Math: Pyramids Assignment - Investigating & Application

Pyramids Investigation & Application Assignment

In this assignment, we basically looked at different parts of a pyramid. Especially the slant height on their sides. We were given the formula on how to find the slant height of a pyramid when given the base and vertical height of a pyramid. We were then to find out how the equation works. The Pythagorean theorem is applied into the formula basically. Then, we looked at some Aztec Pyramids (ones with a flat top) and equations on finding the slant height of an Aztec Pyramid. This time we were asked to explain how the equation works. It also uses the Pythagorean theorem and also the properties of trapezoids. Then, we were asked to apply our knowledge of these equations to find different measurements with the other measurements of a true pyramid. Then, we were asked to make a net for a pyramid only provided with the base and the vertical height of it. In this assignment, I did pretty well - 7/8 for investigation and 7+/8 for Application.

Maths: The Math of Forensics - Unit 3 Assessment

Math of Forensics - Application Assignment

This is an application assignment, meaning we have to apply math to a real-life situation. In this assignment, we are applying math to forensics - the study of crime scene evidence. There are different "branches" of forensics, such as DNA, fingerprinting, car accidents, ballistics (gun-shots).

There were three different parts to it. The first is about the length of bones in our bodies. We were to measure the length of some (fake paper) bones from the different body parts of a "dead person". Then, we were to use math equations for men and women and compare it to the provided measurements of bones of three people. Afterwards, we were to hypothesise whom the bones belonged to and explain. I did very bad on this part since I forgot to take it home the day before this part was due, and so I didn't finish even half of it.

The second part is about a car accident. We received another booklet and we were to follow the instructions of an online activity. We examined car(drawing)s - how and where they are damaged; took notes from (cartoon) witnesses; substituted our (online) measurements into equations to find collision speeds and impact forces on people.

The third part is a "crime scene" that was set up at school by the teacher to represent the road the road outside the school. For this part, we made measurements of tire marks and the distance between body and point of collision. Next, we read some short "witness statements" and took important notes. Afterwards, we substituted our measurements into formulas involving drag factors and brake percentages. The formulas were complicated so we didn't really learn what's behind them. But for this part, we had to understand them a little more to find the thinking distance, and what how long would he need to brake before the pedestrian if he wasn't speeding.

I got 7 for KU, 5 for Comm, 3- for App. I didn't do very well for application because I didn't finish the first part so I couldn't hypothesise with the mathematical data. And I didn't have enough time to answer "would the car have collided with the pedestrian". They were the main parts where math was applied the real life situations to find solutions. But I didn't do them. So I didn't do very well on this assignment. I think I will remember to take my work home to finish and be more responsible. I will also try to work quicker the next time and arrange my time better.

Investigation - The Circumference of a Circle

As you may be able to guess from the title, this investigation is about the circumference of a circle. We are trying to find how many times a diameter of a circle can go into the circumference of a circle. Although some of us already know that before, we are asked to prove if it is correct. And it is of course 3.14 times.

The first task was to get a chalk and tie it to a string about one metre and something long. Then, we measure it and cut it to a meter (recommended to do so when stretched). Then, we draw a circle on the ground and that would make the diameter 2 metres as the radius is 1. However, we have to very careful to not pull the string or pull the string when drawing the circle, depending if the string's cut stretched or not. And then, we have to take out the chalk, cut the string into a metre when not stretched, and then lay it on the circumference perfectly and see how many times it can fit in the circumference. The string would fit in about 6 times as it's the length of the radius, which means the diameter goes into the circumference about 3 times. Technically, it should be 22/7 or at least 3.14, but approximately it is 3 times. (I do think it would be more precise and straightforward if we make the diameter a multiple of 7, and find out if the circumference is the multiple of 22. That would prove it too.)

Then, we did some exercises dividing the circumference by the diameter and finding out if it's around 3.14. Of course, again, technically it should be 22/7, but approximately it is 3.1 times. That's because the measurements are to the nearest tenth.

I had no difficulties and I have figured out the solution quickly before taking the task. I totally understand it also. However, I didn't use any diagrams. We did discuss the purpose of this investigation and the discussed that π is 22/7 with the proof from the numbers we found out in the investigation.

Math Unit #4 - Coordinate Geometries & Reading and Interpreting Graphs

This is the 4th unit for Math. As you can see how the unit is named, we learnt about coordinates, how to read and interpret graphs, and make graphs. This is a useful and interesting unit for me as I haven't really learnt or go deep into coordinates yet. It was also a review about graphs for me. And how graphs are misused is quite interesting. We learnt:

1. Reading Maps
2. Coordinates and the Number Plane
3. Introducing Straight Line Graphs
4. Graphing Straight Lines
5. Lines Parallel to the Axes
6. Further Graphing

1. Graphs and Their Features
2. Reading Graphs
3. Drawing Graphs
4. Travel Graphs
5. Misuse of Graphs

We learnt a lot in this unit.

