps in attacking the problems to find the answer!
Chris, I find it very helpful to plug in a number, particularly for problems like this one. Great review of vocabulary, it was appreciated. This was great, thank you!
It was very helpful going through each possible answer by filling it in with possible numbers for P. Also by having you explain what an integer was made the problem easier to understand.
The video is extremely helpful not only as it explains completely the correct answer but also because it goes over why the other answers don't work
I like that you highlight the importance of knowing the vocabulary that is used in the math problems.
I initially got this question incorrect when practicing before the video. The video demonstrated how important it is to understand the mathematics terminology and how each problem did or did not answer the question. Thank You!
This video was a helpful reminder that knowing the vocabulary can sometimes be half the battle in approaching these questions. Without it I could be grasping at straws.
I like how you took the concept of positive integer and went through each possible answer and used your knowledge of what a positive integer was to find the correct solution. I also like how you tried multiple numbers which answers b-d to show that even if one example works as it did in b, that doesn't necessarily mean that it is the solution.
The break down of the terminology was really helpful and it was nice to visually see the difference in the definitions (integer & natural number)
The explanation on what an integer was helped me to fully understand the question. Also the trial and error of placing numbers in the problems helped to find the right answer.
I like how easy it is to once the problem was broken down.Talking about what is an integer is and is not. Good reminder to try more than 1 to make sure of your answer.
I like how you went through each possible answer and tried plugging in a few numbers to determine if the answer was correct.
It's important to understand the math terms before even trying to solve the problem. Thanks for being thorough!
I really enjoyed the review of math terms and the idea of plugging positive integers into the answer options to see if it works.
very helpful that you broke down the definition of integer, then went through each option to explain why it would/wouldn't work.
Defining the terms is helpful. It makes sense to try each option with multiple numbers to make sure you rule in or out your answer completely.
I was able to apply the knowledge that any positive multiplied by another positive equals a positive to help me see that it must be option D. The definitions of an integer and connecting that to natural numbers was very helpful for me. Thanks!!
I'm so glad this one went through answer by answer and explained why they didn't work. I needed a refresher on integers and this was helpful!
The vocabulary piece can be really hard for me but I love hearing the examples of integers and knowing that natural numbers are positive integers!
Your explanations make sense. I hope they start sticking with me when I try problems on my own.
I really like how you worked through this problem step by step. Very helpful!
Your explanation of what an integer is helped me successfully solve this problem. Thanks for the review on integers.
I like how you went through each option, proving why they worked or did not work.
Great review of integers. I like how you break the wording down and touch upon the vocabulary.
It was very helpful to review what an integer is and understand the vocabulary behind the problem. I like how you went through each of the possible answer choices to find the correct one. It was a helpful visual to see why A, B, and C would not work.
I found it helpful that it broke down the difference between what is a positive vs. negative integer and what is a natural number. The review of rational/irrational numbers was helpful too.I also think the strategy of plugging in with more than one example is something I need to remember.
Good refresher on integers. I also questioned whether zero was positive or negative when I tried the problem on my own before I watched. When I first opened the video I was intimidated but then realized how easy it was.
I'm really glad chris defined the word integer. I have a much better understanding of how to walk through a problem involving vocab words like integer, natural number, rational number, etc.
The explanation of the different types of numbers throughout the problem was helpful! Also, the reminder to try each answer twice is helpful. I always forget to do that because I get overwhelmed.
knowing the vocab for this problem such as integer is the most helpful part. being able to eliminate all negative numbers and focus on just positive numbers-
Knowing the vocabulary was very helpful, the explanation of the trial and error for each answer option was great.
It really is so helpful having a video like this to refresh my memory on the ground rules of integers. Just by knowing the rules, I am able to solve this problem.
I have had difficulty with problems like this before and this video really cleared up my questions and confusion.
This video was a great review. It was easy to cross out B and C as the answer. At first, I thought A was the answer because I overlooked the POSITIVE integer in the question. Shows how easy it is to get the wrong answer if you don't read question carefully.
When I begin to study for this test I think I know the vocabulary but I always get things confused. I find it very helpful that you go into great detail with the vocabulary to enhance my learning of it.
I haven't thought about what in integer is in twenty years. This review, especially plugging the numbers in, was very helpful!
I like how you work out each possibility. Although this is a simple concept, it is even easier to conceptualize when it is worked out in this way.
I liked how you broke down the problem and identifying key words with the problem. I thought considering dividing by ten is a way I did not think about instead of just crossing out zeroes.
This video made me realize/remember what an integer is. Integers are positive or negative and divisible by 1 with no remainder. Looking forward to hearing more about irrational numbers and hoping for more help with the radical sign.
I like how he went though this problem step by step. It made more sense after that.
I realized that knowing the vocabulary is essential for understanding how to solve the problem. This was a good review. Also, plugging in multiple numbers was a good strategy.
This was helpful in refreshing my memory about positive integers. I also realized that it's important to try at least two ways to make sure that it's okay to eliminate an answer. No remainders and divisibility rules were also helpful reminders.
This is a great review of math vocabulary! There is a lot you need to apply in this problem.
Understanding the vocabulary terms helps to understand what the problem is actually asking. It was helpful that you went over vocabulary terms such as. Integer, natural number, and irrational number. I've heard these terms before but didn't fully understand them.
Thanks for the quick hit that natural numbers are the same as positive integers...very helpful!