WAC+Math

Writing Assignments for Math Based on Common Core Math Standards using the links below or other other sources create prompts for writing assignments tied to the standards. List other resources at the listed place at the bottom.

State of Michigan Math WAC guide [|Plainfield WAC Prompts] [|Franklin and Marshall College Math WAC] UPS WAC Glencoe Math WAC

=High School- Numbers and Quantity=


 * **Ideas for how this profession uses writing** ||
 * Teachers incorporate writing in math class to help students reflect on their learning, deepen their understanding of important concepts by explaining and providing examples of those concepts, and make important connections to real-life applications of the math they are learning. Teachers use the writing assignments to assess student understanding of important concepts, student proficiency in explaining and using those concepts and each student's attitude toward learning mathematics. Writing in mathematics is a win-win for both teacher and student. Although it may be difficult to introduce this practice, it is well worth the effort. Look for simple ways to incorporate short writings throughout daily lessons and longer writings over the course of weeks or math units. (MathWire.com)

KWL Chart Exit and Entrance Slips TWPS (think, write, pair, share) Use real-life examples in class Create story problem-makes them think about the real-world experience. Can incorporate narratives and make it really in-depth. Incorporate a certain amount of subjects that have been learned over the year and complete the problems. ||


 * **Standard** || **Writing Assignment Examples** ||
 * N-RN.1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. //For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. // ||  ||
 * N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. ||  ||

Use properties of rational and irrational numbers.

 * **Standard** || **Writing Assignment Examples** ||
 * N-RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. || Create comics about rational and irrational numbers arguing with one another. ||

Reason quantitatively and use units to solve problems.
Flow charts ||
 * **Standard** || **Writing Assignment Examples** ||
 * N-Q.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. || Graphic organizers
 * N-Q.2. Define appropriate quantities for the purpose of descriptive modeling. || Write a paragraph describing your thought process and explain to class. ||
 * N-Q.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. ||  ||

Perform arithmetic operations with complex numbers.

 * **Standard** || **Writing Assignment Examples** ||
 * N-CN.1. Know there is a complex number //i // such that //i //2 = –1, and every complex number has the form //a + bi //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> with //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">a //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> and //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">b //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> real. || create a formula and use a storyboard to show how to solve for i ||
 * N-CN.2.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> Use the relation //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">i //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. || Create a chart to display the following. ||
 * N-CN.3.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. ||  ||

<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif; font-size: 16px;">Represent complex numbers and their operations on the complex plane.

 * **Standard** || **Writing Assignment Examples** ||
 * N-CN.4.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. || Create a poster showing complex numbers that demonstrates and explains why. ||
 * N-CN.5.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°. // || Create a 3D visual demonstrating these properties and explain how they are related. ||
 * N-CN.6.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. || Solve a problem and explain your thought process at each decision point. ||

<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif; font-size: 16px;">Use complex numbers in polynomial identities and equations.

 * **Standard** || **Writing Assignment Examples** ||
 * N-CN.7.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> Solve quadratic equations with real coefficients that have complex solutions. ||  ||
 * N-CN.8.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Extend polynomial identities to the complex numbers. //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">For example, rewrite x2 + 4 as (x + 2i)(x – 2i). // ||  ||
 * N-CN.9.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. ||  ||

<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif; font-size: 16px;">Represent and model with vector quantities.

 * **Standard** || **Writing Assignment Examples** ||
 * N-VM.1.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., **<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">//v// **<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">, | **<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">//v// **<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">|, **<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">//v// **, //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">v //<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">). ||  ||
 * N-VM.2.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. ||  ||
 * N-VM.3.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Solve problems involving velocity and other quantities that can be represented by vectors. ||  ||

<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif; font-size: 16px;">Perform operations on vectors.

 * **Standard** || **Writing Assignment Examples** ||
 * N-VM.4.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Add and subtract vectors.
 * <span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
 * <span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
 * <span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">Understand vector subtraction **//v//** – **//w//** as **//v//** + (–**//w//**), where –**//w//** is the additive inverse of **//w//**, with the same magnitude as **//w//** and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. ||  ||
 * N-VM.5.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Multiply a vector by a scalar.
 * <span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;">Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, ||  ||   ||   ||

<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif; font-size: 16px;">Perform operations on matrices and use matrices in applications.

 * **Standard** || **Writing Assignment Examples** ||
 * N-VM.6.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. ||  ||
 * N-VM.7.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. ||  ||
 * N-VM.8.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Add, subtract, and multiply matrices of appropriate dimensions. ||  ||
 * N-VM.9.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. ||  ||
 * N-VM.10.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. ||  ||
 * N-VM.11.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. ||  ||
 * N-VM.12.<span style="background-color: #ffffff; color: #3b3b3a; font-family: Helvetica,Arial,sans-serif;"> (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. ||  ||


 * **Additional Resources** ||