Third Grade

As students progress, third graders begin to develop their understanding of place value as it relates to rounding numbers to 10s and 100s. Students continue using base ten blocks and place value mats as a kinesthetic tool for their learning. By third grade, students should be able to fluently add and subtract digits and are on their way to explore multiplication. Third graders can use mental math strategies to help them decompose larger digits through 1000. Students can use counters to build groups of an object and to build arrays as they begin to navigate multiplication.

The Progression of Multiplication

This video shows how second grades standards in repeated additional expand to third grade and concepts related to multiplication.

Rounding Numbers

This video shows how to round numbers use multiples of 10 and 100.

Using Mental Math

This video shows how third-graders can use mental math to fluently add and subtract.

Concrete Representation Abstract

CONCRETE: Using manipulatives to model mathematical concepts, numbers, and patterns.

REPRESENTATIONAL: Students draw/use representations models.

ABSTRACT: Present thinking with digits and symbols. In this example, use the symbols for division and multiplication.

Concrete Examples

Base Ten Blocks/Place Value mats
Unifix Cubes
Colored Chips
Fraction Blocks
Marbles
Popsicles Sticks
Candy
Linking Cubes
Algebra Tiles

Representational Examples

Tally Marks
Dots
Circles
Diagrams
Charts

Concrete Representational Abstract Models for Place Value

Concrete

Students use base ten blocks to manipulate numbers through 100s. Students can build different digits through addition and subtraction by sliding the manipulatives over to other columns.

Representational

Students draw representation of concrete model. Students can also use other representations.

Abstract

Students use digits and symbols to write out the number in expanded and simple form. By third grade, students should be able to write numbers to the 1000s place and round digits to the tens and hundreds place value.

Concrete Representational Abstract (CRA) with Subtraction with Regrouping

Concrete Subtraction

This video demonstrates students using base ten blocks manipulatives to begin to develop an abstract understanding through concrete learning.

Representational Subtraction

Students use the represenation of the base ten blocks to begin transfer the learning.

Abstract Subtraction

Students are able to use their skillsets and apply their knowledge to subtract with regrouping using symbols and fluency. By the end of grade 3, students should be able to fluenty subtract digits without regrouping and should be able to use strategies to subtract multi-digit numbers.

Concrete Representational Abstract (CRA) with Addition with Regrouping

Concrete Addition with Regrouping

This video demonstrates how to use base ten blocks to add with regrouping. Students can maniuplate these blocks to determine concrete representations of digits.

Representational Addition with Regrouping

Students use the represenation of the base ten blocks to begin transfer the learning.

Abstract Addition with Regrouping

Students are able to use their skillsets and apply their knowledge to add with regrouping using symbols and fluency. By third grade, students should be able to fluenty add without regrouping using mental math strategies and should be able to apply abstract skills to add multi-digit numbers.

Multiplication with Concrete Representational Abstract Math (CRA)

*Students in grade 3 are being introduced to multiplication. They can start exploring using concrete visuals and manipulatives. As students progress to grade 4 they will begin to develop concrete understanding.

Concrete Multiplication

In this example, students use candy to build arrays.

Representational Multiplication

In this representational model, students can use the visuals to multiply.

Using Math Links Cubes to Multiply

Example of Use

Practice with Adding 3 Digit Numbers

Student Practice

Common Core Standards

"Use place value understanding and properties of operations to perform multi-digit arithmetic".

Students will be able to:

3.NBT.A.2 Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.A.3 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

3.NBT.A.4 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Strategies and Manipulatives for Grade 3 Learning Progressions

In this video students are taught addition using a number line.

Place Value and Expanded form as it relates to grade 2 and 3 progressions.

Introducing students to multiplication by sing arrays to multiply- visual representations.

This interactive video will provide students with an understanding of the Distributive Property of Multiplication.

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