L3 · Comparing percentages within 100%
“I can compare and order percentages - and compare a percent with a fraction or a decimal - by making all the names count out of the same whole of 100.”
Which is greater: 45% or 54%? Step 1: Both percents count out of the same whole - 100. No renaming is needed. Step 2: Compare the counts: 54 squares of the grid against 45 squares. Step 3: 54 > 45, so 54% is greater. Model both ways: two hundred grids shaded to 45 and 54 (the second clearly fuller), and the two points on the pre-segmented 0-2 line - 54% = 0.54 sits to the right of 45% = 0.45, and bigger numbers sit further right. Say the rule plainly: percents are easy to compare BECAUSE they share one whole. Fractions with different denominators do not - that is why we rename them into percents or into a common denominator first.
Why can 45% and 54% be compared right away, with no renaming?
Order from least to greatest: 30%, 12%, 85%. -> 12%, 30%, 85%
"Compare 68% and 86%: the counts are 68 and 86 out of the same 100, and 86 > 68, so ___% is greater." -> 86%
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.