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3.1
Students will understand the base-ten numeration system, place value concepts, simple fractions and perform operations with whole numbers.
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3.1.1
Represent whole numbers up to 10,000, comprehend place value concepts, and identify relationships among whole numbers using base-ten models and symbolic notation.
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3.1.1.a
Read, write, and represent whole numbers using standard and expanded form.
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3.1.1.b
Demonstrate multiple ways to represent numbers using models and symbolic representations (e.g., fifty is the same as two groups of 25, the number of pennies in five dimes, or 75 - 25).
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3.1.1.c
Identify the place and the value of a given digit in a four-digit numeral and round numbers to the nearest ten, hundred, and thousand.
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3.1.1.d
Order and compare whole numbers on a number line and use the symbols <, >, ≠, and = when comparing whole numbers.
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3.1.1.e
Identify factors and multiples of whole numbers.
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3.1.2
Use fractions to describe and compare parts of the whole.
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3.1.2.a
Identify the denominator of a fraction as the number of equal parts of the unit whole and the numerator of a fraction as the number of equal parts being considered.
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3.1.2.b
Define regions and sets of objects as a whole and divide the whole into equal parts using a variety of objects, models, and illustrations.
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3.1.2.c
Name and write a fraction to represent a portion of a unit whole for halves, thirds, fourths, sixths, and eighths.
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3.1.2.d
Place fractions on the number line and compare and order fractions using models, pictures, the number line, and symbols.
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3.1.2.e
Find equivalent fractions using concrete and pictorial representations.
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3.1.3
Model problems involving addition, subtraction, multiplication, and division.
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3.1.3.a
Demonstrate the meaning of multiplication and division of whole numbers through the use of a variety of representations (e.g., equal-sized groups, arrays, area models, and equal jumps on a number line for multiplication, partitioning and sharing for division).
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3.1.3.b
Use a variety of strategies and tools, such as repeated addition or subtraction, equal jumps on the number line, and counters arranged in arrays to model multiplication and division problems.
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3.1.3.c
Demonstrate, using objects, that multiplication and division by the same number are inverse operations (e.g., 3 x ? = 12 is the same as 12 ÷ 3 = ? and ? = 4).
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3.1.3.d
Demonstrate the effect of place value when multiplying whole numbers by 10.
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3.1.3.e
Write a story problem that relates to a given addition, subtraction, or multiplication equation, and write a number sentence to solve a problem related to the students' environment.
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3.1.4
Compute and solve problems involving addition and subtraction of 3- and 4- digit numbers and basic facts of multiplication and division.
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3.1.4.a
Use a variety of methods to facilitate computation (e.g., estimation, mental math strategies, paper and pencil).
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3.1.4.b
Find the sum or difference of numbers, including monetary amounts, using models and strategies such as expanded form, compensation, partial sums, and the standard algorithm.
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3.1.4.c
Compute basic multiplication facts (0-10) and related division facts using a variety of strategies based on properties of addition and multiplication (i.e., commutative, associative, identity, zero, and the distributive properties).
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3.2
Students will use patterns, symbols, operations, and properties of addition and multiplication to represent and describe simple number relationships.
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3.2.1
Create, represent, and analyze growing patterns.
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3.2.1.a
Create and extend growing patterns using objects, numbers, and tables.
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3.2.1.b
Describe how patterns are extended using manipulatives, pictures, and numerical representations.
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3.2.2
Recognize, represent, and simplify simple number relationships using symbols, operations, and properties.
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3.2.2.a
Represent numerical relationships as expressions, equations, and inequalities.
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3.2.2.b
Solve equations involving equivalent expressions (e.g., 6 + 4 = Δ + 7).
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3.2.2.c
Use the >, <, and = symbols to compare two expressions involving addition and subtraction (e.g., 4 + 6 __ 3 + 2; 3 + 5 __ 16 - 9).
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3.2.2.d
Recognize and use the commutative, associative, distributive, and identity properties of addition and multiplication, and the zero property of multiplication.
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3.3
Students will describe and analyze attributes of two-dimensional shapes.
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3.3.1
Describe and compare attributes of two-dimensional shapes.
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3.3.1.a
Identify, describe, and classify polygons (e.g., pentagons, hexagons, octagons).
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3.3.1.b
Identify attributes for classifying triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).
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3.3.1.c
Identify attributes for classifying quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).
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3.3.1.d
Identify right angles in geometric figures, or in appropriate objects, and determine whether other angles are greater or less than a right angle.
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3.3.2
Demonstrate the meaning of congruence through applying transformations.
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3.3.2.a
Demonstrate the effect of reflection, translation, or rotation using objects.
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3.3.2.b
Determine whether two polygons are congruent by reflecting, translating, or rotating one polygon to physically fit on top of the other.
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3.4
Students will select and use appropriate units and measurement tools to solve problems.
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3.4.1
Select and use appropriate tools and units to estimate and measure length, weight, capacity, time, and perimeter of two-dimensional figures.
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3.4.1.a
Describe the part-whole relationships (e.g., 3 feet in a yard, a foot is 1/3 of a yard) between metric units of length (i.e., centimeter, meter), and among customary units of length (i.e., inch, foot, yard), capacity (i.e., cup, quart), and weight (i.e., pound, ounce).
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3.4.1.b
Measure the length of objects to the nearest centimeter, meter, half- and quarter-inch, foot, and yard.
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3.4.1.c
Measure capacity using cups and quarts, and measure weight using pounds and ounces.
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3.4.1.d
Identify the number of minutes in an hour, the number of hours in a day, the number of days in a year, and the number of weeks in a year.
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3.4.1.e
Describe perimeter as a measurable attribute of two-dimensional figures, and estimate and measure perimeter with metric and customary units.
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3.4.2
Solve problems involving measurements.
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3.4.2.a
Determine simple equivalence's of measurements (e.g., 30 inches = 2 feet and 6 inches; 6 cups = 1½ quarts; 90 min. = 1 hr. 30 min.).
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3.4.2.b
Compare given objects according to measurable attributes (i.e., length, weight, capacity).
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3.4.2.c
Solve problems involving perimeter.
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3.4.2.d
Determine elapsed time in hours (e.g., 7:00 a.m. to 2:00 p.m.).
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3.5
Students will collect and organize data to make predictions and identify basic concepts of probability.
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3.5.1
Collect, organize, and display data to make predictions.
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3.5.1.a
Collect, read, represent, and interpret data using tables, graphs, and charts, including keys (e.g., pictographs, bar graphs, frequency tables, line plots).
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3.5.1.b
Make predictions based on a data display.
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3.5.2
Identify basic concepts of probability.
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3.5.2.a
Describe the results of events using the terms "certain," "likely," "unlikely," and "impossible."
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3.5.2.b
Conduct simple probability experiments, record possible outcomes systematically, and display results in an organized way (e.g., chart, graph).
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3.5.2.c
Use results of simple probability experiments to describe the likelihood of a specific outcome in the future.
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