Unit 3
Wrapping Up Addition and Subtraction within 1,000
Unit Goals
- Students use place-value understanding to round whole numbers and add and subtract within 1,000. They also represent and solve two-step word problems, using addition, subtraction, and multiplication, and assess the reasonableness of answers.
Unit Narrative
In this unit, students work toward the goal of fluently adding and subtracting within 1,000. They use mental math strategies developed in grade 2, and learn algorithms based on place value.
In grade 2, students added and subtracted within 1,000, using strategies based on place value, properties of operations, and the relationship between addition and subtraction. When students combine hundreds, tens, and ones, they use place-value understanding. When they decompose numbers to add or subtract, they rely on the commutative and associative properties. When students count up to subtract, they use the relationship between addition and subtraction.
To move toward fluency, students learn a few different algorithms that work with any numbers and are generalizable to greater numbers and decimals. Students work with a variety of algorithms, starting with those that show expanded form, and moving toward algorithms that are more streamlined and closer to the standard algorithm.
Students explore various algorithms but are not required to use a specific one. They should, however, move from the strategy-based work of grade 2 to algorithm-based work, to set the stage for using the standard algorithm in grade 4. If students begin the unit with knowledge of the standard algorithm, it is still important for them to make sense of the place-value basis of the algorithm.
Understanding of place value also comes into play as students round numbers to the nearest multiples of 10 and of 100. Students do not need to know a formal definition of “multiples” until grade 4. At this point, it is enough to recognize that a multiple of 10 is a number called out when counting by 10, or the total in a whole-number of tens (such as 8 tens). Likewise, a multiple of 100 is a number called out when counting by 100, or the total in a whole-number of hundreds (such as 6 hundreds). Students use rounding to estimate answers to two-step problems and to determine if answers are reasonable.