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.
Thanks everyone for joining us tonight. Please keep in touch and let us know how it all goes when you try some new strategies. Now head on over to #elemmathchat and hang out with @SteveWyborney. #octmchat
Thanks everyone for joining us tonight. Please keep in touch and let us know how it all goes when you try some new strategies. Now head on over to #elemmathchat and hang out with @SteveWyborney. #octmchat
My name is Chris Kalmbach. I'm an Elementary Math Coach in Central WA St. I have meetings most of the day tomorrow & I plan on using the words support, goal, plan, and implementation a lot. #ElemMathChat
Hi everyone! My name is Sohnia. I’m a math consultant at Wayne RESA which supports school districts in Wayne County, Michigan. I will be saying TGIF! #elemmathchat
Hello everyone. Excited to be joining in tonight's #ElemMathChat. I'm Maria from Ontario, Canada. Was an instructional until this past Tuesday. Now a math consultant, K-8. Chatting fluency tomorrow at a presentation--so words will include flexibility, accuracy, & efficiency
I cannot over emphasise how powerful "What do you notice and wonder?" are! My students are now asking each other that question when they work in groups!!!!!!! #ElemMathChat
A2: Because kids want to know. They want to know how why where what etc. Especially if they can connect to it. They want to guess, think about, tell you what they think!! They get to talk! Less about their being something they HAVE to do. #ElemMathChat
The sense of mystery...
The sense of challenge...
It's inviting, compelling, enjoyable, and satisfying. May we invite and re-invite our students into wonder and deep math thinking each and every day. #Elemmathchat
A2) Who doesn’t like to be “in the know”!?
We’re naturally curious creatures. We want to know what’s behind door number three, even when we’ve already gotten the car.
#elemmathchat
A2: Missing information is so engaging because it makes your brain actually think critically. For example, Chain reaction, Wheel of Fortune, etc. #elemmathchat
A2 Missing information creates urgency, buy in, a hook. Often time the missing information causes students to ask ?s that take them much deeper into the exploration. #ElemMathChat
A2: Missing information makes us curious. Curiosity is too often an ingredient missing in math classrooms where Ss are told the procedures that focus on answer-getting. #elemmathchat
A2: I think about stories and how if you mix up the chronology and push to the an event like a murder first, then it draws people in and makes us want to know that backstory. #ElemMathChat
All great words Mark. "Relationships" is one, for sure, that is key. Foundational to building conceptual understandings & making connections. #ElemMathChat
A2
"Missing information" is an important aspect of any problem. Really, it's about cognitive engagement. If we want students to think, then there needs to be something worth thinking about.
#elemmathchat
A2- Missing information gives everyone a chance to state an opinion knowing no one knows the answer. A chance to take a risk. They love the thrill that they could be correct. #elemmathchat
A2 I feel like missing info helps Ss decide what info is most valuable in a moment. If it’s missing and they need it they find ways to either solve or gather the info. Helps plan prob solving. #elemMathChat
A2: It takes the stress of solving the problem correctly off the Ss and allows them really think about the puzzle/mystery presented to them. #ElemMathChat
A2 solving a true mystery or puzzle gives all of us a sense of wonder and engages our competitive nature. Even when we are our only competition. #elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A2 everyone always wants to know the whole story or see the big picture. It’s fun and like solving a puzzle!
Maybe a bit of a stretch, but I think of it’s more like family feud- many different ways/attempts to arrive to the answer. #Elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A2: Missing information is so engaging bc it’s almost a challenge! Who can find it out? Kind of like Where in the world is Carmen San Diego! 🙃 #ElemMathChat
A3: strategy 2 - Start at 3 (because there are 3 blue dots) count up 2 more dots would be 5 and then 5 more dots would be 10. So 5 dots and 2 dots would be 7 hiding dots under the splat. #Elemmathchat
A2: Missing information sparks curiosity. A sense of mystery that we want to solve. Makes us want to figure things out, respond to the challenge. e.g. game shows like Wheel of Fortune--I want to figure out the missing letters. Creates excitement. #ElemMathChat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A2: Missing information is so engaging because it’s opposite of what we normally ask if kids. It provides rigor and thinking outside the box similar to a challenging puzzle ! #elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A3: strategy 3.... haha I think I took the bait for the challenge part :P I I forgot what 10 - 3 dots would be... but I know that if there were 8 dots hiding under the splate, I would only need 2 dots showing. So there must only be 7 under the splat instead. #Elemmathchat
Ooooohhhh. Love this. So 16 is the total. I can see two dots. I think. So 14 are the under the splats. Hmmm. So under the two splats could each be 5 because two would be 10. Then that would leave 4 for the red splat. Woah. #elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q2: Its almost like a game and the end result is a prize. Similar to putting together an old school puzzle on your kitchen table. The process is enduring, but the result is so satisfying. #ElemMathChat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A3 I know that I need 10 dots, so I would count the existing dots and then count on from 3 to 10, drawing a new dot each time inside the splat. Then count the 7 dots I just drew. #elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A3: Each concave splat has a dot. If you then add a dot to the other concave parts, you will get 5. Take away the splat and there will be 5 more dots under the convex parts. #ElemMathChat
Q3. I can use my number line and start at 10 and move back 3, then I get 7 or I can start at 3 and count to 10 and I still get 7. So 7 is the answer. #Elemmathchat
A4: So at first I was thinking the total will always be odd because if I put one in each then 3 + 4 is 7. But then I was like nooooo because 2,2, and 2 + the original 4 is 10. Well. All the answers it could be will be 3 apart. 7, 10, 13... #elemMathChat
A4-total could be 16. Total could not be 3. I like stressing a reasonable min and max, such as with a 3 act lesson. For example, total could also not be 100. #Elemmathchat
A2: I also see missing information as more open to interpretation. It presents much less of a threat therefore resulting in greater risk taking. #ElemMathChat
A4: So at first I was thinking the total will always be odd because if I put one in each then 3 + 4 is 7. But then I was like nooooo because 2,2, and 2 + the original 4 is 10. Well. All the answers it could be will be 3 apart. 7, 10, 13... #elemMathChat
Looks like there are 3x+4 dots.
I know there are at least 4 dots (so can't be 2 dots) - unless there are negative dots?
I know there can't be 5, 6, 8, 9, 11, 12, 14, 15..... - unless there are part dots?
#elemmathchat
A4: Total could be 13 if there are 3 under each splat. Total could NOT be 20. Explore patterns that have 3 equal groups with adding a constant or divisibility. Could connect to algebra, like 3x + 4. I'm wondering what @EvanBailey_2 & @mmbailey might answer this. #ElemMathChat
A4: At first I thought all possible numbers would have to have 4 ones. But I think I got fixated on tens and ones and that the splats would be multiples of 10... Mistakes are fun. #ElemMathChat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Student will sometimes arrive at the total must be 4 more than a multiple of 3. (or 1 more)
Then they'll wonder how many less than a multiple of 3 might that be described as.
#Elemmathchat
A4 if each splat has the same value you under it the answer could start at 7 then add three each possibility. 7, 10, 13... if the splats don’t have to hide the same value 7 and larger would work. 5 and 6 will not work. #ElemMathChat
A4: Could be (any multiple of 3)+4 7, 10, 13, 16, 19, etc...
Can not be 8, 9, 11,12... Or can not be less than 4
The idea of equal groups or repeated addition, the idea of a variable
#elemmathchat
Total can be anything greater than or equal to 7 assuming 0 is not used (otherwise anything greater or = 4). It can’t be anything less than 7 (or 4 if 0 is used). #elemmathchat
A4: I love this question because I have s’s right now that will look at this and go, “Well, what’s the right answer?” & this forces them to NOT CARE ABOUT RIGHT ANSWERS. If I could get them all to erase that tendency that would be great #elemmathchat
Here we begin to see a wider and wider variety of responses from students. So many possible ways to approach this - many yet to be discovered. #Elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q4 the answer could be 16,the answer couldn’t be 9 because you see 4 and the leaves 5 and you can’t break 5 into 3 equal parts. Great to start reasoning? #Elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Great point! This is about so much more than the correct answer.
