 • 5
Top Mathematicians
• Number & Operations
• 5.N.1.1
Estimate solutions to division problems in order to assess the reasonableness of results.
• 5.N.1.2
Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.
• 5.N.1.3
Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution.
• 5.N.1.4
Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
• 5.N.2.1
Represent decimal fractions (e.g., 1/10. 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals.
• 5.N.2.2
Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions.
• 5.N.2.3
Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line.
• 5.N.2.4
Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts.
• 5.N.3.1
Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.
• 5.N.3.2
Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods).
• 5.N.3.3
Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data.
• 5.N.3.4
Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.
• Algebraic Reasoning & Algebra
• 5.A.1.1
Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about real-world and mathematical problems.
• 5.A.1.2
Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.
• 5.A.2.1
Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents).
• 5.A.2.2
Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
• 5.A.2.3
Evaluate expressions involving variables when values for the variables are given.
• Geometry & Measurement
• 5.GM.1.1
Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts.
• 5.GM.1.2
Describe and classify three-dimensional figures including cubes, rectangular prisms, and pyramids by the number of edges, faces or vertices as well as the shapes of faces.
• 5.GM.1.3
Recognize and draw a net for a three-dimensional figure (e.g., cubes, rectangular prisms, pyramids).
• 5.GM.2.1
Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a×b×c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a×b×c = p×q×r = n.
• 5.GM.2.2
Recognize that the surface area of a three-dimensional figure with rectangular faces with whole numbered edges can be found by finding the area of each component of the net of that figure. Know that three-dimensional shapes of different dimensions can have the same surface area.
• 5.GM.2.3
Find the perimeter of polygons and create arguments for reasonable values for the perimeter of shapes that include curves.
• 5.GM.3.1
Measure and compare angles according to size.
• 5.GM.3.2
Choose an appropriate instrument and measure the length of an object to the nearest whole centimeter or 1/16-inch.
• 5.GM.3.3
Recognize and use the relationship between inches, feet, and yards to measure and compare objects.
• 5.GM.3.4
Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects.
• Data & Probability
• 5.D.1.1
Find the measures of central tendency (mean, median, or mode) and range of a set of data. Understand that the mean is a "leveling out" or central balance point of the data.
• 5.D.1.2
Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments.