End of Year Reflection


1. I improved as a mathematician because I can solve harder problems and connect them to other problems.

2. I am better at mathematical thinking because I get more complicated concepts.

3. I understand problems more than before. I am quite precise in my answers, even to the third or fourth decimal. I need to improve on my modelling.



1.I know many concepts now and can put them to use in life now.


Fractions as Division

The relationship  between a fraction and division is that the line in the middle of a fraction means divide! This means that when you write 2/3 you actually mean 2 ÷ 3. If you actually did the division, you should end up with 0.66666667 which is the same as 2/3. Isn’t that just cool?

Areas of Parallelograms and Triangles

For a parallelogram: base x height. Remember that height must be perpendicular to base. Example:

For triangle: base x height ÷ 2 because triangle is half of a square. Example: 

Remember that height is perpendicular from base.

The similarities are that they both need base x height to get the area and that the height needs to be drawn as a different line instead of already being there. The differences are that the parallelogram is double the triangle so it is just base x height

Fraction Multiplication Number Sense

To get a number slightly larger than the original you need to multiply it by a number slightly larger than one. If you want a number much greater than the original then multiply it by a number much greater than 1. If you want a number slightly less than the original then multiply it by something slightly smaller than 1. If you want a number a lot less than the original then multiply it by something a lot less than 1.

Multiplying Fractions

I have a square and divide it in to 3 parts because I have 3 pieces, but I want to find 3/4 of 2/3. Of means multiplication when talking about fractions. So I divide the square in 3 parts vertically and 4 parts horizontally to get 12 parts in all. I shade in 2 out of the 3 vertical strips because I need 2/3. Now I don’t need to bother with the last strip left because I need 3/4 of what is already shaded. I shade in the 3 of the 4 horizontal strips and my answer is 1/2.


Today I learnt that if you compare anything on the original and the new, it all gets you to the answer or ratio that you need to solve the problem. For example I can say that the original to the new figure should be 5:9 and my bases are 5:9 and my new height is 27 so to get the answer I can just switch the ratios around and do new to original but I am going to stick with original to new. My original height would be 15 because if I multiply 9 by 3 I get 27 and so 5 multiplied by 3 equals 15. So now I can flip everything and the answer would be the same. I could do 27:15 and say that I am doing new to original so the ratio now is just flipped to 9:5. In my example earlier I showed how ratios can help you get the answer to the problems.

Enlarging Figures

I know that a figure is enlarged correctly if the original figure’s ratio is equivalent as the enlarged because that would mean that all the sides were enlarged by the same amount and not different amounts so the shape stayed exactly the same but only the size changes. Another way I know is if the figure is if I put the original into the enlarged and can see that the corners and sides are all doubled. An example of that would be if I put the original rectangle that I made, into my enlarged one, I should see that the corners and sides are actually exactly double and can fit the original twice everywhere on the enlarged.

Variables and Expressions

A variable is a letter that is used to represent an unknown number. For instance I use the variable t and use it like an unknown number like this: 7 + t = 89. T is and unknown number. An expression is an equation without an equal sign and has a variable. Supposedly this: 20 + d. There is no = in this because then this would be an equation.

Absolute Value

Absolute Value

Absolute Value basically means how far away from 0 the number is. For example there is – 5 and 3. By looking at it now the values say that 3 is greater than – 5 but if we did this in absolute value it would be this: 5 and 3. Now which one is farthest from 0? You would say 5. Get how absolute value works, and what it is?