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3.1
Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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3.1.1
Demonstrate meanings for whole numbers, and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and representing equivalent forms of the same number through the use of physical models, drawings, calculators, and computers.
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3.1.1.a
Identify whether a given number is odd or even.
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3.1.1.b
Identify the fractional part of a drawing or a set (restricted to halves, thirds, fourths).
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3.1.1.c
Using concrete materials or pictures identify different combinations of coins up to $0.99.
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3.1.2
Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.
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3.1.2.a
Read, write, and order numerals 0 - 9,999.
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3.1.2.b
Read the number words for selected numbers from zero to nine thousand, nine hundred ninety-nine.
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3.1.2.c
Identify place value through ten-thousands (for example, in 86,243, '6' is in the thousands place.
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3.1.2.d
Generate equivalent representations for the same number up to a 4-digit number (for example; 25=20+5 or 10+15 or 2 tens and 5 ones).
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3.1.2.e
Compare whole numbers as greater than, less than, or equal to one another using words or symbols.
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3.1.3
Use numbers to count, to measure, to label, and to indicate location.
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3.1.3.a
Locate, label, or count forward from any even number by 2's and from any number by 10's and 100's up to 999.
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3.1.3.b
Locate and label 1/2s between whole numbers on the number line.
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3.1.4
Develop, test, and explain conjectures about properties of whole numbers, and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
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3.1.4.a
Use the multiplication properties of zero and one with whole numbers.
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3.1.4.b
Solve addition and subtraction problems using commutative and associative properties (for example, 2+3+6=6+3+2; the words commutative and associative will not be used in test items).
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3.1.5
Use number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers, and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
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3.1.5.a
Use estimation strategies to determine the reasonableness of solutions to problems.
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3.2
Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
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3.2.1
Reproduce, extend, create, and describe patterns and sequences using a variety of materials (for example, beans, toothpicks, pattern blocks, calculators, unifix cubes, colored tiles).
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3.2.1.a
Reproduce, extend, and create patterns, using pictures or geometric shapes.
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3.2.1.b
Use a pattern to find missing elements (for example, multiples of 2, 3, 4, 5, 10).
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3.2.2
Describe patterns and other relationships using tables, graphs, and open sentences.
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3.2.3
Recognize when a pattern exists and use that information to solve a problem.
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3.2.3.a
Identify a rule using addition or subtraction patterns and solve a new problem using the rule.
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3.2.3.b
Given numbers in a table, extend the table.
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3.2.4
Observe and explain how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the number of wheels).
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3.2.4.a
Using whole numbers, determine how the change in one quantity affects the change in the other by addition or subtraction (for example, one bicycle has 2 wheels, 2 bicycles have 4 wheels, and 3 bicycles have 6 wheels. How many wheels do 4 bicycles have? The solution could be presented in chart or picture form).
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3.3
Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.
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3.3.1
Construct, read, and interpret displays of data including tables, charts, pictographs, and bar graphs.
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3.3.1.a
Organize and display data using tallies, bar graphs, pictographs, or tables.
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3.3.2
Interpret data using the concepts of largest, smallest, most often, and middle.
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3.3.2.a
Determine the mode from a given a set of numbers, the mode is the number that occurs most
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3.3.2.b
Use various displays of data, interpret and draw conclusions.
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3.3.3
Generate, analyze, and make predictions based on data obtained from surveys and chance devices.
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3.3.3.a
Determine which outcomes are the most likely, least likely, or equally likely when using a chance device (for example, a spinner).
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3.3.4
Solve problems using various strategies for making combinations (for example, determining the number of different outfits that can be made using two blouses and three skirts).
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3.3.4.a
Given pictures, determine all the possible combinations of matching a set containing two elements with a set containing three elements.
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3.4
Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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3.4.1
Recognize shapes and their relationships (for example, symmetry, congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).
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3.4.1.a
Identify figures which are congruent.
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3.4.1.b
Identify a line of symmetry for regular polygons and other familiar objects.
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3.4.1.c
Create a figure with at least one line of symmetry.
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3.4.2
Identify, describe, draw, compare, classify, and build physical models of geometric figures.
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3.4.2.a
Identify the characteristics of two-dimensional figures (for example, number of sides or vertices, contains a right angle, contains parallel sides).
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3.4.2.b
Identify points, lines, and line segments.
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3.4.2.c
Identify three dimensional figures (for example, cubes, spheres, cylinders, cones and pyramids).
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3.4.2.d
Identify right angles.
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3.4.2.e
Create and identify the results of combining or subdividing given geometric shapes (for example, pattern blocks, tangrams).
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3.4.3
Relate geometric ideas to measurement and number sense.
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3.4.3.a
Find the perimeter of a polygon.
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3.4.4
Solve problems using geometric relationships and spatial reasoning (for example, using rectangular coordinates to locate objects, constructing models of three-dimensional objects).
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3.4.5
Recognize geometry in their world (for example, in art and in nature).
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3.5
Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
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3.5.1
Know, use, describe and estimate measure of length, perimeter, capacity, weight, time, and temperature.
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3.5.1.a
Use an analog and digital clock, tell time to the nearest 5 minutes.
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3.5.1.b
Read and interpret pictorial representations of measurements of length, weight, temperature, and capacity.
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3.5.1.c
Choose the appropriate tool to measure familiar objects/situations containing length, weight, temperature or time.
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3.5.2
Compare and order objects according to measurable attributes (for example, longest to shortest, lightest to heaviest).
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3.5.2.a
Compare objects according to the measurable attributes of length, capacity, weight, or temperature.
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3.5.3
Demonstrate the process of measuring and explaining the concepts related to units of measurement.
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3.5.3.a
Measure the length of objects including the sides of rectangles and squares to the nearest inch and centimeter.
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3.5.4
Use the approximate measures of familiar objects (for example, the width of your finger, the temperature of a room, the weight of a gallon of milk) to develop a sense of measurement.
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3.5.4.a
Approximate the measurement of familiar objects using standards units (for example, a paper clip is about one inch).
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3.5.5
Select and use appropriate standard and non-standard units of measurement in problem-solving situations.
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3.6
Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.
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3.6.1
Demonstrate conceptual meanings for the four basic arithmetic operations of addition, subtraction, multiplication, and division.
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3.6.1.a
Using pictures, diagrams, numbers or words, demonstrate addition and subtraction of whole numbers with 2- digit numbers.
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3.6.2
Add and subtract commonly-used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75).
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3.6.2.a
Using pictures, demonstrate addition and subtraction of proper fractions with common denominators of four or less
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3.6.2.b
Using money notation, add and subtract commonly used decimals in which sums and differences should not exceed $10.00.
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3.6.3
Demonstrate understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.
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3.6.3.a
Demonstrate understanding of basic multiplication facts of 1's, 2's, 3's, 5's, 10's.
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3.6.3.b
Demonstrate proficiency with basic addition and subtraction facts.
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3.6.4
Construct, use, and explain procedures to compute and estimate with whole numbers.
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3.6.4.a
Use estimation strategies with whole numbers prior to performing the operations of addition and subtraction (for example, front-end estimation, estimation by rounding, friendly numbers, flexible rounding, clustering).
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3.6.4.b
Demonstrate three basic operations of whole numbers (for example, addition and subtraction of three digits, and multiplication of multiples of ten by 1, 2, 3, 5).
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3.6.5
Select and use appropriate methods for computing with whole numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods.
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3.6.5.a
Given a real world problem-solving situation, use addition, subtraction, or multiplication to solve the problem.
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3.6.5.b
Determine from real-world problems, whether an estimated or exact sum, difference, or product is acceptable.
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