1. Algebra Tiles How to sort, making the equation smaller and easier: 2x+1x+3 to 3x+3 How to make zero pairs, 1x+-1x=0, then take them away from the equation to make it smaller How to draw them by making the negative tiles filled in and the positive ones empty We learned how to make the tiles relate to real numbers so we could use them to solve real equations with actual numbers What algebra tiles often look like

2. Brackets We learned how to distribute when a bracket is used, like making 2(4+3) to (8+6) How to know when the brackets are even necessary and can just be taken off: (4+6)-4 is the same as 4+6-4 because of BEDMAS We learned that when dealing with exponents, the exponent needs to be distributed to everything in the bracket

3. Coefficient The Coefficient is the number placed in front of a variable: 8x, 8 is the Coefficient In an equation, if there is variable with a coefficient in front of it, the coefficient shows the amount of variables, so if there’s 8x, there are 8 Xs When dividing by the coefficient in unequal equations, it is used to find how much x is worth, so if you have 5x=8 you would divide 5x by 5, making it x, and divide 8 by x making the final answer x=8/5

4. Division The most useful thing I’ve learned about division this year is how to divide fractions by other fractions When dividing a fraction by another fraction yo simply just switch the second fractions numerator and denominator by the reciprocal and you “just do it” by multipling the numerators and denominators: 4/9 8/12 becomes 4/9 12/8 then you just multiply the numerators and denominators so yu get the answer 48/72

5. Exponents This year we learned a lot on exponents When you have a number in a bracket with an exponent and n exponent outside of that bracket, you can simply at the exponents the make one large exponent that gives you the same result with less work Again like I said in the bracket slide, when an exponent is outside a bracket with multiple numbers in it, it must be distributed to everything in the brackets

6. Fractions This year we learned how to multiply and divide fractions, like I said in the divide slide. We also learned that whole numbers are ust simply that number over one. We also learned how a fraction can be placed on a number line and how fractions are basically just division questions.

7. Geometry This year for geometry we learned a lot about how to get the surface area of complicated shapes, a cylinder stacked on a cube etc. We also learned how to get the surface area/perimeter of strange or awkward shapes by cutting them into simpler shapes that are easy to calculate.

8. Hypotenuse This year we learned Pythagorean’s theorem, we also learned how to switch it around to get exactly what side you need. Related to Pythagorean's theorem, we learned a lot about squaring and square rooting numbers, which I had no idea how to do before. The hypotenuse it the longest side of a right angle triangle.

9. Inequalities We leaned A LOT about inequalities this year, we worked a lot on how to show them visibly with number lines, the easiest way to explain inequalities is when it’s a question with either or = in the middle (or the other one I can’t find on the keyboard)

10. Just Do It! This year we learned one of the most useful things, I think, to remember when doing fraction equations when you need to multiple, JUST DO IT! Just do it basically means to, you know, just do it. When you need to multiply fractions there isn’t any work you need to do other than just multiplying straight across. This also really helps me when dividing fractions because all you need to do is switch the second fraction by the reciprocal then just do it!

11. Kari learned data analysis Even though so far I’ve only had one lesson on data analysis, I learned quite a bit. Data analysis is basically just using common sense and asking questions about simple things related to math in real life. For example if there’s a survey that is bias it can change the answer you will give it and completely change the reliability of the research.

12. Linear equations This year we learned everything I know about linear equations. First we learned how to find the formula and finish a T-Table. Then we learned how to put everything on the T-Table onto a chart, simply by putting the numbers where they cross on the X and Y axis's.

13. Measurement We learned a bit on how to convert measurements, centimeters to meters etc., but most of what we learned about measurement was how to use it when dealing with ratios, scales and scale factors.

14. Numbers When I review it, we actually learned quite a bit about numbers this year. Overall the whole year, in every unit, we spent time using visual images when trying to figure things out. After seeing pretty much every unit in a visual form it really helped me see numbers different. After this year it’s way easier for me to look at normal simple numbers and understand how fractions and decimals are put between them.

15. Order of Rotation When a shape looks the same after a rotation it has rotational symmetry. If it has 3 rotations, with all of them being the exact same, it has a rotational symmetry of 3. : An example of a rotational Symmetry of 3

16. Polynomials We worked a lot this year on polynomials, we spent a while on how to draw polynomials using tiles, cubes, blocks etc. the first step when subtracting polynomials is FLIP. So say your question is (3X+6)-(2X-1+6) you’d turn it into 3X+6-2X+1-6. The second step would then be to sort, 3X-2X 6+1-6, then add them so you have 1X and 1 giving you the final answer of 1X+1.

17. Quotient We didn’t spend very long learning the term quotient since it has such a simple meaning but we did use this term often in the beginning of the year. The definition of a quotient is the answer to a division question.

18. Radius The definition of a radius is a line segment from the center of the circle to the diameter. Though I learned this definition last year, we learned TONS this year about radii. Mostly in the circle geometry unit, but we learned the importance of the radii, when looking for the length of line segments (etc.) in a circle.

19. Surface area Obviously this isn’t the first year any of us had worked on surface area but it was the first year we actually learned how to find really complicated surface areas. The definition of surface area is self explanatory and easy to understand but it can get difficult. The hardest part about doing the complicated shapes we did this year (cylinders stacked on cubes etc.) is definitely not knowing what formulas to use but it’s knowing how to add each answer you get properly and remembering to subtract the overlap.

20. Tug-o-War Tug-o-War is a trick I learned only this year. It’s basically just used to find the answer of simplified/short equations with a positive and negative number. So if your original question is 6+9-3+9-2, you’d cut that down to 24-5 just by sorting, now is the time to use tug-o-war. So since the positive number is 24 and the negative number is -5, you see which number would “win the tug-o-war” (whatever side has more numbers). So since the positives would win because they have more numbers you can now see by how much it would win, which in this equation is 19.

21. Using BEDMAS Though I’ve used bedmas before this year I learned how to actually do the first two steps. We didn’t spend long on doing much bedmas this year but actually learning the first two steps making it way easier for me. Even though bedmas can sound easy at first, just do the steps in order of brackets, exponents, division, multiplication, addition and subtraction, it can actually become quite difficult in some cases, which we worked through this year.

22. Variables Variables are one of the easiest thing to understand that we learned about this year. A variable is used when there is a number you don’t know, that you are mostly likely supposed to try to figure out. An example of a variable is 3X+8+2X, the variable would be X. Any letter can be used as a variable.

23. We need to check our work! Ms Burton, for a while at least, could not stress enough how important it is to check our work! Which is actually very easy to do but most people struggled with it when the equation had variables, even though it’s actually very easy! All you have to do is right the question and replace the variable with the answer you got for it, and if the answer is this the same you know its right.

24. X axis and Y axis Though these our two different letters, it makes sense to combined them. On a chart there is an X axis (horizontal) and a Y axis (vertical). Though it may not look like it, these charts can be almost directly connected to T-charts, as when a T-chart is made with a pattern it will create a straight line when transferred onto a chart.

25. Zero pairs Honestly zero pairs is one of the most useful things I think we worked on this year, so I’m very happened we spent so much time focused on it. Zero pairs can be so very helpful when sorting and simplifying equations, making them way easier and faster to do.