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5.1
Number and Computation
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5.1.1
The student demonstrates number sense for integers, fractions, decimals, and money in a variety of situations.
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5.1.1.1
knows, explains, and uses equivalent representations for:
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5.1.1.1.a
whole numbers from 0 through 1,000,000;
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5.1.1.1.b
fractions greater than or equal to zero (including mixed numbers);
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5.1.1.1.c
decimals greater than or equal to zero through hundredths place and when used as monetary amounts.
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5.1.1.2
compares and orders:
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5.1.1.2.a
integers,
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5.1.1.2.b
fractions greater than or equal to zero (including mixed numbers),
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5.1.1.2.c
decimals greater than or equal to zero through hundredths place.
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5.1.1.3
explains the numerical relationships (relative magnitude) between whole numbers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero through hundredths place.
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5.1.1.4
knows equivalent percents and decimals for one whole, one-half, one-fourth, three-fourths, and one tenth through nine tenths, e.g., 1 = 100% = 1.0, 3/4 = 75% =.75, 3/10 = 30% =.3.
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5.1.1.5
identifies integers and gives real-world problems where integers are used, e.g., making a T-table of the temperature each hour over a twelve hour period in which the temperature at the beginning is 10 degrees and then decreases 2 degrees per hour.
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5.1.2
The student demonstrates an understanding of the whole number system; recognizes, uses, and explains the concepts of properties as they relate to the whole number system; and extends these properties to integers, fractions (including mixed numbers), and decimals.
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5.1.2.1
classifies subsets of numbers as integers, whole number, fractions (including mixed numbers), or decimals.
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5.1.2.2
identifies prime and composite numbers from 0 through 50.
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5.1.2.3
uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects:
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5.1.2.3.a
commutative properties of addition and multiplication, e.g., 43 + 34 = 34 + 43 and 12 x 15 = 15 x 12;
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5.1.2.3.b
associative properties of addition and multiplication, e.g., 4 + (3 + 5) = (4 + 3) + 5;
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5.1.2.3.c
zero property of addition (additive identity) and property of one for multiplication (multiplicative identity), e.g., 342 + 0 = 342 and 576 x 1 = 576;
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5.1.2.3.d
symmetric property of equality, e.g., 35 = 11 + 24 is the same as 11 + 24 = 35;
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5.1.2.3.e
zero property of multiplication, e.g., 438,223 x 0 = 0;
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5.1.2.3.f
distributive property, e.g., 7(3 + 5) = 7(3) + 7(5);
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5.1.2.3.g
substitution property, e.g., if a = 3 and a = b, then b = 3.
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5.1.2.4
recognizes Roman Numerals that are used for dates, on clock faces, and in outlines.
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5.1.2.5
recognizes the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.
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5.1.3
The student uses computational estimation with whole numbers, fractions, decimals, and money in a variety of situations.
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5.1.3.1
estimates whole numbers quantities from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.
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5.1.3.2
uses various estimation strategies to estimate whole number quantities from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 and explains the process used.
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5.1.3.3
recognizes and explains the difference between an exact and an approximate answer.
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5.1.3.4
explains the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer.
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5.1.4
The student models, performs, and explains computation with whole numbers, fractions including mixed numbers, and decimals including the use of concrete objects in a variety of situations.
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5.1.4.1
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.
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5.1.4.2
performs and explains these computational procedures:
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5.1.4.2.a
divides whole numbers through a 2-digit divisor and a 4-digit dividend with the remainder as a whole number or a fraction using paper and pencil, e.g., 7452 ÷ 24 = 310 r 12 or 310 ½;
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5.1.4.2.b
divides whole numbers beyond a 2-digit divisor and a 4-digit dividend using appropriate technology, e.g., 73,368 ÷ 36 = 2,038;
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5.1.4.2.c
adds and subtracts decimals from thousands place through hundredths place;
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5.1.4.2.d
multiplies decimals up to three digits by two digits from hundreds place through hundredths place;
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5.1.4.2.e
adds and subtracts fractions greater than or equal to zero (including mixed numbers) without regrouping and without expressing answers in simplest form;
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5.1.4.2.f
multiplies and divides by 10; 100; 1,000; or single-digit multiples of each, e.g., 20 * 300 or 4,400 ÷ 500.
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5.1.4.3
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 6(4) and 6 x 4 or 10 divided by 2 is the same as 10 ÷ 2 or 10/2
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5.1.4.4
identifies, explains, and finds the greatest common factor and least common multiple of two or more whole numbers through the basic multiplication facts from 1 x 1 through 12 x 12
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5.2
Algebra
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5.2.1
The student recognizes, describes, extends, develops, and explains relationships in patterns in a variety of situations.
