Names of student(s) teaching: Concept statement/main idea: Standards for the lesson: Objectives. Write objectives in LWBAT form.
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1 Teach 1 Teach date: Teach time: Teach length: Names of student(s) teaching: Title of lesson: matrix multiplication Concept statement/main idea: The big idea is to reach an understanding of matrix multiplication beyond the memorized routine most learners have. This will be accomplished through an investigation of the dot product of vectors and ISBN13 and UPC barcodes, and extended to small and large matrices. Standards for the lesson: HS.Modeling ; & beyond the NVACS Objectives. Write objectives in LWBAT form. LWBAT: Learners will be able to use dot product to verify UPC and ISBN13 barcodes and practice matrix multiplication on 2x2, 3x3, and (axn)(nxb) matrix. Evaluation Write at least one question to match the objective you listed or describe what you will look at to be sure that students can do this. How is matrix multiplication and scalar multiplication of matrix related? How can you scale the multiplication of vectors to the multiplication of matrix?
2 Engagement Estimated time: 5 minutes Description of activity: A conversation about the meaning of UPC and ISBN13 BarCodes. Some history, and connection to the topic of vectors. Asks; How many bar codes do you have in your possession right now? Looks for all the barcodes they have in their wallet/ purse/ backpack. Displays all the barcodes on table. student and consider possible student responses Why do you think are there some common numbers? Why do you think are some numbers different? Have you ever wondered what those numbers mean? There is a pattern, a connection between all those numbers. Would you like to know what it is? Paper, Pencils/pens 2
3 Exploration Estimated time: 15 minutes Description of activity: Practice with the vector dot product with varying materials learners brought to class BRIEFLY show the math for dot product of two vectors (also called scalar multiplication.) Depending on how deep you want to go with the exploration, some of the questions on the right may be beyond the class you are teaching. Explores the dot products of varying ISBN13 s and UPC codes. student and consider possible student responses Why is it called scalar multiplication? Why does the scalar always end in a zero? What does it mean if it does not end in a zero? Why did the designers CHOOSE a vector of repeating [3,1 ] Why did the designers choose to have a 1 multiplying the check digit? When could numbers be transposed and the scalar still ends in a zero? (yes, it is possible) Paper, pencils/pens, several ISNB13 s and UPC codes. 3
4 Explanation Estimated time: 10 minutes Description of activity: Teachers asks questions to set up the explanation of Asks questions same Paper, pencils/pens Thinks and discusses in groups, whole class. student and consider possible student responses Are there any other definitions of the process that will lead to a scalar answer? What would they be? Or What other methods could we use to calculate a single number from the two vectors? Explain? Why is the method we used, multiplication and addition, the method that is preferred? What are the advantages of this method over the methods you came up with? We multiplied (1x12)(12x1) vector and ended up with a (1x1) vector; a scalar number. What would happen if we multiplied vectors that are (2x12)(12x2)? Why? What would such a vector represent? 4
5 Elaboration Estimated time: 10 minutes Description of activity: Asks questions Works problems, discusses in groups and whole class student and consider possible student responses Since we predicted the multiplication of (2x12)(12x2) would give us a (2x2) matrix, let s see if we can explain why it works? Multiply a (2x3)(3x2) matrix. Explain how it works, by referring back to the scalar multiplication. What about a (2x2)(2x2), (3x3)(3x3)? What about a (2x3)(2x3)? Will it work? Why not? Refer back to scalar multiplication in your explanation. Given what you know, generalize the definition of Matrix Multiplication to the general form of matrix multiplication; δ ij. Paper, pencils/pens 5
6 Evaluations Estimated time: 5 minutes Description of activity: knowledge check to see if learners mastered the material. Learner must have 100% accuracy on 1 problem. Throughout lesson, teacher will observe and correct misconceptions. Make mistakes and fixes them. student and consider possible student responses Are you confident you did that correctly? Did you check your answer with a classmate? Teacher will give 1 problem at end of class that is a 2x3 matrix multiplication problem. Multiplies the matrices together. Teacher asks for numbers from the class to represent shear and fracture values for materials in a 2x3 and 3x2 matrix. Learners multiply them and check for correct answer. Paper, pencils/pens 6
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