Strengthening Math Fundamentals: Arithmetic and Algebra Review for SAT Readiness

Before jumping into complex algebra and geometry, assess whether your arithmetic and basic algebra are solid. Take a 15-question diagnostic covering: (1) basic arithmetic (fractions, decimals, order of operations), (2) variables and simple equations, (3) properties of exponents, (4) simple linear equations. If you score below 80% on this diagnostic, your foundational skills need strengthening before jumping to SAT-level problems. Weak foundations are why many students struggle on the SAT despite hours of practice: they are practicing advanced techniques on weak foundations, like building a house on sand. Strengthening foundations first, even if it takes 4-6 weeks, yields dramatically faster progress on SAT problems afterward.

The good news: arithmetic and basic algebra are learnable and automatable through short, focused practice. Most students can move from foundational weakness to strong competence in 4-6 weeks of consistent daily drill (20-30 minutes per day).

Commit to 10 minutes of daily arithmetic and algebra drill for the next 4 weeks. Week 1: focus on fractions (adding, subtracting, multiplying, dividing). Week 2: focus on decimals and percentages. Week 3: focus on order of operations and simplifying expressions. Week 4: focus on solving linear equations. Each day, solve 15-20 problems in your week's focus area, timing yourself. Track how many you solve correctly. By week 2, you should solve 15-20% more problems correctly than week 1. By week 4, you should solve 40-50% more correctly than your starting point. This visible progress is motivating and measurable proof that foundational strength is building.

Use free resources for drill: Khan Academy's foundational math sections, IXL, or paper-and-pencil worksheets found online. The resource matters less than consistency; 10 minutes daily beats 70 minutes once per week.

Common arithmetic errors: (1) sign errors when multiplying negatives ((-2)×(-3)=6, not -6). Quick fix: drill sign rules until automatic. (2) Order of operations mistakes (solving 2+3×4 as (2+3)×4 instead of 2+(3×4)). Quick fix: use PEMDAS/BODMAS mnemonic and practice. (3) Fraction mistakes (2/3+1/4 is not 3/7). Quick fix: practice finding common denominators. Common algebra errors: (1) distributing incorrectly (2(x+3) becomes 2x+3 instead of 2x+6). Quick fix: many practice problems until automatic. (2) Forgetting to apply operations to both sides of an equation. Quick fix: write out each step and speak aloud what you are doing.

The fix for all these errors is the same: identify your specific error type, then drill that type repeatedly until you no longer make it. An error log helps: write each mistake down, categorize it, and drill that category the next day.

Here is a 4-week drill schedule. Week 1 (Fractions): Monday-Wednesday drill fraction addition, Thursday-Saturday drill fraction multiplication and division, Sunday review all fractions. Week 2 (Decimals/Percentages): Similar progression with decimals (Mon-Wed), then percentages (Thu-Sat), review Sunday. Week 3 (Order of Operations): simple expressions (Mon-Tue), complex expressions with multiple operations (Wed-Fri), review Saturday-Sunday. Week 4 (Equations): solving one-step equations (Mon), two-step equations (Tue-Wed), multi-step equations (Thu-Fri), review Sat-Sun. After week 4, take an SAT Math diagnostic test to measure improvement. You should score noticeably higher on foundational algebra and arithmetic questions than week 0. Then, continue with SAT-level practice, knowing your foundation is solid.

Track your accuracy and speed on each day's drill in a simple chart. By week 4, you should see your accuracy climb and your speed increase. This visible progress is proof that automaticity is building.