 Hello math learners! This is Mr. Marks, your friendly neighborhood math teacher. Remember, it's not just about getting the right answers, it's about learning and growing along the way. Now today's problem is coming to us from the Pennsylvania Department of Education's Algebra 1 2017 Keystone exam. This problem is an opportunity for us to hone our multiple choice strategies, so let's uncover the mysteries this problem holds together. First, it's a word problem, so let's give it a read. Mary measured the heights of two different plants every day. Plant A was one inch tall when Mary began her measuring, and it grew 0.5 inch per day. Plant B was three inches tall, and it grew 0.25 inch per day, on which day were plant A and plant B the same height. First off, don't worry, I know word problems can be pretty overwhelming, but let's remember to breathe, and let's do this together one step at a time. Help me out by re-reading the problem. Do you recognize any particularly important numbers or statements we should make note of? I see that we are working with two plants, plant A and plant B, and we have some numbers associated with each of them. Alright, let's pause here and start taking some notes. We'll have one area for plant A notes, and we'll have one area for plant B notes. Hey, can you see what numbers and details I should write in for each of these? Now we're talking, we'll write down that plant A began at one inch tall, and plant B began at three inches tall. And we'll also write that plant A grew by 0.5 per day, and plant B grew by 0.25 per day. Wow, we have a great start organizing our information, don't we? Now the question is, how should we proceed with this information? Aha! Do you see it? With our information, we need to determine when these plants will be the same exact height. There are so many ways that we can proceed, it can be quite overwhelming. What ways are you thinking of? For today, I say we create a table of values for tracking the growth of the plants. Hey, it may not be the fastest or the most difficult method that we could choose, but it'll work. We'll track the days and the height of each plant in the columns. We know that on day zero to start, plant A was one inch tall, and plant B was three inches tall. And let's increment our days by one, and we can note the increase in height each day like this. And thus the height of plant A on day one will be 1 plus 0.5 or 1.5. And the height of plant B on day one will be 3 plus 0.25 or 3.25. Alright, now that we know the game plan, let's complete this table together. By day two, plant A will have gone from 1.5 inches tall plus 0.5 inches for a total of 2 inches. And on day two, plant B will have grown from 3.25 plus 0.25 to a total of 3.5 inches tall. On day three, plant A will have a height of 2 plus 0.5 or 2.5 inches. And plant B will have a height of 3.5 plus 0.25 or 3.75. On day four, plant A will have a height of 2.5 plus 0.5 or 3 inches tall. And plant B will have a height of 3.75 plus 0.25 or 4 inches tall. On day five, plant A will have a height of 3 plus 0.5 or 3.5 inches. And plant B will have a height of 4 plus 0.25 or 4.25 inches. On day six, plant A will have a height of 3.5 plus 0.5 or 4 inches tall. And plant B will have a height of 4.25 plus 0.25 or 4.5 inches tall. And on day seven, plant A will have a height of 4 plus 0.5 or 4.5 inches. And plant B will have a height of 4.5 plus 0.25 or 4.75 inches. And on day eight, plant A will be 4.5 plus 0.5 or 5 inches tall. And plant B will be 4.75 plus 0.25 or... Wait, did you notice? Plant B will also be 5 inches tall on day eight. So the answer is that both plant A and plant B will be 5 inches tall, the exact same height on day eight. Wow! By carefully observing, noting, and reasoning, we can see now that the answer is B. This is fantastic, but let's challenge ourselves further. Can you figure out what error somebody would have to think in order to mistakenly choose A as their answer? What about C or D? I hope you choose to challenge yourself to practicing your adaptive thinking skills by wrapping your head around these potential errors. Leave a comment with your thoughts. Bonus if you can recognize the errors in all three options for mistakes. Hey, props to you for taking some time out of your day to do a little bit of math with me. I hope you followed along and if you made mistakes, that is all good. Remember that every mistake that you make is a step towards learning something new. This is Mr. Marks signing off. I'll see you next time with another math problem. What did you think? Did you approach this problem differently? Let me know in the comments. And if you enjoyed this problem, show your support by liking and sharing this video. And don't forget to follow my page to stay up to date on more math related content. Until next time!