Elementary math chat is a weekly math chat where participants come to discuss best practices, examine student work, explore routines for reasoning and research that guides and supports pedagogy centered on problem and student based learning.
Welcome to Elementary Math Chat! We are glad YOU are here!
When answering Q1 (Question), use A1 (Answer) in your response. Remember #ElemMathChat hashtag!
Q0 Introduce yourself, your role, & location.
And share…Where’s a place you’d like to visit?
A0 Hi! I'm Melynee, I teach 6-8th grade math in Claremore, OK. I ALWAYS want to visit the beach! My favorite is Sanibel Island, Fl. I will go to ANY beach that has great shelling! #ElemMathChat
Lori coming to you from the grocery- expecting another snow storm. Elem math interventionist from MO. Get to go to my dream trip to the UK in June! #elemmathchat
Q1: I notice that the numbers are the same in both puzzles. I wonder if the missing numbers HAVE to be the same as the puzzle in the right #elemmathchat
I notice relationships that create rules for each puzzle. I wonder why there is one partially filled out and one all filled. Is the one on left same as one on right. I think so, but is this a trick question? #ElemMathChat
A1. I notice the four blanks and I want to immediately fill them up with numbers that also add up to 11 & 14 by rows and then 12 & 13 by columns but I don't want to use the same numbers. So now I want to play around with numbers #elemmathchat
A1: I notice addends and sums vertically and horizontally. I notice that the middle row is all even numbers--so is the first column. Every other row or column has at least one odd number.#elemmathchat
A1: I notice a puzzle. Addition symbol makes me think I need to add the cells to get the bold numbers. Right image confirms this. Wonder which grades could try this. For sure 3-5. 2nd?
Hmmm... #ElemMathChat
A2
3 8
9 5
and
4 7
8 6
and
5 6
7 7
I notice I can add one from one addend and take one away from the second addend to get different solutions
#elemmathchat
A2 So, I have not started solving because I see 11, 12, 13, 14 & I am wondering if there is a pattern, & relationships that will creat a generalization that can be made that would find all of the solutions without doing guess and check & w/out doing all calculations #ElemMathChat
A2: 56 top row, 77 middle row. 38 top row, 95 mid row. 2 9 top row, 10 4 mid row. I notice that once you get two addends in top row, it is pretty easy to make the mid row addends work horizontally and vertically. I notice that there are no rules for cell numbers. #elemmathchat
A2 I found lots of different solutions! Attaching photos in a sec.
Oh, and I’m jumping in for only a few minutes. :) Jenna from the Boston area. #elemmathchat
A3: I wonder if @MNmMath was on to something with the consecutive numbers identification. I wonder how much difficult would it be if we changed any one of the sums numbers to a different number like 18. #elemmathchat
A2: After trying different solutions (each has a different symbol all round the numbers) I started to realize there was more than 1 solution!! #elemmathchat
I wonder if there is a generalization or a rule we can make about this puzzle. I don't think @RawdingMolly knew how nerdy I would go on her! Patterns, relationships and generalizations are the things I dream about on a great night! LOL NERD in the house! #ElemMathChat
In reply to
@TaraTrifiletti, @RawdingMolly, @RawdingMolly
A4: I think the "prime numbers only" constraint will actually make it faster for me to solve, because I can just look at the prime factorization of each number, and then look for overlaps, like an odd venn diagram #elemmathchat
Addition has many more possibilities
I went for the generalization, too. :) I think there's a generalization we can make about the specific numbers used in this puzzle, given that they're all consecutive integers. #elemmathchat
In reply to
@MNmMath, @TaraTrifiletti, @RawdingMolly
A3: I’m wondering about the relationships between the sums. Two on bottom are 1 apart, two on sides are 3 apart... but all are close. So... what does that mean? 🤷🏻♀️ Does this work with all numbers in same relationship? #elemmathchat
A4: In both grids you need to solve across and down, one is multiplication and one is addition. I wonder if they both have similar rules applied to them for the solutions? #ElemMathChat
Q5 How can you fill in the squares?
What do you notice as you work through this?
Use either game board - the second one has constraints to use only prime numbers.
#ElemMathChat
My conjecture: I think the patterns we found would work for any 4 consecutive integer sides. The sides would have to be with the middle two values along the bottom and the upper and higher bounds on the left, by necessity, I think. #elemmathchat
A4 Same is format 99, 44 multiples of 11. 75, 50 20 & 30 multiples of 5, 20, 30, 50, multiples of 10. In first puzzle the solutions were consecutive #s & sums, this puzzle is products. #ElemMathChat
A4I just noticed the restriction of only being able to use prime numbers for the puzzle on the right. I wonder if without that restriction you can still solve or if you could have multiple answers like you were thinking @TaraTrifiletti#elemmathchat
I'm still puzzling over the first puzzle. I was systematic in finding solutions but then when I started with 9 in top left it didn't work. wondering if I made a mistake.
#ElemMathChat
A4: same structure. Different: operation, use of prime numbers (yay, love prime numbers! 🤓)
Question: what is the same that I can use to help puzzle 2? 🤔
#elemmathchat
A4: The prime factorization of each number has exactly three prime factors. so...maybe that means that you can't solve the puzzle with composite numbers? #ElemMathChat
To make it more challenging, the "prime number" constraint could be lifted. You could still use prime factorization as a strategy, but it would play out differently (and you'd have to add in 1 as a factor) #elemmathchat
These awesome puzzles are called Yohaku. There are constraints below the puzzle.
To make this puzzle more accessible, consider removing that (at least to begin).
@yohakuhttps://t.co/lYqmqPJff6#ElemMathChat
I notice paths I can make with addition to connect the numbers. I notice sum of all is a prime number. I notice sum of top row and second row = but sum of bottom row is one less. #ElemMathChat
I'm wondering if we gave this to students what would they do? Would we want to start by giving them the top number and working their way down? Give them numbers to fit in the puzzle? Just give them blank squares and see what they do? So many options! #elemmathchat
Q7 How might you fill in the squares?
What do you notice as you work through this?
#ElemMathChat
Fill in the squares so that:
It is filled with positive whole numbers
No number occurs more than once in the pyramid
Every number is the sum of the two below it.
Now you have me checking that bottom row connection out. What is the connection w/ sums? I see 8,8, 7. I can do a path for sums that all lead to the top 8. #ElemMathChat
A7: I initially struggled with this on paper because I was trying to make a row with 4 numbers on the bottom instead of 3. Then I fixed it. 9, 6 and 3, then 4,2,1 #ElemMathChat
What I see here from these problems:
- there is always an element of choice
- reasoning is needed to complete each
- there is always room to continue thinking, notice patterns, find limits of possible answers
-there is plenty to discuss once solutions are shared
#elemmathchat
A7b: I thought four lines would make it easier because there would be more solutions, but I am still working on a finding one that works! #ElemMathChat
I think the more rows there are, the better to pick numbers closer to half of the top block - otherwise you might run out of choices by the last row.
#ElemMathChat
A8: Almost always, someone says something that no one else noticed. Then minds start racing and they all look for other ways that might be less obvious to them. Everyone can join in at their comfort level in a #NoticeWonder#elemmathchat
