Course Guide - USAID Teacher Education Project

d) Have students experiment with the number line model for subtraction, “hoppingbackwards” from the starting number (the minuend) to find the answer to 8 - 3 = ?e) Have students refer to the organized chart they created for the problem: “In my block offlats there are 12 cats and dogs. How many might there be of each?” Ask how their chart,which was used to model addition, can be used to describe subtraction.f) Pose the following questions: “If there are 7 cats, then the remainder are dogs. How manyare dogs? If there are 5 cats, then the remainder are dogs. How many are dogs?” Mention tostudents the use of the word “remainder," which implies separating a total quantity into twosets.g) Use this work with the set model to introduce a fifth subtraction model (which did nothave a corresponding model in the Addition session): comparison.Use the 2-column organized chart saved from the prior session, adding a column to the rightlabeled “Difference," in order to begin working with the subtraction model of comparison. Asstudents consider the chart, ask, “Which has more? How many more?” as you add entriesinto the "Difference" column. After the chart is complete ask students:• Do you see any patterns as you look at the differences? (do you mean Difference?)• Is there a symmetrical pattern? If so, why?• Is there an odd or even pattern? If so, why?• What does the chart show about the commutative property of addition?• What does the chart show about the inverse operations of addition and subtraction?h) To end the session, have students consider the numbers 13, 7, and 6, and have them createtwo real life subtraction scenarios:• One where the subtraction model is "take away" and results in a remainder• The other where the scenario involves a comparison, and results in a difference5) AssignmentTo prepare for the next class session have students read:a) “Children’s Understanding of Equality: A Foundation for Algebra." Falkner, K., Levi, L.,& Carpenter, T. Teaching Children Mathematics, Vol. 6, No. 4, Dec. 1999.http://tinyurl.com/Children-EqualityNumber and OperationsUnit 1 Number and OperationsWeek 1, Session 3: Equivalence, Thinking Like Children1. What are the important concepts?a) The notion of Equivalence is one of the major, overarching concepts in all ofmathematics. However, both adults and children often misinterpret the equals sign in anequation as meaning “the answer is….” rather than understanding it to be an indicator of theimportant mathematical notion: that there is a balance, an equivalence, on each side of theequation.b) Cognitively Guided Instruction (CGI) word problems help teachers codify children'sunderstanding of addition, subtraction, and the relationship between these two operations.