Evidence of Understanding

**describe how dimensional changes impact perimeter, area, and volume**- measure and compare different lengths of objects, compare units of measure and understand their size and
**scale**in relation to one another (for example, size of meter vs inch)- set up ratios and proportionsto convert units

- use units to explain the relationship between one, two, and three dimensions
- investigate how
**perimeter**,**area**and**volume**scales under similarity transformations- given different length measures, compare the area or volume of the same object

- determine dimensions of a figure using its perimeter, area, or volume
- use constraints within a situation to solve problems across dimensions and justify solutions

- use constraints within a situation to solve problems across dimensions and justify solutions

- measure and compare different lengths of objects, compare units of measure and understand their size and
**explain perimeter, area, and volume formulas and use them to solve problems**- justify the formulas for the
**circumference**and the area of a circle - make comparisons between areas of different objects using dissection arguments
**partition**three-dimensional shapes into smaller shapes to compare these shapes- make conjectures and justify how 3-D objects that have the same height and
**cross-sections**of equal area will have equal volume - use dissection arguments, Cavalieri’s principle, similarityand informal limit arguments

- make conjectures and justify how 3-D objects that have the same height and
- give an informal argument for the formulas for the volume of a
**cylinder, pyramid, and cone**- describe how area formulas extend into three dimensions to create volume formulas

- identify geometric shapes that best describe a real world shape and determine which dimension to work with
*(*Example: modeling a tree trunk or a human torso as a cylinder)- approximate reasonable solutions to problems using volume formulas
- work backwards from a formula to determine the value of a specific measurement within the context of the situation

- calculate the perimeter, area, or volume of an irregular shape by partitioning it into “familiar” pieces and summing the pieces (or finding the difference between the pieces)

- justify the formulas for the

Develop conceptual understanding:

scale, perimeter, area, volume, circumference, cross-section, cylinder, pyramid, cone

Supporting terms to communicate:

length, units of measure, scale, ratios, radius, proportions, similarity, decompose