6-N-4-1

Student Actions

Teacher Actions

• Develop problem solving strategies by using benchmark fractions (¼, ⅓, ½, ….) to estimate solutions for problems involving fractions and mixed numbers or rounding in problems involving whole numbers and decimals in order to verify the reasonableness of results.

• Develop a deep and flexible conceptual understanding of estimation strategies with rational numbers by exploring which form (fractions or decimals) of a rational number is most useful in obtaining an estimate in real-world and mathematical situations.

• Develop the ability to communicate mathematically through writing and discussion when explaining estimation strategies and justifying solutions as they solve problems involving whole numbers, decimals, fractions and mixed numbers.

• Implement tasks that promote reasoning and problem solving that require obtaining an estimate for problems involving multiplication and division of whole numbers, decimals, fractions and mixed numbers.

• Elicit and use evidence of student thinking to assess progress towards understanding when a particular form of a rational number is useful in a given situation in order to obtain an estimate and adjust instruction to support their understanding.

• Facilitate meaningful mathematical discourse among students to build a shared understanding of estimation strategies involving multiplication and division of whole numbers, decimals, fractions, and mixed numbers.

• Pose purposeful questions about whether a student’s estimation to problems involving multiplication and division of whole numbers, decimals, fractions, and mixed numbers makes sense in the context of the problem. 

Key Understandings

Misconceptions

• Understand estimation of problems involving multiplication and division of whole numbers, decimals, fractions, and mixed numbers can be used to check the reasonableness of results.

• Understand when to use multiplication or division to solve real-world and mathematical problems involving whole numbers, decimals, fractions, and mixed numbers.

• Understand the quotient for real-world and mathematical problems involving division can be larger than the dividend and the divisor. For example, 2  ¼ = 8.

• Understand the product for real-world and mathematical problems involving multiplication can be smaller than the numbers being multiplied. For example, 0.75  0.4 = 0.3.

• Think that estimating the product and quotient of whole numbers, decimals, fractions, and mixed numbers is not an important step in the problem solving process in order to check the reasonableness of the answer.

• Choose the wrong operation when solving real-world and mathematical problems that require multiplication or division of whole numbers, decimals, fractions, and mixed numbers.

• Think that the quotient of two numbers should be smaller than the dividend and the divisor. For example, 2  ¼ = 8.

• Think that when you multiply numbers the product should be larger than the numbers being multiplied. For example, 0.75  0.4 = 0.3.