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FTCE - PreK to 3rd Grade - MATH
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Key Concepts:
Terms in this set (19)
Concrete (concrete to semi-concrete to abstract)
The teacher begins instruction by modeling each mathematical concept with concrete materials (e.g., red and yellow chips, cubes, base-ten blocks, pattern blocks, fraction bars, and geometric figures). Students manipulate the hands on concrete objects to model the math concept/skill.
Representational (Semi-Concrete)
The teacher transforms the concrete model into a representational (semi-concrete) level, which may involve drawing pictures; using circles, dots, and tallies; or using stamps to imprint pictures for counting. Students draw pictures that represent the concrete objects previously used.
Abstract
The teacher models the mathematics concept at a symbolic level, using only numbers, notation, and mathematical symbols to represent the number of circles or groups of circles. The teacher and students use operation symbols (+, -, x, ÷) to indicate addition, subtraction, multiplication, or division.
CRA Model
concrete-to-representational-to-abstract; It is a three-part instructional strategy, with each part building on the previous instruction to promote student learning and retention and to address conceptual knowledge
If students have trouble moving to the abstract
re-teach the mathematics concept/skill using appropriate concrete materials and then explicitly show the relationship between the concrete materials and the abstract representation of the materials
Base 10 Blocks
come with units (one cube), longs (made up of 10 units), flats (made up of 10 longs or 100 units), and cubes (made up of 10 flats or 1000 units).
Can be used for many math procedures:
o Introducing the concept of place value
o Reading and writing numbers
o Zero as a place holder
o Addition
o Subtraction
o Multiplication
o Division
o Fractions
o Decimals/operations with decimals
o Expanded numeration
o Counting/skip counting
o Geometry (area and perimeter)
o Probability, ratios, proportions
Cuisenaire Rods
are colored wooden or plastic rods that have values from one to ten and are colored by the number they represent.
Can be used for:
o Probability and statistics
o Ratios, proportions
o Fractions
o Addition
o Subtraction
Pattern Blocks
are one centimeter thick multicolored blocks that come in six shapes: hexagons, squares, trapezoids, triangles, parallelograms, and rhombi. Each shape is a different color.
Can be used for:
o Fractions
o Patterns
o Geometry
o Symmetry
o Addition
o Multiplication
o Equations
o Ratios
Unifix Cubes
are colorful, interlocking cubes that link in only one way. They come in ten solid colors that make them quite visual for demonstrations and easily allow for patterning and sorting.
Can be used for:
o Counting/skip counting
o Addition
o Subtraction
o Multiplication
o Division
o Patterns
o Number sense
o Equality
o Fact families
o Perfect squares
o Graphing
o Place value
o Fractions
o Measurement
o Probability
Hundred Chart
is a series of 100 squares in a 10 x10 arrangement that forms a larger square. The small squares are labeled from 1 to 100.
Can be used for:
o Visual counting/skip counting
o Visual addition and subtraction
o Fractions
o Decimals
o Percents
Snap Cubes
are similar to Unifix Cubes but they link on all sides (six ways). They come in a variety of colors
Can be used for:
o Counting/skip counting
o Addition
o Subtraction
o Multiplication
o Division
o Patterns
o Number sense
o Equality
o Fact families
o Perfect squares
o Graphing
o Place value
o Fractions
o Measurement
o Probability
o Geometry
o 3D shapes
Fraction Bars
are colored cubes or tiles that are proportional and represent whole, halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths.
Can be used for
o Fractions
- Fraction number sense
- Equivalent fractions
- Operations with fractions
- Mixed numbers
o Proportion
o Ratios
Color 1" Tiles
These are 1" x1" square color tiles. They usually can be purchased with a mix of four colors.
Can be used for:
o Counting and skip counting
o Patterns
o Multiplication
o Division
o Addition
o subtraction
o Geometry (perimeter and area)
o Place value
o Measurement
o Graphing and probability
Two-Sided Counters
are usually circular chips with different colors on each side.
Can be used for:
o Integers
o Addition
o Subtraction
o Multiplication
o Division
o Probability
o Ratios
o Percentages
10 Frames
are a rectangle made up of ten squares (5 by 2). They can have dots on them representing values 1-10 or can be blank.
Can be used for:
o Addition
o Subtraction
o Grouping
o Counting
o Place value
100 Beads
are made by stringing 100 beads on a string. They are made up of 2 colors that alternate every ten.
Can be used for
o Counting and Skip Counting
o Basic math operations
Beans and Cup
comprise of a cup and beans. The teacher will decide how many beans to put in a cup for designated problems.
Can be used for:
o Counting
o Addition
o Subtraction
o Multiplication
o Division
Tangram
is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes.
...
http://www.fl.nesinc.com/studyguide/FL_SG_obj_053.htm
http://www.fl.nesinc.com/PDFs/PK-3_TIG_5thEd_DOE030217.pdf
http://www.ldonline.org/spearswerling/Components_of_Effective_Mathematics_Instruction
http://www.fldoe.org/academics/standards/subject-areas/math-science/mathematics/
https://www.naesp.org/sites/default/files/resources/2/Principal/2007/S-Op51.pdf
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