FTCE Pre K-3 Math (2)

Concrete to representational to abstract sequence of instruction

1. intro to concept modeled with concrete materials
2. translations of concrete models into diagrams or pics
3. translations of models into abstract models using onlyenumbers or symbols

inquiry based learning

a student centered active approach with student assessing manipulatives to grasp concepts

5 steps of problem solving

identify, determine the question, find a strategy, gather materials, solve, explain

guess and check strategy

students make an initial guess at the solution, check the answer, and use that outcome to guide the next guess.

estimation

forming a calculation based on incomplete data

reasonableness

An answer that is based on good number sense.

number sense

the ability to understand numbers and problems

Children learn to read the numbers 0-10 in

kindergarten

Children learn to read the numbers 0-20 in

1st grade

manipulatives

tactile object used to help students grasp mathematical concepts

rulers

help you measure the size of an object on the slide, as well as the amount of space between objects

scales

tool for showing balance

measuring containers

Teach students about fractions & relationships between standard units (pint,quart,gallon) and metric units (millimeter,liter)

money

helps students understand the value associated with denomination

conjectures

an opinion or conclusion formed on the basis of incomplete information, assumption, speculation, hypothesis, supposition, guesswork.

models

Something used to represent an object or an event in order to make it easier to study.

alternative assesment

alternate ways of assessing students other than traditional testing

cooperative learning

Approach to instruction in which students work with a small group of peers to achieve a common goal and help one another learn. Everyone has a job

collaborative learning

The instructional strategy in which a teacher places students of varying abilities & interests to work together in small groups to solve a problem, complete a project, or achieve a common goal is known as:

peer tutoring

Approach to instruction in which one student provides instruction to help another student master a classroom topic.

problem based learning

stimulates real-world problem finding and problem solving by engaging students as stakeholders in situations with undefined problems and incomplete information

instructional games

Drill and practice exercises presented in a game format.

contextual learning

authentic real-life situations (garden)

experiential learning

involves the use of manipulatives that enhance student's understanding of a concept (physical or virtual)

Piaget's Theory

theory statingthat children actively construct their understanding of the world and go through four stages of cognitive development

Bloom's Taxonomy

knowledge, comprehension, analysis, application, synthesis, evaluation

scaffolding

Adjusting the support offered during a teaching session to fit the child's current level of performance

math centers

students move from center to center completing tasks while the teacher focuses on small groups

Individual instruction

allows the teacher to interact closely with the student

algebraic expression for young children

learning about patterns, the attributes of objects, and how to describe objects in detail

Pre-K children should be able to

recognize and extend simple repeating patterns using objects and pictures

Fibonacci sequence

Order as Follows: 0, 1, 1, 2, 3, 5, 8, 13, every term in the series ins a sum of the previous 2 terms

linear programming

a method for finding a minimum or maximum value of some quantity, given a set of constraints

distributive property

a(b + c) = ab + ac

associative property

(a+b)+c=a+(b+c)

commutative property

a+b=b+a or ab=ba

identity property

(a+0=a) or (ax1=a)

closure property

Addition and multiplication. If a and b are real numbers then the sum or product of the numbers will be a real number.

additive property

The sum of any number and zero is that number

seriation

The ability to arrange objects in order based on some common quality, such as height, color, or size. According to Piaget, concrete operational children have mastered this skill.

place value system

One in which the position of a digit in a number determines its value

base ten

As you move to the left each place value is 10 time higher

place value chart

A chart that shows the value of the digits in a number

base 10 regrouping

borrowing

inverse operation

An operation that undoes another operation. For example, multiplication is the inverse operation for division.

length

inch or milimeter

distance

mile or kilometer

area

square inch or square milmeter

volume

cubic inch or square milimeter

mass

grams

weight

ounce or grams

temp

fahrenheit or celcius

pictograph

A visual representation used to make comparisons. A key always appears at the bottom of a pictograph or picture graph showing how many each object represents

acute angle

less than 90 degrees

right angle

90 degrees

obtuse angle

greater than 90 but less than 180 degrees

acute triangle

3 acute angles

right triangle

1 right angle

obtuse triangle

1 obtuse angle

equilaterl triangle

all 3 sides the same length

isosceles triangle

2 sides the same length

scalene triangle

no sides the same length

quadrilateral

A four-sided polygon.

rectangle

2 opposite sides parallel and perpendicular

square

2 opposite sides parallel, perpendicular and equal

symmetry

having the same shape, size, and position on both sides of a dividing line

radial symmetry

Symmetry about a central axis.

point

dimensionless locaation and has no length, width or height

line

A straight path that goes without end in two directions.

line segment

A part of a line with two endpoints

ray

A part of a line, with one endpoint, that continues without end in one direction

angle

A figure formed by two rays with a common endpoint

plane

flat surface defined by 3 points