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2nd
Grade
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3rd
Grade
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4th
Grade
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Number and Number Relations
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1. Model, read, and write
place values for numbers through 999 in word, standard, and expanded
form (N-1-E)
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1. Model, read, and write
place value in word, standard, and expanded form for numbers through
9999 (N-1-E
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1. Read and write place
value in word, standard, and expanded form through 1,000,000 (N-1-E)
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5. Read, write, and relate
decimals through hundredths and connect them with corresponding decimal
fractions (N-1-E)
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2. Model the concepts of
thirds, fourths, fifths and sixths using regions, sets, and fraction
words (e.g., one-third, three-fourths, five-sixths) (N-1-E)
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3. Use region and set models
and symbols to represent, estimate, read, write, and show understanding
of fractions through tenths (N-1-E) (N-2-E)
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6. Model, read, write,
compare, order, and represent fractions with denominators through
twelfths using region and set models (N-1-E) (A-1-E)
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7. Give decimal equivalents
of halves, fourths, and tenths (N-2-E) (N-1-E)
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8. Use common equivalent
reference points for percents (i.e., ¼, ½, ¾, and
1 whole) (N-2-E)
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9. Estimate fractional
amounts through twelfths, using pictures, models, and diagrams (N-2-E)
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3. Make reasonable estimates
of the number of objects in a collection with fewer than 100 objects
(N-2-E)
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13. Determine when and how to
estimate, and when and how to use mental math, calculators, or
paper/pencil strategies to solve addition and subtraction problems
(N-8-E) (N-9-E)
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13. Determine when and how to
estimate, and when and how to use mental math, calculators, or
paper/pencil strategies to solve multiplication and division problems
(N-8-E)
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4. Count and write the value
of amounts of money up to $1.00 using ¢ and $ (N-2-E) (N-6-E)
(M-1-E) (M-5-E)
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10. Calculate the value of a
combination of bills and coins and make change up to $5.00 (N-6-E)
(M-1-E) (M-5-E)
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12. Count money, determine
change, and solve simple word problems involving money amounts using
decimal notation (N-6-E) (N-9-E) (M-1-E) (M-5-E)
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5. Read, write, compare, and
order whole numbers through 999 using words, number lines, and models
(N-3-E) (N-1-E)
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2. Read, write, compare, and
order whole numbers through 9999 using symbols (i.e., <, =, >)
and models (N-1-E) (N-3-E)
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2. Read, write, compare, and
order whole numbers using place value concepts, standard notation, and
models through 1,000,000 (N-1-E) (N-3-E) (A-1-E)
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6. From a given number,
count forward and backward and count to 100 by 2s (N-3-E) (N-1-E)
(N-4-E)
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7. Know all basic facts for
addition and subtraction and use them to solve real-life problems
(N-5-E) (N-6-E) (N-7-E) (N-8-E) (N-9-E)
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9. Know basic multiplication
and division facts [0s, 1s, 2s, 5s, 9s, and turn-arounds (commutative
facts), including multiplying by 10s] (N-6-E) (N-4-E)
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4. Know all basic facts for
multiplication and division through 12 x 12 and 144 ¸ 12, and recognize
factors of composite numbers less than 50 (N-1-E) (N-6-E) (N-7-E)
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8. Recognize, select,
connect, and use operations, operational words and symbols (+, -) for addition (join,
part/part/whole) or subtraction (take away, comparison, missing addend,
and set/subset) situations (N-6-E) (N-5-E)
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8. Recognize, select,
connect, and use operations, operational words, and symbols (i.e., +, -, x, ¸) to solve real-life
situations (N-5-E) (N-6-E) (N-9-E)
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9. Add and subtract 1- and
2-digit numbers (N-6-E) (N-7-E)
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11. Add and subtract numbers
of 3 digits or less (N-6-E) (N-7-E)
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10. Round numbers to the
nearest 10 or 100 and identify situations in which rounding is
appropriate (N-7-E) (N-9-E)
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12. Round to the nearest 1000
and identify situations in which such rounding is appropriate (N-7-E)
(N-9-E)
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11. Use the concept of
one-to-several correspondence to trade single items for a greater
quantity of items with unequal value (1 nickel for 5 pennies, 1 dime
