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5.1
Number Sense
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5.1.1
Convert between numbers in words and numbers in figures, for numbers up to millions and decimals to thousandths.
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5.1.2
Round whole numbers and decimals to any place value.
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5.1.3
Arrange in numerical order and compare whole numbers or decimals to two decimal places by using the symbols for less than (<), equals (=), and greater than (>).
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5.1.4
Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
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5.1.5
Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.
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5.1.6
Describe and identify prime and composite numbers.
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5.1.7
Identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive decimals.
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5.2
Computation
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5.2.1
Solve problems involving multiplication and division of any whole numbers.
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5.2.2
Add and subtract fractions (including mixed numbers) with different denominators.
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5.2.3
Use models to show an understanding of multiplication and division of fractions.
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5.2.4
Multiply and divide fractions to solve problems.
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5.2.5
Add and subtract decimals and verify the reasonableness of the results.
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5.2.6
Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems.
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5.2.7
Use mental arithmetic to add or subtract simple decimals.
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5.3
Algebra and Functions
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5.3.1
Use a variable to represent an unknown number.
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5.3.2
Write simple algebraic expressions in one or two variables and evaluate them by substitution.
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5.3.3
Use the distributive property in numerical equations and expressions.
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5.3.4
Identify and graph ordered pairs of positive numbers.
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5.3.5
Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.
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5.3.6
Understand that the length of a horizontal line segment on a coordinate plane equals the difference between the x-coordinates and that the length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.
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5.3.7
Use information taken from a graph or equation to answer questions about a problem situation.
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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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5.4
Geometry
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5.4.1
Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, triangles, and circles by using appropriate tools (e.g., ruler, compass, protractor, appropriate technology, media tools).
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5.4.2
Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangular.
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5.4.3
Identify congruent triangles and justify your decisions by referring to sides and angles.
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5.4.4
Identify, describe, draw, and classify polygons, such as pentagons and hexagons.
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5.4.5
Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.
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5.4.6
Identify shapes that have reflectional and rotational symmetry.
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5.4.7
Understand that 90°, 180°, 270°, and 360° are associated with quarter, half, three-quarters, and full turns, respectively.
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5.4.8
Construct prisms and pyramids using appropriate materials.
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5.4.9
Given a picture of a three-dimensional object, build the object with blocks.
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5.5
Measurement
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5.5.1
Understand and apply the formulas for the area of a triangle, parallelogram, and trapezoid.
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5.5.2
Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
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5.5.3
Use formulas for the areas of rectangles and triangles to find the area of complex shapes by dividing them into basic shapes.
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5.5.4
Find the surface area and volume of rectangular solids using appropriate units.
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5.5.5
Understand and use the smaller and larger units for measuring weight (ounce, gram, and ton) and their relationship to pounds and kilograms.
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5.5.6
Compare temperatures in Celsius and Fahrenheit, knowing that the freezing point of water is 0°C and 32°F and that the boiling point is 100°C and 212°F.
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5.5.7
Add and subtract with money in decimal notation.
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5.6
Data Analysis and Probability
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5.6.1
Explain which types of displays are appropriate for various sets of data.
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5.6.2
Find the mean, median, mode, and range of a set of data and describe what each does and does not tell about the data set.
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5.6.3
Understand that probability can take any value between 0 and 1, events that are not going to occur have probability 0, events certain to occur have probability 1, and more likely events have a higher probability than less likely events.
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5.6.4
Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4, 3/4).
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5.7
Problem Solving
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Students make decisions about how to approach problems and communicate their ideas.
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5.7.1
Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
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5.7.2
Decide when and how to break a problem into simpler parts.
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Students use strategies, skills, and concepts in finding and communicating solutions to problems.
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5.7.3
Apply strategies and results from simpler problems to solve more complex problems.
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5.7.4
Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
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5.7.5
Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
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5.7.6
Know and apply appropriate methods for estimating results of rational-number computations.
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5.7.7
Make precise calculations and check the validity of the results in the context of the problem.
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Students determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.
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5.7.8
Decide whether a solution is reasonable in the context of the original situation.
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5.7.9
Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
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