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5.M5N
Number and Operations
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5.M5N1
Students will further develop their understanding of whole numbers.
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5.M5N1.a
Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).
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5.M5N1.b
Find multiples and factors.
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5.M5N1.c
Analyze and use divisibility rules.
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5.M5N2
Students will further develop their understanding of decimal fractions as part of the base-ten number system.
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5.M5N2.a
Understand place value.
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5.M5N2.b
Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, and 0.01.
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5.M5N3
Students will further develop their understanding of the meaning of multiplication and division with decimal fractions and use them.
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5.M5N3.a
Model multiplication and division of decimal fractions by another decimal fraction.
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5.M5N3.b
Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimal fractions.
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5.M5N3.c
Multiply and divide with decimal fractions including decimal fractions less than one and greater than one.
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5.M5N3.d
Understand the relationships and rules for multiplication and division of whole numbers also apply to decimal fractions.
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5.M5N4
Students will continue to develop their understanding of the meaning of common fractions and compute with them.
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5.M5N4.a
Understand division of whole numbers can be represented as a fraction (a/b = a ÷ b).
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5.M5N4.b
Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.
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5.M5N4.c
Find equivalent fractions and simplify fractions.
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5.M5N4.d
Model the multiplication and division of common fractions.
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5.M5N4.e
Explore finding common denominators using concrete, pictorial, and computational models.
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5.M5N4.f
Use <, >, or = to compare fractions and justify the comparison.
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5.M5N4.g
Add and subtract common fractions and mixed numbers with unlike denominators.
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5.M5N4.h
Use fractions (proper and improper) and decimal fractions interchangeably.
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5.M5N4.i
Estimate products and quotients.
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5.M5N5
Students will understand the meaning of percentage.
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5.M5N5.a
Model percent on 10 by 10 grids.
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5.M5N5.b
Apply percentage to circle graphs.
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5.M5M
Measurement
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5.M5M1
Students will extend their understanding of area of fundamental geometric plane figures.
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5.M5M1.a
Estimate the area of fundamental geometric plane figures.
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5.M5M1.b
Derive the formula for the area of a parallelogram (e.g., cut the parallelogram apart and rearrange it into a rectangle of the same area).
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5.M5M1.c
Derive the formula for the area of a triangle (e.g. demonstrate and explain its relationship to the area of a rectangle with the same base and height).
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5.M5M1.d
Find the areas of triangles and parallelograms using formulae.
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5.M5M1.e
Estimate the area of a circle through partitioning and tiling and then with formula (let pi = 3.14). (Discuss square units as they apply to circles.)
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5.M5M1.f
Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.
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5.M5M3
Students will measure capacity with appropriately chosen units and tools.
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5.M5M3.a
Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.
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5.M5M3.b
Compare one unit to another within a single system of measurement (e.g., 1 quart = 2 pints).
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5.M5M4
Students will understand and compute the volume of a simple geometric solid.
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5.M5M4.a
Understand a cubic unit (u³) is represented by a cube in which each edge has the length of 1 unit.
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5.M5M4.b
Identify the units used in computing volume as cubic centimeters (cm³), cubic meters (m³), cubic inches (in³), cubic feet (ft³), and cubic yards (yd³).
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5.M5M4.c
Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.
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5.M5M4.d
Compute the volume of a cube and a rectangular prism using formulae.
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5.M5M4.e
Estimate the volume of a simple geometric solid.
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5.M5M4.f
Understand the similarities and differences between volume and capacity.
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5.M5G
Geometry
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5.M5G1
Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles.
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5.M5G2
Students will understand the relationship of the circumference of a circle to its diameter is pi (pi is approximately 3.14).
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5.M5A
Algebra
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5.M5A1
Students will represent and interpret the relationships between quantities algebraically.
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5.M5A1.a
Use variables, such as n or x, for unknown quantities in algebraic expressions.
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5.M5A1.b
Investigate simple algebraic expressions by substituting numbers for the unknown.
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5.M5A1.c
Determine that a formula will be reliable regardless of the type of number (whole numbers or decimal fractions) substituted for the variable.
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5.M5D
Data Analysis
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5.M5D1
Students will analyze graphs.
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5.M5D1.a
Analyze data presented in a graph.
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Data, charts, and graphs: Line graphs (Fifth grade - R.2)
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Data, charts, and graphs: Bar graphs (Fifth grade - R.3)
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Data, charts, and graphs: Pictographs (Fifth grade - R.4)
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Data, charts, and graphs: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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5.M5D1.b
Compare and contrast multiple graphic representations (circle graphs, line graphs, bar graphs, etc.) for a single set of data and discuss the advantages/disadvantages of each.
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5.M5D2
Students will collect, organize, and display data using the most appropriate graph.
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