By Yan Ping Xin

Are you having hassle to find Tier II intervention fabrics for straight forward scholars who're suffering in math? Are you hungry for powerful tutorial innovations that may handle students' conceptual hole in additive and multiplicative math challenge fixing? Are you trying to find a strong and generalizable challenge fixing procedure that may aid people who find themselves left in the back of in assembly the typical middle nation criteria for arithmetic (CCSSM)? if that is so, this ebook is the reply for you. • The conceptual model-based challenge fixing (COMPS) software emphasizes mathematical modeling and algebraic illustration of mathematical family members in equations, that are in accordance with the recent universal middle. • "Through development such a lot primary suggestions pertinent to additive and multiplicative reasoning and making the relationship among concrete and summary modeling, scholars have been ready to head above and past concrete point of operation and manage to use mathematical types to resolve extra complicated real-world difficulties. because the connection is made among the concrete version (or students' current wisdom scheme) and the symbolic mathematical set of rules, the summary mathematical types are not any longer "alien" to the students." As Ms. Karen Combs, Director of user-friendly schooling of Lafayette college company in Indiana, testified: "It fairly labored with our kids!" • "One hallmark of mathematical realizing is the power to justify,... why a selected mathematical assertion is right or the place a mathematical rule comes from" (http://illustrativemathematics.org/standards). via making connections among mathematical rules, the COMPS application makes particular the reasoning in the back of math, which has the capability to advertise a robust move of information by means of using the realized perception to unravel different difficulties in new contexts. • Dr. Yan Ping Xin's booklet comprises crucial instruments for lecturers to aid scholars with studying disabilities or problems shut the distance in arithmetic note challenge fixing. i've got witnessed many suffering scholars use those innovations to unravel note difficulties and achieve self assurance as freshmen of arithmetic. This publication is a useful source for basic and unique schooling academics of arithmetic. - Casey Hord, PhD, college of Cincinnati

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**Extra info for Conceptual Model-Based Problem Solving: Teach Students with Learning Difficulties to Solve Math Problems**

**Example text**

The big box is for the total number of tickets Lauren has (the bigger quantity). I will write 110 in the big box that is labeled “whole” for the bigger quantity. You will do the same in your worksheet. See Slide 4-3-2-c for the completed bar model and the PPW diagram equation model. Slide 3-4-2-c 60 50 110 Whole Part 60 Smaller Part + 50 = 110 Difference Bigger Teacher: As shown in the above PPW diagram equation, for representing the comparison story onto the PPW diagram equation, the smaller quantity (Alex in this case) of the two being compared (Lauren and Alex) AND the difference amount between the bigger and smaller quantities (or between Lauren and Alex’s Carnival tickets in this story) will make up the “whole,” which is the bigger quantity (Lauren in this case), as shown in the bar model.

How many pieces of candy did Larry originally have? (45 + 57 = a) 9. Gilbert had several paperback books. Then his brother, Sean, gave him 57 more paperback books. Now Gilbert has 113 paperback books. How many paperback books did Gilbert have in the beginning? (a + 57 = 113) 47 UNIT 3 REPRESENTING ADDITIVE COMPARE (AC) PROBLEMS LESSON 4: REPRESENTING AC-MORE PROBLEMS Learning Outcome: Be able to represent AC word problem stories with the bar model and the PPW diagram equation Materials Needed: Diagram Overhead Modeling Student Worksheets Part-Part-Whole (PPW) Diagram Equation for AC Modeling AC-more problem representation 1, 2, & 3 Modeling AC-more problem representation 1, 2, & 3 Try It Out: AC–more problem representation 4, 5, & 6 Independent Worksheet: AC-more problem representation 7, 8, & 9 Reference Guide Reference Guide: AC-more problem representation 1–9 __________________________________________________________________ Teacher: In the last Unit, we learned how to use a bar model and diagram equation to represent and solve PPW problems.

DIRECTIONS FOR INDEPENDENT WORKSHEET Teacher: In the below worksheets, you will use the PPW diagram equation to represent and solve the problem. After reading and understand the problem, find out the total amount, or the whole, and the two parts. Map the information accordingly to the PPW diagram. After completing the representation, you will rewrite the math sentence by “peeling off” all the boxes in the diagram equation. You will solve for the unknown quantity (or a) in the equation. To check for the accuracy of your calculation, you can replace a in the diagram with your answer, and check whether the sum on the left side of the equation equals the sum on the right side of the equation.