## Friday, July 10, 2015

### Pythagorean Stacks

I absolutely love this post from great maths teaching ideas for a  trigonometry-pile-up. However, I don't teach trigonometry in my 8th grade math classes but I do teach Pythagorean Theorem. I decided to make triangle stacks that cover this topic. The first unit for my Algebra students is Pythagorean Theorem. It isn't a topic we usually cover in Algebra but the students are eighth graders and they will be tested on this material so we will cover it at the beginning of the year. Toward the end of the school year I will use this activity with my Pre-Algebra students as well.

 Silly students, don't look for answers here. You will not find them as I don't post answers that can be copied.  (The diagram is definitely not to scale.) The correct worksheet is the downloaded copy. It has the corrections. Sorry for the confusion. I need to update that picture one of these days.
All of the answers are integers so I may use this in conjunction with the Pythagorean Triple lessons that I will be doing with the students. Students will place numbers in each of the triangles starting at the bottom so it will be easy to follow their work. They willstart at the bottom of the puzzle to find answers and work their way up to the top triangle to find the missing side. I plan to have the students place this in their interactive notebooks.

I can't tell you how many times I made this diagram. I thought it was perfect until the area where the green, blue, yellow and purple triangles intersect. I was 1 cm off, Yikes! So I adjusted the picture and hope you understand what it means. All in all I am very pleased with how it turned out. It will be interesting to see how it works with the two different groups of students. My concern is that it will be too easy for the Algebra kids but too hard for many of the Pre-Algebra kids. I'll let you know.

Hope you all are enjoying your summer! School starts in one month for us. Too much planning to do and so little time. UGH!

Til next time,
Jan

1. I'm planning my Pythagorean Theorem unit, and this activity is part of it (as well as the scarecrow activity). Is there any way I can get a copy of the answers emailed to me? I can work it; I would just like to double-check myself. :)

1. Thanks Mickie for your help in checking the problems. Good thing you did. I missed those two mistakes. The corrected link is in the post now. You are a lifesaver:)

2. Hello Jan,

this is awesome! Would it be possible to also get answers to double check? I'm a teacher as well. thanks
Karen

2. I love this! I can't wait to use it!

1. I'm excited to use it too. I think it is challenging enough for my higher level students, not just the regular drill. I do think my lower level students should be able to complete it as well. I will have them working with their shoulder partners on this activity. Thanks for stopping by:)

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3. how do id find the top triangle

3. I need a hint on where to start :/

1. Start with the bottom triangle and find the missing side using Pythagorean Theorem. Then to find the missing side on the gold triangle, subtract 2 but add three for the additional length. Then use Pythagorean Theorem on that triangle and work your way up to the missing side at the top. Hope that helps.

2. you are taking a long time answering my E-mail. please hurry up

4. What happens when you get to the pink triangle and the length is 15? Do you split it in half equally with the blue and yellow triangles?

5. Look at the small pink triangle above the blue triangle. You can use that triangle to find the length of the missing side of the blue triangle. Use the length of the blue triangle to find what remains which will give the length of the gold triangle. Does that help?

6. Is there a way that I can double check my answer with someone! Thanks

1. Email me through the contact form at the bottom right of the blog. We can talk there.

7. What's the answer? HAHA I'm so close.

1. Keep trying,you can do it:)

8. Is the correct worksheet the one pictured or the one available for download? I was attempting to start solving the problem and on the second triable (the gold one) you get 15^2=5^2+x^2 and you do not get an integer you get a decimal. I wanted to make sure that I was using the correct numbers before I gave this out ot my students.

1. The correct version is the worksheet you download. That one has the correct numbers. Sorry for the confusion. Let me know how your students like the activity. Thanks for stopping by.

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10. im so confused can someone help me

1. Do you have a specific question you can ask me. Then I can help you get started.

11. Are you suppose to assume that the small pink and blue (gray) triangles are congruent, and therefore share the 10 cm hypotenuse? If so, then you would also use the same logic for the orange and purple triangle with the 25cm hypotenuse?
I think I have the answer. How can I verify?
Thanks.

1. This is the step that stumped me. Thanks for asking and once I figured out that there are two rectangles, I got it! I can't wait til my 11th graders tackle this one.... I might not tell them the trick and see if they can get it on their own.

12. Love this activity. My students were totally engaged. I loved the student discourse too! Thank you for sharing this activity.

1. Thanks Diane. My students loved this activity too.

13. how could i get the right answers.

1. Is the answer 28.72 unit

14. how could i get the right answers.

1. Use Pythagorean Theorem to solve the problems. Do you have a specific question I can help you with? I do not publish the answers but will help you get started on the problem.

