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.
#elemmathchat
Hi! Margie from PA
Math Coach
So excited to have @MFAnnie and @maxrayriek leading tonight!
My favorite flower is an Iris - they are blooming in my garden
I'm Annie, a sometimes K-5 math coach. I'm right outside Philly, and my neighbors have a huge white double dogwood that's in full bloom that I can see from my desk! #ElemMathChat
Marian from Atlanta joining for the first time. I teach 4th/5th Montessori. My students are pretty proud of their grass heads they’re growing in the classroom. #elemmathchat
@pearse_margie I swear we are soul sisters! My favorite flower is an Iris too! I teach 6-8 students with disabilities. I love them beyond all measure, and I am still ready for summer break to get here! #ElemMathChat
Hi #Elemmathchat. I’m Max from Philly and I learned last year about moss phlox which is very pretty, easy to recognize, and fun to shout when you spot it. Moss Phlox!
I'm Stacie. I'm a student at Chapman University pursuing a degree in Integrated Educational Studies. There's some really pretty flowers blooming on campus. @YehCathery#ElemMathChat
A1 notice: 1 row with 4 rectangles, 1 row with 3
the length of 3 is equal to the width of 4
a length and a width together is one of the dimensions of the larger rectangle. #elemmathchat
A1: I notice that it is divided into 7 rectangles. I notice that the exterior is a rectangle. I notice that 4 of the rectangles are standing vertically, and 3 are laying horizontally. I wonder if it is divided into sevenths? #elemmathchat
A1: There are 4 on the top row and 3 on the bottom. I wonder if there is some way I can figure out the dimensions or at least the ratio of one side to the other, given the arrangement. #elemmathchat
#elemmathchat first timer. I'm Skye Darnell, teaching grades 6-8 math and intervention in Hawaii. Spent the day decorating my son's cafeteria with foliage for May Day performances tomorrow
A1 The orientations of top and bottom rows are perpendicular, each row has a different number of small rectangles, total area of each row must be equal. #elemmathchat
A1: I notice that some of the rectangles are standing horizontally and other vertically. I wonder how my formula-loving students who enter my classroom in September might compute area. #elemmathchat
A1 I notice several rectangles. I wonder if this is an area problem. We are doing rates and ratios right now. I wonder what the relationship is among these rectangles. Are they proportional? I this one of those how many do you see problems? #ElemMathChat
A1: Seeing different arrangements. Definitely noticing how things look different size depending on alignment and orientation. Wondering about how you could build on to makes arrays #ElemMathChat
A1: I notice the top has one less rectangle than the bottom. I also notice that even though they are different size rectangles, they cover the same area. The 1x3 covers the same area as the 1x4, it is just split up into 3rds or 4ths. Next row 3 or 5 rectangles? #elemmathchat
A2 Notice we could figure out the area of the smaller rectangles now.
756 is divisible by 7.
wonder if that will be enough info to get dimensions #elemmathchat
A2: I notice that the are of each small rectangle must be 108 cm squared. I wonder what the dimensions of the small rectangles are or the dimensions of the large rectangle are. #elemmathchat
A2: I wonder if there is more than one answer for “what are the dimensions of the smaller rectangles.” How many combinations could there be that would be reasonable? #elemmathchat
A2. I notice that each rectangle would have area 756/ 7 = 108. Since 9*12 = 108 and 12/9 = 4/3, then the dimensions of each rectangle is 9 cm by 12 cm. #elemmathchat
A2 notice 756 is an even number. There are 7 rectangles odd number. wondering about factor pairs for 756 Wondering how to rearrange these rectangles to find the area of each with what we know. Wondering why it is so hard for me to move images around in my brain! #ElemMathChat
A2 I wonder how my Ss would approach this. Would they start by finding possible length and width of the large rectangle? Would they related the total area to area of 7 small rectangles? #elemmathchat
@RawdingMolly wonders if we had enough information to find the dimensions. This an intriguing question that I'm exploring as we... tweet? #ElemMathChat
A2 I notice the 756cm^2 long side is 3 long sides of the 108^2 and the short side is 1 long side and one short side of the 108cm^2. I wonder if we have enough info to find the lengths. #elemmathchat
I’m a little late, but I notice that 3 lengths = 4 widths. I wonder what the least amount of information would be to figure out area, perimeter, etc. #ElemMathChat
A2 more... Even though my brain knows rectangles are congruent, my eyes don't believe it. 756/7 = 108 So now I wonder how we find the perimeter measurements of each of the little rectangles. I notice the lines and fractions that should help! #ElemMathChat
A2 I notice that each small has an area of 108. I wonder what the dimensions of the large rectangle would be of the small ones were 2x54? Or 4x27? #ElemMathChat
A4. If we let x < y be the dimensions, then the perimeter is 2(x+y) + 4x + 3y = 6x + 5y. If we know the area as before, then x = 9, y = 12 and the perimeter is 54 + 60 or 104 cm. #elemmathchat
A3 I notice I want to talk to Margie more to ask her how she sees this. I need to hear her tell me how she knows this :) I am thinking in fractions. I wonder if she is thinking differently! #ElemMathChat
#elemmathchat I wonder if the large rectangle is a reptile because it's tiled with smaller rectangles. I wonder if they're proportional to each other. I wonder how we could determine the ratio between the side lengths - I wonder if we have enough information or if we need more.