• We learnt how to find places using the grids on the map and the coordinates on provided.
• We learnt how to write the coordinate of a place on the map.
• We learnt about the number plane.
• We learnt how to find a point on the number plane, and how to find the coordinate from the point.
• We learnt how to draw a slope from an equation, and form an equation from the slope.
• We learnt what are the lines parallel to the axes, and how to draw them from the equation.
• We learnt the point to intersection of lines.

• We learnt the divided bar graph, the sector graph, the line graph, the conversion graph, and the step graph and their features and what they're used for.
• We learnt how to read them, interpret them, and get different informations from them.
• We learnt how to draw the different graphs using the information given.
• We learnt how to choose the most suitable graph for different kinds of information and data.
• We specifically looked at the travel graphs, and how to read them.
• We learnt how to find out the misusing parts of a graph.

Math Unit #3 - Algebra Equations

This unit taught me how to solve different equations with different things in it, and finally, all in one equation, it also taught me inequations which was something I didn't know. It helped me practise solving algebraic equations. By now, after this unit, I feel like I can do an algebraic equation very very quickly. As I do more and more of them, I realise that I finally understand and became familiar with something I was a bit uncleared about before. This unit is useful, I learnt quite a few things from it, and it is a good practice and it allowed me to gain more understanding of algebra. In this unit, we learnt:

1. Inverse operations
2. Solving equations
3. Solving equations with pronumerals on both sides
4. Solving equations with grouping symbol
5. Formulae
6. Solving problems using equations
7. Graphing inequations
8. Solving inequations

• We learnt inverse operations in order to have a better understanding in solving equations.

• We learnt how to solve an equation using inverse operations.

• We learnt how to solve an equation with pronumerals on both sides.

• We learnt how to solve an equation with grouping symbols.

• We learnt how to substitute a numeral to a pronumeral to solve an equation.

• We learnt how to solve problems using equations.

• We learnt the four steps to do so solve problems using equations.

• We learnt how to form an equation and solve it by looking at a shape with different... like the below.

 

• We learnt what are inequations and how to graph them.

• We learnt how to solve an inequation.

Math Unit #2 - Patterns And Algebra

In this unit, parts of it are things that I knew already, and parts of them are new ways to calculate. This unit is also a good unit for me to practise to do algebras, and it helped me do algebra very quickly, and how to sometimes do it in less steps. In this unit, we learnt:

1. Vocabulary of algebra
2. Gathering like terms (combining like terms by adding and subtracting like terms)
3. Multiplying pronumerals
4. Indicies/exponents
5. Expanding (multiplying with grouping symbols)
6. Factoring
7. Using algebra

• We learnt how to find patterns and how to use a pattern to solve an equation.

• We learnt 20 definition of algebra vocabularies.

• We learnt combining (adding and subtracting) like terms.

• We learnt how to group/multiply pronumerals.

(12)(3n)=36n   (3a)(bc)=3abc   (3a)a=3a²

• We learnt how to do division of pronumerals.

• We learnt multiplying and dividing pronumerals in one expression in order to simplify it.

• We learnt how to use algebra (like creating an expression for the perimeter of a square).

• We learnt what is a power, what is an exponent, and what is a base.

• We learnt six laws of indices (e.g. subtract the exponent if you are dividing two power with the same base).

• We learnt how to solve an expression with indices with a substitute. We learnt how to simplify multiplications into powers.

• We learnt how to expand and factorize an expression.

• We learnt algebraic fractions.

Math Unit #1 - Fractions, Decimals and Ratios

The first unit of the year is "Fractions, Decimals and Ratios". I actually learnt most of the things in this unit before so I actually take this unit as a review, and I am sure I got better in what we learn in this unit somehow. I was good in the whole unit and I know everything I learnt and is confident in it. In this unit, we learnt:

1. Fraction
2. Percentages
3. Ratios
4. Rate
5. Scale
6. Sector graph (pie chart) and histogram

• We reviewed how to make or form or estimate a percentage, decimal, ratio or fraction by looking at an object: Like how many percent is in colour, how full is a bottle, how much is the wall painted...

• We learnt how to convert percentages, decimals, and fractions, to each other.

• We leant how to calculate a number by "multiplying, dividing, adding, and subtracting" it with a decimal, fraction, percentage, ratio.

37%     18/39 3.6

• We learnt how to create a ratio and the different forms of ratio.

• We learnt how to convert a rate to different units, calculate and form a rate...

1 2/3 km/min=100km/h=100000m/h

• We leant how to make a scale or use a scale to calculate sizes, length...

1:100=1cm:1m

• We learnt use percentages to make a pie chart. We learnt how to make a histogram.