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4.1
Number and Computation
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4.1.1
The student demonstrates number sense for whole numbers, fractions (including mixed numbers), decimals, and money including the use of concrete objects in a variety of situations.
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4.1.1.1
knows, explains, and uses equivalent representations for:
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4.1.1.1.a
whole numbers from 0 through 100,000;
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4.1.1.1.b
fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers;
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4.1.1.1.c
decimals greater than or equal to zero through hundredths place and when used as monetary amounts, e.g., 7¢ = $.07 = 7/100 of a dollar or a hundreds grid with 7 sections colored.
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4.1.1.2
compares and orders:
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4.1.1.2.a
whole numbers from 0 through 100,000;
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4.1.1.2.b
fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers with a special emphasis on concrete objects;
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4.1.1.2.c
decimals greater than or equal to zero through hundredths place and when used as monetary amounts.
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4.1.2
The student demonstrates an understanding of whole numbers with a special emphasis on place value; recognizes, uses, and explains the concepts of properties as they relate to whole numbers; and extends these properties to fractions (including mixed numbers), decimals, and money.
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4.1.2.1
identifies, models, reads, and writes numbers using numerals, words, and expanded notation from hundredths place through one-hundred thousands place, e.g., four hundred sixty-two thousand, two hundred eighty-four and fifty hundredths = 462,284.50 or 462,284.50 = (4 x 100,000) + (6 x 10,000) + (2 x 1,000) + (2 x 100) + (8 x 10) + (4 x 1) + (5 x .1) + (0 x .01) = 400,000 + 60,000 + 2,000 + 200 + 80 + 4 +.5 +.00.
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4.1.2.2
classifies various subsets of numbers as whole numbers, fractions (including mixed numbers), or decimals.
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4.1.2.3
identifies the place value of various digits from hundredths place through one hundred thousands place.
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4.1.2.4
identifies any whole number as even or odd.
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4.1.2.5
uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects:
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4.1.2.5.a
commutative properties of addition and multiplication, e.g., 12 + 18 = 18 + 12 and 8 x 9 = 9 x 8;
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4.1.2.5.b
zero property of addition (additive identity) and property of one for multiplication (multiplicative identity), e.g., 24 + 0 = 24 and 75 x 1 = 75;
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4.1.2.5.c
associative properties of addition and multiplication, e.g., 4 + (2 + 3) = (4 + 2) + 3 and 2 x (3 x 4) = (2 x 3) x 4;
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4.1.2.5.d
symmetric property of equality applied to addition and multiplication, e.g., 100 = 20 + 80 is the same as 20 + 80 = 100 and 21 = 7 x 3 is the same as 3 x 7 = 21;
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4.1.2.5.e
zero property of multiplication, e.g., 9 x 0 = 0 or 0 x 112 = 0;
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4.1.2.5.f
distributive property, e.g., 6(7 + 3) = (6 x 7) + (6 x 3).
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4.1.3
The student uses computational estimation with whole numbers, fractions (including mixed numbers) and money in a variety of situations.
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4.1.3.1
estimates whole number quantities from 0 through 10,000; fractions (halves, fourths, thirds); and monetary amounts through $1,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.
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4.1.3.2
uses various estimation strategies and explains how they are used when estimating whole numbers quantities from 0 through 10,000; fractions [(halves, fourths, thirds) including mixed numbers)]; and monetary amounts through $1,000.
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4.1.3.3
recognizes and explains the difference between an exact and an approximate answer, e.g., when asked how many desks are in the room, the student gives an estimate of about 30 and then counts the desks and indicates an exact answer is 28 desks.
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4.1.3.4
selects from an appropriate range of estimation strategies and determines if the estimate is an overestimate or underestimate.
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4.1.4
The student models, performs, and explains computation with whole numbers, fractions, and money including the use of concrete objects in a variety of situations.
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4.1.4.1
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.
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4.1.4.2
states and uses with efficiency and accuracy multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.
