# Category Archives: Mathematics

# DES: Waste Not, Want Not II

This is a screenshot of my packaging design in Sketchup.

*How can our understanding of geometry help us reduce our carbon footprint?*

Our understanding of geometry can help us reduce our carbon footprint because if we know how to maximize our use of space, then we won’t be wasting as many materials, such as paper, which contributes to deforestation. Also, if we know how to create a net with correct precision then we won’t have to waste materials trying to figure out the correct net for the packaging. To reduce our carbon footprint, we can also try to use more eco-friendly materials. However, with different materials you might have to adapt the geometric design of the packaging to suit the material better.

# DES: Waste Not, Want Not

During Design Day today, we had to create a packaging for a fruit (banana) according to the criteria we came up with for a good packaging. I think our packaging mostly followed the criteria because we wrote at the back how you could open it, so the customer wouldn’t have to go through much trouble trying to access it. You can rip this since it isn’t meant for reusing, so afterwards you can just recycle it. The content is also obvious because the packaging says what is in it. It easy to hold as it can be held as a purse and the contents won’t fall out if you turn the package around. It is also an appropriate size for a banana because there isn’t a bunch of extra space in the package which could cause bulkiness. The packaging is light as it is paper, and durable enough for short trips, such as from home to school/work. However, it isn’t too secure or durable because the material is only paper and could easily rip if roughly handled. The banana could also bruise easily in this packaging. This isn’t too attractive, but it is a minimalistic design which can work for selling bananas as they aren’t fancy products. If we had more time, we could have added some more designs to make it more attractive. Also, we should have made some holes in the packaging to let air in so the banana wouldn’t become rotten if kept in for a long amount of time.

Criteria for packaging success:

1. easy to open

2. secure

3. contents should be obvious

4. ergonomic

5. protective

6. appropriate size

7. attractive

8. light

9. durable

# MATH: Managing Markups and Percents

1. What were the two big “take aways” from Managing Markups assessment?

The two big take aways from the Managing Markups assessment for me were how business come up with pricing plans and how I should be more specific and clear in some of my explanations. I gained a better understanding of . I also realized that sometimes in my explanations of my findings, I talk about things that are clear to me but might not be clear to the reader.

2. How have you become a more educated investor? Be specific about how you would invest your money.

I now know that it is better to invest in a company with better pricing plans and more profit. A good pricing plan would be finding out how to maximize profit, and having a good backup plan in times of a financial crisis, such as, deciding whether selling the product at cost or maintaining the markup (with a decrease in demand) would be more efficient. If I don’t invest in a company with good pricing plans, then I wouldn’t be able to earn money from the company I invest in.

3. Describe, with examples, how you improved some of your math skills.

A math skill I improved through this assessment is being faster at creating formulas. I have improved my skills in creating formulas because in excel, it’s easiest to create a formula that works for everything in the table instead of putting in all the numbers separately. For example, a formula I had to create to find out what the new retail price was after an additional markup was 5000+(5000*new retail price). This formula is different from what I would usually use (new retail price*1.85) because I had to make sure it would work for all the other cells when I dragged it down.

4. Why doesn’t a 20% discount followed by a 20% markup get you back to where you a started?

A 20% discount followed by a 20% markup wouldn’t get you back to where you started because the number you discount from is different from the number you markup from, so the 20% wouldn’t be the same.

5. How do companies make profit?

Companies make profit by making their retail price higher than the wholesale price. They have to find the best way to maximize their monthly revenue and minimize their costs because a monthly revenue subtracted by the costs is a company’s profits. Companies also have to consider a reasonable retail price because if it is too expensive then customers might not want to buy it.

6. Is it possible for everyone to win the marketplace?

I don’t think it is possible for everyone to win the marketplace because when companies are competing against each other with different products, the majority of customers may favourite a specific product, therefore allowing that company to profit and the other companies to not profit as much or have loss.

