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 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....

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 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...

 Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical...

 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...

 In Topic A, students look at incidence relationships in networks and encode information about them via highdimensional matrices. Questions on counting routes, the results of combining networks,...

 Topic B explores the geometric context for higherdimensional matrices. The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students...

 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 C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...

 In Topic B, students develop an understanding that when complex numbers are considered points in the Cartesian plane, complex number multiplication has the geometric effect of a rotation followed by...

 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 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...

 Topic A begins the study of linearity looking at common misconceptions made by math students. This study leads to complex solutions which launches the study of products, quotients of complex numbers...

 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...

 In Topic C, children shift focus to subtraction stories with numbers 1 to 5, again acting them out, using fingers, manipulating objects, drawing, and counting pictorial representations to model the...

 In Topic C, the concept of volume and the vocabulary used to describe and compare it (i.e., big, small, more, and less) are discussed. This is perhaps the most familiar to young children, compared to...

 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...

 Topic E builds on the work of previous topics, providing opportunities for children to solve subtraction story problems with abstract representations (MP.4). As in Topic D, children decontextualize...

 Topic D begins by building upon the work of Module 1 by having students count 5 bears in a scattered configuration while identifying the first and last bear counted (PK.CC.6). This concept is a...

 Topic D builds on the work of Topic B, again providing opportunities for children to solve addition story problems while taking a step forward by representing the objects in the story with fingers,...

 In Modules 1 and 3 students did extensive work to develop understanding of numbers to 10. The first half of Module 4 was dedicated to comparison of measurement. Topic F brings together this work...

 So far, PreKindergarten students have done a lot of onetoone counting, have compared measurable attributes, and have identified the first and last in a group of objects. Topic E brings these...