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Common Core: Math
Topic: Common Core Learning Standards
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 In Topic A of Module 5, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. The module begins by explaining...

 In Topic B, students apply their knowledge of volume from previous grade levels (5.MD.C.3, 5.MD.C.5) to the learning of the volume formulas for cones, cylinders, and spheres (8.G.C.9). First,...

 In Topic B, students’ understanding of integer exponents is expanded to include the concept of magnitude as a measurement. Students learn to estimate how big or how small a number is using magnitude...

 Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these...

 Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while...

 In Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions...

 Optional Topic D begins the learning of Pythagorean Theorem. Students are shown the “square within a square” proof of the Pythagorean Theorem. The proof uses concepts learned in previous topics of...

 In Topic A, students begin by learning the precise definition of exponential notation where the exponent is restricted to being a positive integer. In Lessons 2 and 3, students discern the structure...

 Student Outcomes Students use the Pythagorean Theorem to determine an unknown dimension of a cone or a sphere. Students know that a pyramid is a special type of cone with triangular faces and a...

 Student Outcomes Students know that truncated cones and pyramids are solids obtained by removing the top portion above a plane parallel to the base. Students find the volume of truncated cones.

 Student Outcomes Students know how to determine the volume of a figure composed of combinations of cylinders, cones, and spheres.

 Student Outcomes Students know how to compute the average rate of change in the height of water level when water is poured into a conical container at a constant rate.

 Student Outcomes Using square roots, students determine the position of the bottom of a ladder as its top slides down a wall at a constant rate.

 Student Outcomes Students calculate the decimal expansion of pi using basic properties of area. Students estimate the value of expressions such as pi2.

 Student Outcomes Students know that the Pythagorean Theorem can be interpreted as a statement about the areas of similar geometric figures constructed on the sides of a right triangle. Students...

 Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems.

 Student Outcomes Students determine the distance between two points on a coordinate plane using the Pythagorean Theorem.

 Student Outcomes Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

 Student Outcomes Students apply knowledge of equivalent fractions, long division, and the distributive property to write the decimal expansion of fractions.

 Student Outcomes Students know the intuitive reason why every repeating decimal is equal to a fraction. Students convert a decimal expansion that eventually repeats into a fraction. Students know...

 Student Outcomes Students use rational approximation to get the approximate decimal expansion of numbers like the square root of 3 and the square root of 28. Students distinguish between rational and...

 Student Outcomes Students apply the method of rational approximation to determine the decimal expansion of a fraction. Students relate the method of rational approximation to the long division...

 Student Outcomes Students use rational approximations of irrational numbers to compare the size of irrational numbers. Students place irrational numbers in their approximate locations on a number...

 Student Outcomes Students use factors of a number to simplify a square root.