In this section, students use strategies based on place value to add three-digit numbers. They learn that it is sometimes necessary to compose a hundred from 10 tens to find the values of such sums.

Students begin with sums that allow them to decide when to make a ten. They then work with greater values in the tens place and determine when to compose a hundred. As the lessons progress, they encounter sums of two- and three-digit numbers that involve composing two units. 

Throughout the section, students analyze and use representations, such as base-ten blocks, base-ten diagrams, expanded form, and other equations, to build conceptual understanding and show place-value reasoning. They also develop their understanding of the properties of operations as they observe that the order in which they add the units doesn’t affect the value of the sum.

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What is the same and what is different about how Priya and Lin found ?

Later in the section, students add within 1,000, using any method they have learned and thinking flexibly about the numbers they are adding.

In this section, students add and subtract within 1,000, using methods where they do not explicitly compose or decompose a ten or a hundred.

The number line is used early in this section to help students recognize that when numbers are relatively close, students can count on or count back to find the value of the difference. For example, they may count on from 559 to 562 to find .

Students also analyze counting sequences of three-digit numbers that increase or decrease by 10 or 100. They observe patterns in place value before adding and subtracting multiples of 10 or by 100.

Fill in the missing numbers. Does the number line show counting on by 10 or by 100?

Students then engage with problems and expressions that encourage them to reason about sums and differences, using the relationship between addition and subtraction and the properties of operations.

Diego has 6 tens. Tyler has 8 hundreds, 3 tens, and 6 ones.
What is the value of their blocks together?

Later in the section, students analyze and make connections between methods that use different representations, such as number lines, base-ten diagrams, and equations. They then use methods or representations that make sense to them to add and subtract three-digit numbers.

As they have done when adding, students subtract numbers within 1,000, using place-value strategies that involve decomposing a ten, a hundred, or both. This work builds on their previous experience of subtracting two-digit numbers by place value and decomposing a ten. 

Students use base-ten blocks to subtract hundreds from hundreds, tens from tens, and ones from ones, which offers a concrete experience of exchanging a ten for 10 ones or a hundred for 10 tens as needed.

Along the way, they begin to think strategically about how to decompose the minuend when using base-ten blocks or diagrams. They learn that by analyzing the value of the digits in each place, they can initially represent the minuend in a way that would require decomposing fewer units when subtracting by place. 

For example, this is a helpful way to represent 244 if we are subtracting a number with more than 4 ones, such as when finding  :

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Throughout the section, students compare the steps they use to decompose units and the different ways to represent and record the units that are decomposed.

The section ends with students choosing subtraction methods flexibly. They apply their understanding of place value, the relationship between addition and subtraction, and the properties of operations, to analyze number relationships and decide how to find the value of a difference within 1,000.