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4.1.4.3
performs and explains these computational procedures:
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4.1.4.3.a
adds and subtracts whole numbers from 0 through 100,000 and when used as monetary amounts;
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4.1.4.3.b
multiplies through a three-digit whole number by a two-digit whole number;
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4.1.4.3.c
multiplies whole dollar monetary amounts (through three-digits) by a one- or two-digit whole number, e.g., $45 x 16;
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4.1.4.3.d
multiplies monetary amounts less than $100.00 by whole numbers less than ten, e.g., $14.12 x 7;
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4.1.4.3.e
divides through a two-digit whole number by a one-digit whole number with a one-digit whole number quotient with or without a remainder, e.g., 47 ÷ 5 = 9 r 2;
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4.1.4.3.f
adds and subtracts fractions greater than or equal to zero with like denominators;
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4.1.4.3.g
figures correct change through $20.00.
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4.1.4.4
identifies multiplication and division fact families.
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4.1.4.5
reads and writes horizontally, vertically, and with different operational symbols the same addition, subtraction, multiplication, or division expression, e.g., 6 * 4 is the same as 6 x 4 is the same as 4 and 6(4) or 10 divided by 2 is the same as 10 ÷ 2 or 10/2
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4.1.4.6
shows the relationship between these operations with the basic fact families (addition facts with sums from 0 through 20 and corresponding subtraction facts, multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts) including the use of mathematical models
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4.1.4.6.a
addition and subtraction,
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4.1.4.6.b
addition and multiplication,
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4.1.4.6.c
multiplication and division,
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4.1.4.6.d
subtraction and division.
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4.1.4.7
finds factors and multiples of whole numbers from 1 through 100.
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4.2
Algebra
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4.2.1
The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.
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4.2.1.1
uses concrete objects, drawings, and other representations to work with types of patterns:
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4.2.1.1.a
repeating patterns, e.g., an AB pattern is like 1-2, 1-2, ...; an ABC pattern is like dog-horse-pig, dog-horse-pig, ...; an AAB pattern is like ^^>, ^^>, ...;
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4.2.1.1.b
growing patterns e.g., 2, 5, 11, 20, ...
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4.2.1.2
uses these attributes to generate patterns:
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4.2.1.2.a
counting numbers related to number theory, e.g., multiples and factors through 12 or multiplying by 10, 100, or 1,000;
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4.2.1.2.b
whole numbers that increase or decrease, e.g., 20, 15, 10,;
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4.2.1.2.c
geometric shapes including one or two attributes changes
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4.2.1.2.d
measurements, e.g., 3 ft., 6 ft., 9 ft., ;
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4.2.1.2.e
money and time, e.g., $.25, $.50, $.75, or 1:05 p.m., 1:10 p.m., 1:15 p.m., ;
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4.2.1.2.f
things related to daily life, e.g., water cycle, food cycle, or life cycle;
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4.2.1.2.g
things related to size, shape, color, texture, or movement, e.g., rough, smooth, rough, smooth, rough, smooth, ...; or clapping hands (kinesthetic patterns);
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4.2.1.3
identifies, states, and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written.
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4.2.1.4
generates:
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4.2.1.4.a
a pattern (repeating, growing);
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4.2.1.4.b
a pattern using a function table (input/output machines, T-tables).
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4.2.2
The student uses variables, symbols, and whole numbers to solve equations including the use of concrete objects in a variety of situations.
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4.2.2.1
explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000.
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4.2.2.2
solves one-step equations using whole numbers with one variable and a whole number solution that:
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4.2.2.2.a
find the unknown in a multiplication or division equation based on the multiplication facts from 1 x 1 through 12 X 12 and corresponding division facts, e.g., 60 = 10 x n;
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4.2.2.2.b
find the unknown in a money equation using multiplication and division based upon the facts and addition and subtraction with values through $10, e.g., 8 quarters + 10 dimes = y dollars;
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4.2.2.2.c
find the unknown in a time equation involving whole minutes, hours, days, and weeks with values through 200, e.g., 180 minutes = y hours.
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4.2.2.3
compares two whole numbers from 0 through 10,000 using the equality and inequality symbols (=, is not equal to, <, >) and their corresponding meanings (is equal to, is not equal to, is less than, is greater than).
