Grade 2 - California Department of Education

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State Board of Education-Adopted Grade Two Page 20 of 45 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 generalizable methods to compute sums and differences of whole numbers in base-ten notation. While students become fluent in such methods within 100 at grade two, they also use these methods for sums and differences within 1000. The narrative will first present general written strategies for numbers within 1000, since they are simply extensions of those for numbers within 100. Of course, all methods for adding and subtracting two- and three-digit numbers should be based on place value and should be learned by students with an emphasis on understanding. Math drawings should accompany such written methods as students become familiar with them. Written methods for addition and subtraction are based on two important features of the base-10 number system: • When adding or subtracting numbers in the base-10 system, like units are added or subtracted (e.g., ones are added to ones, tens to tens, hundreds to hundreds). • Adding and subtracting multi-digit numbers written in base-10 can be facilitated by composing and decomposing units appropriately, so as to reduce the methods to simply doing additions and subtractions within 20 (e.g., 10 ones make 1 ten, 100 ones make 1 hundred, 1 hundred makes 10 tens). The following table illustrates two written methods for addition, with accompanying illustrations (base-10 blocks can also be used to illustrate). Students first work with math drawings or manipulatives alongside the written methods; they will eventually move on to just using written methods, mentally constructing pictures as necessary and using other strategies. Teachers should note the importance of these methods; they generalize to larger numbers and decimals and emphasize the regrouping nature of combining units. Note that these two methods are only examples and are not meant to represent all such place value methods. The Mathematics Framework was adopted by the California State Board of Education on November 6, 2013. The Mathematics Framework has not been edited for publication.
State Board of Education-Adopted Grade Two Page 21 of 45 346 347 348 349 350 351 352 353 354 355 356 357 The following table also illustrates two methods for subtraction, one where all decomposing is done first, the other where decomposing is done as needed. Students will encounter situations where students “don’t have enough” to subtract. Note that this is more precise than saying, “You can’t subtract a larger number from a smaller number,” or the like, as the latter statement is a false mathematical statement. Eventually, students will subtract and obtain negative numbers. Note the accompanying diagrams that show the decomposing steps in each written subtraction method. Again, these methods generalize to numbers of all sizes, and are based on decomposing larger units into smaller units when necessary. The Mathematics Framework was adopted by the California State Board of Education on November 6, 2013. The Mathematics Framework has not been edited for publication.
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Grade 2 - California Department of Education

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