It's about the reasoning, investigation, number sense, and many other things ... mixed with wonder, curiosity, and if you've used it in class a lot of joy. #Elemmathchat
A4: I love this question because I have s’s right now that will look at this and go, “Well, what’s the right answer?” & this forces them to NOT CARE ABOUT RIGHT ANSWERS. If I could get them all to erase that tendency that would be great #elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A4: so then I started still thinking about number four because if half was under each splat then it would be 5 1/2 so the rule changes if fractions are allowed. Hmmm. Maybe. Well 3x + 4 still works but not a difference of 3 between any answer. #elemmathchat
A5: strategy 1 - Start at 21 and count back 6 ... so now I have 15 more dots hiding. Pretend in my mind to put one in each splat while counting to 15. I will need 5 under each splat to use all 15 missing dots. #elemmathchat
I just saw the disclaimer on the original tweet of no fractions, so hmmmmmm I guess 5 and 6 would be out. and then then you would have to then think in multiples of 3 with no fractions. I don't know if no fractions makes this easier or harder! LOL #ElemMathChat
A5: (21-6)/3 = 15/3 = 5 (However, I don't like that i have to represent this symbolically! I really want to grab the counters out of my basement and model it!) #ElemMathChat
A5: I trial and error... first I try 2 dots in each splat, but that gets me to 6+6 and that is only 12. If I double my first attempt and do 4 dots in each splat that would be 12+6 and I get 21. Now I only need 3 more dots - so 1 more per splat. 5 in each splat! #elemmathchat
I would say that each shape of blue dots could be a diamond shape, making the total possibly 7. The concept of spacial mapping comes to mind. #elemmathchat
A5: Guess and check and revise based on what you discover. I was lucky. I started with 5 because counting by fives is something I’m good at! 😀 #elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A5: Start with 6. Draw 3 open circles. Keep adding one to each circle as you count up from 6 and stop when you reach 21. The number of tallies in each circle represents the number of dots under the splat. #ElemMathChat
Ooooooohhhhhhh so like just 21/3 and then when it’s 7 you just take away 2 because each splat sort of has 2 dots next to it. So 5. #elemMathChat Clear as mud. Right?
A5: Start with 6. Draw 3 open circles. Keep adding one to each circle as you count up from 6 and stop when you reach 21. The number of tallies in each circle represents the number of dots under the splat. #ElemMathChat
A5 A way that is new for me. Count up the existing dots, then one by one, draw a new dot in each splat in a clockwise fashion. Keep going until that total amount of dots is 21. #elemmathchat
A5: Take 5 showing dots and cover them with a fourth splat then having one left over reason that the remaining must also be groups of 5 making since all groups are equal #elemmathchat
A6: provides students a way to check their work and make connections. They don’t have to rely on Someone else to tell them they are right #ElemMathChat
A:5 A student with little access might try trial and error. 6 + ___ + ___ + ___ = 21 2+2+2 = 6 6+6= 12 way to low. Tries 4's 4+4+4 = 12 12 +6 = 18 Close just need to add 3 - one to each group. 6 +5+5+5 =21 Yeah! #elemmathchat
A6: It is critical because it forces you to reason and it opens up the conversations so that everyone in the room is considering what is possible. #elemmathchat
A5 there are 3 splats and 6 dots. Dividing them into 3 groups I have a splat and 2 dots in each group. I can divide 21 by 3 and get 7. So a splat and 2 dots is the same a 7. I can represent 7 with 7 dots and then take away 2, leaving 5 dots the same as a splat #elemmathchat
A6: Asking " how else could you know" in a math class is important to have assurance that your student actually understands and know how to do the work. If a student can get to the same answer in more than one way they have mastered it. #elemmathchat
A5 3n+6=21 is most efficient way for me to solve. I could see Ss using table with 6 in the first column & multiples of 3 in next column until they found the solution of 21 #ElemMathChat
6+3 no
6+6 no
6+9 no
6+12 no
6+15 ding ding ding!
#Elemmathchat
A6 “How else could you know” pushes the focus on multiple valid strategies, allowing all children to realize that their own thinking is valid #elemmathchat
A4 I love how these tasks allow the facilitator to say, “yes but what else could it be?”
Allows for multiple solutions and to easily move to generalizing.
#elemMathChat
Hello everyone. I'm going to play catch up. Apologies in advance for some possibly contrarian answers.
A1: 5 most important words in a maths lesson: "Socialism kills every time it's been tried."
#elemmathchat
A6 “How else could you know” pushes the focus on multiple valid strategies, allowing all children to realize that their own thinking is valid #elemmathchat
You know the total is 21. If you can see 6 dots then 15 of them must be hidden. Placing 15 equally into the 3 splats gives you 5 dots per splat. #elemmathchat
Lots of ways to solve a problem, lots of ways to attack a problem. All of them have merit, asking how else proves this, stretches thinking, builds persistence and math reasoning. #ElemMathChat
A6: How else could you know opens the situation up to so many more mathematical representations. This is so important because not every problem has a clear cut solution or path to that solution. #elemmathchat
A5 there are 3 splats and 6 dots. Dividing them into 3 groups I have a splat and 2 dots in each group. I can divide 21 by 3 and get 7. So a splat and 2 dots is the same a 7. I can represent 7 with 7 dots and then take away 2, leaving 5 dots the same as a splat #elemmathchat
A6: " How else could u know?" helps to build flexibility, a variety strategies. Opens up to having conversations abt how each is related to the other. A way to push thinking towards considering relationships. Values that there isn't just 1 way to approach things #elemmathchat
A6: Pushes students to think deeper. The first strategy we see is typically “easy” for us to find. There has been little productive struggle until we are pushed to find another way (aka see A5...I really had to think to get my second way) #Elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
These also allow for the “undoing” of arithmetic. Look at the total value, the visible dots, subtract and then divide.
Important for Ss to both do and undo
#ElemmathChat
A6: Encouraging multiple ways of thinking about a problem also helps Ss see the connectedness of mathematical thought/concepts for the individual S and also the class as a whole. #elemmathchat
A6: for the exact reason that just happened to me... to allow the opportunity for kids to say/think ¨OH!!! I never thought about it that way. Now I get it!¨ #elemmathchat
Asking, "How else could you know?"
is a great way for us to make sure our students are seeing the relationships and connections needed for relational understanding. If we are aiming to help our Ss understand, then we need to expect them to make sense of things.
#elemmathchat
A2: It appeals to our deep, instinctive curiosity to know.
Eg. provide a diagram of 5 of 7 triangle types and ask Ss to identify the missing two.
#elemmathchat
A6: Not everyone sees things the same way. Asking Ss how else they see it pushes them to look beyond the standard way. The first couple of answers aren't that interesting - they're often typical. The magic happens as you have to be creative to find new ways. #elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A6: So important because then even the teacher gets to learn new strategies from the students ALONG with the kids in the class. #truestory#elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Really challenge yourself here. Ask yourself, "How else could I know." Aim for at least 3 approaches, even if you aren't able to fit them into a tweet.
#Elemmathchat
A7: Strategy 1 - Well first I need 1 more fourth to get to having 2 full dots. So under the splat I need 2 more whole dots and 1/4 to get a total of 4 or maybe even 9 fourths underneath the splat. #elemmathchat
A:6 Helps students think with more flexibility, which can help them when they are faced with a math challenge that they have not experienced before. Also, teaches them that there is more than one way to approach a problem. Could help them become more efficient. #elemmathchat
A7: keep adding counters “whole numbers” until I get close to 4 and then add the difference so add 2 to get to 3 3/4 and then add 1/4 more. #ElemMathChat
Yes, and the visual can really support the vocabulary in development. #Elemmathchat
Students frequently point to the parts of the Splats as they try out the new vocabulary. #Elemmathchat
To me, it offers an opportunity to students who have thoughts on how to solve a problem "unconventional" but dont know if that's acceptable. #morethanoneway#elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A7: Strategy 2 - I am thinking like count around the circle activity. 1 3/4, 2, 2 1/4, 2 2/4, 2 3/4, 3, 3 1/4, 3 2/4, 3 3/4, 4! I counted up 9/4ths to get to 4 #elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A7 I see 1 whole and 3 quarters, to get to 4 I need another quarter to make 2 and two more wholes to get to 4 so that’s 2 1/4 under the splat! #elemmathchat
A7: Strategy 2 - I am thinking like count around the circle activity. 1 3/4, 2, 2 1/4, 2 2/4, 2 3/4, 3, 3 1/4, 3 2/4, 3 3/4, 4! I counted up 9/4ths to get to 4 #elemmathchat
A6 Asking for multiple ways gives my Ss confidence. They figure out that the way they did it is still right & might not make sense to the S who is always right. Everyone has something to add to the discussion #ElemMathChat
A3: having a science and engineering background with a strong interest in philosophy I'd wonder whether or not there still are any dots. What are the dots made of, what substance has made the splat. How do the two chemically react?
#elemmathchat
Q3. Look at the picture and describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A7: Well. 1 3/4 plus ? equals 4. So wow. For sure you need 2 wholes which is 8/4 then you need an extra 1/4 to make the 2 wholes in the first place. So. 9/4. Ooooooh. Or. 4 is the same as 16/4. Cool. You can see 7/4. Ohhh baby. So 9/4 are missing. 😲 #elemMathChat
Q8. Look at the picture and describe the steps you could take to find the number under each Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
This question makes me think of @gfletchy emphasis on the vocab of "3 one-fourths". I could add another "one fourth" to make 2 and then add 2 wholes to make 4. The language supports the visual. Great question, @SteveWyborney! #elemmathchat
Really challenge yourself here. Ask yourself, "How else could I know." Aim for at least 3 approaches, even if you aren't able to fit them into a tweet.
#Elemmathchat
A3 I see that some dots are in quarters. First, I would count the dots already shown (1 3/4). I would draw 1 dot and continue counting (2 3/4), then another dot (3 and 3/4.) Then, to get to 4, I would draw another 1/4. I found up my drawings: 2 1/4 #elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A8
16-1 = 15 then "attach" one 1/4 to each of the splat. 15 /3 is 5 so including that 1/4 the total is 5, then subtract the 1/4 to get 4 3/4.
#elemmathchat
Q8. Look at the picture and describe the steps you could take to find the number under each Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q8. Look at the picture and describe the steps you could take to find the number under each Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Q7. Look at the picture and describe the steps you could take to find the number under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
Yes! asking for multiple ways encourages Ss to not stop thinking the minute they have one answer. The same way @SteveWyborney challenges us to come up with 3 ways, I just can not help myself from trying to explain a creative way that no one else might have tried. #elemmathchat
You could do this numerically with subtraction or visually by counting out how many dots are missing. If you have 1 3/4 dots then I would add one and count until I hit four, which is 2 1/2
#splat#elemmathchat
A8: add what’s showing, subtract it from the total, divide the remaining by the number of splats. This is what I revert to because it is my initial preferred method so it is easiest for me to describe in words. #elemmathchat
A7: another way. Count up.
1, 1 and 3 quarters, then 1 more quarter gets me to 2. Another 2 gets me to 4. So the splat has 2 and 1 quarter under it.
#ElemMathChat
A:7 First the fourths equaling 3/4 and then I saw the total of 4 so I know that there have to be fractions under the splats. So uncovered there are 1 3/4 dots leaving 2 1/4 under the splat or 9 -1/4s or any number of 1/4s and whole numbers that would equal 2 1/4. #elemmathchat
This attaching concept is very helpful. That is a great lesson all by itself. The usefulness of putting numbers together and taking numbers apart. We really see it in this context. #Elemmathchat
A8
16-1 = 15 then "attach" one 1/4 to each of the splat. 15 /3 is 5 so including that 1/4 the total is 5, then subtract the 1/4 to get 4 3/4.
#elemmathchat
Q8. Look at the picture and describe the steps you could take to find the number under each Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
The total must satisfy: 4 + 3*S (where S = number of dots under one Splat, assuming there are any still there)
Concept of combined multiplication and addition emerges.
#elemmathchat
Q8. Look at the picture and describe the steps you could take to find the number under each Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A8 This is really fun! I see that we’re working with 1/4 pieces. So I’ll do that too. Just keep distributing 1/4 pieces to each splat until I have a total of 16 for all the pieces. Then, count what is each splat. Counted 19 1/4 pieces, or 4 3/4. #ElemMathChat
A8 another way....
add 3 one-fourths (one to each splat) until you have a whole number of fourths - then add that one dot shown - then see if the difference is a whole number divisible by 3 - if so, add that number of dots to each splat
#thinkingINprogress#ElemMathChat
A8 This is really fun! I see that we’re working with 1/4 pieces. So I’ll do that too. Just keep distributing 1/4 pieces to each splat until I have a total of 16 for all the pieces. Then, count what is each splat. Counted 19 1/4 pieces, or 4 3/4. #ElemMathChat
Any time you value multiple pathways you show that you value student thinking over answers.
