Mathematics Study Skills
Mathematics Overview
The 4 Mathematics lessons will be especially helpful for students who think that they’re bad at math. Very often, these students haven’t put in place the good habits that let them catch their mistakes or push past intimidating questions. They have a misconception about what being good at math is supposed to feel like, so they interpret their confusion as a sign that math is just not something they’re capable of understanding. Often, these students actually understand complicated algebra well enough, but they have weak arithmetic fundamentals, which makes every question feel like a slog. Lack of confidence around multiplication and division/fractions, in particular, ripples throughout other math topics, but these students don’t recognize that this is the source of their math issues.
Memorizing the Times Tables
The root of so many students’ math issues is a failure to confidently learn the times tables when they were young. Almost every math topic involves multiplication in some way, yet high school students don’t recognize that the times tables are holding them back. Luckily, it’s never too late to learn! This lesson goes back to basics, walking students through strategies that can help them memorize the 10-by-10 times tables.
Lesson [10:03] — https://youtu.be/lJTQ8Vxn06s
1. Multiplication is Everywhere — demonstration of various topics that heavily involve multiplication
2. Memorize the Times Tables — fill out the standard 10x10 times tables, one row at a time; connects multiplication and division
Worksheet — fill out a chronological times table, then fill out a jumbled times table; practice quickly knowing whether numbers are divisible by 2, 3 and 5
Review [23:56] — https://youtu.be/LEvlwAt5ilg
Fraction Rules
One of the reasons that students hate fractions is that they aren’t confident with the times tables. However, fraction rules create confusion on their own. This lesson reviews the main fraction rules, emphasizing the concepts that are used most often in high school algebra.
Lesson [11:29] — https://youtu.be/NwiOVqsRF2I
1. Fractions are Division — seeing fractions as division problems that we’re too lazy to complete puts all of the other fraction rules in context
2. Reducing — do as much of the division as possible
3. Mixed Numbers are Dead — high school algebra rarely uses mixed numbers, yet students have developed strong habits to convert
4. Multiplication — the easiest operation to perform with fractions; encourage students to reduce before they multiply
5. Division — keep, change, flip
6. Addition & Subtraction — emphasizes that these are the hardest fraction operations
7. Moving & Eliminating — discourages cross-multiplying, which undermines normal fraction multiplication; encourages use of the reciprocal
Worksheet — mixture of fraction algebra problems of all types
Review [32:52] — https://youtu.be/5SguxBVrKAA
How Math Feels
Many students assume that they’re bad at math because it doesn’t feel automatic. They need to go slowly and show their work for every step. The steps to solve problems aren’t obvious to them. This lesson tells them that all of this is not only okay, but actually what being good at math is supposed to feel like. The lesson walks students through a complicated linear algebra question, replicating the thought process and steps that “math geniuses” would go through to solve it.
Lesson [11:15] — https://youtu.be/V4nS1EhWHnk
1. Just Start Walking — you do not need to know Step 5 to start Step 1; start Step 1 with the confidence that the remaining steps will reveal themselves
2. Write Stuff Down — no matter how obvious something seems, it should be written down on the page; don’t erase dead ends
3. Solve for Variables — generally, getting rid of variables by substituting and solving will help you move forward through the question
Worksheet — four difficult math problems that can be solved with confidence in Step 1, without worrying about the entire plan
Review [30:53] — https://youtu.be/6nsYAIOT30E
How to Check Your Work
Students wrongly assume that checking your work means redoing a problem the same way from start to finish to see if you get the same answer. This lesson shows other ways to check your work that are more efficient. It also emphasizes checking your work “as you go” so that you catch mistakes before they carry through to the next steps of long problems.
Lesson [10:57] — https://youtu.be/W_fR_xxDzco
1. Check Your Work As You Go — redoing problems at the end is not efficient; know which kinds of steps are most likely to cause errors; check for mistakes before moving on to the next step
2. Plug Values Into Equations — check algebra answers by plugging numbers into variables, turning abstract algebra into easier arithmetic
Worksheet — five deliberately error-prone algebraic expressions that encourage students to slow down and check each step; check a solution to an equation or system by plugging the values into the variables
Review [18:46] — https://youtu.be/xd113URIMrk
