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3.1
Number and Computation
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3.1.1
The student demonstrates number sense for whole numbers, fractions, decimals, and money using concrete objects in a variety of situations.
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3.1.1.1
knows, explains, and represents:
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3.1.1.1.a
whole numbers from 0 through 10,000;
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3.1.1.1.b
fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, sixteenths);
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3.1.1.1.c
decimals greater than or equal to zero through tenths place.
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3.1.1.2
compares and orders:
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3.1.1.2.a
whole numbers from 0 through 10,000 with and without the use of concrete objects;
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3.1.1.2.b
fractions greater than or equal to zero with like denominators (halves, fourths, thirds, eighths, tenths, sixteenths) using concrete objects;
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3.1.1.2.c
decimals greater than or equal to zero through tenths place using concrete objects.
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3.1.1.3
knows, explains, and uses equivalent representations including the use of mathematical models for:
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3.1.1.3.a
addition and subtraction of whole numbers from 0 through 1,000.
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3.1.1.3.b
multiplication using the basic facts through the 5s and the multiplication facts of the 10s, e.g., 3 x 2 can be represented as 4 + 2 or as an array, XXX-XXX;
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3.1.1.3.c
addition and subtraction of money, e.g., three half dollars equals 50¢ + 50¢ + 50¢ or 50¢ + 100¢.
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3.1.1.4
determines the value of mixed coins and bills with a total value of $50 or less.
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3.1.2
The student demonstrates an understanding of whole numbers with a special emphasis on place value and recognizes, uses, and explains the concepts of properties as they relate to whole numbers, fractions, decimals, and money in a variety of situations.
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3.1.2.1
identifies, reads, and writes numbers using numerals and words from tenths place through ten thousands place, e.g., sixty-four thousand, three hundred eighty and five tenths is written in numerical form as 64,380.5.
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3.1.2.2
identifies, models, reads, and writes numbers using expanded form from tenths place through ten thousands place, e.g., 56,277.3 = (5 x 10,000) + (6 x 1,000) + (2 x 100) + (7 x 10) + (7 x 1) + (3 x .1) = 50,000 + 6,000 + 200 + 70 + 7 + .3
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3.1.2.3
classifies various subsets of numbers as whole numbers, fractions (including mixed numbers), or decimals.
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3.1.2.4
identifies the place value of various digits from tenths to one hundred thousands place.
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3.1.2.5
identifies any whole number through 1,000 as even or odd
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3.1.2.6
uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects:
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3.1.2.7.a
commutative properties of addition and multiplication, e.g., 7 + 8 = 8 + 7 or 3 x 6 = 6 x 3;
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3.1.2.7.b
zero property of addition (additive identity), e.g., 4 + 0 = 4;
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3.1.2.7.c
property of one for multiplication (multiplicative identity), 1 x 3 = 3;
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3.1.2.7.d
associative property of addition, e.g., (3 + 2) + 4 = 3 + (2 + 4);
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3.1.2.7.e
symmetric property of equality applied to addition and multiplication, e.g., 100 = 20 + 80 is the same as 20 + 80 = 100 and 3 x 4 = 12 is the same as 12 = 3 x 4;
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3.1.2.7.f
zero property of multiplication, e.g., 9 x 0 = 0 or 0 x 32 = 0.
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3.1.2.7
divides whole numbers from 0 through 99,999 into groups of 10,000s; 1,000s; 100s; 10s, and 1s using base ten models.
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3.1.3
The student uses computational estimation with whole numbers, fractions, and money in a variety of situations.
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3.1.3.1
estimates whole numbers quantities from 0 through 1,000; fractions (halves, fourths); and monetary amounts through $500 using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
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3.1.3.2
uses various estimation strategies to estimate using whole number quantities from 0 through 1,000 and explains the process used; e.g., 362 rounded to the nearest ten is 360 and 362 rounded to the nearest hundred is 400. Using front-end estimation, 362 is about 300 or 400 depending on the context of the problem. Using a "nice" number, 362 is about 350 because of the benchmark number - 350, since 350 is the halfway point between 300 and 400.
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3.1.3.3
recognizes and explains the difference between an exact and an approximate answer, e.g., When asked how many students are in a classroom, an exact answer could be 24. Whereas, an approximate answer could be 20 since 24 could be rounded down to the nearest ten (underestimated) or rounded up to 30 (overestimated).
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3.1.4
The student models, performs, and explains computation with whole numbers and money including the use of concrete objects in a variety of situations.
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3.1.4.1
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
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3.1.4.2
states and uses with efficiency and accuracy the multiplication facts through the 5s and the multiplication facts of the 10s and corresponding division facts.
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3.1.4.3
skip counts (multiples) by 2s, 3s, 4s, 5s, and 10s.
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3.1.4.4
performs and explains these computational procedures:
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3.1.4.4.a
adds and subtracts whole numbers from 0 through 10,000;
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3.1.4.4.b
multiplies whole numbers when one factor is 5 or less and the other factor is a multiple of 10 through 1,000 with or without the use of concrete objects, e.g., 400 x 3 = 120 or 70 x 5 = 350;
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3.1.4.4.c
adds and subtracts monetary amounts using dollar and cents notation through $500.00, e.g., $47.07 + $356.96 = $404.03.
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3.1.4.5
fair shares/measures out (divides) a total amount through 100 concrete objects into equal groups, e.g., fair sharing 52 pieces of candy with 8 friends resulting in eight groups of 6 with four pieces left over or measuring out into groups of eight 52 pieces of candy with four pieces left over.
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3.1.4.6
explains the relationship between addition and subtraction.
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3.1.4.7
identifies multiplication and division fact families through the 5s and the multiplication and division fact families of the 10s, e.g., when given 6 x __ = 18, the student recognizes the remaining members of the fact family.
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3.1.4.8
reads and writes horizontally, vertically, and with different operational symbols the same addition, subtraction, multiplication, or division expression e.g., 4 * 6 is the same as 4 x 6 or 4(6) or 6 x 4 and 10 divided by 2 is the same as 10 ÷ 2 or 10/2.
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3.2
Algebra
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3.2.1
The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.
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3.2.1.1
uses concrete objects, drawings, and other representations to work with types of patterns:
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3.2.1.1.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.
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3.2.1.1.b
growing patterns, e.g., 1, 4, 7, 10,
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3.2.1.2
uses these attributes to generate patterns:
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3.2.1.2.a
counting numbers related to number theory, e.g., evens, odds, or multiples through the 5s;
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3.2.1.2.b
whole numbers that increase or decrease, e.g., 3, 6, 9, ...; 20, 15, 10, ...;
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3.2.1.2.c
geometric shapes including one attribute change, e.g., where the pattern is solid square, square, triangle, solid triangle, solid square, square triangle, solid triangle, solid square, square, triangle, solid triangle; or when using attribute blocks the change is size only, then shape only.
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3.2.1.2.d
measurements, e.g., 1 ft, 2 ft, 3 ft, ; 3 lbs, 6 lbs, 9 lbs; or 2 cups, 4 cups, 6 cups, ;
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3.2.1.2.e
money and time patterns, e.g., $.25, $.50, $.75, or 1:05 p.m., 1:10 p.m., 1:15 p.m., ;
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3.2.1.2.f
things related to daily life, e.g., water cycle, food cycle, or life cycle;
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3.2.1.2.g
things related to size, shape, color, texture, or movement, e.g., red-green, red-green, red-green, ...; snapping fingers; clapping hands; stomping feet; or tossing a bean bag over the head, under the leg, and behind the back (kinesthetic patterns).
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3.2.1.3
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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3.2.1.4
generates:
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3.2.1.4.a
repeating patterns,
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3.2.1.4.b
growing (extending) patterns,
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3.2.1.4.c
patterns using function tables (input/output machines, T-tables).
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3.2.2
The student uses symbols and whole numbers to solve equations including the use of concrete objects in a variety of situations.
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3.2.2.1
explains and uses symbols to represent unknown whole number quantities from 0 through 1,000.
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3.2.2.2
finds the sum or difference in one-step equations with:
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3.2.2.2.a
whole numbers from 0 through 99, e.g., 89 = 76 + y or y - 23 = 32;
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3.2.2.2.b
monetary values through a dollar, e.g., 25¢ + 10¢ + 5¢ = n.
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3.2.2.3
finds the unknown in the multiplication and division fact families through the 5s and the 10s, e.g., 3 * ___; = 4 * 6.
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3.2.2.4
compares two whole numbers from 0 through 1,000 using the equality and inequality symbols (=, <, >) and their corresponding meanings (is equal to, is less than, is greater than).
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3.2.3
The student recognizes and describes whole number relationships using concrete objects in a variety of situations.
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3.2.3.1
states mathematical relationships between whole numbers from 0 through 200 using various methods including mental math, paper and pencil, concrete objects, and appropriate technology, e.g., every time a quarter is added to the amount; 25¢ is added to the total.
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3.2.3.2
finds the values and determines the rule with one operation (addition, subtraction) of whole numbers from 0 through 200 using a horizontal or vertical function table (input/output machine, T-table).
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3.2.3.3
generalizes numerical patterns using whole numbers from 0 through 200 with one operation (addition, subtraction) by stating the rule using words, e.g., if the sequence is 30, 50, 70, 90, ; in words, the rule is add twenty to the number before.
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3.2.3.4
uses a function table (input/output machine, T-table) to identify and plot ordered pairs in the first quadrant of a coordinate plane.
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3.2.4
The student develops and uses mathematical models including the use of concrete objects to represent and show mathematical relationships in a variety of situations.