for 2 nickels) (N-9-E)
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4. Use the concepts of
associative and commutative properties of multiplication to simplify
computations (N-4-E) (N-7-E)
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5. Recognize and model
multiplication as a rectangular array or as repeated addition (N-4-E)
(N-7-E)
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6. Recognize and model
division as separating quantities into equal subsets (fair shares) or
as repeated subtraction (N-4-E) (N-7-E)
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3. Illustrate with
manipulatives when a number is divisible by 2, 3, 5, or 10 (N-1-E)
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7. Recognize and apply
multiplication and division as inverse operations (N-4-E)
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10. Solve multiplication and
division number sentences including interpreting remainders
(N-4-E)(A-3-E)
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11. Multiply 3-digit by
1-digit numbers, 2-digit by 2-digit numbers, and divide 3-digit numbers
by 1-digit numbers, with and without remainders (N-6-E) (N-7-E)
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14. Solve real-life problems,
including those in which some information is not given (N-9-E)
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Algebra
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12. Use number sentences to
represent real-life problems involving addition and subtraction (A-1-E)
(A-2-E)
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16. Use number sentences to
represent real-life problems involving multiplication and division
(A-1-E) (N-4-E)
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15. Write number sentences or
formulas containing a variable to represent real-life problems (A-1-E)
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13. Find the missing number
in an equation involving addition or subtraction (e.g., # + 4 = 7, 8 -
# = 3) (A-2-E) (N-4-E)
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14. Use the symbols <,
>, and ¹ to express inequalities
(A-1-E)
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15. Use objects, pictures,
numbers, symbols, and words to represent multiplication and division
problem situations (A-1-E)
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17. Analyze and describe
situations where proportional trades or correspondences are required
(e.g., trade 2 pieces of candy for 3 pieces of gum, make equivalent
actions on pans to keep balance scale in equilibrium, plan for the
number of pieces of bread needed for x sandwiches) (A-1-E)
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18. Use letters as variables
in mathematical statements that represent real-life problems (e.g., 2 x n = 8)
(A-2-E)
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16. Write a related story
problem for a given algebraic sentence (A-1-E)
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17. Use manipulatives to
represent the distributive property of multiplication over addition to
explain multiplying numbers (A-1-E) (A-2-E)
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18. Identify and create
true/false and open/closed number sentences (A-2-E)
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19. Solve one-step equations
with whole number solutions (A-2-E) (N-4-E)
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Measurement
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14. Measure and appropriately
label measures of length and perimeter (i.e., inch, centimeter, foot),
capacity (i.e., cup, quart, liter), and weight/mass (i.e., pound,
kilogram) (M-1-E
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19. Measure length to the
nearest yard, meter, and half-inch (M-1-E)
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20. Measure length to the
nearest quarter-inch and mm (M-2-E) (M-1-E)
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20. Measure capacity using
pints and gallons (M-1-E)
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21. Describe the concept of
volume, and measure volume using cubic in. and cubic cm and capacity
using fl. oz. and ml (M-2-E) (M-3-E)
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21. Measure weight using
grams and ounces (M-1-E)
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22. Find the perimeter of a
geometric shape given the length of its sides (M-1-E)
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25. Use estimates and
measurements to calculate perimeter and area of rectangular objects
(including squares) in U.S. (including square feet)
and metric units (M-3-E)
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15. Read a thermometer in
degrees Fahrenheit and Celsius and interpret the temperature (M-1-E)
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16. Tell time to the nearest
5 minutes, and identify the time one hour before or after a given time
(M-1-E) (M-3-E)
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24. Find elapsed time
involving hours and minutes, without regrouping, and tell time to the
nearest minute (M-1-E) (M-5-E)
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23. Set up, solve, and
interpret elapsed time problems (M-2-E) (M-5-E)
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17. Select and use
appropriate tools and units to measure length, time, capacity, and
weight (e.g., scales for pounds and kilograms; rulers for inches and