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4.2.2.4
reads and writes whole number equations and inequalities using mathematical vocabulary and notation, e.g., 15 = 3 x 5 is the same as fifteen equals three times five or 4,564 > 1,000 is the same as four thousand, five hundred sixty-four is greater than one thousand.
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4.2.3
The student recognizes and describes whole number relationships including the use of concrete objects in a variety of situations.
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4.2.3.1
states mathematical relationships between whole numbers from 0 through 1,000 using various methods including mental math, paper and pencil, concrete materials, and appropriate technology.
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4.2.3.2
find the values, determines the rule, and states the rule using symbolic notation with one operation of whole numbers from 0 through 200 using a horizontal or vertical function table (input/output machine, T-table).
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4.2.3.3
generalizes numerical patterns using whole numbers from 0 through 200 with one operation by stating the rule using words, e.g., if the pattern is 46, 68,90, 112, 134, ...; in words, the rule is add 22 to the number before.
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4.2.3.4
uses a function table (input/output machine, T-table) to identify, plot, and label the ordered pairs in the first quadrant of a coordinate plane.
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4.2.4
The student develops and uses mathematical models including the use of concrete objects to represent and explain mathematical relationships in a variety of situations.
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4.2.4.1
knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
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4.2.4.1.a
process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures, mathematical relationships, and equations;
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4.2.4.1.b
place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;
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4.2.4.1.c
fraction and mixed number models (fraction strips or pattern blocks) and decimal models (base ten blocks or coins) to compare, order, and represent numerical quantities;
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4.2.4.1.d
money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
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4.2.4.1.e
function tables (input/output machines, T-tables) to model numerical and algebraic relationships;
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4.2.4.1.f
two-dimensional geometric models (geoboards, dot paper, pattern blocks, or tangrams) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model properties of geometric shapes;
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4.2.4.1.g
two-dimensional geometric models (spinners), three-dimensional models (number cubes), and process models (concrete objects) to model probability;
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4.2.4.1.h
graphs using concrete objects, pictographs, frequency tables, horizontal and vertical bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables to organize and display data;
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Data, charts, and graphs: Read a table (Fourth grade - J.1)
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Data, charts, and graphs: Line graphs (Fourth grade - J.2)
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Data, charts, and graphs: Bar graphs (Fourth grade - J.3)
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Data, charts, and graphs: Frequency charts (Fourth grade - J.4)
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Data, charts, and graphs: Stem-and-leaf plots (Fourth grade - J.5)
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Data, charts, and graphs: Circle graphs (Fourth grade - J.6)
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Data, charts, and graphs: Choose the best type of graph (Fourth grade - J.7)
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4.2.4.1.i
Venn diagrams to sort data and to show relationships.
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4.2.4.2
creates a mathematical model to show the relationship between two or more things, e.g., using pattern blocks, a whole (1) can be represented as a(1/1) or two (2/2) or three (3/3) or six (6/6).
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4.3
Geometry
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4.3.1
The student recognizes geometric shapes and investigates their properties including the use of concrete objects in a variety of situations.
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4.3.1.1
recognizes and investigates properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons) using concrete objects, drawings, and appropriate technology.
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4.3.1.2
recognizes, draws, and describes plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons).
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4.3.1.3
describes the solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms) using the terms faces, edges, and vertices (corners).
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4.3.1.4
recognizes and describes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.
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4.3.1.5
recognizes:
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4.3.1.5.a
squares, rectangles, rhombi, parallelograms, trapezoids as special quadrilaterals;
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4.3.1.5.b
similar and congruent figures;
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4.3.1.5.c
points, lines (intersecting, parallel, perpendicular), line segments, and rays.
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4.3.1.6
determines if geometric shapes and real-world objects contain line(s) of symmetry and draws the line(s) of symmetry if the line(s) exist(s).
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4.3.2
The student estimates and measures using standard and nonstandard units of measure including the use of concrete objects in a variety of situations.
