Design a community garden where every job is fraction multiplication or division in disguise.
REMEMBER:“Of” means multiply: 2/3 of 3/4 is 2/3 × 3/4. A
fraction is a division: 3/4 = 3 ÷ 4 (3 pizzas shared by 4 people). Multiplying by a
fraction less than 1 shrinks, by a fraction greater than 1 grows, and by 1
keeps the size — you can predict that before computing. Dividing by a unit
fraction asks “how many of these fit?” (2 ÷ 1/3 = 6 scoops), and dividing a unit
fraction by a whole number splits it into smaller pieces (1/2 ÷ 3 = 1/6).
Part 1 · Plant the Plot
The garden plot is one square acre. First shade the part of the acre you are working with
(the columns). Then plant a fraction of that part (the rows). The double-shaded region is
the product — count its pieces.
Keep both fractions at most 1 (numerator no bigger than denominator), denominators up to 12.
Tile a Plot
A rectangular bed has fractional sides. Tile it with small squares whose sides are unit fractions, count the tiles,
and multiply by the area of one tile.
The Watering Station
Two kinds of division live here. Pick one, set the numbers, and watch the bar.
Part 2 · The Scaling Greenhouse
A plant goes into the greenhouse and gets multiplied by a factor. Before it runs, predict:
will it come out bigger, smaller, or the same size? Lock in, then watch. Some rounds ask about sharing instead.
Part 3 · The Machines
Three step-by-step machines. Each step says what to do and why.
Multiply fractions and mixed numbers
Share whole things equally (a ÷ b = a/b)
Divide with a unit fraction
Part 4 · Master Gardener Quiz
Ten questions. Each wrong answer tells you which part of the garden to revisit.
Question 1 of 10Score: 0
Word Box
Fraction as division
a/b means a ÷ b. Three pizzas shared by four people: each gets 3 ÷ 4 = 3/4 of a pizza.
“Of” means multiply
2/3 of 3/4 = 2/3 × 3/4. Take a fraction of a fraction by multiplying.
Area model
A unit square cut into columns for one fraction and rows for the other. The double-shaded region is the product.
Unit fraction
A fraction with numerator 1: 1/2, 1/3, 1/4. The building block of every other fraction.
Tiling
Covering a rectangle with unit-fraction squares to find its area: count tiles × area of one tile.
Scaling
Multiplying as resizing. Factor > 1 enlarges, factor < 1 shrinks, factor = 1 keeps the size.
Mixed number · Improper fraction
2 1/2 = 5/2. Convert to improper before multiplying: whole × denominator + numerator.
Quotient
The answer to a division. 2 ÷ 1/3 = 6 means six 1/3-cup scoops fill 2 cups.