Carefully writing up representations of modeling with manipulatives will be a very important part of your course and is meant to be a lasting reference for you. These write-ups will allow you to demonstrate your knowledge of modeling mathematics with manipulatives through series of careful, well explained pictures.PORTFOLIO PRESENTATION OUTLINE (more detailed explanations below)Whole Number AdditionModel the problem:CAREFUL WRITE UP OFPAGE LABELING EXAMPLEWhole Number AdditionWhole Number AdditionWhole Number AdditionPortfolio ExampleMultiplication of Whole NumbersProblem: Model 3 x 5 with Cuisenaire RodsNotice the general elements of this portfolio problem, these should be included in all portfolio presentations.Notice the specific elements of this portfolio problem:Math 391PORTFOLIO GENERAL DIRECTIONSYour Math 391 course syllabus states:- For each activity you will be required to write up, in careful, thorough, well-explained detail, several examples of the types of manipulative modelingproblems that we are exploring in class. Each activity will have two or threeportfolio assignments (1.1, 1.2, 1.3, etc.). These problems will be similar to theproblems assigned in class for poster making and poster presentations.- Carefully writing up representations of modeling with manipulatives will be a veryimportant part of your course and is meant to be a lasting reference for you.These write-ups will allow you to demonstrate your knowledge of modelingmathematics with manipulatives through series of careful, well explainedpictures.- You should work on your portfolio problems after you have completed the corresponding activity (see the Portfolio Help & Turn In Guide).PORTFOLIO PRESENTATION OUTLINE (more detailed explanations below)EACH OF THE FOLLOWING ITEMS IS ONLY AN EXAMPLEPortfolio 2.1Whole Number AdditionProblem: Model 123 + 354 with Multibase blocksGeneral Manipulative Description: For this problem we will use Multibase Blockswhich are ....Model the problem: CAREFUL WRITE UP OFMODELING OF THE PROBLEM & THE PROBLEM SOLUTIONOften; describe specific manipulative use orvalues towards the beginning of this sectionSolution: Give the final solution last, sometimes embedded at the end of modelingLabel page, more than 1-page directionsfollowWrite out theexact problemGenerallydescribemanipulativeShow detailedModelingSee directionsGive SolutionPORTFOLIO WRITE UP PROCEDUREFirst: LABEL THE PAGE(S) WITH ONLY THE FOLLOWING (your name will be on your cover sheet)For each problem, in the Upper Right Hand Corner of the First Page- Write the portfolio reference number (1.1, 1.1, 2.1, etc.)- Write the type of the problem (Whole Number Addition, etc.)(Per problem) If your work extends beyond one page label the pages with numbersas shown in this example:PAGE LABELING EXAMPLEOne page (side) totalPortfolio 2.1Whole Number AdditionMore than one page (side) total (front and/or front and back)Portfolio 2.1, page 1Whole Number AdditionPortfolio 2.1, page 2Whole Number AdditionAfter labeling the page(s), follow the following steps for each portfolioassignment.1. WRITE OUT THE PROBLEM - Write the problem out EXACTLY as it is stated on your assignment.- Your work is not useful as a reference if you don’t know what problem you aresolving when you look back at the work.2. GENERALLY DESCRIBE THE MANIPULATIVE- Briefly but generally describe the manipulative used so that any adult can seewhat you are using.- Pictures with a few words are acceptable- DO NOT describe the manipulative as it relates to your specific problem. Thatcomes in the modeling. DO NOT mention the manipulative values here.REUSABLE MANIPULATIVE DESCRIPTION PAGES- You will need to describe most of the manipulatives we use more than one timeover the course of the term. IF YOU WRITE OUT THE PORTFOLIOS BY HAND- You are encouraged to create a MANIPULATIVE DESCRIPTION PAGE for eachmanipulative and to REUSE this page for each portfolio that uses that particularmanipulative. If you do this, as usual, the description must be completelygeneric, it must NOT mention any specific problem aspects and it must containONLY a general manipulative description. Portfolio Direction, Page 2Top RIGHT of pageREUSABLE MANIPULATIVE DESCRIPTION PAGES continued- LABEL each reusable manipulative page ONLY with the manipulative type. Forexample:- If you create reusable manipulative pages you may turn your portfolio in like this:- Cover Sheet- Reusable manipulative page- Problem Write up, with:Exact Problem (as usual)General Manipulative Description: For this problem we will use ... which is described on the previous page.IF YOU WORD PROCESS THE PORTFOLIOS - You may wish to create reusable manipulative description pages OR just cutprevious general descriptions and paste them into your current document.- Most of the class course pack documents (such as this one) are linked to theMath 391 webpage. You are welcome to cut & paste pictures from coursedocuments.4. MODEL THE PROBLEM- Carefully write up the modeling of the problem.This is your opportunity to communicate that you have - Depth and clarity of knowledge regarding the mathematics that are beingmodeled.- Depth and clarity of knowledge regarding the manipulative procedures at hand.Portfolio Direction, Page 3Cuisenaire Rods Description PageCuisenaire Rods are 10 color-coded rods that increaseuniformly in size from the smallest white rod to thelongest orange rod. They are:Orange Rod = 10 whiterodsBlue Rod = 9 white rodsBrown Rod = 8 whiterodsBlack = 7 whiterodsDark Green = Yellow = Purple =RedW6 white rods5 white rods4 white rods= 2 white rods3 white rodsThe white rodFill in correct manipulative typeLight Green =4. MODEL THE PROBLEM continuedFor each portfolio,  YOUR MODELING SHOULD BE A SERIES OF CAREFUL EXPLANATIONS AND WELL-DRAWN, CLEARLY LABELED PICTURES. - This should read as if you are sitting at a class table showing and explaining tosomeone how to work through a problem with a manipulative. - In particular, everything that you would say out loud in a class setting must belabeled in your problem presentation. In a conversation, after saying the values,you and your partner “remember” the values of the manipulatives. In contrast,for a