Fourth Grade

In fourth grade, students must be fluent in adding and subtracting numerals and in multiplying and dividing single and double digits, in order to extend their understanding of the base-ten system.

Students need to:

Understand and use place value to manipulate whole numbers and to read numbers up to 1,000,000
Compare numbers up to 1,000,000
Understand and write decimals and fractions based on the base-ten system (e.g., 1/10 and 1/100), including the expanded form of non-whole numbers (e.g., 23 7/10 = 2 x 10+ 3 x 1+ 7x 1/10).
Use place value understanding and properties of operations to perform multi-digit arithmetic:
1. Fluently add and subtract numbers through 1,000,000
2. Compute products of one-digit numbers and multi-digit numbers (up to four digits)
3. Compute products of two-digit numbers
4. Divide multi-digit numbers (up to four) by one-digit numbers
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Concrete Model

Representational

Abstract

Place Value Using Concrete Models

Operations and Concrete Models

Operations and Abstract Models

Reasoning in Math

Click on the button below to access the Common Core Standards in more detail.

Number & Operations in Base Ten Common Core Standards

Concrete Model

Concrete models use manipulatives and digital representations of the actual numbers to help students solve problems.

Example:

Teachers may use pictures of base ten blocks or actual base ten blocks to model how to compute double-digit numbers to extend to larger numbers. To watch it being done with digital base ten blocks click here.

Representational

Representational models move away from using manipulatives to using pictorial representations of concrete models (e.g., sticks and pictures) to help students solve math problems.

Example:

Teachers may use a place value chart to have students draw representations of base ten blocks to solve double-digit multiplication problems and extend to larger numbers. See the complete procedure and PDF here.

Abstract

During the abstract phase of doing a math problem an algorithm may be introduced, such as the traditional way of adding or subtracting numbers or by using arrays.

Example:

Once students understand how to model the product of double-digit numbers using a concrete and representational model, they may transfer learning to the traditional algorithm or use arrays. See an example here.

Place Value Using Concrete Models

Place Value to One Million

Watch the video to review place value up to millions using concrete virtual models.

Using a Place Value Chart

This video explains the relationship between place values (i.e., multiply or divide by 10) using a place value chart.

Expanded Notation

The video uses a virtual place value chart with an expanded notation scaffold to show how to write expanded form of whole numbers up to one hundred thousand (it may be expanded to millions).

Comparing Numbers Using a Place Value Chart

The video illustrates how to use a place value chart to compare numbers up to one million.

Concrete Model to read and write Decimals

The video shows a teacher presenting a concrete model of decimals place values.

Modeling Decimals with Virtual Manipulatives

The video introduces how to use base-ten virtual models to represent and write fractions and decimals, including mixed numbers.

Place Value Song with Decimals

A song video to explain place values, including decimals.

Operations and Concrete Models

Adding using the Place Value Chart and Standard Algorithm

The teacher in the video demonstrates how to create and use a simple place value chart to help students understand the standard algorithm for addition. The process may be extended to larger numbers.

Subtraction - Regrouping using Place Value Discs

The teacher in the video demonstrates how to use place value discs to model how regrouping works before transferring student learning to the standard algorithm. The example displays a chart up to the hundreds place, but it may be extended to larger numbers.

Using a Place Value Chart and Discs to Model Regrouping of Large Numbers

The video demonstrates how you may use place value discs to model and subtract larger numbers up to one million.

Operations and Abstract Models

Multiplication Sketch Array

In this video the teacher demonstrates how to use a multiplication sketch array to multiply a two digit number by a one-digit number.

Multi-Digit Multiplication using the Distributive Property

The teacher models how to use the distributive property, manipulatives, and a multiplication array to solve a multi-digit multiplication problem. The process uses the CRA model (i.e., concrete, representational, and abstract).

Using Arrays to Multiply Double-Digit Numbers

In this video the teacher demonstrates how to use the area and array model to multiply double-digit numbers.

Area Model for Division

The teacher reviews how to use the area model for division of large numbers up to one thousand. It also includes using mental math and reasoning to begin to solve the problem.

Whole Number Division with the Open Area Model

In the video the teacher demonstrates how to use the open area model, similar to the area model, but it uses decomposing of numbers to arrive at the answer.

Reasoning in Math

Number Talks

The above resource includes a series of ideas, videos, and strategies for teachers of fourth grade to facilitate number talks.

Writing to Explain in Math

The article describes a variety of ways to use writing to develop students' explanations in resolving math problems.

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