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3.2.4.1
knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
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3.2.4.1.a
process models (concrete objects, pictures, number lines, coordinate planes/grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures and mathematical relationships;
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3.2.4.1.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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3.2.4.1.c
fraction 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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3.2.4.1.d
money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
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3.2.4.1.e
function tables (input/output machines, T-tables) to find numerical relationships;
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3.2.4.1.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 attributes of geometric shapes;
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3.2.4.1.g
two-dimensional geometric models (spinners), three-dimensional models (number cubes), and process models (concrete objects) to model probability;
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3.2.4.1.h
graphs using concrete objects, representational objects, or abstract representations, pictographs, frequency tables, horizontal and vertical bar graphs, Venn diagrams or other pictorial displays, line plots, charts, and tables to organize and display data;
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3.2.4.1.i
Venn diagrams to sort data and show relationships.
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3.2.4.2
creates a mathematical model to show the relationship between two or more things.
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3.3
Geometry
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3.3.1
The student recognizes geometric shapes and investigates their properties using concrete objects in a variety of situations.
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3.3.1.1
recognizes and investigates properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons) using concrete objects, drawings, and appropriate technology.
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3.3.1.2
recognizes, draws, and describes plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons).
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3.3.1.3
recognizes the solids (cubes, rectangular prisms, cylinders, cones, spheres).
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3.3.1.4
recognizes and describes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.
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3.3.1.5
recognizes and describes a quadrilateral as any four-sided figure.
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3.3.1.6
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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3.3.2
The student estimates and measures using standard and nonstandard units of measure using concrete objects in a variety of situations.
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3.3.2.1
uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, and perimeter using standard and nonstandard units of measure.
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3.3.2.2
reads and tells time to the minute using analog and digital clocks.
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3.3.2.3
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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3.3.2.3.a
length width, and height to the nearest half inch, inch, foot, and yard; and to the nearest whole unit of nonstandard unit;
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3.3.2.3.b
length, width, and height to the nearest centimeter and meter;
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3.3.2.3.c
weight to the nearest whole unit of a nonstandard unit;
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3.3.2.3.d
volume to the nearest cup, pint, quart, and gallon;
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3.3.2.3.e
volume to the nearest liter;
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3.3.2.3.f
temperature to the nearest degree.
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3.3.2.4
states:
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3.3.2.4.a
the number of hours in a day and days in a year;
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3.3.2.4.b
the number of inches in a foot, inches in a yard, and feet in a yard;
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3.3.2.4.c
the number of centimeters in a meter;
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3.3.2.4.d
the number of cups in a pint, pints in a quart, and quarts in a gallon.
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3.3.2.5
finds the perimeter of squares, rectangles, and triangles given the measures of all the sides.
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3.3.3
The student recognizes and performs one transformation on simple shapes or concrete objects in a variety of situations.
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3.3.3.1
knows and uses cardinal points (north, south, east, west) and intermediate points (northeast, southeast, northwest, southwest).
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3.3.3.2
recognizes and performs one transformation (reflection/flip, rotation/turn, and translation/slide) on a two-dimensional figure.
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3.3.4
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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3.3.4.1
uses a number line (horizontal/vertical) to model the basic multiplication facts through the 5s and the multiplication facts of the 10s.
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3.3.4.2
identifies points on a coordinate plane (coordinate grid) using:
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3.3.4.2.a
two positive whole numbers,
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3.3.4.2.b
a letter and a positive whole number.
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3.3.4.3
identifies points as ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
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3.4
Data
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3.4.1
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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3.4.1.1
recognizes any outcome of a simple event in an experiment or simulation as impossible, possible, certain, likely, unlikely, or equally likely.
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3.4.1.2
lists some of the possible outcomes of a simple event in an experiment or simulation including the use of concrete objects.
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3.4.2
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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3.4.2.1
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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3.4.2.1.a
graphs using concrete objects;
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3.4.2.1.b
pictographs with a whole symbol or picture representing one, two, five, ten, twenty-five, or one-hundred (no partial symbols or pictures);
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3.4.2.1.c
frequency tables (tally marks);
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3.4.2.1.d
horizontal and vertical bar graphs;
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3.4.2.1.e
Venn diagrams or other pictorial displays, e.g., glyphs;
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3.4.2.1.f
line plots;
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3.4.2.1.g
charts and tables.
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3.4.2.2
collects data using different techniques (observations, polls, surveys, or interviews) and explains the results.
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3.4.2.3
finds these statistical measures of a data set with less than ten data points using whole numbers from 0 through 1,000:
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3.4.2.3.a
minimum and maximum data values,
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3.4.2.3.b
range,
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3.4.2.3.c
mode (uni-modal only),
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3.4.2.3.d
median when data set has an odd number of data points.
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