# MATH: Assessment – Algebra Reflection

After looking at my pre-assessment and unit assessment, I can see that the main skill I learnt in this unit is simplifying equations. In my pre-assessment, I simplified “10m – 7m + 3m” as “(10-7+3)m”. Now, I know that the simplified version of that is supposed to be 6m. I also learnt about solving equations with variables on both sides. Before this unit, I wasn’t too sure about how to get all the variables on one side, but now I understand that you can just make a zero pair with the variable and do the same on the other side. For example, in the pre-assessment, I didn’t know how to solve “5 (x + 3) = 4x + 5” because I wasn’t sure about what to do with the variables. Now, I know you can subtract x from 4x and get all variables on one side.

Some concepts I found confusing in this unit was simplifying problems with multiplication and division. Sometimes, I got confused about how to join the variables together or get rid of them because it’s different from addition and subtraction. To study for them, I found extra practice problems in the textbook and worked on them until I felt like I could simplify easily. If I forgot how to do it, I would look back at the problems we did in class to refresh my memory.

# MATH: Polygon Area Patterns

Some strategies I learned when approaching this Crit B (Patterns) task was that to be able to find the pattern easily, I had to organize my data well. For example, I would increase one number by one each time, rather then trying random numbers. Last time I did a Crit B task, I didn’t organize my data well so I couldn’t find the pattern. However, this time, I used a chart and organized everything well, so I was able to spot the pattern easily.

If I could do this assessment again, I would improve my explanations and descriptions by adding diagrams because it was hard to explain some things with just words. Adding a diagram would have helped explain the pattern and make it easier to understand. For example, while explaining why the pattern was like that, I could have added a diagram of the way the area increased when an exterior point or interior point was added.

# MATH: Unit 2 Test – Rational Numbers Test

The rational numbers skills that I am best at are operations and using models/number lines to show the equation. I am able to solve operations by following BEDMAS and knowing how to add/subtract/multiply/divide for decimals or fractions. When given an equation I can draw out a number line or model to show how I got to the answer.

The skills I need to improve on are powers and estimating and spotting the mistake. When there is a rational number cubed or squared in a problem, I should make sure I know clearly whether it is cubed or squared because sometimes I make careless mistakes and forget or I do the multiplication wrong. I could improve on this by doing more practice by myself. I could improve on estimating and spotting the mistake by making sure I know how to do the problems correctly first, and then looking at them more closely.

A strategy that worked for me when learning the content in this unit is doing practice problems, and then going back later to check if my answers were correct or wrong. This worked for me because I was able to get practice and learn from my mistakes. I would like to try and not get distracted so easily while studying at home and focus more on what I am doing.

# MATH: Swimming Problem Assessment Reflection

For this assessment, something I did well was recognizing the patterns. I found it quite easy as all I had to do was look at the pattern closely and see how it changed. Being able to recognize the patterns also helped me with some other problems, such as, seeing what the number of laps would be after a few days. Something else I did well was figuring out how to solve it when I was stuck. The best way I found was to just use trial and error because if I kept trying with reasonable numbers, then I would eventually figure out the answer, even though it might take up some time.

However, something I could improve on would be to calculate the total number of laps more accurately. Even though I used a calculator, I should still check over my answers more carefully next time. I could also improve on writing my explanations a bit more clearly because sometimes I felt like it would be hard to understand. To improve on this, I could try to use more math vocabulary and write my answers in a more straight forward way.

If I were to rank myself in terms of participation in class and collaboration with my group from 1 – 10, I would rank myself a 7.5. I did participate in class most of the time, but I think I could have participated even more. When collaborating with my group, I think I did well because I tried to help out and solve the problem with them. I also asked questions when I didn’t understand something.

Something I learnt about myself as a problem solver in this unit was that I could recognize patterns most of time if I looked at it closely. Although sometimes it took longer than other times, and sometimes I worked with someone else, I would still end up figuring it out. I also learnt that I could improve on trying to find formulas for patterns and writing clearer explanations.