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4.NO
Number, operation, and quantitative reasoning.
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4.111.16.4.1
The student uses place value to represent whole numbers and decimals.
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4.111.16.4.1.A
use place value to read, write, compare, and order whole numbers through 999,999,999; and
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4.111.16.4.1.B
use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete objects and pictorial models.
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4.111.16.4.2
The student describes and compares fractional parts of whole objects or sets of objects.
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4.111.16.4.2.A
use concrete objects and pictorial models to generate equivalent fractions;
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4.111.16.4.2.B
model fraction quantities greater than one using concrete objects and pictorial models;
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4.111.16.4.2.C
compare and order fractions using concrete objects and pictorial models; and
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4.111.16.4.2.D
relate decimals to fractions that name tenths and hundredths using concrete objects and pictorial models.
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4.111.16.4.3
The student adds and subtracts to solve meaningful problems involving whole numbers and decimals.
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4.111.16.4.3.A
use addition and subtraction to solve problems involving whole numbers; and
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4.111.16.4.3.B
add and subtract decimals to the hundredths place using concrete objects and pictorial models.
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4.111.16.4.4
The student multiplies and divides to solve meaningful problems involving whole numbers.
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4.111.16.4.4.A
model factors and products using arrays and area models;
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4.111.16.4.4.B
represent multiplication and division situations in picture, word, and number form;
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4.111.16.4.4.C
recall and apply multiplication facts through 12 x 12;
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4.111.16.4.4.D
use multiplication to solve problems (no more than two digits times two digits without technology); and
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4.111.16.4.4.E
use division to solve problems (no more than one-digit divisors and three-digit dividends without technology).
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4.111.16.4.5
The student estimates to determine reasonable results.
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4.111.16.4.5.A
round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations; and
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4.111.16.4.5.B
use strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems.
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4.PAT
Patterns, relationships, and algebraic thinking.
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4.111.16.4.6
The student uses patterns in multiplication and division.
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4.111.16.4.6.A
use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division number sentences (fact families) such as 9 x 9 = 81 and 81 รท 9 = 9); and
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4.111.16.4.6.B
use patterns to multiply by 10 and 100.
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4.111.16.4.7
The student uses organizational structures to analyze and describe patterns and relationships.
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4.111.16.4.7.A
The student is expected to describe the relationship between two sets of related data such as ordered pairs in a table.
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4.GEO
Geometry and spatial reasoning.
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4.111.16.4.8
The student identifies and describes attributes of geometric figures using formal geometric language.
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4.111.16.4.8.A
identify and describe right, acute, and obtuse angles;
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4.111.16.4.8.B
identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models; and
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4.111.16.4.8.C
use essential attributes to define two- and three-dimensional geometric figures.
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4.111.16.4.9
The student connects transformations to congruence and symmetry.
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4.111.16.4.9.A
demonstrate translations, reflections, and rotations using concrete models;
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4.111.16.4.9.B
use translations, reflections, and rotations to verify that two shapes are congruent; and
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4.111.16.4.9.C
use reflections to verify that a shape has symmetry.
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4.111.16.4.10
The student recognizes the connection between numbers and their properties and points on a line.
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4.111.16.4.10.A
The student is expected to locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths.
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4.MEA
Measurement.
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4.111.16.4.11
The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass.
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4.111.16.4.11.A
estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary;
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4.111.16.4.11.B
perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system;
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4.111.16.4.11.C
use concrete models of standard cubic units to measure volume;
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4.111.16.4.11.D
estimate volume in cubic units; and
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4.111.16.4.11.E
explain the difference between weight and mass.
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4.111.16.4.12
The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius).
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4.111.16.4.12.A
use a thermometer to measure temperature and changes in temperature; and
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4.111.16.4.12.B
use tools such as a clock with gears or a stopwatch to solve problems involving elapsed time.
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4.PROB
Probability and statistics.
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4.111.16.4.13
The student solves problems by collecting, organizing, displaying, and interpreting sets of data.
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4.111.16.4.13.A
use concrete objects or pictures to make generalizations about determining all possible combinations of a given set of data or of objects in a problem situation; and
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4.111.16.4.13.B
interpret bar graphs.
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4.PROC
Underlying processes and mathematical tools.
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4.111.16.4.14
The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.
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4.111.16.4.14.A
identify the mathematics in everyday situations;
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Functions: Function tables (Fourth grade - H.2)
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Data, charts, and graphs: Line graphs (Fourth grade - J.2)
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Data, charts, and graphs: Bar graphs (Fourth grade - J.3)
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Data, charts, and graphs: Frequency charts (Fourth grade - J.4)
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Data, charts, and graphs: Stem-and-leaf plots (Fourth grade - J.5)
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Data, charts, and graphs: Circle graphs (Fourth grade - J.6)
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Logical reasoning: Find the order (Fourth grade - K.3)
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Money: Round money amounts (Fourth grade - M.2)
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Money: Add and subtract money amounts (Fourth grade - M.3)
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Money: Making change (Fourth grade - M.5)
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Money: Price lists with addition and subtraction (Fourth grade - M.6)
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Measurement: Compare customary units by multiplying (Fourth grade - N.3)
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Time: Time zones (Fourth grade - O.4)
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Time: Transportation schedules (Fourth grade - O.7)
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Add and subtract fractions: Recipes (Fourth grade - R.14)
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4.111.16.4.14.B
solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;
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4.111.16.4.14.C
select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and
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4.111.16.4.14.D
use tools such as real objects, manipulatives, and technology to solve problems.
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4.111.16.4.15
The student communicates about Grade 4 mathematics using informal language.
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4.111.16.4.15.A
explain and record observations using objects, words, pictures, numbers, and technology; and
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4.111.16.4.15.B
relate informal language to mathematical language and symbols.
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4.111.16.4.16
The student uses logical reasoning.
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4.111.16.4.16.A
make generalizations from patterns or sets of examples and nonexamples; and
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4.111.16.4.16.B
justify why an answer is reasonable and explain the solution process.
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