The most important part of solving a problem is, first, finding out what the problem is. Next, you think of a plan on how to solve it. Then, you actually figure out the problem. When you are solving a problem, always remember: Never give up. Mrs Marley, my Gr.2 teacher, always said to have a growth mindset instead of a fixed mindset. If you have a fixed mindset, you are probably not going to finish it, and probably get a bad mark. You are probably going to be really miserable. If you have a growth mindset, you are probably get it finished, and get a really good mark, and be really happy.
When it comes to math, I find it difficult to learn math in a new way. For example, before I knew what division was, I did not completely understand. And it’s not just math equations. It’s things like angles, and area in circles. I don’t exactly know why you have to multiply “Pi r squared”. I wonder why it has to be the number Pi? And how, in angles, is 360 degrees not just 0 degrees? I do not understand. Things like that.
When it comes to math I find it easy to add and subtract using strategies like place value chart, and add up to subtract. They give me easier math equations like 7 + 6 or 9 – 3. Then, using those small equations, I can answer the one big equation more easily.
When I think of math by itself, I think of answering math equations. I do not think of answering any specific math equations* or things like addition, or multiplication, just math equations itself. *I do not think of answering any math equations of any kind, just, again, math equations itself.
But, when I think about it more deeply, I see math almost every day!
For example, I like to figure out how much time there is before bed, so I can have a treat before bed. Also, I went to buy a few things at the dollar store a couple months ago, and I had to figure out how much tax I had to pay, and the change I would get back. Another example is that sometimes I want to play video games by myself, and I have to figure out a fair time for when my brother can play.
At the movies Sadie ate one-fourth of the popcorn. Her mom ate two-eighths of the popcorn. Did they eat the same amount of popcorn? Explain the strategy you used to solve this challenge.
Sadie ate the same amount of popcorn as her mom. To figure out the question, I first drew a circle to represent how much popcorn there was. Then, I split the circle into eighths.
When I was drawing the lines inside of the circle, I drew it first in quarters. When I was finished drawing the lines inside the circle, I saw that 2 eighths was a quarter. I did not need and strategy at all to figure the question out. Here is an example of what I was thinking:
In this picture there are different shapes put together to make one big hexagon. In the middle there are 3 smaller yellow hexagons. Around those hexagons are 3 blue rhombuses. Around the hexagons and rhombuses are 6 pink trapezoids. Beside those trapezoids are more blue rhombuses. If you count all of them one by one, you will find that there is 18 shapes to make up the one big hexagon.
Most of the hexagon is made up of blue rhombuses. This is because there are 9 of the rhombuses, but 6 of the trapezoids and 3 of the hexagons.
In this picture there are 2 growing patterns. Here is one of them:
3 hexagons, 6 trapezoids and 9 rhombuses. You see, there are 6 of the first shape. Then, in the next shape, 3 are added to make 6. In the last shape, 3 more are added to make 9.
Here is the other:
3 hexagons, 3 rhombuses, 6 trapezoids, 6 rhombuses. In the middle, there are 3 hexagons and 3 rhombuses. They both have 3. On the outside, 3 are added to make 6. There are 6 trapezoids and 6 rhombuses. Again, they both have 6.
Chicken and Sheep, Heads and Feet
Samantha has chickens and sheep on her farm. Each chicken has two legs and
each sheep has four legs. Each chicken has one head and each sheep has
one head. She looked out one day and counted 48 animal heads and 134 legs.
How many of each animal live on the farm?
There are 19 sheep and 29 chickens. This is how I figured that out:
We know there are 48 animals in total, because Samantha counted 48 animals heads, and each sheep and chicken have 1 head. First I started guessing that there were 24 sheep. Then, to figure out the number of chickens, I subtracted 24 from 48, which is 24. Then I multiplied the number of sheep x4, the number of chickens x2, and added both those numbers together to figure out the total of legs. If there are 24 sheep and 24 chickens, there would be 120 legs, which is not 134 legs, as it says in the problem.
I then made a chart, and used the same technique with different numbers of sheep and chickens. As I got closer to the right answer, I used numbers closer to the ones I had before. When I used 19 sheep and 29 chickens, I got the right answer.
In this picture there are 96 towels. This is how I figured it out: First, I counted 6 towels in 1 stack. Next, I counted how many stacks there were in the top row. There were 4 stacks in the top row. Then, I counted the left column. Also 4 stacks. This means there are 4 stacks in each row and column. There are 16 stacks in the picture. I know this because I used the equation 4 x 4 = 16. I know this equation because I have memorized it. But the question is to find out how I figured out that there were 96 towels in the picture. Well, we know that there are 6 towels in each stack, so I took the 10 out of 16. 10 x 6 = 60. I know this, because I have memorized a strategy for the 10x table: You add a 0 to the other number you are multiplying. Then, I took the 6 out of 16. 6 x 6 = 36. I know this, because I have memorized the equations 6 x 4 = 24, and 6 x 2 = 12. I took the 10 out of 12, and added it to 24, to make 34. Then I took the 2 out of the 12, and added it to 34, to make 36. 60 + 36 = 96. I know this, because, first, to figure out the equation, I took the 6 out of 36. Then, I took the 0s out of 60 and 30. 6 + 3 = 9. After that, I put the 0s back. 60 + 30 = 90. Lastly, I put the 6 in 36 back, to make 96.
I think Avril’s estimate makes sense. I think this, because there is a $5 bill in the picture. Then there is a toonie. A toonie costs $2. $5 + $2 = $7. Next there is a loonie. A loonie costs $1. $7 + $1 = $8. After that, there is 3 quarters. Each quarter costs $0.25. $0.25 x 3 = $0.75. I figured that out by counting by 25’s: “25, 50, 75”. I have now counted $8.75. I estimated the rest of the coins would make around $9. The exact amount of Avril’s money is $9.15. I know this, because I know there is at least $8.75. So I started at $8.75. In the picture, there was 2 dimes. A dime costs $0.10. $0.10 $0.10 = $0.20. I figured that out because that is one of the math equations I have already memorized. $8.75 + $0.20 = $8.95. I figured that out by counting by 10’s starting at 875: “875, 885, 895”. Next there are 4 nickels. A nickel costs $0.05. $0.05 x 4 = $0.20. I figured that out because that is another math equation I have memorized. $8.95 + $0.20 = $9.15. I figured that out by splitting the $0.20 in half, so I could count by 10’s: “895, 905, 915”.
In this picture there are 35 pretzels. I know there are 35 because I counted by 1’s across from left to right. “1, 2, 3, 4, 5”. Then I counted by 5’s from top to bottom. ¨5, 10, 15, 20, 25, 30, 35¨ In this picture there are 4 x 4 holes in each pretzel. 4 x 4 = 16. 1 + 1 = 2. 2 + 2 = 4. 4 + 4 = 8. 8 + 8 = 16. If I eat 5 of these pretzels, there will be 30 left. 35 – 5 = 30. If I eat these pretzels 5 at a time 6 more times, there will be none left. I ate 7 of these pretzels from top to bottom. If I eat these pretzels 7 at a time 4 more times, there will be none left.