In Grades 4 and 5, students used concrete models, pictorial representations, and properties to divide whole numbers (4.NBT.6, 5.NBT.6). They became efficient in applying the standard algorithm for long division. They broke dividends apart into like base-ten units, applying the distributive property to find quotients place by place. In Module 2, Topic C, students connect estimation to place value and determine that the standard algorithm is simply a tally system arranged in place value columns (6.NS.2). Students understand that when they “bring down” the next digit in the algorithm, they are essentially distributing, recording, and shifting to the next place value. They understand that the steps in the algorithm continually provide better approximations to the answer. Students further their understanding of division as they develop fluency in the use of the standard algorithm to divide multi-digit decimals (6.NS.3). They make connections to the division of fractions and rely on mental math strategies to implement the division algorithm when finding the quotients of decimals.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 6

5. Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Unpacked Content

Evidence Of Student Attainment:

Students: Given a context which calls for the division of two whole numbers,

Choose the most appropriate strategy for computing the answer.

Produce accurate results using a standard algorithm when appropriate.

Teacher Vocabulary:

Standard algorithm

Dividend

Divisor

Quotient

Knowledge:

Students know:

strategies for computing answers to division mathematical and real-world problems using the standard division algorithm.

Skills:

Students are able to:

Strategically choose and apply appropriate strategies for dividing.

Accurately find quotients using the standard division algorithm.

Understanding:

Students understand that:

Mathematical problems can be solved using a variety of strategies, models, and representations.

Efficient application of computation strategies is based on the numbers and operations in the problems,

The steps used in the standard algorithms for division can be justified by using properties of operations and understanding of place value.

Among all techniques and algorithms that may be chosen for accurately performing multi-digit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M. 6.5.1: Define factors and multiples.
M. 6.5.2: Discuss the steps for solving a division problem.
M. 6.5.3: Recognize division and multiplication as inverse operations.
M. 6.5.4: Recall basic division and multiplication facts.
M. 6.5.5: Solve real-world division problems with and without models or a calculator.

Prior Knowledge Skills:

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Write number sentences for word problems.

Identify key terms to solve multiplication word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Recall basic multiplication facts.

Recognize key terms to solve word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Label numerator, denominator, and fraction bar.

Recognize a fraction as a number on the number line.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.6.5 Apply the concepts of dividing multi-digit numbers without remainders to real-world problems.

Mathematics MA2019 (2019) Grade: 6

6. Add, subtract, multiply, and divide decimals using a standard algorithm.

Unpacked Content

Evidence Of Student Attainment:

Students: Given a context which calls for complex computation involving multi-digit decimals,

Choose the most appropriate strategy for computing the answer.

Produce accurate results efficiently using a standard algorithm for each operation when appropriate.

Teacher Vocabulary:

Standard algorithms (addition, subtraction, multiplication, and division)

Quotient

Sum

Product

Difference

Tenths

Hundredths

Thousandths

Ten thousandths

Hundred thousandths

Knowledge:

Students know:

Place value conventions (i.e., a digit in one place represents 10 times as much as it would represent in the place to its right and 1/10 of what it represents in the place to its left).

Strategies for computing answers to complex addition, subtraction, multiplication, and division problems involving multi-digit decimals, including a standard algorithm for each operation.

Skills:

Students are able to:

Strategically choose and apply appropriate computation strategies.

Accurately find sums, differences, products, and quotients using the standard algorithms for each operation.

Understanding:

Students understand that:

Place value patterns and values continue to the right of the decimal point and allow the standard algorithm for addition and subtraction to be applied in the same manner as with whole numbers.

Mathematical problems can be solved using a variety of strategies, models, and representations.

Efficient application of computation strategies is based on the numbers and operations in the problem.

The steps used in the standard algorithms for the four operations can be justified by using properties of operations and understanding of place value.

Among all techniques and algorithms that may be chosen for accurately performing multi-digit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.6.6.1: Solve division problems involving multi-digit whole numbers and decimal numbers with or without a calculator.
M.6.6.2: Solve multiplication problems involving multi-digit whole numbers and decimal numbers with or without a calculator.
M.6.6.3: Recall basic multiplication and division facts.
M.6.6.4: Solve addition and subtraction of multi-digit decimal numbers (emphasis on alignment).
M.6.6.5: Solve addition and subtraction of multi-digit whole numbers.
M.6.6.6: Recognize place value of whole numbers and decimals.
M.6.6.7: Demonstrate addition, subtraction, multiplication, and division of whole numbers and decimals using manipulatives.

Prior Knowledge Skills:

Recall basic multiplication facts.

Recall basic addition, subtraction, multiplication, and division facts.

Use place value understanding to round whole numbers to the nearest 10 or 100.

Identify place value of decimals to the tenths and hundredths.

Recall basic addition and subtraction facts.

Recall basic addition and subtraction facts.

Recall basic addition, subtraction, and multiplication facts.

Multiply within 100, using strategies such as the relationship between multiplication and division.

Multiply within 100, using strategies such as properties of operations.

Divide within 100, using strategies such as properties of operations.

Divide within 100, using strategies such as the relationship between multiplication and division.

Add and subtract within 1000.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.6.6 Solve two-factor multiplication problems with products up to 100 (whole numbers only).