Unit 3A: Whole Numbers & Expressions with Area

The big ideas for Unit 3 are number operations, expressions, and geometry.  The strands that connect them all are area & volume.  How do you understand expressions themselves & equivalent expressions?  Area models until you get to expressions like a3 (cubes), abc (any rectangular prism) or a2b (a rectangular prism with a square base), then it’s volume.  Even certain cases of the greatest common factor and the least common multiple can be understood through area & volume models, respectively (see more under FAQs).  The distributive property is simply an example of length times width.  6th grade can connect area models from elementary school to multiplying and factoring polynomials in Algebra 1 if algebra tiles are used when exploring algebraic examples of the distributive property and even by employing base-ten blocks with the numeric examples of the distributive property.  Geometry is embedded throughout the unit, and it is the tie that binds this large unit together.  

Numeric & algebraic operations are both tied to area & volume.  Expressions students evaluate like a²b are in fact an abstraction of the volume of any rectangular prism if drawn out or created with blocks.  Likewise, x² is a representation of the area of any square.  The distributive property has two factors, length & width, and can be represented by area as well.