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5.2.1.1
uses concrete objects, drawings, and other representations to work with types of patterns. The types of patterns are:
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5.2.1.1.a
repeating patterns, e.g., 9, 10, 11, 9, 10, 11, ...;
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5.2.1.1.b
growing patterns, e.g., 20, 30, 28, 38, 36, ... where the rule is add 10, then subtract 2; or 2, 5, 8, ... as an example of an arithmetic sequence - each term after the first is found by adding the same number to the preceding term.
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5.2.1.2
uses these attributes to generate patterns:
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5.2.1.2.a
counting numbers related to number theory, e.g., multiples or perfect squares;
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5.2.1.2.b
whole numbers, e.g., 10; 100; 1,000; 10,000; 100,000; ... (powers of ten);
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5.2.1.2.c
geometric shapes through two attribute changes, e.g., when the next shape has one more side; or when both the color and the shape change at the same time;
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5.2.1.2.d
measurements, e.g., 3 m, 6 m, 9 m, ;
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5.2.1.2.e
things related to daily life, e.g., sports scores, longitude and latitude, elections, eras, or appropriate topics across the curriculum;
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5.2.1.2.f
things related to size, shape, color, texture, or movement, e.g., square dancing moves (kinesthetic patterns);
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5.2.1.3
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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5.2.1.4
generates:
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5.2.1.4.a
a pattern (repeating, growing).
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5.2.1.4.b
a pattern using a function table (input/output machines, T-tables).
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5.2.2
The student uses variables, symbols, whole numbers, and algebraic expressions in one variable to solve linear equations in a variety of situations.
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5.2.2.1
explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000 and variable relationships.
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5.2.2.2
solves one-step linear equations with one variable and a whole number solution using addition and subtraction with whole numbers from 0 through 100 and multiplication with the basic facts, e.g., 3y = 12, 45 = 17 + q, or r - 42 = 36.
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5.2.2.3
explains and uses equality and inequality symbols (=, not equal to, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) with whole numbers from 0 to 100,000.
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5.2.2.4
recognizes ratio as a comparison of part-to-part and part-to-whole relationships, e.g., the relationship between the number of boys and the number of girls (part-to-part) or the relationship between the number of girls to the total number of students in the classroom (part-to-whole).
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5.2.3
The student recognizes, describes, and examines whole number relationships in a variety of situations.
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5.2.3.1
states mathematical relationships between whole numbers from 0 through 10,000 using various methods including mental math, paper and pencil, concrete objects, and appropriate technology.
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5.2.3.2
finds the values, determines the rule, and states the rule using symbolic notation with one operation of whole numbers from 0 through 10,000 using a vertical or horizontal function table (input/output machine, T-table),
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5.2.3.3
generalizes numerical patterns using whole numbers from 0 through 5,000 up to two operations by stating the rule using words, e.g., If the sequence is 2400, 1200, 600, 300, 150, ...; in words, the rule could be split the number in half or divide the number before by 2 or if the sequence is 4, 11, 25, 53, 109, ...; in words, the rule could be double the number and add 3 to get the next number or multiply the number by 2 and add 3.
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5.2.3.4
uses a function table (input/output machine, T-table) to identify, plot, and label whole number ordered pairs in the first quadrant of a coordinate plane.
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5.2.3.5
plots and locates points for integers (positive and negative whole numbers) on a horizontal number line and vertical number line.
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5.2.3.6
describes whole number relationships using letters and symbols.
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5.2.4
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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5.2.4.1
knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
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5.2.4.1.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 and mathematical relationships and to solve equations;
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5.2.4.1.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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5.2.4.1.c
fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
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5.2.4.1.d
factor trees to find least common multiple and greatest common factor;
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5.2.4.1.e
equations and inequalities to model numerical relationships;
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5.2.4.1.f
function tables (input/output machines, T-tables) to model numerical and algebraic relationships;
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5.2.4.1.g
two-dimensional geometric models (geoboards or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional models (nets or solids) and real-world objects to compare size and to model volume and properties of geometric shapes;
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5.2.4.1.h
tree diagrams to organize attributes through three different sets and determine the number of possible combinations;
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5.2.4.1.i
two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability;
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5.2.4.1.j
graphs using concrete objects, pictographs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, tables, and single stem-and-leaf plots to organize and display data;
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Data, charts, and graphs: Read a table (Fifth grade - R.1)
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Data, charts, and graphs: Line graphs (Fifth grade - R.2)
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Data, charts, and graphs: Bar graphs (Fifth grade - R.3)
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Data, charts, and graphs: Pictographs (Fifth grade - R.4)
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Data, charts, and graphs: Frequency charts (Fifth grade - R.5)
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Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - R.6)
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Data, charts, and graphs: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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Data, charts, and graphs: Choose the best type of graph (Fifth grade - R.9)
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5.2.4.1.k
Venn diagrams to sort data and to show relationships.
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5.2.4.2
creates mathematical models to show the relationship between two or more things, e.g., using trapezoids to represent numerical quantities
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5.3
Geometry
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5.3.1
The student recognizes geometric shapes and compares their properties in a variety of situations.
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5.3.1.1
recognizes and investigates properties of plane figures and solids using concrete objects, drawings, and appropriate technology.
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5.3.1.2
recognizes and describes:
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5.3.1.2.a
regular polygons having up to and including ten sides;
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5.3.1.2.b
similar and congruent figures.
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5.3.1.3
recognizes and describes the solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids, triangular pyramids) using the terms faces, edges, and vertices (corners).
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5.3.1.4
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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5.3.1.5
recognizes, draws, and describes:
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5.3.1.5.a
points, lines, line segments, and rays;
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5.3.1.5.b
angles as right, obtuse, or acute.
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5.3.1.6
recognizes and describes the difference between intersecting, parallel, and perpendicular lines.
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5.3.1.7
identifies circumference, radius, and diameter of a circle.
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5.3.2
The student estimates, measures, and uses measurement formulas in a variety of situations.
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5.3.2.1
determines and 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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5.3.2.2
selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using:
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5.3.2.2.a
customary units of measure to the nearest fourth and eighth inch,
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5.3.2.2.b
metric units of measure to the nearest centimeter,
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5.3.2.2.c
nonstandard units of measure to the nearest whole unit,
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5.3.2.2.d
time including elapsed time.
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5.3.2.3
states the number of feet and yards in a mile.
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5.3.2.4
converts:
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5.3.2.4.a
within the customary system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons, pounds and ounces;
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5.3.2.4.b
within the metric system: centimeters and meters, meters and kilometers, milliliters and liters, grams and kilograms.
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5.3.2.5
knows and uses perimeter and area formulas for squares and rectangles.
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5.3.3
The student recognizes and performs transformations on geometric shapes including the use of concrete objects in a variety of situations.
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5.3.3.1
recognizes and performs through two transformations (reflection, rotation, translation) on a two-dimensional figure.
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5.3.3.2
recognizes when an object is reduced or enlarged.
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5.3.3.3
recognizes three-dimensional figures (rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids) from various perspectives (top, bottom, side, corners).
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5.3.4
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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5.3.4.1
locates and plots points on a number line (vertical/horizontal) using integers (positive and negative whole numbers).
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5.3.4.2
explains mathematical relationships between whole numbers, fractions, and decimals and where they appear on a number line.
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5.3.4.3
identifies and plots points as ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
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5.3.4.4
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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5.4
Data
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5.4.1
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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5.4.1.1
recognizes that all probabilities range from zero (impossible) through one (certain).
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5.4.1.2
lists all possible outcomes of a simple event in an experiment or simulation in an organized manner including the use of concrete objects.
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5.4.1.3
recognizes a simple event in an experiment or simulation where the probabilities of all outcomes are equal.
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5.4.1.4
represents the probability of a simple event in an experiment or simulation using fractions.
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5.4.2
The student collects, organizes, displays, explains, and interprets numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.
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5.4.2.1
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 and decimal intervals using these data displays:
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5.4.2.1.a
graphs using concrete objects,
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5.4.2.1.b
pictographs,
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5.4.2.1.c
frequency tables,
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5.4.2.1.d
bar and line graphs,
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5.4.2.1.e
Venn diagrams and other pictorial displays, e.g., glyphs,
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5.4.2.1.f
line plots,
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5.4.2.1.g
charts and tables,
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5.4.2.1.h
circle graphs,
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5.4.2.1.i
single stem-and-leaf plots.
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5.4.2.2
collects data using different techniques (observations, polls, tallying, interviews, surveys, or random sampling) and explains the results.
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5.4.2.3
identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,000:
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5.4.2.3.a
minimum and maximum values,
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5.4.2.3.b
range,
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5.4.2.3.c
mode (no-, uni-, bi-),
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5.4.2.3.d
median (including answers expressed as a decimal or a fraction without reducing to simplest form),
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5.4.2.3.e
mean (including answers expressed as a decimal or a fraction without reducing to simplest form).
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