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2.1
Number and Computation
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2.1.1
The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations.
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2.1.1.1
knows, explains, and represents whole numbers from 0 through 1,000 using concrete objects.
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2.1.1.2
compares and orders:
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2.1.1.2.a
whole numbers from 0 through 1,000 using concrete objects;
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2.1.1.2.b
fractions greater than or equal to zero with like denominators (halves, fourths, thirds, eighths) using concrete objects.
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2.1.1.3
uses addition and subtraction to show equivalent representations for whole numbers from 0 through 100, e.g., 8 - 5 = 2 + 1 or 20 + 40 = 70 - 10.
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2.1.1.4
identifies and uses ordinal positions from first (1st) through twentieth (20th).
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2.1.1.5
identifies coins, states their values, and determines the total value to $1.00 of a mixed group of coins using pennies, nickels, dimes, quarters, and half-dollars.
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2.1.1.6
counts a like combination of currency ($1, $5, $10, $20) to $100.
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2.1.2
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 in a variety of situations.
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2.1.2.1
reads and writes:
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2.1.2.1.a
whole numbers from 0 through 1,000 in numerical form, e.g., 942 is read as nine hundred forty-two and is written in numerical form as 942;
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2.1.2.1.b
whole numbers from 0 through 100 in words, e.g., 76 is read as seventy-six and is written in words as seventy-six.
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2.1.2.1.c
whole numbers from 0 through 1,000 in numerical form when presented in word form, e.g., nine hundred forty-six is read as nine hundred forty-six and is written as 946.
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2.1.2.2
represents whole numbers from 0 through 1,000 using various groupings and place value models emphasizing 1s, 10s, and 100s; explains the groups; and states the value of the digit in ones place, tens place, and hundreds place, e.g., in 385, the 3 represents 3 hundreds, 30 tens, or 300 ones; the 8 represents 8 tens or 80 ones; and the 5 represents 5 ones.
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2.1.2.3
counts subsets of whole numbers from 0 through 1,000 forwards and backwards, e.g., 311, 312, ..., 320; or 210, 209, ..., 204.
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2.1.2.4
identifies the place value of the digits in whole numbers from 0 through 1,000.
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2.1.2.5
identifies any whole number from 0 through 100 as even or odd.
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2.1.2.6
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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2.1.2.6.a
commutative property of addition, e.g., 5 + 6 = 6 + 5;
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2.1.2.6.b
zero property of addition (additive identity), e.g., 4 + 0 = 4;
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2.1.2.6.c
associative property of addition, e.g., (3 + 2) + 4 = 3 + (2 + 4);
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2.1.2.6.d
symmetric property of equality applied to basic addition and subtraction facts, e.g., 10 = 2 + 8 is the same as 2 + 8 = 10 or 7 = 10 - 3 is the same as 10 - 3 = 7.
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2.1.3
The student uses computational estimation with whole numbers and money in a variety of situations.
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2.1.3.1
estimates whole number quantities from 0 through 1,000 and monetary amounts through $50 using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
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2.1.3.2
uses various estimation strategies to estimate whole number quantities from 0 through 1,000.
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2.1.4
The student models, performs, and explains computation with whole numbers and money using concrete objects in a variety of situations.
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2.1.4.1
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
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2.1.4.2
states and uses with efficiency and accuracy basic addition facts with sums from 0 through 20 and corresponding subtraction facts.
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2.1.4.3
skip counts by 2s, 5s, and 10s through 100 and skip counts by 3s through 36.
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2.1.4.4
uses repeated addition (multiplication) with whole numbers to find the sum when given the number of groups (ten or less) and given the same number of concrete objects in each group (twenty or less), e.g., five classes of 15 students visit the zoo; 15 + 15 + 15 + 15 + 15 = 75.
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2.1.4.5
uses repeated subtraction (division) with whole numbers when given the total number of concrete objects in each group to find the number of groups, e.g., There are 25 cookies. If each student gets 3 cookies, how many students get cookies? 25 - 3 - 3 - 3 - 3 - 3 - 3 - 3 - 3 or 25 minus 3 eight times means eight students get 3 cookies each and there is 1 cookie left over.
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2.1.4.6
fair shares/measures out (divides) a total amount through 100 concrete objects into equal groups, e.g., fair sharing 48 eggs into four groups resulting in four groups of 12 eggs or measuring out 48 eggs with 12 eggs in each group resulting in four groups of 12 eggs.
