Rounding, Addition, and Subtraction

1. Subtract three-digit numbers with one decomposition.
2. Solve one-step word problems involving three-digit subtraction with one decomposition.

• As noted previously, when discussing how to line up numbers in order to add or subtract them vertically, emphasize that units need to be lined up because one can only add or subtract like units (ones with ones and tens with tens), as opposed to saying that numbers need to be lined up from right to left. This is an important distinction since lining numbers up from right to left no longer works when students begin working with decimals (e.g., adding 6.4 and 2.08 would result in an incorrect sum if lined up from right to left). 
• It is important not to say things like "you cannot take a bigger number from a smaller number" when discussing subtraction, since this is in fact possible to do. It would just result in a negative number, which students won’t see until Grade 7 (7.NS.1). Instead, you can say things like "there are not enough ones/tens/etc., to subtract."
• When subtraction requires decomposition, doing all necessary decomposition before subtracting will help to avoid errors. Take 425 – 278, for example. "The total 425 does not have enough tens or ones to subtract the 7 tens or 8 ones in 278. Therefore one hundred is decomposed to make ten tens and one ten is decomposed to make ten ones. These decompositions can be done and written in either order; starting from the left is shown because many students prefer to operate in that order. In the middle step, one hundred has been decomposed (making 3 hundreds, 11 tens, 15 ones) so that the 2 hundreds 7 tens and 8 ones in 278 can be subtracted. These subtractions of like units can also be done in any order. When students alternate decomposing and subtracting like units, they may forget to decompose entirely or in a given column after they have just subtracted (e.g., after subtracting 8 from 15 to get 7, they move left to the tens column and see a 1 on the top and a 7 on the bottom and write 6 because they are in subtraction mode, having just subtracted the ones)" (NBT Progression, p. 10). Thus, decomposing first allows students to both decompose in any order and avoid common errors. This process would look like this:

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• Students have solved one-step word problems involving subtraction in previous grade levels (1.OA.1, 2.OA.1), just not yet with whole numbers of this magnitude. So, the intention of the word problems in this lesson is to have students solve contextual problems that involve computations expected of this grade level (3.NBT.2) as well as prepare students to solve two-step word problems involving addition and subtraction later in the unit, and eventually all four operations in Units 2 and 3 (3.OA.8).

• Problem Set

• Problem Set Answer Key