centimeters; measuring containers for cup, quarts, and liters) (M-2-E)
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25. Select and use the
appropriate standard units of measure, abbreviations, and tools to
measure length and perimeter (i.e., in., cm, ft., yd., m), area (square
inch, square centimeter), capacity (i.e., cup, pint, quart, gallon,
liter), and weight/mass (i.e., oz., lb., g, kg, ton) (M-2-E)
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22. Select and use the
appropriate standard units of measure, abbreviations, and tools to
measure length and perimeter (i.e., in., cm, ft., yd., mile, m, km),
area (i.e., square inch, square foot, square centimeter), capacity
(i.e., fl. oz., cup, pt., qt., gal., l, ml), weight/mass (i.e., oz.,
lb., g, kg, ton), and volume (i.e., cubic cm, cubic in.) (M-2-E) (M-1-E)
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18. Use non-standard units to
cover a given region (M-2-E)
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19. Estimate length in
standard units (inch, foot, and centimeter) (M-3-E)
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28. Estimate length,
weight/mass, and capacity (M-3-E
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25. Use estimates and
measurements to calculate perimeter and area of rectangular objects
(including squares) in U.S. (including square feet)
and metric units (M-3-E)
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20. Compare units within the same
system (inch is shorter than a foot, minute is shorter than an hour,
day is shorter than a month, cup holds less than a quart) (M-3-E)
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26. Order a set of measures
within the same system (M-3-E)
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27. Use unit conversions
within the same system to solve real-life problems (e.g., 60 sec. = 1
min., 12 objects = 1 dozen, 12 in. = 1 ft., 100 cm = 1 m, 1 pt. = 2
cups) (M-4-E) (N-2-E) (M-5-E)
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23. Find the area in square
units of a given rectangle (including squares) drawn on a grid or by
covering the region with square tiles (M-1-E)
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26. Estimate the area of an
irregular shape drawn on a unit grid (M-3-E)
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27. Compare U.S. and metric measurements
using approximate reference points without using conversions (e.g., a
meter is longer than a yard) (M-3-E) (M-4-E)
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24. Recognize the attributes
to be measured in a real-life situation (M-2-E) (M-5-E)
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Geometry
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21. Compare and contrast
3-dimensional shapes (i.e., sphere, cube, cylinder, cone, prism,
pyramid) according to their attributes (e.g., number of faces, shape of
faces) (G-2-E)
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29. Classify and describe 2-
and 3-dimensional objects according to given attributes (triangle vs.
quadrilateral, parallelogram vs. prism) (G-2-E) (G-1-E) (G-4-E)
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28. Identify the top, bottom,
or side view of a given 3-dimensional object (G-1-E) (G-3-E)
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29. Identify, describe the
properties of, and draw circles and polygons (triangle, quadrilateral,
parallelogram, trapezoid, rectangle, square, rhombus, pentagon,
hexagon, octagon, and decagon) (G-2-E)
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22. Identify a reduction or
enlargement of a given shape (G-2-E)
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23. Identify congruent
3-dimensional solids in a variety of positions and orientations (G-3-E)
(G-4-E) (G-2-E)
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30. Apply concepts of
congruence, similarity, and symmetry in real-life situations (G-2-E
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24. Identify and draw
horizontal and vertical line segments (G-5-E)
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31. Draw or reconstruct
figures from visual memory or verbal descriptions (G-3-E)
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32. Recognize and execute
specified flips, turns, and slides of geometric figures using
manipulatives and correct terminology (including clockwise and counterclockwise)
(G-3-E)
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30. Make and test predictions
regarding transformations (i.e., slides, flips, and turns) of plane
geometric shapes (G-3-E)
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31. Identify, manipulate, and
predict the results of rotations of 90, 180, 270, and 360 degrees on a
given figure (G-3-E)
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33. Construct and draw
rectangles (including squares) with given dimensions (e.g., grid paper,
square tiles) (G-4-E)
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34. Fold a 2-dimensional net
into a 3-dimensional object (G-4-E) (G-1-E)
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35. Identify, give properties
of, and distinguish among points, lines, line segments, planes, rays,
and angles (G-5-E)
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36. Identify and draw
segments, rays, and lines that are perpendicular, parallel, and
intersecting (G-5-E)
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32. Draw, identify, and
classify angles that are acute, right, and obtuse (G-5-E) (G-1-E)
