Course Guide - USAID Teacher Education Project

4. Class Activitiesa) Begin by asking students in pairs (or groups of no more than four) to brainstorm for fiveminutes about all the mathematics that may be implicit in the equation 5 + 7 = 12. Askstudents to share their thoughts while you record the ideas on chart paper for future reference.After this activity, note with a check mark ideas that will be discussed during the rest of theweek. Congratulate students for their willingness to go beyond their first impression anddelve more deeply into the mathematics! (Add to the list any topics for the week that studentsdid not mention.)b) Introduce the four models for addition: joining sets, counting on, "hopping" forward on anumber line, creating equivalence.c) Give students the following scenario and ask them to "count on" by using their fingers (asyoung children would) to solve this problem. "I get up early and eat breakfast at 5 in themorning; 7 hours later I eat lunch. When do I eat lunch?" Ask how "counting on" issomewhat different from "counting from 0."d) Distribute the number line handout and have students use the number line to add 5 + 7.Notice which students started from 0, hopped to 5, and then hopped 7 more places? Whichstudents began at 5 and "counted on." Relate these two different ways of modeling theproblem to the "starting from 0" and the "counting on" methods. (Also note that youngchildren are often unsure about whether they should begin counting from 0 or from 1.) Havestudents think of a ruler as a model for a number line, one that includes not only wholenumbers, but also fractions or decimals. How might they use rulers to help children thinkabout adding (and later subtracting)?d) Introduce the concept of decomposing a number.e) Have students solve the problem: “In my apartment building there are 12 cats and dogs.How many might there be of each?” Ask for random answers and record these on chartpaper. When all combinations have been given, have students create an organized list of theresults in their notebooks. Discuss why helping young children organize mathematicalinformation is an important step in noting patterns, not just for computation, but later on forpatterns in algebra function tables (a + b = 12). Mention that they will use this chart in thenext session to discuss subtraction.5. Assignment (to be determined)