Sunday, October 9, 2011

Number and Operations in Base Ten (1.NBT.4~6)

In the Grade 1 Number and Operations in Base Ten domain, you will see the following cluster.

Use place value understanding and properties of operations to add and subtract.
4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

As I discussed briefly in the previous post, these standards are based on students' understanding of ten as a unit, which are the major focus of 1.NBT.2. While in Kindergarten, students considered 10 as a "benchmark" or a "mile marker" to understand numbers 11 through 19, in Grade 1, students learn to count ten, that is, ten as a unit. Thus, extending the idea of composing and decomposing number further, instead of thinking 64 as just 60+4, we want students to think of 60 as 10+10+10+10+10+10, or six 10's. Being able to coordinate two units, i.e., ones and tens, is not a trivial task for young children. Many children at this age can recite the sequence of decade number words correctly, "ten, twenty, thirty, forty, ..." However, some children will have to count by ones to answer, "what is 10 more than 36?" For many young children, the decade number word sequence is just a memorized set of words with no numerical significance. They do not yet understand when they go from "thirty" to "forty," the number increased by 10. Thus, these standards, although they are based on 1.NBT.2, are not necessarily something that comes after students master 1.NBT.2. As students think about addition of 2 multiples of 10 or subtract a multiple of 10 from another multiple of 10, we want to encourage students to think in terms of 10's. So, questions like, "how many 10's are in __?" and "how many 10's are we adding (or taking away)?" must be an important part of teachers' questioning repertoire.