In Part One, we left off with Chubaka feeling like a mathematician and Artoo dreading the math portion of the SAT:
Artoo has the SAT coming up in two months and wants to go to Michigan, which wants to see a 700 from her math score. What should she do? Short answer? Start math over from scratch.
Making a Review Sheet & “Taking Notes”
When you’re first exposed to a topic, you might take word-for-word notes from the various books/articles/lectures engaging you. In math, preschoolers and kindergarteners add the numbers 1 through 10 dozens of times before reciting from memory. I remember doing pages of worksheets just asking me to add two-digit numbers, and I’m proud that in the example content review below, I’ve included all of that effort as simply “addition.” I’ve achieved this through an iterative process of whittling my ideas about addition:
I learned to add the ones place, then I learned spillover from the ones place goes to the tens place, then spillover from the tens place goes to the hundreds place, and then I said “I think I’ve got it!” I recommend Artoo literally start by working through PEMDAS examples and taking pride in her achievements. Then, she should identify where exactly it starts to get frustrating, then she should practice that content and ask for help/Google when she gets stuck.
Artoo is in the process of rebuilding her math identity from the ground-up, and she will surprise herself with how much she already knows and how small the misconceptions were that were leading to her frustration. Here are two places you can start reviewing all of math:
When you do practice problems for these tests, take note of what TYPE of math is being asked, and what STRATEGY you’re applying to solve it. By the end of each topic, you should have a list of strategies that you can summarize on a more long-term review sheet. Then, categorize the types in a way that makes sense to you.
I imagine Artoo doing this exercise and feeling like math is actually a lot less material than what she expected from 13 years of school.
Example Content Review + Strategy Guide through Algebra II
Test taking
- Flexible mental model between equation, word problem, graph, and table
- Plug in numbers (when numbers in answer choices)
- Make up numbers
- Estimate
- Elimination
- Calculator
Arithmetic
- Parentheses, addition, subtraction, multiplication, division, exponents, factorials, sums
- Sequences: arithmetic, geometric, periodic, Fibonacci
- Prime numbers, composite numbers, factors & multiples, remainder & modulo
- Invalid operations (divide by 0, sqrt(-1))
- Units (dimensional analysis)
Algebra
- Functions (linear, quadratic, exponential, sqrt(x), absolute value, rational, polynomial, trig)
- Graphing: inverse, even, odd, translations, transformations
- Interpreting constants and coefficients (slope, x&y intercepts, amplitude)
Geometry
- Definition of two & three dimensions; length, area, volume
- Triangles (half a rectangle, bh/2, similarity & congruence, 180 degrees, acute, obtuse, right; scalene, isosceles, equilateral; right triangle trig; law of sines and cosines)
- Circles
- Proportionality: part/whole = radians/2pi = sectorArea/pi(r^2) = arclength/2pi(r) = degrees/360)
- (x-h)^2 + (y-k)^2 = r^2 is the Pythagorean theorem
- Inscribed angle theorem, tangent to a circle is perpendicular
- Regular polygons (break into isosceles triangles from center)
Probability
- AND OR probability, 1-p(e), total probability adds to 1
- n!, permutations, combinations, arrangement in groups
- redundancy, replacement, ordering,
- binomial theorem & pascals triangle
By the end of her review process, math may not be Artoo’s favorite subject, but she can go into the SAT feeling confident in her ability to solve the problems she’ll see there.
Math can seem huge and daunting, but a lot of success in math comes from your own confidence – or identity – as mathematician. Remember to start with the basics, celebrate your successes, and build gradually. Don’t forget to create study materials as you go, like notecards, study guides, and strategy lists. And, it’s okay if it seems too daunting – a math tutor or SAT tutor can help you get organized, face your stress around math, and crush your tests!
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