High School Geometry Goals

• Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CCSS.MATH.CONTENT.HSG.SRT.C.8

• Pythagorean theorem basics

Given access to formulas and a calculator, Lysandra can find the area of triangles, but she needs significant teacher support to apply the Pythagorean theorem.

• Given a calculator and the formula, Name will use the Pythagorean Theorem to solve right triangles in applied problems with 80% accuracy on two of three trials as measured by teacher records and observations CCSS.MATH.CONTENT.HSG.SRT.C.8

• Make it easier: Limit the length of the sides in the right triangle problems; remove “applied” from the goal.
• Make it harder: Remove the supports of formulas and calculators.

• Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot) MATH.CONTENT.HSG.MG.A.2

• Density worksheet 1, no formulas
• Density worksheet 2, no formulas

Given the formula for density and word problems involving density and determining if something can float on water, Sunni can solve the problems with 30% accuracy. 

• Given a calculator and formulas, Name will apply concepts of density based on area and volume in modeling situations, determining the density of objects given their mass and volume and comparing the density of those objects to water with 80% accuracy as measured by teacher records and observations MATH.CONTENT.HSG.MG.A.2

• Make it easier: Just have the student calculate the density of the objects.
• Make it harder: Remove the supports of notes and calculators. Specify that the student needs to include the correct units.

• Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula CCSS.MATH.CONTENT.HSG.GPE.B.7

• Perimeter and surface area in a coordinate plane, no explanation
• Perimeter and surface area in a coordinate plane, with explanation

Don can calculate the area and perimeter of rectangles and area of triangles given their heights and widths and given a calculator and the formulas with 80% accuracy. He needs more support to find the perimeter of a triangle and to find either area or perimeter for the shapes using the coordinate plane (20% accuracy).

• Given a calculator and the distance formula, Name will use coordinates to compute perimeters and areas of triangles and rectangles, with 80% accuracy as measured by teacher records and observations CCSS.MATH.CONTENT.HSG.GPE.B.7

• Make it easier: Focus on just area or perimeter.
• Make it harder: Remove the supports of notes and calculators. Add “perimeters of polygons and areas of triangles and rectangles.”

• Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. CCSS.MATH.CONTENT.HSG.GMD.A.3

• Volume of cones, spheres, and cylinders, no formulas
• Volume of cones, spheres, and cylinders, with formulas
• Volume of cones and pyramids, no formulas

Given the formula and measurements such as the height of a pyramid, John can find the volume of cylinders, spheres, pyramids, and cones with 30% accuracy.

• Given a calculator and access to notes, Name will use volume formulas for cylinders, pyramids, cones, and spheres to solve problems with 80% accuracy as measured by teacher records and observations CCSS.MATH.CONTENT.HSG.GMD.A.3

• Make it easier: Reduce the number of shapes the student needs to work with to spheres and pyramids or spheres and cylinders.
• Make it harder: Remove the supports of notes and calculators.