A3: the area of the small rectangles is 756 divided by 7, which is 108. Now let’s find the numbers that will multiply to make 108 and see if we can discover the dimensions. Brainstorm how to make 108 with students. #elemmathchat
Since we know each individual area, we can generate a list of possible dimensions. And since we know the ratio of the dimensions, there’s probably only one set that works. Then we can find perimeter! #ElemMathChat
Ah! But a couple of people have mentioned 3s and 4s and their relationship (including @MrsPollardprime). Do you see how they might be related to the big rectangle? Fun to have to switch thinking! Good exercise. #ElemMathChat
In reply to
@bupeBSD, @jkgibson6, @MrsPollardprime
A4. Not knowing anything about the total area, I am interested in the possible ratios of the total perimeter of all seven rectangles to the perimeter of the largest rectangle. #elemmathchat
#elemmathchat A2 I notice area of each small rectangle would be 108... Wonder if middle school students could use system of equations? Multi tasking is not a good idea right now...😀😎🙃
A4: if we have the area of the larger rectangle from that figure the area of each of the smaller rectangles, we can use that information to gain knowledge of the possible perimeter of the larger rectangle. #elemmathchat
I once had a T say in a workshop about another activity, "Once I see it my way, it's REALLY hard to see it my partner's way!" A great argument for sharing, and discussing, many multiple paths to the same answer (see Number Talks, for example). #ElemMathChat
A5: just the area of the large rectangle. Once I knew that I could use the relationships of the sides to help me figure out the dimensions of the small ones. #elemmathchat
Trial and error. I knew that 756 was divisible by 7 which means it was divisible by 14 and 21. I tried both and thought 21 would be the more reasonable width and that makes the length 36 because 756 divided by 21 is 36. #elemmathchat
If the length is 36 then I looked across the top and divided it by 4 which means the width of each small rectangle is 9. Then the width has to be 12 if the area of the small rec. is 108. #elemmathchat
A4 I am thinking about factor pairs for the area, and the way to make arrays with those that would both add and multiple to meet the parameters for this rectangle. Not all of the factor pari arrays could work. #ElemMathChat
There was a slide that might have snuck by adding some numbers to this numberless picture problem! @MFAnnie said the area of the big rectangle is 756cm^2 #ElemMathChat
A5: had to know some things about rectangles and area. Had to know about perimeter and had to have a basic understanding of division. #ElemMathChat#NoticeWonder
A5 seems like one of those problems that is accessible at many levels. Like dividing fractions problems: a fourth grader can draw and model a situation where we're dividing into fractional sized groups even though they don't formally know how to do it #ElemMathChat
A5: You needed to know how to find area and perimeter. You also needed to understand that multiplication and division are inverse operations and the same for addition and subtraction. #elemmathchat
Yes. Because for example when trying 6 x 18 for the small dimensions it doesn’t work. The sides of the large rectangle would be 24 (6+18) but the bottom would be 54 (3 x 18)and the top would be 24 (4 x 6) which would not be a rectangle. Only 9x12 didn’t do this.
Q5: I have to know that there are 7 equivalent shapes that make up the big rect. Understand the area formula & how to break down the 2 variables. You can use substitution in the later grades to solve, or some trial and error for younger students. I teach ms math #elemmathchat
When I first saw dinner I was like "why is dinner so late" Then saw the time. I always forget that we are all in different time zones. I will be heading off to bed as soon as this chat is over. lol #elemmathchat
Q6: Another relationship is that 4x=3y for the top and bottom of the large retangle. Interesting relationships and lots of number talking happens with these #noticewonder problems love love! #ElemMathChat
#elemmathchat So I went right for an algebraic solution and a MS teacher might present such a problem to see if students use that "tool" but a fourth grade teacher might be working on factors, multiples, area, making a table etc. and be anticipating students use diff strategy
Q7: What are some math ideas that you are reflecting on more now after thinking about all the different ways to find the perimeter of the large rectangle? #ElemMathChat
Would have to understand that a rectangles area is a result of the two side lengths multiplied together. Would also be helpful to understand that rectangles have opposite equal sides.
