Course Guide - USAID Teacher Education Project

Unit 1 Number and OperationsWeek 2, Session 1: Place Value in Base 101. What are the important concepts?a) Although all equations are "equal," not all equations are equally useful as teaching tools.Selecting the equation 5 + 7 = 12 for exploration last week was a conscious instructionaldecision, because the equation connects to the concept of place value this week. Thisconnection indicates how teachers need to consider the implications of the numbers they usewhen using exemplars to introduce maths topics.b) Many maths problems have "one right answer," such as 5 + 7 = 12. There are, however,different strategies that children might use to arrive at that "one right answer." Some of theirstrategies may seem more or less efficient to us adults. But efficiency is an end goal, oncemathematical understanding is in place.c) Valuing and discussing alternative solution strategies is an important way to help studentsmake mathematical connections and see mathematical equivalency among different solutionstrategies. (This will become even more evident when considering proofs in algebra andgeometry, which is why it is important for children to discuss alternative solution methodseven in the Number and Operations unit.)d) When young children need to go beyond the number 9 in counting and addition, theymove toward multi-digit number sense, encountering the concept of tens and units.e) There is a major difference between digits and numbers. For example, the "1" in thenumber 13 is simply a digit representing the number "10."f) Young children can begin working with place value by using handfuls of small objectssuch as pebbles, beans, etc., arranging them into groups of 10 with perhaps some left over. Atsome point, however, the number of physical items becomes unwieldy, suggesting othermodels would be better, more efficient ways to further concept development.g) To help children develop multi-digit number sense, two simple “ten frames” can be usedto model why we need to use two digits to describe the number “12” in our base-10 numbersystem, since each frame can only accommodate 10 items. Ten Frame Mats:http://tinyurl.com/TensFrames