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2.1.4.7
performs and explains these computational procedures:
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2.1.4.7.a
adds and subtracts three-digit whole numbers with and without regrouping including the use of concrete objects,
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2.1.4.7.b
adds and subtracts monetary amounts through 99¢ using cent notation (25¢ + 52¢) and money models.
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2.1.4.8
identifies basic addition and subtraction fact families
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2.1.4.9
reads and writes horizontally and vertically the same addition or subtraction expression e.g., 6 - 3 is the same as 6 - 3.
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2.2
Algebra
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2.2.1
The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.
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2.2.1.1
uses concrete objects, drawings, and other representations to work with types of patterns:
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2.2.1.1.a
repeating patterns, e.g., an AB pattern is like left-right, left-right, ...; an ABC pattern is like dog-horse-pig, dog-horse-pig,
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2.2.1.1.b
growing (extending) patterns, e.g., 7, 9, 11, where the rule could be add 2 or the odd numbers beginning with 7.
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2.2.1.2
uses the following attributes to generate patterns:
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2.2.1.2.a
counting numbers related to number theory, e.g., evens, odds, or skip counting by 3s, or 4s;
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2.2.1.2.b
whole numbers that increase or decrease, e.g., 11, 22, 33,... or 98, 88, 78, ;
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2.2.1.2.c
geometric shapes
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2.2.1.2.d
measurements, e.g., 1", 3", 5", or 5 lbs, 10 lbs, 15 lbs,;
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2.2.1.2.e
the calendar, e.g., Sunday, Monday, Tuesday,;
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2.2.1.2.f
money and time, e.g., $5, $10, $15,... or 1:15, 1:30, 1:45, ;
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2.2.1.2.g
things related to daily life, e.g., seasons, temperature, or weather;
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2.2.1.2.h
things related to size, shape, color, texture, or movement, e.g., snapping fingers, clapping hands, or stomping feet or over, under, or behind using a bean bag toss (kinesthetic patterns).
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2.2.1.3
identifies 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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2.2.1.4
generates:
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2.2.1.4.a
repeating patterns, e.g., 1-2, 1-2, 1-2, ... where the elements repeat;
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2.2.1.4.b
growing (extending) patterns, e.g., 1, 4, 7, ...where the rule is add 3.
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2.2.2
The student uses symbols and whole numbers to solve addition and subtraction equations using concrete objects in a variety of situations.
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2.2.2.1
explains and uses symbols to represent unknown whole number quantities from 0 through 100.
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2.2.2.2
finds the sum or difference in one-step equations with:
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2.2.2.2.a
whole numbers from 0 through 99, e.g., 32 + 19 = ___ or ___ = 79 - 46;
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2.2.2.2.b
up to two different coins, e.g., nickel + penny = __¢.
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2.2.2.3
finds unknown addend or subtrahend using basic addition and subtraction facts (fact family), e.g., 12 = __ + 7 or 12 - __ = 7.
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2.2.2.4
describes and compares two whole numbers from 0 through 1,000 using the terms: is equal to, is less than, is greater than.
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2.2.3
The student recognizes and describes whole number relationships using concrete objects in a variety of situations.
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2.2.3.1
states mathematical relationships between whole numbers from 0 through 100 using various methods including mental math, paper and pencil, and concrete objects, e.g., every time a dog is added to the pack, 2 more ears are added to the total.
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2.2.3.2
finds the values and determines the rule that involve addition or subtraction of whole numbers from 0 through 100 using a horizontal or vertical function table (input/output machine, T-table).
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2.2.3.3
generalizes numerical patterns using whole numbers from 0 through 100 with one operation (addition, subtraction) by stating the rule using words, e.g., if a set of numbers is 2, 4, 6, 8,10, ...; the rule is add two.
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2.2.4
The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations.
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2.2.4.1
knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
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2.2.4.1.a
process models (concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or measurement tools) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to represent fractional parts;
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2.2.4.1.b
place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures;
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2.2.4.1.c
fraction models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities;
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2.2.4.1.d
money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
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2.2.4.1.e
function tables (input/output machines, T-tables) to model numerical relationships;
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2.2.4.1.f
two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks) to model perimeter 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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2.2.4.1.g
two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability;
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2.2.4.1.h
graphs using concrete objects, representational objects, or abstract representations, pictographs, frequency tables, horizontal and vertical bar graphs, Venn diagrams or other pictorial displays, and line plots to organize and display data;
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2.2.4.1.i
Venn diagrams to sort data.
