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5.1
Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.
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5.1.1
Represent whole numbers and decimals from thousandths to one billion, fractions, percents, and integers.
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5.1.1.a
Read and write numbers in standard and expanded form.
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5.1.1.b
Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and symbolic representations (e.g., 108 = 2 x 50 + 8; 108 = 10² + 8; 90% = 90 out of 100 squares on a hundred chart).
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5.1.1.c
Identify, read, and locate fractions, mixed numbers, decimals, and integers on the number line.
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5.1.1.d
Represent repeated factors using exponents.
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5.1.1.e
Describe situations where integers could be used in the students' environment.
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5.1.2
Explain relationships and equivalencies among integers, fractions, decimals, and percents.
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5.1.2.a
Compare fractions by finding a common denominator.
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5.1.2.b
Order integers, fractions (including mixed numbers), and decimals using a variety of methods, including the number line.
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5.1.2.c
Rewrite mixed numbers and improper fractions from one form to the other and represent each using regions, sets of objects, or line segments.
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5.1.2.d
Represent commonly used fractions as decimals and percents in a variety of ways (e.g., models, fraction strips, pictures, calculators, algorithms).
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5.1.2.e
Model and calculate equivalent forms of a fraction (including simplest form).
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5.1.2.f
Rename whole numbers as fractions with different denominators (e.g., 5 = 5/1, 3 = 6/2, 1 = 7/7).
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5.1.3
Use number theory concepts to develop and use divisibility tests; classify whole numbers to 50 as prime, composite, or neither; and find common multiples and factors.
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5.1.3.a
Identify patterns with skip counting and multiples to develop and use divisibility tests for determining whether a whole number is divisible by 2, 3, 5, 6, 9, and 10.
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5.1.3.b
Use strategies for classifying whole numbers to 50 as prime, composite, or neither.
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5.1.3.c
Rewrite a composite number between 2 and 50 as a product of only prime numbers.
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5.1.3.d
Find common multiples and factors and apply to adding and subtracting fractions.
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5.1.4
Model and illustrate meanings of multiplication and division.
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5.1.4.a
Represent division-with-remainder using whole numbers, decimals, or fractions.
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5.1.4.b
Describe the effect of place value when multiplying and dividing whole numbers and decimals by 10, 100, and 1,000.
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5.1.4.c
Model multiplication of fractions and decimals (e.g., tenths multiplied by tenths, a whole number multiplied by tenths, or a whole number with tenths multiplied by tenths) in a variety of ways (e.g., manipulatives, number line and area models, patterns).
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5.1.5
Solve problems involving one or two operations.
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5.1.5.a
Determine when it is appropriate to use estimation, mental math strategies, paper and pencil, and algorithms.
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5.1.5.b
Make reasonable estimations of fraction and decimal sums, differences, and products, including knowing whether results obtained using a calculator are reasonable.
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5.1.5.c
Write number sentences that can be used to solve a two-step problem.
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5.1.5.d
Interpret division-with-remainder problems as they apply to the environment (e.g., If there are 53 people, how many vans are needed if each van holds 8 people?).
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5.1.6
Demonstrate proficiency with multiplication and division of whole numbers and compute problems involving addition, subtraction, and multiplication of decimals and fractions.
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5.1.6.a
Multiply multi-digit whole numbers by a two-digit whole number with fluency, using efficient procedures.
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5.1.6.b
Divide multi-digit dividends by a one-digit divisor with fluency, using efficient procedures.
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5.1.6.c
Add and subtract decimals with fluency, using efficient procedures.
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5.1.6.d
Add and subtract fractions with fluency.
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5.1.6.e
Multiply fractions.
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5.2
Students will use patterns and relations to represent and analyze mathematical problems and number relationships using algebraic symbols.
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5.2.1
Identify, analyze and determine a rule for predicting and extending numerical patterns involving operations whole numbers, decimals, and fractions.
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5.2.1.a
Analyze and make predictions about numeric patterns, including decimals and fractions.
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5.2.1.b
Determine a rule for the pattern using organized lists, tables, objects, and variables.
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5.2.2
Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.