15. This is AWESOME!!! Thank you for creating this!

1. I'm glad you like it!

16. I have worked on the solutions. Where do I verify my answer before I give my students the worksheet?

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1. You were both correct with your answer. I removed the comments because I do not post answers on my blog. If anyone wants to check your answer use the contact form and I will respond via email. Thank you for stopping by my blog. I am glad you enjoyed the problem!

2. I would love to use this in my class could you email me the answer sheet to make sure I have it right so I don't have my students Ork it out and not have the right answer to check theirs with

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20. Using this in my summer school class tomorrow, could I get the answer key?

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23. Using this in my summer school class tomorrow, could I get the answer key?

1. Hi Deanna,
Please email me through the contact form. We can talk there. I do not publish the answers on my blog. I will tell you that all the answers are integers. Thanks for stopping by and let me know how your students like the activity.

24. Are there decimals

1. No they are all integers.

25. I've been having problems with it.

1. Please email me through the contact form on the side with specific questions. I can help you get started. I do not post answers on my blog. Thanks for contacting me.

26. I can not find your email! Would love to email you to check my answer :)

27. On the right hand side go to the Contact Form. It will send me an email and I will write you back.

28. My son is working on this & I absolutely am no help at all. He is stumped on the third triangle up from bottom. The dark coral one. He has 12cm & 17cm as the first two...can you help me help him?

29. what your email i wanna to call you.can i?

1. You can email me on the contact form on the right side of my blog. I will contact you through email.

30. Thanks for all these great resources. We (the teachers) really enjoyed working them out!

31. 657 square root. It is?

1. No, all the answers are integers.

32. On the second Triangle, I get 121-25=96 and when I square root it I get a decimal! What am I doing wrong?!

1. When you find the missing side of the first triangle, the hypotenuse c, you will need to add or subtract to find the hypotenuse of the yellow triangle. Then use Pythagorean Theorem to find sides a and b.

33. I NEED HELPPP!

1. Contact me through the contact form at the right. We will talk there. Tell me what you have so far in the email.

2. When you find the missing side of the first triangle, the hypotenuse c, you will need to add or subtract to find the hypotenuse of the yellow triangle. Then use Pythagorean Theorem to find sides a and b.

3. When you find the missing side of the first triangle, the hypotenuse c, you will need to add or subtract to find the hypotenuse of the yellow triangle. Then use Pythagorean Theorem to find sides a and b

34. I am a teacher and wanting to use this worksheet with my 8th grade students. Anyway you can send me the answer key. I have completed some of the triangles, but would like to make sure they are correct before I have my students work on this.

Thank you

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37. Hi Jan! This is my first year teaching tenth grade geometry, I've been following you for a while and I was wondering if I could get emailed the answers to confirm my grading!

-Debbie (jaappdebbie@gmail.com)

1. Hi Debbie,
Email me through the contact form at the right. We can talk through email. I do not post answers online. Thanks.

38. Wait.. was the answer 8cm??

1. No it is not. Email me through the contact form in the sidebar of my blog. We can talk there.

39. EVERYBODY THE ANSWER IS 23!

40. No it is not 23.

41. Hello. I am going to give this to my algebra students but I want to make sure I did it correctly because this is the first time I've heard of these. Can you please send me the correct answers and the work so I can teach myself and my students how to do it. You can email me through my school email - 774473220@turnerusd202.org

1. Please email me through the contact form on the side with specific questions. I do not post answers on my blog. Thanks for contacting me.

42. Hi i really need help my teacher doesn’t teach correctly and i missed when she was explaining

43. Do you have to assume that the yellow and orange triangles meet the blue triangle at the same point?

1. Yes they do meet at the same point. I'll see f I can redo those points to make it more clear.

44. can someone send me answers for this

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1. Please email me through the contact form on the right sidebar of my blog. We can talk there.
Jan

46. What is the answer? pls we need to check

47. Please email me through the contact form on the right sidebar of my blog. We can talk there.
Jan

1. Sorry, that is not correct.

49. Is the answer 28.72 unit?

1. No, all answers are integers. The main mistake people make is on the green triangle. The length of the side is 12, not 12- 1.

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51. Who to solve it

1. Use Pythagorean Theorem to find the missing side of the first triangle, the hypotenuse c, you will need to add or subtract to find the hypotenuse of the yellow triangle. Then use Pythagorean Theorem to find sides a and

52. Hello! I love this activity, and I am planning on using it with my students soon. Is there any way you could email me an answer key? I am going to work it out myself but I want to make sure I get all the right answers. Thank you!

53. Please email me through the contact form on the right sidebar of my blog. We can talk there.
Jan

1. Hi I don't know to email you but I wish to know the answer for this if you don't mind. Thank you so much. This activity is really great. My email is dayyanana05@yahoo.com.

54. I there any way you can give me the answer, we finished in class but did not go over it. thanks

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56. I need to get a answer Key for my sub to show my students can I get one from you or someone