Category: Math

 

Jack and Dan competed against each other in a round of running. They both ran a kilometer. Jack took about 8 minutes to finish the race while Dan took around 5. What’s their speed in kilometers per hour? Imagine if they ran for another 3 hours at half their original speed. How far would they go and who would go farther?

To find speed, we must take the distance and divide it by the time. In the case for Jack, it would be: 1 (kilometers) ÷ 8 (minutes). Do the math and you would get 0.125, so Jack’s speed is 0.125 km in a minute. But we want km/h. We just need to convert it. To convert it, basically multiply by 60 because an hour is 60 minutes, so 0.125 (km per minute) x 60 (number of minutes in an hour) and you would get 7.5 km/h. That is Jack’s speed in kilometers per hour.

Let’s quickly find Dan’s speed:

1 km (how far Dan ran) ÷ 5 minutes (how long he took) = 0.2 km/minute (his speed)

0.2 km/minute x 60 (number of minutes in an hour) = 12 km/h (his speed converted from km/minute into km/h)

Now how far would they go if they ran for another 3 hours half their original speed?

First I would find their new speed. That’s easy, just divide their original speed by two.

Jack’s new speed: 7.5 ÷ 2 = 3.75 km/h

Dan’s new speed: 12 ÷ 2 = 6 km/h

To find out how far they would go, we need to multiply their speed by how long they would run.

For Jack, 3.75 km/h (his speed) times 3 (time of running) would find out his distance. It’s 11.25 km. In Dan’s case, his distance would be 18 km.

So if they both ran for another 3 hours at half their original speed, Jack would run 11.25 kilometers and Dan would run 18 kilometers. Who ran farther? You know how to do this one, it’s Dan because 18 is obviously bigger than 11.25; just find the number that’s bigger.

You’re walking in the mall and you’re trying to find a thick hoodie because you have a trip to the arctic next week. Some of the shops you’ve passed did sell hoodies, but they didn’t have what you wanted and the price didn’t match the quality either. You look to your right and spot a hoodie you like. It costs $25, but you only have $20. You’re about​ leave, but you see a sign that says “Special Offer: All is 25% Off!”. Now, you actually might be able to afford the jacket and avoid 3 more hours of walking and searching for another hoodie in another store in this gigantic mall. But how much is 25% off? How much is the hoodie now? And how much will you have left?

So the price of the hoodie without the discount is 25$. The discount is 25% off, so we need to find 25% of 25$. Then will you be able to figure out how much is left and how much the hoodie costs with the discount. 100% of the hoodie’s price is 25$, so 100/100 = 25$. 25% of 25$ isn’t known yet, but we know that 25% = 25/100 just like the 100%. To find 25% of 25$, just basically take 25$ times 25/100. We also know that 25/100 = 25 ÷ 100. This can be done using many different methods. Here is the one I’m using:

25 (the price) x 25 (the discount %) = 625 ÷ 100 = 6.25$ (25% of 25$)

Now we know that 25% of 25$ is 6.25$. All we need to do now is find the new price and then will we know if we can buy the hoodie or not. 6.25$ is just the discount. The new price is the difference of the normal price subtracted by the discount. So it’s done like:

25$ - 6.25% = 18.75$

The price of the hoodie now is 18.75$. You have 20$. You have just enough! Well lucky you. How much will you have left after buying the hoodie? I’ll leave that one for you to figure out. Just simple subtraction.

And that about sums up what we did in round 4 of math. We learned about percentages and to write a portfolio about it, I chose to create this short problem! I learned a lot about percentages as well as enjoyed it. It’s really fun to learn about, doing problems like these and it’ll make figuring out discounts (and solve other real life problems) much easier. The next time you visit a place that sells something you like and has a discount, you know how to figure it out! Thanks for reading!

As given by the title, this portfolio piece for math this round (2nd round) is about geometry! There were a few lessons about fractions that we needed to cover, so the first week was spent finishing that up and then we got into geometry.

In class, we learned how to find the area and perimeter of different shapes. It started off with simple shapes like squares and triangles then we went into circles and some other shapes. Those shapes just looked complex and weird, but nevertheless, they were still shapes. Finding the area or perimeter of simple shapes were simple and straightforward, but with made-up and complex shapes, we needed to something else, so we learned how to divide them into smaller simpler shapes and then find its perimeter or area. Just like last round, after each lesson, we split into groups to do math problems to put our knowledge of math to the test and also just for practice. There were also other in-class activities, we had the usual options whenever we finish work early which still included Khan Academy, and sometimes games.

Near the end of the round, we learned about ratios which I thought was fun. And then came round 3. Round 2 math was great. I enjoyed learning about geometry, a bit of fractions, and a bit of ratios! The next round is coming up and I hope that it’ll be fun, too.

In the first round of math this year, we didn’t focus on anything specific since it was the beginning of the year and also because we had a new math teacher. Most of the round was spent learning fractions. The other part was spent reviewing. In the first few weeks, we reviewed a bit on last year’s math, did a little bit of pre-algebra and we made posters that said “Make the most of your learning” to remind students to do so in class. Then we turned to fractions. We had a short review of fractions and then dove deeper into it. It wasn’t that different from last year’s fractions, except that we learned new complex and useful concepts which included multiplying fractions. Other than just learning about fractions, we did many activities in class related to it. Most of the time at the beginning of every class, we would get grouped to do exercises in the workbook together. When we finished, we would either play fun games or work on this free-learning website called Khan academy. This round was like an introduction to what we will be doing in math this year and I had lots of fun in reviewing and catching up on all the things we did in math last year as well as learning new concepts related to fractions. There are many new lessons yet to come in the following rounds and I look forward to them.