I am excited about the combined #mtedchat#OregonMathChat tonight! Let's talk about math and inviting students - and ourselves - into the wonder of math!
I'm Steve, a district math coach from Oregon. I'll be posting questions tonight.
I'm from the small part of Oregon that is in the Mountain Time Zone.
#mtedchat#Oregonmathchat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
If you are using the Twitter website, did you know you can put both hashtags in the search area to automatically add them to every tweet and follow the dialogue? I copy the tags so I can paste them in tweets as well ;) #mtedchat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Take a second to tag a friend who would be interested in taking on the challenge Steve will be introducing tonight!! I LOVE that we are doing this series! #mtedchat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q2 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q2. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
A1 b) My 8-yr-old says: 💜
I will pretend there are 5 in each red group. That would make 25. Take away the extra 5, so 20 red. Then, there are 45 in all, so I know there are 25 blue. 20+25=45 #MTedchat#OregonMathChat
Q1 Here are 45 cubes. How many different ways can you see 45?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
A1: Of course there’s 9x5 but I have to say that the colors made it hard to see. It’s something to consider for color blind people. #MTedchat#OregonMathChat
Q2. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
I agree. That is an excellent point. I've tried different colors (yellow) an different backgrounds and am looking for the best combo. When I use this in class, I literally have it fade away and here I captioned a moment in the middle of the fade.
#mtedchat#Oregonmathchat
Q2 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q2. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
A2: In each group there are 7 blue cubes and 3 red cubes, making 10 cubes in each group. Since there are 4 groups with 10 cubes in each group, there are 40 total cubes. #MTedchat#OregonMathChat
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q2 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Q3. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A3: This is going with an assumption that there are 2 more cubes you can’t see on 2nd row of the base - there are 3 blocks in each group with 2 groups that form the base and 4 groups making the “frame.” 3 blocks per group x 6 groups = 18 total blocks. #MtEdChat#OregonMathChat
A3: I see this:
6 groups of 3 blocks.
I assume the last group in the back is 3 because the ones above it are level.
So, 3*6 =18.
#mtedchat#Oregonmathchat
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A3: This is going with an assumption that there are 2 more cubes you can’t see on 2nd row of the base - there are 3 blocks in each group with 2 groups that form the base and 4 groups making the “frame.” 3 blocks per group x 6 groups = 18 total blocks. #MtEdChat#OregonMathChat
A2: I love these questions. Definitely putting my decomposing strategies to the test. I'm seeing 4 groups of 5 (20) + 4 groups of 3 (12) + 4 groups of 2 (8) = 40
#mtedchat#Oregonmathchat
A2 My 8-yr-old:
I see the red first. 3-6-9-12.
Then I see 7 blue in each group.
7+7=14. Then 14+14=28.
12+28=40.
Then we saw @NVradenburg's explanation, and she says: "Oh, that's way easier. I should've done that! Let's do another!"
#MTedchat#OregonMathChat
Q2. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
A2: I love these questions. Definitely putting my decomposing strategies to the test. I'm seeing 4 groups of 5 (20) + 4 groups of 3 (12) + 4 groups of 2 (8) = 40
#mtedchat#Oregonmathchat
A2 My 8-yr-old:
I see the red first. 3-6-9-12.
Then I see 7 blue in each group.
7+7=14. Then 14+14=28.
12+28=40.
Then we saw @NVradenburg's explanation, and she says: "Oh, that's way easier. I should've done that! Let's do another!"
#MTedchat#OregonMathChat
Q2. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste the at the end of your tweet.)
#MtEdChat#OregonMathChat
Is that a rhetorical question? ;) #mtedchat#OregonMathChat The answer is 18...so numerically yes... You can't currently split the figure into symmetrical halves without cutting individual cubes.
A3partb: Splitting it in half could be done by seeing 3 groups of 3 blocks each for the base and 3 groups of 3 blocks for each side of the “frame.” #MTedchat#OregonMathChat
#OregonMathChat#mtedchat Since there are cubes, they can slide, rotate etc & create different views like 9 sets of 2 or vice versus. Since the cubes could be tofu, they can easily be split into two halves vertically.
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Sometimes the students will "slice the cubes in half" because that is a useful approach to them. It's pretty fascinating and eye-opening. #mtedchat#Oregonmathchat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q3 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q3: Love it. Tetris is paying off. I see 2 empty rows of black that the other cubes can slide into. Sliding one of the rows up, I can see the hidden row. This gives me 3 rows of 4 cubes, showing 12 cubes + 3 cubes = 15 cubes.
#mtedchat#Oregonmathchat
Q4. How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
What I’ve learned since doing activities like this with my class is that they are able to “see” math more easily than I am. I am a product of the memorization generation and I can tell my brain has to work a lot harder to do things like this. #mtedchat#OregonMathChat
Nope. because the definition of cube was not explicit.
Many are going on the assumption of the blue and red cubes as the cubes.
We are becoming more aware of negative space. #mtedchat#Oregonmathchat
In reply to
@BenGarciaSOPTV, @oregonmathchat, @NVradenburg
Q3: Correction. Love it. Tetris is paying off. I see 2 empty rows of black that the other cubes can slide into. Sliding one of the rows up, I can see the hidden row. This gives me 3 rows of 5 cubes, showing 15 cubes + 3 cubes = 18 cubes.
#mtedchat#Oregonmathchat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
When we give our students opportunities to describe multiple mathematical perspectives they often begin to move fluidly among those vantage points. #mtedchat#Oregonmathchat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Ooh, so true. This helps me see how I could slide the top part of the 'frame' down a row, and move one row of the 'base' up to fill the space in the middle. Fun manipulative the visual! #MTedchat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A4: There are 12 blocks in the 3 by 4. The side wall is 3 by 3, making 9 blocks. There are 5 more blocks forming the remaining parts 12+9+5 is the same as 12+10+4 (decompose & make friendly ten). Total is 26 blocks. #MtEdChat#OregonMathChat
Q5. How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A4: When I look at the figure, I see 3 shapes. The back shape is an O made up of 12 cubes. Then I see 2 L shapes. The Ls are 7 blocks each. So 12 + 14 = 26.
A 2nd look I saw the left wall as 12 blocks + The bottom 9 + the sideways 5 = 26.
#MtEdChat#OregonMathChat
#OregonMathChat#mtedchat I like this as it could be used as a growing pattern or the total cubes like here. The growing pattern is +3 so counting the 3's, 1 set, 2 sets, 3 sets plus each figure has a constant 2. I see 6 threes + 3 twos = 24 or combine as 4 sixes = 24
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
24... but I’ve never taught math... I haven’t had a math class since graduate school like 10 years ago. Am I suppose to see more cubes than I counted for face value? I feel like all these questions are tricking me somehow... #mtedchat and #orMathchat@NVradenburg@techyturner
In reply to
@oregonmathchat, @NVradenburg, @techyturner
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
I looked at this first as 3 crosses with 5 blocks each. And like me, the 2nd and 3rd ones got wider. The second with one extra group of 3, and the other with 2 groups of 3. So I saw this as 15 + 3 + 6 = 24
#MtEdChat#OregonMathChat
Nice use of annotation, Amanda!
#mtedchat#Oregonmathchat
This helps me to see how you see it growing. You could probably identify what a 4th term would look like pretty quickly using this visual.
Q4 How many cubes are there in all? Describe what you see and how you know?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
Q6 Look! Some of the cubes are melting! When they finish, the next layer will melt. How many cubes will be left? Why do you think so?
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#MtEdChat#OregonMathChat
Q6. Look! Some of the cubes are melting! When they finish, the next layer will melt. How many cubes will be left? Why do you think so?
Remember to use both hashtags.
#MtEdChat#OregonMathChat
Q6 Look! Some of the cubes are melting! When they finish, the next layer will melt. How many cubes will be left? Why do you think so?
Remember to use both hashtags.
#MtEdChat#OregonMathChat
A4 Ohh, this one is making us THINK! Anna and I get 24. She saw 5+8+11=24. I saw the 5 shape (plus sign on left) repeat in each of the following groups (5x3=15). Plus 3 in the middle (15+3=18) plus 6 added on on right (18+6). Hard 2 explain in a tweet! #MTedchat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A4 #MTEdchat 26 cubes. Base is 12, left side is 9. Added 3from right side to the base to make 15. Added 1 from top to left side to get 10. 1 is left. 15+10+1=26 #OregonMathChat
Q6 Look! Some of the cubes are melting! When they finish, the next layer will melt. How many cubes will be left? Why do you think so?
Remember to use both hashtags.
#MtEdChat#OregonMathChat
Q5 How many cubes are there in all? How do you know? How else could you approach this question?
Remember to use both hashtags.
(Hint: Copy them onto your clipboard then paste them at the end of your tweet.)
#MtEdChat#OregonMathChat
A6: it looks like only 4 are not currentlytouchkng a red, so I’m going with 4. But it’s also getting late and my math brain is getting slow.
#MtEdChat#OregonMathChat
So, I see the error of my thinking and rushing. (Even though I wasn't)
The block walls are 3*4!
Left wall-12
Rear wall-4*4=16-4-4=8
Base-12-3-3=6
Total-26 cubes! #mtedchat#Oregonmathchat
#OregonMathChat#mtedchat A7 from 14 to 25 added 11 in that layer and then there might be almost double added to that layer. 25 + 22ish = 47
(But history shows I tend to estimate low so 49 makes a nice square number)
#OregonMathChat#mtedchat A7 from 14 to 25 added 11 in that layer and then there might be almost double added to that layer. 25 + 22ish = 47
(But history shows I tend to estimate low so 49 makes a nice square number)
A7 Seems like the 1st cup is over half full, while the 2nd is just under. The third is over the lip of the cup so I think 40 is my estimate. #MTedchat#OregonMathChat
Oh! It's not you, it's totally me.
I like to read and see what others got and then figure out how they got their answer.
Seek first to understand... #mtedchat#OregonMathChat
A7 5th grader thinks the 14 gems were poured into the glass of 25, so an estimate of 39. 3rd grader thinks 45, because 25+25 is 50, but that it's likely a bit less than that. #MTedchat#OregonMathChat
Thank you @SteveWyborney for chat that made me scratch my head tonight! Great fun! Thanks for sharing your expertise! Can't wait for next week! #MTedchat#OregonMathChat
Thanks, friends, for the opportunity to share out some questions and hear amazing perspectives. You can use these 40 lessons to hear the perspectives from your students: https://t.co/mvjMH0n84J#mtedchat#OregonMathChat
