5th Grade Power Standards (also refer to 4th, 3rd, 2nd and 1st grade skills)
- Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. 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.
- Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
- Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
- 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.
- Subtraction skills
- Multiply two- and three-digit numbers by a two-digit number.
- Understand the inverse relationship between multiplication and division.
- Fluent in multiplication and division facts.
- Divide multi-digit numbers by 1-digit divisors with and without remainders.
- Estimation skills.
- Place value understanding- including expanded form.
- Understanding of division problem types; equal groups, area and array, multiplicative comparison, and combination.
- Understand properties.
- Understand and use the fraction bar as division notation.
- Understand and apply the standard algorithm for division.
- Represent the quotient in a variety of ways including whole number with a remainder, fraction or mixed number, or a decimal.
- Recognize that the context of a problem determines how to interpret quotients with remainders when solving real world problems.
- Estimate quotients and/or products in order to assess the reasonableness of their answer.
- Understand that the fraction bar represents division.
- Use various strategies, including the inverse relationship between operations, in solving problems.
- Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
- Model addition and subtraction of fractions and decimals using a variety of representations.
- Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
- Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
- Understand the concept of and generate equivalent fractions
- Relate decimal fractions to fraction notation
- Understand that the size of a fractional part is relative to the size of the whole
- Understand the relationship between the size of the denominator and the size of the parts, i.e., as the denominator gets larger the size of the parts gets smaller.
- Fractions can be parts of a whole, parts of a set, points or distances on a number line.
- Understand that fractions and decimals are numbers and can be represented on a number line.
- Locate fractions, including improper fractions, and mixed numbers on a number line.
- Use models to show addition and subtraction of fractions with like denominators and generate a rule for addition and subtraction of fractions with like denominators
- Add and subtract decimals to the millionths place using multiple representations including standard algorithms.
- Add or subtract 0.1, 0.01, 0.001, 0.0001, 0.00001or 0.000001 to a given whole number or decimal.
- Estimate decimal sums and differences to check for reasonableness of results.
- Use the relationship of addition and subtraction to add and subtract fractions including standard algorithms.
- Model the addition and subtraction of fractions using a variety of representations.
- Estimate fraction sums and differences to check for reasonableness of results.
- Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
- For example: An end-of-the-year party for 5th grade costs $100 to rent the room and $4.50 for each student. Know how to use a spreadsheet to create an input-output table that records the total cost of the party for any number of students between 90 and 150.
- Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
- Recognize and describe patterns of change involving more than one operation.
- Record inputs and outputs in a chart or a table.
- Create input-output rules involving addition, subtraction, multiplication and division.
- Use input-output rules to solve real-world and mathematical problems.
- Use addition, subtraction, multiplication and division to solve problems.
- Create tables, spreadsheets and coordinate graphs to represent patterns of change.
- Create a rule for a pattern of change and represent it in more than one way.
- Describe a given pattern of change using a rule.
- Represent a given pattern of change in more than one way using rules, tables, spreadsheets, and coordinate graphs.
- Use a rule or a table to represent ordered pairs of positive integers (input, output).
- Graph ordered pairs of positive integers on a coordinate system.
- Solve problems based on a pattern of change that has been represented using tables, spreadsheets, rules and/or the coordinate system.
- Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
- Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
- Evaluate expressions and solve equations involving variables when values for the variables are given.
- interpreting number sentences involving multiplication and division and unknowns.
- representing a given problem situation with a number sentence.
- using real-world situations to represent a given number sentences.
- concretely modeling and describing mathematical relationships in open number sentences.
- finding the value for unknowns in order to make number sentences true.
- solving simple equations with the unknown represented as a variable.
- seeing unknown numbers represented as variables, boxes or blanks.
- Use algebraic concepts and processes to represent and solve problems that involve variable quantities.
- Represent real-world situations using equations and inequalities involving variables.
- Create real-world situations corresponding to equations and inequalities.
- Determine whether an equation or inequality is true or false for a given variable value.
- Solve equations when values for variables are given.
- Use the < and > symbols.
- Solve equations and inequalities that are not embedded in a context.
- Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
- Recognize and draw a net for a three-dimensional figure.
- Name, describe, and classify polygons.
- Identify parallel and perpendicular lines in various contexts and use them to describe geometric shapes.
- Sketch polygons with a given number of sides or vertices.
- Describe, compare, and classify 2 and 3-dimensional figures according to number and shape of faces, and the number of sides, edges, and vertices.
- Identify basic 2 and 3-dimensional shapes.
- Move fluently between 2-dimensional representations of 3-dimensional shapes.
- Able to decompose a 3-dimensional shape into its 2-dimensional components.
- Create nets by correctly arranging the 2-dimensional faces that can be folded into a given 3-dimensional shape.
- Describe and classify 3-dimensional shapes by their properties: faces, edges, and vertices. For example, all prisms contain 2 congruent parallel shapes connected by rectangular faces, while pyramids have a base face with triangular faces that create an apex.
- Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
- Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. For example: Use a net or decompose the surface into rectangles. Another example: Measure the volume of a cereal box by using a ruler to measure its height, width and length, or by filling it with cereal and then emptying the cereal into containers of known volume.
- Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. For example: Use cubes to find the volume of a small box.
- Develop and use the formulas V = ℓwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
- Understand that area of two-dimensional figures can be found by counting the total number of same size square units that cover a shape without gaps or overlaps
- Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns
- Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes.
- Use square units to label measurements.
- Recognize and draw a net for a three-dimensional figure (current grade level).
- Understand, develop and use formulas to determine the area of triangles, trapezoids, parallelograms and other figures that can be decomposed into triangles.
- Find the area of any polygon by breaking the polygon into triangles or rectangles. Find the area of each triangle or rectangle, and then add the areas together to find the area of the polygon.
- Measure the volume of rectangular prisms.
- Measure the surface area of rectangular prisms - strategy may include decomposing the prism into its net.
- Find the volume of rectangular prisms by finding the area of the base and then counting the number of layers of cubes needed to fill the prism. Use multiplication to find the number of cubes needed to fill the prism.
- Understand, develop and use a formula to determine volume.
- Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data.
- Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.
- Collect, organize, and display data.
- Interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales.
- Use appropriate titles, labels and units.
- Use tables, bar graphs, time-lines and Venn diagrams to display data sets.
- Work with data involving fractions or decimals.
- Understand that spreadsheet tables and graphs can be used to display data.
- Use information in a data display to answer questions.
- Find the mean, median, and range of a data set.
- Demonstrate understanding that the mean is a "leveling out" of data.
- Create and analyze double-bar graphs and line graphs.
- Use technology to create spreadsheet tables and graphs to organize and display data.
- Adjust the scale of the graph to accommodate rational numbers.