This question was **closed** Dec 07, 2013 at 05:41 PM by Maria Droujkova for the following reason: The course is over.

Here are problems for techniques seven through ten. As in the previous assignments, write down the brief plans for what you will do with your kids. 1. Look at the PDF document [mpsMOOC13_Problems_7_8_9_10][1] 2. Reply here: how do you plan to adapt the problems for your kids? [1]:
https://docs.google.com/file/d/0B6enMfoYXJb3dkJrR211WTBYbTQ/edit?usp=sharing

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**Answer** by Denise Gaskins
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Jul 22, 2013 at 03:57 PM

**First thoughts for my K-1 group:** The "perseverance" problems will take more time than we have. Leave those for another day. The "land or water?" puzzle looks like something the kids will enjoy. Here's hoping it's cool enough to meet at the park again. Sidewalk chalk on the drive should work well, with a stuffed animal to put in the maze. The "strange cake parties" puzzle sounds good, too. Looks like we're celebrating our inner toddler this week :) We won't have an escalator to play with, no matter where we meet, so we can't do the toddler level on the last puzzle. I think I'll try modifying the "51 two-digit numbers" problem down to single digits. Perhaps we'll start with a half-deck of cards and play [Tens Concentration][1] first, then spread out the whole deck (minus face cards) number-side-up and ask: "Can you draw out 6 cards so that no pair of them add up to make 10?" [1]:
http://letsplaymath.net/2007/07/10/tens-concentration/

**Answer** by mirandamiranda
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Jul 23, 2013 at 12:33 AM

**Problem 7** Double shape puzzles. I am trying to think of the best way to facilitate trying many different times. I think I would like to laminate and then cut out the shapes. So kids can try drawing lines on them and erasing them if they need to. My other idea was that they could use the cut out shapes as templates to make copies out of paper. Then they could cut out the two shapes and check they were the same (I am not sure whether everyone will be able to tell the shapes are the same just by looking).
I also think I might save the 'make-your-own' suggestion until after they've had a try with the first ones - otherwise they may just ignore my carefully prepared laminates!
I also like the square number puzzle, my eldest and i are keen on square numbers. But I do not feel confident working on this one with a group - we are a bit too loud and chaotic! Maybe we will try it on our own, although I am not sure her multiplication is good enough, I might adapt with smaller numbers...
**Problem 8** Islands. I wonder if kids will want to just colour them in. I like the idea of drawing islands though, I could use the white board. I think I will need to practice! I also think this would be a good one for the kids to join in creating islands. Maybe someone will come up with the island-in-a-lake-in-an-island extension without prompting!
I think I will try on the white board and then use paper for this. I might get some little toys out too. I like the idea of playground chalk but not sure I can do this where we are. Large pieces of paper? I think I have some somewhere...
**Problem 9** Cutting up pieces. This feels similar to problem 7. I wonder if I should group them together or if it would be better to separate them. I will definitely use the cake story - I think *I* find things easier to introduce with a story - but I will use the kids present instead. "I am cutting up cake for you three. Oh, look, x wants some too! How can we cut it up now?"
Laminated 'cake' might work here too. Maybe I can make a few and divide up into groups of different sizes. That way I can differentiate by skill level a little too. Then I will bring in the imaginary 100 people joining our class!
**Problem 10** I am not sure we will reach this one. I like the idea of doing the two-digit number puzzle with smaller numbers, like 1 - 10. Except - I am presuming this is not possible, please someone tell me if I'm wrong! - and I'm not sure I like setting them a problem that is impossible to solve. I might have the escalator one up my sleeve just in case.

The digit puzzles are possible/impossible depending on how you interpret them. In the puzzle as originally given, a student who thinks of the "negative numbers" loophole could do it.
In my smaller puzzle, I had originally thought the kids could use zero to make a 6th number---but if we're using the playing cards, we don't have a zero, so they would need to draw one of the 10s (which would not make a "pair" with any other number). We might start smaller though: "Can you pick 3? 4? Can anyone find 5? Would 6 be possible?" and see whether they think using a 10 card is fair or cheating.

Good point, I had thought about the 10s but as three digit numbers were out in the original I just extrapolated and assumed single digits for the cards. It definitely could make for a good discussion.

If you have a problem that may be impossible to solve, you could change your wording to "Is it possible... ?" It can be a wonderful eye-opening experience for students to learn that some problems are impossible and that "is it possible" is a valid mathematical question. My students have often been caught up in the worldview that there always is an answer, just one answer, and the teacher knows what it is.

