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Common Core: Math
Subject: Math
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 Drawing Figures in the Coordinate Plane

 Topic G culminates not only Module 6, but also a full year of learning for Grade 1 students. It is a joyous celebration of the great progress of all students. During each lesson, students recognize...

 Topic F provides students the opportunity to focus on solving various problem types and learn from their peers’ strategies. Lessons 25 and 26 focus on the most challenging Grade 1 problem types:...

 Through Topic E, students learn about the four most predominant U.S. coins in circulation, the penny, the nickel, the dime, and the quarter. Students identify and use the coins based on their image,...

 During Topic D, students discuss and compare the various place value strategies they use when adding to 100 (1.NBT.4). Students have the opportunity to explain their thinking and better understand...

 During Topic C, students apply all of their place value and Level 3 strategy knowledge to add pairs of twodigit numbers to sums within 100. To this point, students have only added pairs of twodigit...

 Topic B extends students’ use of counting sequences and understanding of tens and ones to numbers up to and including 120. In Lesson 3, students apply their understanding of tens and ones to two...

 Topic A of Module 6 opens with students exploring one of the most challenging problem types for their grade level, comparison word problems (1.OA.1). Students were informally introduced to the...

 Throughout their math experiences, students will look for and make use of structure (MP.7). In Topic F, children model repeating and growth patterns using objects, sounds, and movements.

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts (S.MD.B....

 In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...

 In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

 The graphs of the trigonometric functions are revisited in Topic C. Students visualize these graphs with the aid of the appropriate software and briefly recall how changing various parameters of a...

 Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...

 In Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. ...

 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 In Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They...

 Topic B defines the measure of an arc and establishes results relating chord lengths and the measures of the arcs they subtend. Students build on their knowledge of circles from Module 2 and prove...

 Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

 In Topic E students apply the knowledge developed in this module to understand how firstperson video games use matrix operations to project threedimensional objects onto twodimensional screens and...