A fraction, a decimal, and a percent are three ways to write the same amount. One quarter, 0.25, and 25% all say "a quarter of the way."
They grow out of fractions. A decimal is a fraction out of 10, 100, or 1000. A percent is a fraction out of 100.
They are on the grade-level path. Fifth graders read, write, compare, and round decimals to the thousandths. Sixth graders use percents as rates out of 100.
They are everywhere. Money, sales and tips, sports stats, test scores, and phone batteries all use decimals and percents.
In every round, Emma climbs and a ruler measures how far she went. Students see the same height three ways, so the connection between the forms is something they can picture, not just a rule to memorize.
How Far Did Emma Go? Match words and numbers to Emma's climb, move Emma to a target, then write how far she went three ways: as a fraction, a percent, and a decimal.
Place Value: Emma walks across the place value chart and shows what a number 0 to 9 is worth in each box: multiplied by 1000, 100, 10, or 1 on the left of the decimal point, divided by 10, 100, or 1000 on the right.
Times & Divided by Ten: meet June, Emma's friend. She fetches the decimal point and places it to make a number. Students show her where it goes, first from numbers and then from number words. Then June moves the point: times ten, one place to the right; divide by ten, one place to the left (and two or three places for 100 and 1000). Last, June fills empty places with zeros from her Zero Bowl, as in 4.5 × 100 = 450 and 3.2 ÷ 10 = 0.32.
Fraction ↔ Decimal ↔ Percent: Emma and June together. June turns decimals into percents and back (× 100 or ÷ 100, two places), and Emma climbs the wall to show how far that is. Then students write any amount all three ways at once.