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4.1
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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4.1.1
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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4.1.1.a
Using concrete materials and visual representations, compare, order, and represent decimal fractions of tenths, hundreds, and commonly-used fractions with unlike denominators such as: halves, fourths, and tenths (for example, may use base-ten blocks, pictures, fraction strips, fraction circles).
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4.1.1.b
Recognize different combinations of currency and coins for a set amount up to $10.00.
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4.1.2
Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.
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4.1.2.a
Read, write, and order numerals and number words from 0 - 99,999.
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4.1.2.b
Identify place value through 99,999.
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4.1.2.c
Generate equivalent representations for whole numbers up to 99,999 (for example; 87459 = 7,000 + 400 + 50 + 9 or 36 = 30 + 6 or 2 tens +16 ones).
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4.1.3
Use numbers to count, to measure, to label, and to indicate location.
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4.1.3.a
Using a number line, a hundreds chart or other number chart, locate, label, or count from any number by 2s, 3s, 5s, 10s, or 100s.
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4.1.3.b
Locate and label halves, multiples of fourths, and thirds, between whole numbers on a number line.
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4.1.4
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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4.1.4.a
Show division of whole numbers is not commutative (1-digit into 2-digits).
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4.1.4.b
Use number properties with any of the four basic operations (commutative, associative, properties of zero and one).
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4.1.5
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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4.1.5.a
Use estimation strategies to determine the reasonableness of solutions involving the four basic operations.
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4.1.5.b
Use estimation to round to the nearest dollar in context and determine reasonableness.
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4.2
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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4.2.1
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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4.2.1.a
Reproduce, extend, create or describe patterns, using pictures, geometric shapes or numbers. Objectives
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4.2.1.b
Determine the missing element in a pattern using pictures, geometric shapes, or numbers.
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4.2.2
Describe patterns and other relationships using tables, graphs, and open sentences.
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4.2.2.a
Display numbers in tables or graphs, to show patterns.
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4.2.2.b
Describe patterns given in tables and graphs.
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4.2.3
Recognize when a pattern exists and use that information to solve a problem.
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4.2.3.a
Identify a rule using addition, subtraction, or multiplication and solve a problem using the rule (for example, function boxes, input/output boxes, T charts).
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4.2.4
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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4.2.4.a
Using whole numbers, determine how the change in one quantity affects the change in another by addition, subtraction, or multiplication (for example, Maria is making ladybugs. For 1 ladybug she needs 6 black dots, for 2 ladybugs she needs 12 dots. How many black dots will she need for 4 ladybugs?).
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4.3
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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4.3.1
Construct, read, and interpret displays of data including tables, charts, pictographs, and bar graphs.
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4.3.1.a
Organize, construct, read and interpret a table, line plot, bar graph and/or pictograph from given data.
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4.3.2
Interpret data using the concepts of largest, smallest, most often, and middle.
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4.3.2.a
Draw conclusions from a given data display.
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4.3.2.b
Find the median, mode, the smallest and the largest element in a set of data.
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4.3.3
Generate, analyze, and make predictions based on data obtained from surveys and chance devices.
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4.3.3.a
Predict the outcomes of flipping a coin, spinning a spinner with four congruent sectors and/or a number cube.
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4.3.3.b
Determine and support which outcomes are most likely, least likely or equally likely when using a chance device.
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4.3.4
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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4.3.4.a
Given pictures, describe all possible combinations of matching the elements of two sets.
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4.4
Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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4.4.1
Recognize shapes and their relationships (for example, symmetry, congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).
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4.4.1.a
Identify and give examples of congruency.
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4.4.1.b
Identify one line of symmetry for a given shape.
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4.4.2
Identify, describe, draw, compare, classify, and build physical models of geometric figures.
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4.4.2.a
Identify, classify, and compare 2-dimensional shapes and use vocabulary to describe the attributes (for example, number of sides, vertices, angles, parallel sides).
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4.4.2.b
Identify parallel, and intersecting lines and right angles.
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4.4.2.c
Identify 2- and 3-dimensional figures; such as, trapezoids, parallelograms, rhombuses and other polygons.
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4.4.2.d
Recognize common attributes of squares and rectangles.
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4.4.3
Relate geometric ideas to measurement and number sense.
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4.4.3.a
Solve for perimeter and area of rectangles and squares using a drawing on a grid.
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4.4.4
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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4.4.4.a
Locate objects on a coordinate grid (1st quadrant only) and label ordered pairs.
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4.4.5
Recognize geometry in their world (for example, in art and in nature).
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4.5
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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4.5.1
Know, use, describe and estimate measure of length, perimeter, capacity, weight, time, and temperature.
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4.5.1.a
Tell time in hours and minutes, including a.m. and p.m. using both analog and digital displays.
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4.5.1.b
Choose the appropriate tool to measure familiar objects in situations that contain length, weight, capacity, time and temperature.
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4.5.2
Compare and order objects according to measurable attributes (for example, longest to shortest, lightest to heaviest).
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4.5.2.a
Compare objects according to measurable attributes of length, area, volume, capacity, weight, and/or temperature in US customary and/or metric units.
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4.5.3
Demonstrate the process of measuring and explaining the concepts related to units of measurement.
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4.5.3.a
Measure and determine perimeter of polygons to the nearest half inch or centimeter.
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4.5.3.b
Determine the areas of squares and rectangles on a grid.
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4.5.4
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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4.5.4.a
Relate units of measurement of length, area, volume, capacity, weight, and/or temperature in US customary and/or metric units to every day objects or situations (for example, yard to a stride, liter to a quart).
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4.5.5
Select and use appropriate standard and non-standard units of measurement in problem-solving situations.
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4.5.5.a
Choose appropriate units of measure for length, area, volume, capacity, weight, temperature, and/or time to solve problems.
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4.6
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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4.6.1
Demonstrate conceptual meanings for the four basic arithmetic operations of addition, subtraction, multiplication, and division.
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4.6.1.a
Demonstrate the conceptual meaning (using pictures, words, diagrams, or numbers) of addition, subtraction, multiplication, and division of whole numbers.
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4.6.2
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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4.6.2.a
Using pictures, demonstrate addition and subtraction of commonly used fractions with the same denominators where sums/differences are equal or less than a whole (1/2, 1/3, 1/4, 1/8, 1/10).
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4.6.2.b
Using money notation, add and subtract decimals in which sums and differences should not exceed $100.00.
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4.6.3
Demonstrate understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.
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4.6.3.a
Demonstrate understanding of basic multiplication and division facts.
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4.6.3.b
Continue to demonstrate proficiency of basic addition and subtraction facts.
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4.6.3.c
Use a multiplication facts table to locate all the factors for a particular product (for example, for a product of six: 1, 6, 2, and 3 are all factors).
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4.6.4
Construct, use, and explain procedures to compute and estimate with whole numbers.
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4.6.4.a
Use reasonable estimation techniques before performing basic math operations (for example, front-end estimation, estimation by rounding, friendly numbers, compatible numbers, flexible rounding, clustering).
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4.6.4.b
Using paper and pencil, demonstrate the four basic operations of whole numbers including: addition; subtraction; multiplication of 2 or 3-digit numbers by a 1-digit number; division of 2-digit number by a 1-digit divisor.
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4.6.5
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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4.6.5.a
Given a real-world problem-solving situation, use an appropriate operation (any four basic math operation) and an appropriate method (paper-pencil, mental math, estimation, calculator, computer) to solve the problem.
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4.6.5.b
Determine from a real-world problem whether an estimated or exact sum, difference, product, or quotient is acceptable.
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