**Answer** by Rodi.Steinig
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Jul 25, 2013 at 10:42 PM

**Problem 7 (Perserverence)** I will cut strips of paper in 2 colors for weaving. The question: “Is it possible to find patterns other than *‘over one, under one’* that make non-adjacent squares?”
**Problem 8 (Second guess the author)** We’ll play the logic game “Knights and Liars” with puppets and arithmetic statements similar to Dr. T’s problem about the reversal of digits.
**Problem 9 (Avoid hard work)** I’ll ask the kids for 5 consecutive numbers that add up to 100, and then maybe 5 that add up to 1,000, or if needed, that add up to 30.
**Problem 10 (Go to extremes)** I’m having trouble adapting these for my group, and also doubt that we’ll get to them in the 90 minutes that we have. I may think of something using the pigeon-hole principle at the last minute, but really like the elevator question so will probably use that.

**Answer** by Denise Gaskins
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Jul 25, 2013 at 11:02 PM

Here is a printable version of the cake puzzle: [How can we share the cake?][1] [1]: /storage/temp/133-cake+
puzzle.pdf

cake puzzle.pdf
(205.3 kB)

**Answer** by abrador
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Jul 27, 2013 at 12:29 PM

This meeting will be special, because my family -- who have been hosting the meetings -- are going away on sabbatical. So I want to make sure that it is a fun meeting that involves everyone, and that means I might be creative... For Problem #7, though, I will build a puzzle per instructions, and then encourage the kids to build their own puzzles. The idea is to spark thoughts about tessellation. But then we are going to do something that was not in our plan for today -- we are going to play choosing games! We will begin from two people using ini-mini-mini-mo to decide who does something fun, like getting the last jellybean, but also something not fun, like emptying the trashcan. If you begin the ini-mini, can you set it up so that you get what you want?.. But then how about when you have three people -- how do you make sure to get what you want then? Four people?... Do we need a different rhyme for 5, 6, or 7 people?

**Answer** by ccross
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Aug 01, 2013 at 10:58 AM

One thing I didn't like about this section was not having the actual answers, especially to the second/young kid or teen problem. I just don't trust that I figured them out correctly, and I didn't want students to be working out the problems and for me not to be able to say definitively that they were right or wrong.
In general, I think you need more answer sheets and/or vocabulary sheets to use these problems with more math-impaired or math-phobic moms like me. It may be fine for more math-savvy audiences, but those of us who are unsure of our own math capabilities need a little more support and/or information before I think many of them would be comfortable about using these things with their own kids or students.
Just my opinion....
Carol

**Answer** by ccross
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Aug 01, 2013 at 11:02 AM

Also, in the MAA teen problem for #10, I didn't understand how Going to Extremes helped with the problem-solving process. I was a little iffy on this entire problem-solving technique. I could see how it was helpful in the first problem, but I didn't really see that absurd answers helped that much in solving the other two.

**Answer** by Silina
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Aug 04, 2013 at 04:06 AM

For my almost 12 year old we will 7. Try to find or proof that there is not a square number ending with 8 8. do the a*b & b*a problem 9. Find the sum of the first 100 odd numbers
10.do 51 different two-digit number problem

**Answer** by Lobr23
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Aug 05, 2013 at 04:11 PM

Problem 7: We'll try solving the problems by making our own. First, I'll make an example. Then, I'll have each child make their own puzzle out of cardstock, then give it to one of the other children as a challenge. Problem 8: I liked Denise's suggestion of using sidewalk chalk. I think we will do something similar with the islands and sea.We'll make the puzzles big enough to walk on them. Problem 9: Looking at the Toddler time, I think for this problem we'll use paper and our Lego figures or favorite dolls to share the cake. Problem 10: No playing on escalators for us, trying to think of another way to illustrate this technique (going to extremes) for my age group (ages 7, 6,and 4).

**Answer** by Silina
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Aug 10, 2013 at 07:22 PM

For my 22 months old: 7) we will cut animals out of paper, make them touch each other, then trace and see what it will look like. 8)we will draw land-water-land curves on the sidewalk, walk through them and see if we can figure out where the land is. 9) I will cut L-shaped pie between three different animals and see if we can divide those pieces between their friends. 10) we will visit an escalator and see if she can guess the relationship between our speed and the number of the steps we use.

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