Mathematics 9 Square Roots and surface area
Specific Curriculum Outcomes
N05 Students will be expected to determine the exact square root of positive rational numbers.
N06 Students will be expected to determine an approximate square root of positive rational numbers.
G01 Students will be expected to determine the surface area of composite 3D objects to solve problems (note that this outcome is limited to right cylinders, right rectangular prisms, and right triangular prisms).
N05 Students will be expected to determine the exact square root of positive rational numbers.
N06 Students will be expected to determine an approximate square root of positive rational numbers.
G01 Students will be expected to determine the surface area of composite 3D objects to solve problems (note that this outcome is limited to right cylinders, right rectangular prisms, and right triangular prisms).
activities
 Solid Fusing Task from Nat Banting  Students are given a set of six solids. It includes a cube; two cylinders; a right, square pyramid; a right cone; and a hemisphere (note: you can adjust list of solids to make it specific to outcome G01). Rather than provide them with a preordained arrangement of the solids, the task makes the arrangement the key mathematical decision to be made. Combine any number of the six solids provided to you to create a shape that has a surface area (in square units) as close as possible to its volume (in cubic units). Nat has some additional resources on his blog.

 File Cabinet from Andrew Stadel  Andrew was staring at this file cabinet at the back of his room, saw a stack of PostIts on his desk and thought, how many PostIts would it take to cover this rectangular sonofaprism... and so it began. Extension: ask students to calculate how many postit note it would take to completely cover their desk. Give them exactly that many postits and see if it works.
 Surface Area Tin Man Project  Each pair of students built a tin man out of boxes, toilet paper rolls, paper towel rolls, Styrofoam balls, and cones. They had to use a formula sheet to first measure the surface area of the parts, showing all of their work for each part. Next they had to tape the parts together. Then I would give them the exact amount of foil they measured for, no more and no less. They had to cover their tin man as completely as possible without running out of tinfoil or having extra leftover.