A tape diagram models an equation as a relationship among quantities: a whole represents a total, adjoining parts represent addition, equal-sized repeated parts represent multiplication, and equal partitions can represent division. The variable labels an unknown length or quantity, while numbers label known parts, totals, or differences; translating between the diagram and equation preserves equality and clarifies the distinction between an unknown and its coefficient. At this level, representations are limited to numerical one- and two-step relationships rather than abstract symbolic generalizations.
A tape diagram shows how quantities fit together.
Suppose a problem says:
Three equal boxes and 4 extra items make 19 items altogether. How many items are in each box?
Let represent the number of items in one box.
The tape diagram is:
19 items
┌─────┬─────┬─────┬───┐
│ x │ x │ x │ 4 │
└─────┴─────┴─────┴───┘
or, using multiplication,
To find , first remove the extra :
Then divide the 15 items equally among the 3 equal boxes:
Each box contains items. Checking the diagram:
The three equal sections show the coefficient , while labels the unknown amount in one section.
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