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37. Identify, describe, and
draw intersecting, horizontal, vertical, parallel, diagonal, and
perpendicular lines, rays, and right angles in the real world (G-5-E)
(G-6-E)
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38. Find the length of a path
(that does not include diagonals) between two points on a grid (G-6-E)
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33. Specify locations of
points in the first quadrant of coordinate systems and describe paths
on maps (G-6-E)
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Data Analysis, Probability, and Discrete
Math
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25. Collect and organize data
using observations, surveys, and experiments (D-1-E)
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26. Construct and read line
plots and tables (D-2-E)
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42. Match a data set to a
graph, table, or chart and vice versa (D-2-E)
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27. Interpret pictographs in
which each picture represents more than one object (D-2-E)
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43. Represent and solve
problems using data from a variety of sources (e.g., tables, graphs,
maps, advertisements) (D-3-E)
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34. Summarize information and
relationships revealed by patterns or trends in a graph, and use the
information to make predictions (D-1-E)
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36. Analyze, describe,
interpret, and construct various types of charts and graphs using
appropriate titles, axis labels, scales, and legends (D-2-E) (D-1-E)
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37. Determine which type of
graph best represents a given set of discrete data (D-2-E) (D-1-E)
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28. Generate questions that
can be answered by collecting and analyzing data (D-3-E)
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29. Solve logic problems
involving two sets by using elementary set logic (i.e., and, or, and
is/is not statements) (D-3-E)
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38. Solve problems involving
simple deductive reasoning (D-3-E)
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39. Identify categories and
sort objects based on qualitative (categorical) and quantitative
(numerical) characteristics (D-1-E)
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40. Read, describe, and
organize a two-circle Venn diagram (D-1-E) (D-2-E)
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41. Explain the word average
and use it appropriately in discussing what is “typical” of a
data set (D-1-E)
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35. Find and interpret the
meaning of mean, mode, and median of a small set of numbers (using
concrete objects) when the answer is a whole number (D-1-E)
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44. Discuss chance situations
in terms of certain/impossible and equally likely (D-5-E)
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45. Use manipulatives to
discuss the probability of an event (e.g., number cubes, spinners to
determine what is most likely or least likely) (D-5-E)
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41. Apply appropriate
probabilistic reasoning in real-life contexts using games and other
activities (e.g., examining fair and unfair situations) (D-5-E) (D-6-E)
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39. Use lists, tables, and
tree diagrams to generate and record all possible combinations for 2
sets of 3 or fewer objects (e.g., combinations of pants and shirts,
days and games) and for given experiments (D-3-E) (D-4-E)
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40. Determine the total
number of possible outcomes for a given experiment using lists, tables,
and tree diagrams (e.g., spinning a spinner, tossing 2 coins) (D-4-E)
(D-5-E)
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Patterns, Relations, and Functions
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30. Recognize, extend,
create, and explain patterns of addition and subtraction as represented
in charts and tables and in varied forms of skip-counting (P-1-E)
(P-2-E)
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47. Find patterns to complete
tables, state the rule governing the shift between successive terms,
and continue the pattern (including growing patterns) (P-1-E) (P-2-E)
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43. Identify missing elements
in a number pattern (P-1-E)
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31. Recognize, extend,
create, and explain patterns that involve simple rotations or size
changes with geometric objects (P-1-E) (P-2-E)
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32. Recognize and apply
patterns in problem-solving in other content areas and real-life
situations (P-3-E) (N-9-E)
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46. Identify and model even
and odd numbers with objects, pictures, and words (P-1-E)
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42. Find and describe
patterns resulting from operations involving even and odd numbers (such
as even + even = even) (P-1-E)
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44. Represent the
relationship in an input-output situation using a simple equation,
graph, table, or word description (P-2-E)
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