I just #NoticeWonder there's a ratio btwn side lengths: 4 of the short ones must be equivalent to 3 of the long ones. Which means I think one side of a small rectangle is 9 and the long side is 12 for an area of 108 each. 9 x 4 = 12 x 3, so top and bottom are equal #elemmathchat
A7: I'm thinking about how I can recreate this problem with my 3rd graders. They are struggling with remembering the difference between area and perimeter. It might be good for them to explore a problem similar to this. #elemmathchat
I drew the line straight down to make a square and then thought about the square numbers within 108, recorded 81 and subtracted to get 27 for the other piece. Then I had finite answers to work with to get the perimeter (which I now realize I did not record on that picture) 😂
A1: There are 4 on the top row and 3 on the bottom. I wonder if there is some way I can figure out the dimensions or at least the ratio of one side to the other, given the arrangement. #elemmathchat
Would you try solving a similar problem that way? Or do you have a way you like better? (or, what would be the benefit of trying to solve it that way?) #ElemMathChat
In reply to
@themathgirl, @katrina_cade, @maxrayriek
I knew I had to find common factors for 108 and 756 and the width of the smaller rectangles had to be close to 3/4 the length so I played around with dimensions of the smaller rectangles (9 cm and 12 cm) Making the dimensions of the larger rectangle 21 cm by 36 cm
I'm not sure if I'd approach it the same way if I were on my own. It helped seeing what other people noticed and wondered before I dove into the problem. #elemmathchat
A7 Less math and more what a fine art we practice in selecting problems to challenge our students and in anticipating the type of solving we think we might get all with the goal of hitting each child in a sweet spot of maximal learning. I think we rock! . #ElemMathChat
(And since this happens to people, I remember exactly when I first saw this method, and where the girl was sitting, and what room we were in, etc. And how cool I thought it was to see a "new" method!) #ElemMathChat
I love the extra line or "altitude" you dropped to cut the rotated rectangle into a square! I think adding in lines to help us reason is a critical geometry skill that not enough students cultivate or have the opportunity to practice/try out! #elemmathchat
A7: I’m thinking about playfulness. You don’t need procedures to solve this problem if you’re willing to play with numbers and have some strong ideas about the attributes of rectangles and understand area and perimeter. #elemmathchat
I am behind! I'm over here like filling pages and pages with drawings and lists of numbers and calculations. I am wondering if there is more than one answer to this investigation. What relationships do the factors of 756 and 108 have How does 4 and 3 play into that #ElemMathChat
A8 BY thinking about ways to find the perimeter of the larger rectangle, I am working on finding a new understanding of congruent polygons, using my current knowledge of area by doing mutliplication. #elemmathchat
A8: I am working on finding a new understanding of proportional reasoning, using my current understanding of congruent rectangles by playing with ratios and matching factor pairs. #ElemMathChat#NoticeWonder
I found it! And I didn't recognize it at first. Trying to think about why (and not because there are Too Many Great Ideas Going By Too Fast!). Thinking I usually see folks extend the middle top line down. Still thinking... #ElemMathChat
A6 I know I am thinking about this in a random me kind of way! I am trying to find patterns, I am trying to find more. I always am. I am that kid that needs A LOT of think time because I want to know everything before I know the answer! #ElemMathChat
A7: there are many, different and unusual ways to think about the area &perimeter of these rectangles. I love that students can talk about and parse the information & work backwards. Brainstorm thinking. #Metacognition#ElemMathChat
Q9: Take some time to read each other’s learning stories. Pick someone’s and say one thing you notice and one thing you’re wondering based on their story. #NoticeWonder#ElemMathChat
I'm not sure what the best way to keep up with a chat is... This #elemmathchat is the first time I've ever actively participated in a "live" chat - usually, by the time I notice it, it's already over!
What a great chat tonight! Wishing everyone a happy Friday and Happy Teacher Appreciation Week. Based on the conversations in #elemmathchat each week, there are some really lucky students out there with all of you as teachers and math coaches. Thank you for all you do!
A9 Notice @RawdingMolly mentioned slow reveal and wonder how I can / think I should tap into suspense of that technique on a more regular basis. #ElemMathChat
There isn't. Get involved in the bits that are appealing. Read through tomorrow to see what U missed and write some replies. Be real. #ElemMathChat (I have gone whole chats without answering a single Q, or even reading them, and just having awesome side convos!) #ElemMathChat
A8: By thinking about ways to find the perimeter ofthe larger rectangle, I am working on finding a new understanding of perimeter & area, using my current knowledge of Algebra, by finding & naming variables & their relationship to the large & small shapes. #ElemMathChat
I hope some more people will try answering Q8 at a later time, and then revisit other people's ideas. It's an interesting thing to think about...and will lead into our next #ElemMathChat in two weeks!
At first, I was thinking I had to add up each individual rectangle's sides and then figure out which sides were actually included. Then I realized I could find the perimeter of the smaller rectangle and use my knowledge of similar triangles to scale it up by 7! #elemmathchat
