lesson
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If you bake 3 whole pans of brownies and eat 52 of each pan, how many total pans of brownies did you eat?
Even though you are multiplying, you end up with less than the 3 pans you started with.
Building the Area Model
An area model represents multiplication by showing the total space inside a rectangle with a given length and height ( extArea=length×height).
To find 3×52, line up 3 unit squares side-by-side to make a total length of 3 and split each unit square into 5 equal columns.
📊Create an interactive visual diagram showing an area model for 3 * (2/5). Display three side-by-side unit squares with width 1 and height 1 each, forming a total width of 3. Each square is divided vertically into 5 equal vertical strips. In each of the 3 squares, exactly 2 out of the 5 strips are shaded in vibrant blue (#2563eb). Below the 3 squares, show an animation or toggle that rearranges the 6 shaded fifths together into 1 completely filled whole unit square plus 1 unit square with 1 fifth shaded, labeled 'Total = 6/5 = 1 1/5'. Clean typography, light background (#f8fafc), dark text (#1e293b).
Each whole square has 2 out of 5 parts shaded, giving a total of 3×2=6 shaded parts, or 56.
When you slide those 6 shaded fifths together, they fill 1 full whole square plus 51 of another, giving 151.
What happens if the fraction is greater than 1 whole?
Fractions Greater Than One
An improper fraction is a fraction where the top number is greater than or equal to the bottom number, such as 34.
To model 2×34, create 2 columns of width 1 and extend their height to 34 (which is 1 whole plus 31).
📊Create a diagram showing 2 * (4/3) using an area model. Show 2 side-by-side unit columns (width 2 total). Vertically, divide the height into thirds, extending 4 thirds high (1 whole plus 1 extra third row above the dashed baseline). All 2 columns x 4 vertical thirds are shaded in emerald green (#059669), giving 8 total unit-thirds shaded. On the right side, show these 8 thirds rearranged into 2 completely full unit squares plus 2/3 of a third square, labeled '8/3 = 2 2/3'. Responsive 350px container with clear labels.