Domain

NUMBER & OPERATION IN BASE 10

Generalize place value understanding for multi-digit whole numbers .

• NC.4.NBT.1

Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000.

• NC.4.NBT.2

Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form .

• NC.4.NBT.4

Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding .

• NC.4.NBT.5

Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm.

• NC.4.NBT.6

Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or the relationship between multiplication and division.

• NC.4.NBT.7

Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Unpacking

NC.4.NBT.1

This standard calls for students to extend their understanding of place value related to multiplying and dividing by multiples of 10. In this standard, students should reason about the magnitude of digits in a number. In the base-ten system, the value of each place is 10 times the value of the place to the immediate right. Students should reason and analyze the relationships of numbers that they are working with.

NC.4.NBT.2

This standard asks for students to write numbers in various forms. Students should have flexibility with the different forms of a number. Written form or number name is to write out a number in words like “two hundred eighty-five.” Traditional expanded form is 285 = 200 + 80 + 5. However, students should have opportunities to explore the idea that 285 could also be 28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones. They should also be comfortable with expanding a number by place value such as (2 x 100) + (8 x 10) + (5 x 1). To read numerals between 1,000 and 100,000, students need to understand the role of commas. Each section between commas is read a hundreds, tens, and ones followed by the appropriate unit (thousands). 97,345 would be read ninety-seven thousand, three hundred forty-five.

NC.4.NBT.4

In this standard, students build on their conceptual understanding of addition and subtraction, their use of place value and their flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place value in describing and justifying the processes they use to add and subtract. Students are expected to explain their thinking to show understanding of the algorithm. This is the first grade level in which students are expected to be proficient at using the standard algorithm to add and subtract. However, other previously learned strategies are still appropriate for students to use. In mathematics, an algorithm is defined by its steps and not by the way those steps are recorded in writing. With this in mind, minor variations in methods of recording standard algorithms are acceptable. Students may ask if it is possible to subtract a larger number from a smaller number. While it is not the focus or expectation of this standard in this grade, students should know that it is mathematically possible, and they will be learning more about that concept in later grades. If the misconception that larger numbers cannot be subtracted from smaller numbers is confirmed or reinforced, students may struggle to make the transition to negative numbers in later grades.

NC.4.NBT.5

In this standard, students extend their understanding of multiplying a singledigit factor times a multiple of ten to multiplying a single-digit factor times multi-digit factors. Students will also begin their exploration of multiplying two two-digit factors. Students should be able to apply their understanding of place value and various forms of a number to compute products. Students will also use area models, partial products and properties of operations to solve multiplication problems Connections should be made between models and written equations, but it is not necessary for fourth grade students to use the standard algorithm. The standard algorithm for multiplication is not an expectation until fifth grade.

NC.4.NBT.6

In this standard, students build on their understanding of the meaning of division and the relationship to multiplication by modeling, writing, and explaining division by a one-digit divisor. This standard calls for students to explore division through various strategies. Students should be able to apply their understanding of place value and various forms of a number to compute quotients. Students will also use arrays and area models, repeated subtraction, partial quotients and properties of operations to solve division problems This standard also references interpreting remainders. Remainders should be put into context for interpretation. Ways to address remainders:

• Remain as a left over

• Partitioned into fractions or decimals

• Discarded leaving only the whole number answer

• Increase the whole number answer up one

• Round to the nearest whole number for an approximate result.

The focus of this standard is to build conceptual understanding of division. Students are expected to use various strategies and explain their thinking. Students are not expected to master the traditional algorithm until middle school.

NC.4.NBT.7

In this standard, students use their understanding of groups and value of digits to compare two numbers by examining the value of the digits. Students are expected to be able to compare numbers presented in various forms. Students should have ample experiences communicating their comparisons in words before using symbols. Students were introduced to the symbols greater than (>), less than (<) and equal to (=) in First Grade and continue to use them. While students may have the skills to order more than 2 numbers, this standard focuses on comparing two numbers and using reasoning about place value to support the use of the various symbols.