Backwards Math

Today was Backwards Day!  In math we were given the answer to a question.  We had to figure out what the question might have been.  Check out our work!

Math Talk

We had a great discussion about this picture in Math today.  Our discussion showed our understanding of estimating, comparing, and adding numbers; measurement; and even probability:

I don’t think 18 belongs because it’s a little smaller number than the blue and I think there’s more in there than 18. (Ekmeet)

I think the green one has 18 marbles because those ones are longer and the other ones are shorter so I think you would have a bigger number like 55. I think the green ones have 18 because they’re longer and that’s my estimate. (Chloe)

I don’t think 139 belongs because it probably will be way too much of the actual limit.  I think 11 might belong because the green has bigger marbles than the blue so it could be 11 and I’m pretty sure it’s 18 in the blue one or more but it only makes 20-something, 29 and there’s no 29 in the answers.  I think 11, 18, one of them is probably not the right answer.  And also it couldn’t be 73 because that’s way too much so I think it’s either 66 or 55. (Parker)

I think 139 might be the total or 73 because those are the two highest. I think 55 is the one in the blue and 18 is the one in the green one. (Owin)

I think 139 is too big because it’s a 3-digit number and all the other ones are not.  I think 11 is the amount in the green one and the blue one has 18. I think 55 or 73 could be the total. I think the blue one has the most because it has smaller beads. (Lily)

I think it’s likely 55 or 73 to be the total and I think there could also be 18 in the green bowl and there  also could be 55 in the blue ones. (Delaney)

I think the blue one is higher because I think the blue one has 66 and the green one has 18. (Nattas)

I think 66 and 139 and 11 do not match because 11 is way too small.  139 is way too big.  66 is big enough to just be as big to not fit in the blue bowl. So I think it’s either 18 or 55. (Stevan)

Mrs. Ho: How might we check the reasonableness of our guesses?  We know we need to put two numbers together to make the total.  Can you think of a way to check to see if the numbers we’re combining make sense?

I did some math and I think 55 and 18 go together and it made 73 so I think that’s the answer. (Owin)

I also think it’s 73 because the green one looks like it has 18 and the blue one looks like it has 55 so I also think it’s 73. (Chloe)

It might be likely that it’s 73 but you can’t see the marbles in the back. (Chloe)

You can see more from the other side so if you see one on the back you can count two more. (Nattas)

I put 73 + 66 and it made 139 so my two guesses are 18, 55 and 73 or 66, 73 and 139. (Owin)

Mrs. Ho: I noticed that if I start with 55 and add 11 more, I will have the answer 66 because there’s 1 more one and 1 more ten.  So three possible answers are:




Which is the most reasonable and why?

I think it’s 55 and 18 is 73 because in the green bowl it looks like there’s 18 because it looks like there’s around the same in the front and the back. I think around 9 would be around in the front and around 9 in the back so I think it’s the same. In the blue bowl the marbles are smaller so I think you can fit more in the bowl and it’s filled up so there would be a lot of them. (Delaney)

I think 11 and 55 are equally likely to be the answer because 55 might be the amount in the blue bowl and 11 in the green bowl. (Owin)

Crossing the River

After we had a chance to play, we reflected on the game.

We noticed it was impossible to get a 1 because there were two dices.  Even if you get a 1 on one, you still need to roll the other dice. (Delaney)

I noticed that how the mat was made, it went up to 12. Because if you have 6+6=12 it would be would be impossible for the number you rolled to be out of the numbers on the map. (Owin)

I noticed the same as Owin and Delaney, Matthew and me, because it was impossible to get 1 and it would also be impossible to get higher than 12.  (Tristan)

The number that me and Stevan mostly got was 2 and 4 because we tried to roll a 6 but we did it the opposite way that the 6 was. So we didn’t get any 1s because there’s two dice and if you roll with two dices you get 1 and a 1 on both dices so you would get 2 instead of a 1. (Chloe)

Next, we went through each dock number and tried to figure out what numbers we would need to roll to make that dock number.  Here is what we found out:

1 Impossible
2 1+1
3 1+2, 2+1
4 2+2, 3+1, 1+3
5 3+2, 4+1, 2+3, 1+4
6 3+3, 4+2, 5+1, 2+4, 1+5
7 5+2, 4+3, 2+5, 3+4, 6+1, 1+6
8 4+4, 5+3, 6+2, 2+6, 3+5
9 3+6, 4+5, 6+3, 5+4
10 5+5, 6+4, 4+6
11 6+5, 5+6
12 6+6


I noticed that every time it goes 1 bigger. (Delaney)

If you go on 2 you have 1 answer and so it’s like a growing and shrinking pattern. (Chloe)

Mrs. Ho: If you were to play this game again, how might you decide where to put your boats?

I’d put one of my boats on 7 because it has the most answers. I wouldn’t put any of my boats on 1 because you can’t get it when you roll two dices. I’d do any number higher than 1.  (Stevan)

I would put mine on 8 because it’s sort of the same as Stevan’s but it’s just one down. (Armeet)

I would do all the even numbers or I would put it on two of the odd numbers like 5 and 9 because it’s more likely that you’re going to roll an even number because last time when me and Stevan played I mostly got even numbers. (Chloe)

I’d put four on 7 because 7 has the most. I’d put two on 8 because 7 has the most and 8 is just one less. (Owin)

I think I would put it on numbers higher than 2 or 1 because 2 it has a chance but it’s very hard to get it because last time when I was against I put it on 2 and that was the only one I have left to do. It was very hard to get it. (Delaney)

I’d probably not put it on 6 or 2 because it would probably be more unlikely to roll a 6 because it only has one answer. (Parker)

Probability Experiment

We look at the weather forecast every morning during Morning Announcements. We used probability words (likely, unlikely, certain, impossible, equally likely) to describe the chance of different things happening.  For example, what is the probability we’ll have an indoor recess today?

Today in math we did a probability experiment.  Mrs. Ho told us that each bag has exactly 20 cubes in it.  Only one bag has exactly 10 blue cubes and 10 red cubes.  We took turns picking a bag for Mrs. Ho to draw one cube out of, and stopped at different points to discuss the possible outcomes.

Bag C is likely to have 10 reds and 10 blues because it has a blue and a red. (Parker)

It’s impossible for Bag A because it has a green. (Tristan)

I think bag B and D are also likely because there’s still red. (Chloe)


I think it’s very likely that C is going to be the one because we already have 5 blues and 2 reds on C and on the other ones there’s only 1 or 2 reds. (Student #20)

I think that C is actually unlikely and in middle of likely and unlikely [equally likely] because you pulled out 5 blues and 2 reds and you said you need to have 10 of each colour but it’s mostly been blues that have been pulled out. (Stevan)

I think D or B is the answer because we haven’t checked the whole bag yet so I think we should keep checking all the bags so we make sure because people keep picking C. (Owin)


I think it’s likely for it to be C because what we pulled out so far has only been red and blue and I think it’s impossible for it to be A because we pulled out a green there are supposed to be 10 blues and 10 reds and if you have a green there is only 9 of one colour. (Delaney)

I think likely for C to win because I saw 10 blues and there’s 9 reds. If we get one more than it is likely to C is going to win. (Daniel)

I think C because it has more blues than reds. (Steven)

 After the experiment Mrs. Ho revealed what was in each bag.  Bag C had exactly 10 reds and 10 blues.