C2.3 Identify and use equivalent relationships for whole numbers up to 1000, in various contexts.
Activity: Representing Quantities to Understand Equivalence Relations
When numbers are decomposed, the parts are equivalent to their whole.
The various activities below lead students to understand that, even if the quantity is broken down in different ways, it remains the same. The concrete and semi-concrete representations can later be combined with a symbolic representation.
Examples
500 = 250 + 250
494 + 1 = 1 + 494
200 + 200 = 100 + 100 + 100 + 100
- Represent $500 in different ways with various bills or coins. If you don't have enough materials for all students, visit the mathies website.
- Represent 250 with different jumps on a number line or on a beaded line.
- Mystery number: Ask students, in teams of two, to represent a number in different ways (concrete material, semi-concrete, symbolically). Create a gallery where students circulate and see how other teams have represented it.