One-to-One Correspondence

One-to-One Correspondence One-to-one correspondence is the most _______________ component of the concept of ________________ understanding that one ____________ has the ___________ number of things as another ____________

Examples of One-to-One Correspondence Activities Naturalistic Activities Informal Activities Structured Activities

Five Characteristics to Vary One-to-One Correspondence Activities Number of items to be matched Physically joined or not physically joined Groups of the same or not the same number

Evaluation of One-to-One Correspondence Activities Notice each child’s response during structured activities Notice during free play if the child passes out materials to other children one at a time Notice whether children can put items away by matching each item with a drawing of the item

Number Sense and Counting

Number Sense: Understanding Number Number sense is a concept makes the connection between ___________ and _____________ underlies the understanding of other math concepts helps children estimate ___________ and _________________

Number Sense (cont.) Subitizing Perceptual Subitizing – Can state how many are in a group without _______________, usually up to four Conceptual Subitizing – Seeing _____________ ___________ within a group

Counting Counting is a skill assists children in the process of understanding ___________ includes two operations rote counting rational counting

Counting Principles One-One Principle Stable-Order Principle Only _________number word is assigned to each object being counted Stable-Order Principle The number words used to correspond to items in an array must be used in a _______________ order Cardinal Principle (Cardinality) The ____________ number used in the counting of a set represents the _______________of that set Order-Irrelevance Principle The _____________ in which items are counted doesn’t matter Abstraction Principle The preceding principles can be applied to any array or collection of entities

Examples of Number Sense and Counting Activities Naturalistic Activities Informal Activities Structured Activities

Evaluation Number Sense Can the children subitize perceptually, that is, recognize small groups for four or five without counting? Knowing the amount in one group, can they use the information to figure out how many are in another group? Can they make reasonable estimates of the amount in a group and revise their estimate after counting some items?

Evaluation (cont.) Counting To what amount can children work with What kinds of errors do children make? Are they consistent or random? Are they accurate? Do they check their results? Do they remember the number they counted to and realize that is the amount in the group (cardinal number)

Basic Concepts of Algebra Logic

Classifying Classifying Adding Subtracting Being able to _______ and __________ based on an ____________ Adding Subtracting

Features of Groups Color Shape Size Material Patterns Texture Big/small; fat/thin; short/tall Material Things made out of different materials Patterns Things with different visual patterns Texture How things feels (smooth/rough; soft/hard; wet/dry)

Features of Groups (cont.) Function Items do the same thing, are used for the same thing etc. Association Things that do a job together (candle/match; milk/glass; shoe/foot) or come from the same place (bought at a store; seen at a zoo) or belong to a special person (fire hose, fire truck, fire man’s hat) Class Name Names that belong to several different things (people, animals, food, vehicles, clothing, homes) Common Features All have handles or windows or wheels etc. Number All are groups of a specific number

Examples of Classification Activities Naturalistic Activitiess Informal Activities Structured Activitiest

Assessment Does each child sort and group during play? Does each child use feature names during play?

Comparing

Discoveries Made through Comparison The _____________ between two things or groups of things on the _________ of a specific _____________ informal measurement length weight speed quantity measurement are two groups the _________ or does one group have _____________ things? Comparison is the basis for __________ and ___________________

Comparison Terms Number more—less/fewer Informal measurement large—small big—little long—short tall—short fat—skinny heavy—light fast—slow cold—hot thick—thin wide—narrow near—far late—sooner (earlier) older—younger (newer) higher—lower loud—soft (sound) Number more—less/fewer

Examples of Comparison Activities Naturalistic Activities Informal Activities Structured Activitiest

Assessment Does the child compare during play? Does the child understand and use basic comparison words? Ask questions without disrupting play Are there more cows or chickens in your barn? Who is older, your brother or you? Who is taller, your father or your brother?

Ordering and Patterning

Ordering Involves comparing more than two things or more than two sets Placing things in a _____________ from first to _____________

Patterning Related to ordering children need a basic understanding of ___________ to do _____________ Involves making or discovering auditory, visual, and motor regularities

Ordering and Patterning Words Next Biggest Smallest Fattest Shortest Before After

Examples of Ordering and Patterning Activities Naturalistic Activities Informal Activities Structured Activities

Assessment and Evaluation Does the child use ordering and patterning words during daily activities? Do patterns appear in the child’s art work? Ask questions, make comments or suggestions such as Which doll is taller? Which block is shorter? John is first in line. Line up from the shortest to the tallest. Conduct individual evaluation interviews