Introduction

(a benchmark) and judging that a large containerholds about 8 cups allows a person to estimatethe number of marbles in the large container. Inmeasurement, knowing that the width of the littlefinger is about one centimetre (the benchmark)helps to estimate the length of a book cover.big ideas. In mathematics, the important conceptsor major underlying principles. For example,the big ideas for Kindergarten to Grade 3 in theNumber Sense and Numeration strand of theOntario curriculum are counting, operationalsense, quantity, relationships, and representation.calculation. The process of figuring out ananswer using one or more computations.cardinality. The idea that the last count of a setof objects represents the total number of objectsin the set.cardinal number. A number that describeshow many are in a set of objects.classifying. Making decisions about how to sort orcategorize things. Classifying objects and numbersin different ways helps students recognize attributesand characteristics of objects and numbers, anddevelops flexible thinking.cluster (of curriculum expectations). A groupof curriculum expectations that relate to animportant concept. By clustering expectations,teachers are able to design learning activities thathighlight key concepts and address curriculumexpectations in an integrated way, rather than havingto plan separate instructional activities for eachindividual expectation. For example, curriculumexpectations can be clustered around big ideas.clustering. See under estimation strategies.cognitive dissonance. In learning, a psychologicaldiscomfort felt by the learner when new conceptsseem inconsistent with the learner’s currentunderstanding. Because of cognitive dissonance,the learner strives to make sense of new conceptsby linking them with what is already understoodand, if necessary, altering existing understandings.combinations problem. A problem that involvesdetermining the number of possible pairings orcombinations between two sets. The following arethe 6 possible outfit combinations, given 3 shirts –red, yellow, and green – and 2 pairs of pants –blue and black:red shirt and blue pantsred shirt and black pantsyellow shirt and blue pantsyellow shirt and black pantsgreen shirt and blue pantsgreen shirt and black pantscombining. The act or process of joining quantities.Addition involves combining equal or unequalquantities. Multiplication involves joining groupsof equal quantities. See also partitioning.commutative property. A property of additionand multiplication that allows the numbers to beadded or multiplied in any order, without affectingthe sum or product of the operation. Forexample, 2+3=3+2 and 2 x 3=3 x 2. Using thecommutative property can simplify computation.This property does not generally hold for subtractionor division.commutativity. See commulative property.comparison model. A representation, used insubtraction, in which two sets of items or quantitiesare set side by side and the difference betweenthem is determined.compatible numbers. See under estimationstrategies.compensation. A mental arithmetic techniquein which part of the value of one number is givento another number to facilitate computation(e.g., 6+9 can be expressed as 5+10; that is,1 from the 6 is transferred to the 9 to make 10).Glossary 89