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4.3.2.1
uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.
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4.3.2.2
selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure:
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4.3.2.2.a
length, width, and height to the nearest fourth of an inch or to the nearest centimeter;
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4.3.2.2.b
volume to the nearest cup, pint, quart, or gallon; to the nearest liter; or to the nearest whole unit of a nonstandard unit;
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4.3.2.2.c
weight to the nearest ounce or pound or to the nearest whole unit of a nonstandard unit of measure;
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4.3.2.2.d
temperature to the nearest degree;
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4.3.2.2.e
time including elapsed time.
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4.3.2.3
states
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4.3.2.3.a
the number of weeks in a year;
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4.3.2.3.b
the number of ounces in a pound;
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4.3.2.3.c
the number of milliliters in a liter, grams in a kilogram, and meters in a kilometer.
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4.3.2.3.d
the number of items in a dozen.
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4.3.2.4
converts:
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4.3.2.4.a
within the customary system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons;
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4.3.2.4.b
within the metric system: centimeters and meters.
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4.3.2.5
finds
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4.3.2.5.a
the perimeter of two-dimensional figures given the measures of all the sides.
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4.3.2.5.b
the area of squares and rectangles using concrete objects.
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4.3.3
The student recognizes and performs one transformation on simple shapes or concrete objects in a variety of situations.
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4.3.3.1
describes a transformation using cardinal points or positional directions, e.g., go north three blocks and then west four blocks or move the triangle three units to the right and two units up.
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4.3.3.2
recognizes, performs, and describes one transformation (reflection/flip, rotation/turn, translation/slide) on a two-dimensional figure or concrete object.
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4.3.3.3
recognizes three-dimensional figures (rectangular prisms, cylinders) and concrete objects from various perspectives (top, bottom, sides, corners).
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4.3.4
The student relates geometric concepts to a number line and the first quadrant of a coordinate plane in a variety of situations.
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4.3.4.1
uses a number line (horizontal/vertical) to model whole number multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.
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4.3.4.2
uses points in the first quadrant of a coordinate plane (coordinate grid) to identify locations.
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4.3.4.3
identifies and plots points as whole number ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
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4.3.4.4
organizes whole number data using a T-table and plots the ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
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4.4
Data
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4.4.1
The student applies the concepts of probability to draw conclusions and to make predictions and decisions including the use of concrete objects in a variety of situations.
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4.4.1.1
recognizes that the probability of an impossible event is zero and that the probability of a certain event is one.
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4.4.1.2
lists all possible outcomes of a simple event in an experiment or simulation including the use of concrete objects.
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4.4.1.3
recognizes and states the probability of a simple event in an experiment or simulation, e.g., when a coin is flipped, the probability of landing heads up is 1/2 and the probability of landing tails up is 1/2. This can be read as one out of two or one half.
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4.4.2
The student collects, organizes, displays, explains, and interprets numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations.
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4.4.2.1
organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays:
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4.4.2.1.a
graphs using concrete objects;
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4.4.2.1.b
pictographs with a symbol or picture representing one, two, five, ten, twenty-five, or one-hundred including partial symbols when the symbol represents an even amount;
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4.4.2.1.c
frequency tables (tally marks);
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4.4.2.1.d
horizontal and vertical bar graphs;
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4.4.2.1.e
Venn diagrams or other pictorial displays, e.g., glyphs;
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4.4.2.1.f
line plots;
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4.4.2.1.g
charts and tables;
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4.4.2.1.h
line graphs;
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4.4.2.1.i
circle graphs.
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4.4.2.2
collects data using different techniques (observations, polls, surveys, interviews, or random sampling) and explains the results.
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4.4.2.3
identifies, explains, and calculates or finds these statistical measures of a data set with less than ten whole number data points using whole numbers from 0 through 1,000:
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4.4.2.3.a
minimum and maximum values,
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4.4.2.3.b
range,
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4.4.2.3.c
mode,
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4.4.2.3.d
median when data set has an odd number of data points,
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4.4.2.3.e
mean when data set has a whole number mean.
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