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5.2.2.a
Use properties and the order of operations involving addition, subtraction, multiplication, division, and the use of parentheses to compute with whole numbers, decimals, and fractions.
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5.2.2.b
Use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities with whole number solutions (e.g., 6x = 54; x + 3 = 7).
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5.3
Students will use spatial reasoning to recognize, describe, and analyze geometric shapes and principles.
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5.3.1
Describe relationships between two- and three-dimensional shapes and analyze attributes and properties of geometric shapes.
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5.3.1.a
Draw, label, and describe line segments, rays, lines, parallel lines, and perpendicular lines.
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5.3.1.b
Draw, label, and define an angle as two rays sharing a common endpoint (vertex).
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5.3.1.c
Classify triangles and quadrilaterals and analyze the relationships among the shapes in each classification (e.g., a square is a rectangle).
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5.3.1.d
Relate pyramids and right prisms to the two-dimensional shapes (nets) from which they were created.
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5.3.1.e
Identify properties and attributes of solids (i.e., right prisms, pyramids, cylinders, cones) and describe them by the number of edges, faces, and vertices as well as the types of faces.
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5.3.2
Specify locations in a coordinate plane.
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5.3.2.a
Locate points defined by ordered pairs of integers.
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5.3.2.b
Write an ordered pair for a point in a coordinate plane with integer coordinates.
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5.3.2.c
Specify possible paths between locations on a coordinate plane and compare distances of the various paths.
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5.4
Students will determine area of polygons and surface area and volume of three-dimensional shapes.
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5.4.1
Determine the area of polygons and apply to real-world problems.
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5.4.1.a
Determine the area of a trapezoid by the composition and decomposition of rectangles, triangles, and parallelograms.
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5.4.1.b
Determine the area of irregular and regular polygons by the composition and decomposition of rectangles, triangles, and parallelograms.
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5.4.1.c
Compare areas of polygons using different units of measure within the same measurement system (e.g., square feet, square yards).
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5.4.2
Recognize, describe, and determine surface area and volume of three-dimensional shapes.
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5.4.2.a
Quantify volume by finding the total number of same-sized units of volume needed to fill the space without gaps or overlaps.
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5.4.2.b
Recognize that a cube having a 1 unit edge is the standard unit for measuring volume expressed as a cubic unit.
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5.4.2.c
Derive and use the formula to determine the volume of a right prism with a triangular or rectangular base.
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5.4.2.d
Relate the formulas for the areas of triangles, rectangles, or parallelograms to the surface area of a right prism.
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5.4.2.e
Derive and use the formula to determine the surface area of a right prism and express surface area in square units.
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5.5
Students will construct, analyze, and construct reasonable conclusions from data and apply basic concepts of probability.
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5.5.1
Formulate and answer questions using statistical methods to compare data, and propose and justify inferences based on data.
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5.5.1.a
Construct, analyze, and display data using an appropriate format (e.g., line plots, bar graphs, line graphs).
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Problem solving: Use Venn diagrams to solve problems (Fifth grade - J.5)
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Data, charts, and graphs: Read a table (Fifth grade - S.1)
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Data, charts, and graphs: Interpret line graphs (Fifth grade - S.2)
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Data, charts, and graphs: Interpret bar graphs (Fifth grade - S.4)
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Data, charts, and graphs: Interpret pictographs (Fifth grade - S.6)
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Data, charts, and graphs: Interpret histograms (Fifth grade - S.8)
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Data, charts, and graphs: Frequency charts (Fifth grade - S.12)
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Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - S.13)
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Data, charts, and graphs: Circle graphs (Fifth grade - S.14)
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5.5.1.b
Recognize the differences in representing categorical and numerical data.
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5.5.1.c
Identify minimum and maximum values for a set of data.
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5.5.1.d
Identify and calculate the mean, median, mode, and range.
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5.5.2
Apply basic concepts of probability.
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5.5.2.a
Describe the results of experiments involving random outcomes using a variety of notations (e.g., 4 out of 9, 4/9).
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5.5.2.b
Recognize that probability is always a value between 0 and 1 (inclusively).
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5.5.2.c
Express the likelihood of an outcome in a simple experiment as a value between 0 and 1 (inclusively).
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