Every S response is an opportunity for assessment.
#ElemmathChat
A8 another way....
add 3 one-fourths (one to each splat) until you have a whole number of fourths - then add that one dot shown - then see if the difference is a whole number divisible by 3 - if so, add that number of dots to each splat
#thinkingINprogress#ElemMathChat
A8: I want to do same and different with the one earlier in the chat. So 16-1 whole is 15. Then because there is 1/4 next to each of the 3 splats you can divide 15/3 and know there are 5 - 1/4 under each. So 4 3/4. #elemMathChat
A8 Using a similar strategy as before, if I remove the first dot then my target is 15. 15/3 = 5 . I have 3 splats and 1/4 so a splat and 1/4 is the same as 5. With this thinking, a splat is worth 4 and 3/4 #elemmathchat
A5: At this point I'd be taking steps to hack the school firewall to play Fortnite.
Why would a child care how many dots are under a splat!? Or, perhaps more importantly, why would we want them to care? What sort of abstract-concrete hybrid world is this?
#elemmathchat
Q5. Describe the steps you could take to find the number of dots under the Splat!
CHALLENGE: Answer this question at least 3 different ways with at least 3 different tweets!
#elemmathchat
A9 A strategy that is part of my pedagogy is to allow for productive struggle. Because when students struggle productively they learn and discover WAY more than if just told how! We are tessalating tomorrow. The struggle is real! #ElemMathChat
A8: I could think 16 - 1 is 15. Then 15 ÷ 3 is 5. Each of the 3 splats is 5 less one quarter (since there are 3 one quarters). Therefore, each splat is covering 4 and three quarters. #elemmathchat
A9: Me too! The more strategies and ways of thinking about something, the more likely we'll have Ss "getting it" and being able to connect to new ideas. #ElemMathChat
A9: Since I am a student still, hypothetically, I would teach my class that it is almost always another way to get an answer in math & then probably introduce Splat !! #elemmathchat
A9 A strategy that is part of my pedagogy is to allow for productive struggle. Because when students struggle productively they learn and discover WAY more than if just told how! We are tessalating tomorrow. The struggle is real! #ElemMathChat
Ahh and there lies a dangerous trap. Chasing all the “neat ways” Ss can solve a task. Sometimes we need to stay focused on the learning goal.
What is the important math my Ss will learn today? Do my actions support this goal?
#elemMathChat
Yes! asking for multiple ways encourages Ss to not stop thinking the minute they have one answer. The same way @SteveWyborney challenges us to come up with 3 ways, I just can not help myself from trying to explain a creative way that no one else might have tried. #elemmathchat
A8: 16 - 1 is 15. So there is going to be less than 5 under each splat for sure. If I start at 4 whole dots in each splat, that would give me 13 and 3/4. Then start adding groups of 3/4 (1/4 in each splat). 6/4, 9/4, 12/4 (3 dots) 4 3/4 under each splat. #elemmathchat
Love it! I'm going to be encouraging Ts to incorporate Numberless Word Problems into our new curriculum in order to focus Ss on meaning making of the problem b4 solving. #ElemMathChat
I am going to set some time aside to go back and look at all the multiple ways to solve these splats! I couldn't keep up with all of them, but am loving what has emerged. #elemmathchat
On maternity leave but I will be emailing teachers to ask them how including Take some time to think. and How else could you know? in their math classrooms could increase student engagement and math discourse. #elemmathchat@mscarissaspeaks be on the lookout for my email! 😎
Thank you, everyone! I'm reading your ideas as quickly as I can!
Great thinking!!!
I really appreciate your taking the time to be a part of the discussion this evening! #elemmathchat
A:8 16 - 1 3/4 = Ss might think counting up 1/4 gets to 2 then 16-2= 14 so it is 14 and 1/4 or 57 fourths. 57 divided by 3 is 19 fourths. then could think mixed numbers 16 fourths is 4 leaving 3/4s. checking 4+4+4 +3/4 +3/4+3/4 = 12 + 6/4 +3/4= 12 +8/4 +1/4= 14 1/4 #elemmathchat
