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Beyond High School

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Performance Expectations
Math - Fifth Grade

5.1. Core Content: Multi-digit division (Operations, Algebra)

Students learn efficient ways to divide whole numbers. They apply what they know about division to solve problems, using estimation and mental math skills to decide whether their results are reasonable. This emphasis on division gives students a complete set of tools for adding, subtracting, multiplying, and dividing whole numbers—basic skills for everyday life and further study of mathematics.

Performance Expectations - Students are expected to:

  • 5.1.A - Represent multi-digit division using place value models and connect the representation to the related equation.
  • 5.1.B - Determine quotients for multiples of 10 and 100 by applying knowledge of place value and properties of operations.
  • 5.1.C - Fluently and accurately divide up to a four-digit number by one- or two-digit divisors using the standard long-division algorithm.
  • 5.1.D - Estimate quotients to approximate solutions and determine reasonableness of answers in problems involving up to two-digit divisors.
  • 5.1.E - Mentally divide two-digit numbers by one-digit divisors and explain the strategies used.
  • 5.1.F - Solve single- and multi-step word problems involving multi-digit division and verify
  • the solutions.

5.2. Core Content: Addition and subtraction of fractions and decimals (Numbers, Operations, Algebra)

Students extend their knowledge about adding and subtracting whole numbers to learning procedures for adding and subtracting fractions and decimals. Students apply these procedures, along with mental math and estimation, to solve a wide range of problems that involve more of the types of numbers students see in other school subjects and in their lives.

Performance Expectations - Students are expected to:

  • 5.2.A - Represent addition and subtraction of fractions and mixed numbers using visual and numerical models, and connect the representation to the related equation.
  • 5.2.B - Represent addition and subtraction of decimals using place value models and connect the representation to the related equation.
  • 5.2.C - Given two fractions with unlike denominators, rewrite the fractions with a common denominator.
  • 5.2.D - Determine the greatest common factor and the least common multiple of two or more whole numbers.
  • 5.2.E - Fluently and accurately add and subtract fractions, including mixed numbers.
  • 5.2.F - Fluently and accurately add and subtract decimals.
  • 5.2.G - Estimate sums and differences of fractions, mixed numbers, and decimals to approximate solutions to problems and determine reasonableness of answers.
  • 5.2.H - Solve single- and multi-step word problems involving addition and subtraction of whole numbers, fractions (including mixed numbers), and decimals, and verify the solutions.

5.3. Core Content: Triangles and quadrilaterals (Geometry/Measurement, Algebra)

Students focus on triangles and quadrilaterals to formalize and extend their understanding of these geometric shapes. They classify different types of triangles and quadrilaterals and develop formulas for their areas. In working with these formulas, students reinforce an important connection between algebra and geometry. They explore symmetry of these figures and use what they learn about triangles and quadrilaterals to solve a variety of problems in geometric contexts.

Performance Expectations - Students are expected to:

  • 5.3.A - Classify quadrilaterals.
  • 5.3.B - Identify, sketch, and measure acute, right, and obtuse angles.
  • 5.3.C - Identify, describe, and classify triangles by angle measure and number of congruent sides.
  • 5.3.D - Determine the formula for the area of a parallel-ogram by relating it to the area of a rectangle.
  • 5.3.E - Determine the formula for the area of a triangle by relating it to the area of a parallelogram.
  • 5.3.F - Determine the perimeters and areas of triangles and parallelograms.
  • 5.3.G - Draw quadrilaterals and triangles from given information about sides and angles.
  • 5.3.H - Determine the number and location of lines of symmetry in triangles and quadrilaterals.
  • 5.3.I - Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions.

5.4. Core Content: Representations of algebraic relationships (Operations, Algebra)

Students continue their development of algebraic thinking as they move toward more in-depth study of algebra in middle school. They use variables to write simple algebraic expressions describing patterns or solutions to problems. They use what they have learned about numbers and operations to evaluate simple algebraic expressions and to solve simple equations. Students make tables and graphs from linear equations to strengthen their understanding of algebraic relationships and to see the mathematical connections between algebra and geometry. These foundational algebraic skills allow students to see where mathematics, including algebra, can be used in real situations, and these skills prepare students for success in future grades.

Performance Expectations - Students are expected to:

  • 5.4.A - Describe and create a rule for numerical and geometric patterns and extend the patterns.
  • 5.4.B - Write a rule to describe the relationship between two sets of data that are linearly related.
  • 5.4.C - Write algebraic expressions that represent simple situations and evaluate the expressions, using substitution when variables are involved.
  • 5.4.D - Graph ordered pairs in the coordinate plane for two sets of data related by a linear rule and draw the line they determine.

5.5. Additional Key Content (Numbers, Data/Statistics/Probability)

Students extend their work with common factors and common multiples as they deal with prime numbers. Students extend and reinforce their use of numbers, operations, and graphing to describe and compare data sets for increasingly complex situations they may encounter in other school subjects and in their lives.

Performance Expectations - Students are expected to:

  • 5.5.A - Classify numbers as prime or composite.
  • 5.5.B - Determine and interpret the mean of a small data set of whole numbers.
  • 5.5.C - Construct and interpret line graphs.

5.6. Core Processes: Reasoning, problem solving, and communication

Performance Expectations - Students are expected to:

  • 5.6.A - Determine the question(s) to be answered given a problem situation.
  • 5.6.B - Identify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem.
  • 5.6.C - Determine whether additional information is needed to solve the problem.
  • 5.6.D - Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.
  • 5.6.E - Select and use one or more appropriate strategies to solve a problem, and explain the choice of strategy.
  • 5.6.F - Represent a problem situation using words, numbers, pictures, physical objects, or symbols.
  • 5.6.G - Explain why a specific problem-solving strategy or procedure was used to determine a solution.
  • 5.6.H - Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.
  • 5.6.I - Summarize mathematical information, draw conclusions, and explain reasoning.
  • 5.6.J - Make and test conjectures based on data (or information) collected from explorations and experiments.