Mathematical Reflections #2

In math class, we've recently started a new unit on integers and rational numbers. In the last unit, we started off with the first mathematical reflection, so here's another. The first question asked was (1.A.) "How do you decide which of two numbers is greater when both numbers are positive?" Well, when you first look at a number, if one number has more digits than the other, then that number with more digits is greater. If they both have the same number of digits, then look at the first digit of the number, if it's greater than the other, then that number would be greater. If the first digit is equal to the other number's first digit, then look at their second digit. Looking at the second digit and so forth, and seeing if they are greater or less than the other number's helps identify the greater number. (1.B.) "How do you decide which of two numbers is greater when both numbers are negative?" You can tell if one negative number is greater than the other by looking at a number line and looking at which one is close to zero. If you're not looking at a number line, just ignore the negative sign, and look at the actual number (digits.) The smaller number is greater while the greater number is smaller. For example, -10 and -5, -5 is greater. (1.C.) "How do you decide which of two numbers is greater when one number is positive and one number is negative?" We all know that the positive number is always the greatest. When you look at a number line it could help you determine the greater number by looking at the placement of the numbers. The positive number would be on the right and the negative number would be on the left.

(2) "How does a number line help you compare numbers?" A number line can help you compare numbers because as said before the negative numbers are on the left and the positive numbers are on the right. When comparing one negative number and a positive number you can just look at where the number is, either on the left or on the right. If you are comparing two positive numbers, you can look at a number line and see which one is closer to zero, if it is closer to zero than it is less than the other number. Something similar would go for the negative numbers, the number closer to zero would be greatest. Something that could help you on the number line, is using the jumping method. No, you don't actually jump on a number line. When you are using the jumping method, you see how many jumps it would take one number to get to another.

(3) "When you add a positive number and a negative number, how do you determine the sign of the answer?" When you add a positive number and a negative number, the answer will also be a positive number. For example, if you're looking at a number line, and the problem you're trying to figure out is +7+-5=? You would start at 7 and you would count towards the zero, since negative numbers are on the left, you would "jump" to the left. You would end up landing on 2. Alway remembering that whenever you add a positive with a negative, you end up with a positive number.

(4) "If you are doing a subtraction problem on a chip board, and the board does not have enough chips of the colour you wish to subtract, what can you do to make the subtraction possible?"
Knowing that when you add negative one to positive one, those numbers cancel each other out, meaning that they would equal zero. If you add an amount of pairs (negative one and positive one) to the problem, it would just be adding zeros, so it wouldn't harm the equation. Then, by breaking these pairs up, you get enough chips for both the positive and the negative, by erasing the extra chips, you are able to make the subtraction possible.

This picture of a number line, was taken from Creative Commons. 

This picture of negative and positive number chips, was taken from Creative Commons.

Building Quadrilaterals

Quadrilateral Rule  

If you add the 3 smallest sides of a quadrilateral, the sum must be BIGGER than the longest side. 

Mathematical Reflection 1

Recently, in math we've been developing our understanding of polygons and angles. Now we've finished that unit, so I'm here to reflect on my learning through the lessons and questions. One major thing we talked about was the answer to this question, (1) "what are the common properties of all polygons." We were reminded several times, and constantly came up with the answer of, "all polygons must have closed sides, there may not be any intersecting lines, there also may not be any curved lines, meaning all sides are straight."
(2) "What are the measure in degrees tell you about an angle?" The measure in degrees tell us how big or how small the angle is supposed to be. It can also tell you whether the angle is obtuse, acute, or right. "What are some common benchmark angles?" Some of the more commonly used benchmark angles are, 45°, 90°(a right angle),180°, 270°, and 360°.
(3) "What strategies can be used to estimate angle measures?" One strategy someone could use to estimate angle measures, is to use benchmark fractions, you could use them by asking yourself, "is this angle greater than or less than 90°?"
"What strategies can be used to deduce angle measures from given information?" If you are trying to find the total angle sum, you just have to multiply the size of the angles with the number of sides the shape has. Just remember that the greater the angles in the shape is, means that there are more sides. But if you wanted to find the size of the angle without actually using a protractor to measure it, then you can divide the total angle sum with the number of sides. Continuing on with that, if you wanted to find out the number of sides of a shape, you could divide the sum of the angles with the size of the angle.
The last question is, "what strategies can be used to find accurate measurements with tools." Well, the tools you can use to find accurate measurements is either a protractor or a angle ruler. Usually, a protractor has two sets of numbers on them, so pay attention to your measurements, keep on thinking, "is this angle greater than or less than 90°."

This picture of a protractor, was taken from Creative Commons.

These are a few of the types of angles, also taken from Creative Commons. 

Got GRIT?

Using Your Laptop

Finding the Volume of a Cylinder!

This is a video that I made teaching you guys how to find the volume of a cylinder. I think I did a better job on this movie than the other movie I made a while ago. Something I think I didn't really do well on was pronouncing my words properly. One thing I improved on was I talked louder than usual. I apologize that my video is a bit blurry. Any ways I hope you learned how to find the volume!

Multiplying Fractions!

This is my first math video. Its not perfect, but its okay. I just decided to make this video about multiplying fractions. It was fun to teach people who don't know how to multiply fractions. One thing I should work on next time would be to speak louder and speak clearer. I also think I should not pause that often. I had lots of fun making this video!