Examples · Study
Study, on a board
Not to get the answer out, but to change a number and see why it comes out that way.
A calculator is finished once it has produced the answer. CalcAnyway keeps the working on the screen as cards, so you can change a number and compare what the formula and the picture do.
What happens to the bar diagram when the numerator changes. How the area moves when the base or the height does. Which way the mean and the median go when one score is changed. Where a formula on its own is hard to read, moving the numbers and the picture together shows the relation.
Articles
Percentage change — the new value, and the rise needed to get back
1,000 to 800 is −20%. A 20% rise from 800 only reaches 960; getting back to 1,000 takes 25%.
Division and fractions — quotient and remainder, fraction, decimal
13 ÷ 4 is 3 remainder 1, 3 1/4 or 3.25. Why the three forms match, and why the remainder is smaller than the divisor.
Rounding — to the nearest, up and down
34,567 to the thousands: 35,000 to the nearest or rounded up, 34,000 rounded down. The hundreds digit decides.
Area of a triangle — why it is base × height ÷ 2
A triangle with base 6 and height 4 is 6 × 4 ÷ 2 = 12: exactly half of the parallelogram (24) with the same base and height.
Unit conversion — length, area and time
350 cm is 3.5 m, 1 m² is 10,000 cm², and 142 minutes is 2 h 22 min (about 2.37 hours) — with the reason behind each factor.
Mean and median — how they differ and how to find each
Eight scores: mean 78.25, median 81. With one score changed to 0, the mean drops to 70.5 and the median stays at 81.
Scaling a recipe — the factor from servings or from an ingredient
A recipe for 4 cooked for 6 is ×1.5: 400 g of meat becomes 600 g. Also the factor from the meat you have, and why one factor keeps the ingredients in the same proportions.
Average speed for a round trip — total distance over total time
Total distance ÷ total time. 60 km/h out and 30 km/h back gives 40 km/h, not the 45 km/h from averaging the two speeds.
Concentration — finding it, diluting and mixing
20 g of salt in 180 g of water is 10%: the divisor is the whole solution, not the water. Also the water to add when diluting, and how much of two solutions to mix.
Balancing a lever — weight times distance from the pivot
Weight × distance from the pivot has to match on both sides: 60 g at 20 cm balances 40 g at 30 cm. Also several weights on one side, and the force to lift a load with a bar.
Resistors in parallel — the combined resistance from the branch currents
Add the branch currents, then divide the voltage by the total. 4 Ω and 6 Ω in parallel across 12 V draw 5 A, so the combined resistance is 2.4 Ω.