Introduction

number sense. The ability to interpret numbersand use them correctly and confidently.numeral. A word or symbol that represents anumber.numeration. A system of symbols or numeralsrepresenting numbers. Our number system uses10 symbols, the digits from 0 to 9. The placementof these digits within a number determines thevalue of that numeral. See also place value.numerator. In common fractions, the numberwritten above the line. It represents the numberof equal parts being considered.observations. Records of what students do, say,and show, gathered by teachers as evidence of howwell students are learning mathematical conceptsand skills.ones unit. In base ten blocks, the small cubethat represents 1.one-to-one correspondence. The correspondenceof one object to one symbol or picture. Incounting, one-to-one correspondence is the ideathat each object being counted must be given onecount and only one count.open-ended problems. Problems that require theuse of reasoning, that often have more than onesolution, or that can be solved in a variety of ways.open number line. A line that is drawn to representrelationships between numbers or numberoperations. Only the points and numbers that aresignificant to the situation are indicated. Theplacement of points between numbers is not toscale.46 56 66 76 78An open number line showing 46 +32.operational sense. Understanding of themathematical concepts and procedures involvedin operations on numbers (addition, subtraction,multiplication, and division) and of the applicationof operations to solve problems.oral communication. Expression of mathematicalideas through the spoken word. Oral communicationinvolves expressing ideas through talkand receiving information through listening.Some students have difficulty articulating theirunderstanding of mathematical ideas. Thesestudents can be helped to improve by ongoingexperiences in oral communication and by exposureto teacher modelling. See also think-aloud.order irrelevance. The idea that the countingof objects can begin with any object in a set andthe total will still be the same.ordinal number. A number that shows relativeposition or place – for example, first, second,third, fourth.partitioning. One of the two meanings of division;sharing. For example, when 14 apples are partitioned(shared equally) among 4 children, eachchild receives 3 apples and there are 2 applesremaining (left over). A more sophisticated partitioning(or sharing) process is to partition theremaining parts so that each child, for example,receives 3 1 /2 apples.The other meaning of division is often referredto as “measurement”. In a problem involvingmeasurement division, the number in each groupis known, but the number of groups is unknown.For example: Some children share 15 applesequally so that each child receives 3 apples. Howmany children are there?part-part-whole. The idea that a numbercan be composed of two parts. For example,a set of 7 counters can be separated intoparts – 1 counter and 6 counters, 2 counters and5 counters, 3 counters and 4 counters, and so forth.patterning. The sequencing of numbers, objects,shapes, events, actions, sounds, ideas, and soforth, in regular ways. Recognizing patterns andGlossary 97