5.3.5: Number Relationships: Describe, Interpret and use quantities, relationships between quantities, representations of quantities, and number systems. Describe operations and the relationship between operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.

Number Relationships: Describe, Interpret and use quantities, relationships between quantities, representations of quantities, and number systems. Describe operations and the relationship between operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.

5.3.5.01Multiply two multi-digit numbers using an efficient strategy. Strategies include decomposing factors into factors, decomposing factors into sums or using an area model. Justify the chosen strategy using properties of operations and place value.5.3.5.02Divide multi-digit numbers by a one-digit or two-digit divisor using efficient and generalizable procedures based on knowledge of place value and the properties of operations that may include partial quotients and standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction, a mixed number or a decimal.5.3.5.03Consider the context of a problem involving division to select the most useful form of the quotient and the remainder.5.3.5.04Solve multi-step contextual situations 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 situation to assess the reasonableness of results.5.3.5.05Generate equivalent fractions of the forms a/b = (n x a)/(n x b) and a/b = (a / n)/(b / n) and justify relationships using visual models.5.3.5.06Given a value, mentally find 0.1 more or 0.1 less, 0.01 more or 0.01 less and 0.001 more or 0.001 less than the number. Justify reasoning by referencing a visual model.5.3.5.07Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.5.3.5.08Recognize and flexibly generate equivalences between fractions and decimals to the thousandths place and justify using visual models, place value language and symbols.5.3.5.09Compare and order decimal values to the thousandths. Justify using place value language and visual models.5.3.5.10Estimate sums and differences of fractions and mixed numbers to the nearest half. Justify reasoning using benchmarks.5.3.5.11Fluently add and subtract fractions with unlike denominators (including mixed numbers) and justify using equivalent fractions, visual models and the number line.5.3.5.12Estimate sums and differences of decimals.5.3.5.13Solve contextual situations using addition and subtraction of positive rational numbers represented as fractions (including mixed numbers) or decimals using visual models, equations and properties of operations.5.3.5.14Represent multiplication of a whole number of fractional groups, n x a/b, using visual models, including a number line, and explain how the picture shows the product.5.3.5.15Represent contextual multiplication situations of a fractional amount of a whole number amount, a/b of a group of n, using visual models, including a number line, and explain how the picture shows the product.5.3.5.16Represent contextual measurement situations using division of the form n / (a/b) where n is the total and a/b is the amount per group. Use a visual model and explain how the picture shows the number of groups.5.3.5.17Solve multi-step contextual situations using addition and subtraction of positive rational numbers. Use various strategies, including the inverse relationships between operations and the context of the situation, to assess the reasonableness of results.5.3.5.18Use the four operations to compare and contrast different ways of paying and receiving payments. Identify the advantages and disadvantages of each method of payment, including checks, credit cards, debit cards and electronic payments.5.3.5.19Use the four operations to create an individual or group budget based on wants and needs and explore examples of debt and manageability of debt and its long-term impact.

1-on-1 AI tutoring aligned to 5.3.5. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →