Students continue to work on developing and deepening conceptual comprehension and fluency throughout Module 5.

Topic A concerns place value techniques for adding and subtracting inside 1,000.  (2.NBT.B.7).  Students associate 100 more and 100 less with 100 addition and subtraction (2.NBT.B.8).  They add and subtract multiples of 100, including counting on to remove (for example, for 650 – 300, they begin with 300 and think, “300 more takes me to 600, and 50 more gets me to 650, so… 350”).  Students also employ addition and subtraction simplification procedures.  They extend the make-a-ten strategy to make a hundred by mentally decomposing one addend to make a hundred with the other (for example, 299 + 6 becomes 299 + 1 + 5, or 300 + 5, which equals 305) and use compensation to subtract from three-digit numbers (for example, 376 – 59, add 1 to each, 377 – 60 = 317).  The topic concludes with students sharing and criticizing addition and subtraction problem solution ideas.  Students utilize place value language and operations characteristics to describe why their solutions work throughout the topic (2.NBT.B.9).

Students continue to expand on Module 4’s work in Topics B and C, now constructing and decomposing tens and hundreds inside 1,000 words (2.NBT.B.7).  Students begin each topic by relating manipulative representations to the algorithm and then go to making math drawings in place of the manipulatives.  Students utilize place value reasoning and operations characteristics to describe their work like they usually do.

Students use addition and subtraction fluency within 100 throughout Module 5.  These lessons focus on adding and subtracting within 1,000 by utilizing models or drawings and strategies based on place value, operations qualities, the link between addition and subtraction, and written methods.  Number bonds, chip models, arrow notation, the algorithm, and tape diagrams are all examples of written methods.  Many pupils need to keep track of these tactics to solve them appropriately.  The courses are structured to provide plenty of opportunity for conversations about student thinking, such as why their addition and subtraction procedures work (2.NBT.B.9).  Students, for example, can utilize the link between addition and subtraction to show why their subtraction solution is correct.

The module concludes with topic D, where students synthesize their learning of addition and subtraction procedures and select the most efficient strategy for presented problems.  They use place value language and their comprehension of operation properties to argue their decisions (2.NBT.B.9).

Beginning in Topic C and continuing throughout the year, each day’s Fluency Practice gives a chance for review and mastery of sums and differences with totals up to 20 using the Core Fluency Practice Sets or Sprints.

The Mid-Module Assessment follows topic B.  Topic D is followed by the End-of-Module Assessment.

Mathematical Practice Focus Standards

MP.3 Create credible arguments and evaluate the logic of others.  Students explain how each step in their painting connects to a stage in the algorithm using place value reasoning.  They choose and present numerous problem-solving solutions, such as number bonds, chip models, vertical form, arrow notation, and tape diagrams.  When kids listen to peers explain their problem-solving tactics and then debate the usefulness of those strategies, they analyze the reasoning of others.

MP.6 Pay attention to detail.  When students use place value language to explain their math drawings and calculations, they pay attention to precision.  They express the mathematical properties they employ to solve various issues.  For example, when adding 435 + 70, a student could demonstrate comprehension of the associative principle by explaining, “I know that 30 + 70 = 100; so, I added 400 + 100 + 5, which is 505.”

MP.7 Look for and utilize structure.  Students search for and employ the base ten structure when composing and deconstructing.  They expand their understanding from Module 4 by seeing ten tens as constituting a new unit called a hundred, just as ten ones create one ten.  When adding and subtracting three-digit integers, they use their grasp of base ten structure by frequently bundling and unbundling groups of ten.  Students also use structure when they apply simplifying tactics like compensation to construct a multiple of ten or a hundred.

MP.8 In repeated reasoning, look for and convey regularity.  Students notice the cyclic pattern of the addition or removal of like units and the following possible composition or breakdown of units through the place values when they repeatedly handle models and record the work abstractly.  They recognize that the vertical shape symbolizes the same cycle as the manipulatives.