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2.2.4.2
creates a mathematical model to show the relationship between two or more things e.g., using pattern blocks, a whole (1) can be represented using a (1/1) or two (2/2) or thhree (3/3) or six (6/6).
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2.3
Geometry
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2.3.1
The student recognizes geometric shapes and describes their properties using concrete objects in a variety of situations.
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2.3.1.1
recognizes and investigates properties of circles, squares, rectangles, triangles, and ellipses (ovals) (plane figures/two-dimensional shapes) using concrete objects, drawings, and appropriate technology.
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2.3.1.2
recognizes, draws, and describes circles, squares, rectangles, triangles, ellipses (ovals) (plane figures).
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2.3.1.3
recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids/three-dimensional figures).
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2.3.1.4
recognizes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.
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2.3.1.5
compares geometric shapes (circles, squares, rectangles, triangles, ellipses) to one another.
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2.3.1.6
recognizes whether a shape has a line of symmetry.
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2.3.2
The student estimates and measures using standard and nonstandard units of measure with concrete objects in a variety of situations.
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2.3.2.1
uses whole number approximations (estimations) for length, weight, and volume using standard and nonstandard units of measure, e.g., the height of the classroom door is 14 chalkboard erasers laid end to end or 7 feet high or an apple weighs about 42 unifix cubes.
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2.3.2.2
reads and tells time by five-minute intervals using analog and digital clocks.
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2.3.2.3
selects and uses appropriate measurement tools and units of measure for length, weight, volume, and temperature for a given situation.
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2.3.2.4
measures:
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2.3.2.4.a
length to the nearest inch or foot and to the nearest whole unit of a nonstandard unit;
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2.3.2.4.b
weight to the nearest nonstandard unit;
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2.3.2.4.c
volume to the nearest cup, pint, quart, or gallon;
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2.3.2.4.d
temperature to the nearest degree.
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2.3.2.5
states:
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2.3.2.5.a
the number of minutes in an hour,
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2.3.2.5.b
the number of days in each month.
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2.3.3
The student recognizes and shows one transformation on simple shapes and concrete objects in a variety of situations.
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2.3.3.1
knows and uses the cardinal points (north, south, east, west).
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2.3.3.2
recognizes that changing an object's position or orientation including whether the object is nearer or farther away does not change the name, size, or shape of the object.
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2.3.3.3
recognizes when a shape has undergone one transformation (flip/reflection, turn/rotation, slide/translation).
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2.3.4
The student identifies one or more points on a number line in a variety of situations.
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2.3.4.1
locates and plots whole numbers from 0 through 1,000 on a segment of a number line (horizontal/vertical), e.g., using a segment of a number line from 800 to 820 to locate the whole number 805.
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2.3.4.2
represents the distance between two whole numbers from 0 through 1,000 on a segment of a number line.
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2.3.4.3
uses a segment of a number line to model addition and subtraction using whole numbers from 0 through 1,000, e.g., 333 + n = 349 or 333 + 16 = n or 400 - n = 352 or 400 - 48 = n.
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2.4
Data
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2.4.1
The student applies the concepts of probability using concrete objects in a variety of situations.
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2.4.1.1
recognizes any outcome of a simple event in an experiment or simulation as impossible, possible, certain, likely, or unlikely.
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2.4.1.2
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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2.4.2
The student collects, organizes, displays, and explains numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations.
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2.4.2.1
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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2.4.2.1.a
graphs using concrete objects;
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2.4.2.1.b
pictographs with a whole symbol or picture representing one, two, or ten (no partial symbols or pictures);
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2.4.2.1.c
frequency tables (tally marks);
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2.4.2.1.d
horizontal and vertical bar graphs;
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2.4.2.1.e
Venn diagrams or other pictorial displays, e.g., glyphs;
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2.4.2.1.f
line plots.
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2.4.2.2
collects data using different techniques (observations, interviews, or surveys) and explains the results.
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2.4.2.3
identifies the minimum (lowest) and maximum (highest) values in a whole number data set.
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2.4.2.4
finds the range for a data set using two-digit whole numbers.
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2.4.2.5
finds the mode (most) for a data set using concrete objects that include:
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2.4.2.5.a
quantitative/numerical data (whole numbers through 100);
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2.4.2.5.b
qualitative/non-numerical data (category that occurs most often).
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