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Module 1

Place Value, Rounding, and Algorithms for Addition and Subtraction

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In this 25-day module of Grade 4, students extend their work with whole numbers.  They begin with large numbers using familiar units (hundreds and thousands) and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1).  They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion).[1]

The place value chart will be fundamental in Topic A.  Building upon their previous knowledge of bundling, students learn that 10 hundreds can be composed into 1 thousand and, therefore, 30 hundreds can be composed into 3 thousands because a digit’s value is ten times what it would be one place to its right (4.NBT.1).  Conversely, students learn to recognize that in a number such as 7,777 each 7 has a value that is 10 times the value of its neighbor to the immediate right. 1 thousand can be decomposed into 10 hundreds, therefore 7 thousands can be decomposed into 70 hundreds.

Similarly, multiplying by 10 will shift digits one place to the left, and dividing by 10 will shift digits one place to the right.

3,000 = 300 x 10 3,000 ÷ 10 = 300

In Topic B, students use place value as a basis for comparison of whole numbers.  Although this is not a new topic, it becomes more complex because the numbers are larger.  For example, it becomes clear that 34,156 is 3 thousand greater than 31,156.

Comparison leads directly into rounding, where their skill with isolating units is applied and extended. Rounding to the nearest ten and hundred was mastered with 3 digit numbers in Grade 3.  Now Grade 4 students moving into Topic C learn to round to any place value (4.NBT.3) initially using the vertical number line though ultimately moving away from the visual model altogether.  Topic C also includes word problems where students apply rounding to real life situations.

In Grade 4, students become fluent with the standard algorithms for addition and subtraction.  In Topics D and E students focus on single like-unit calculations (ones with ones, thousands with thousands, etc.) at times requiring the composition of greater units when adding (10 hundreds are composed into 1 thousand) and decomposition into smaller units when subtracting (1 thousand is decomposed into 10 hundreds) (4.NBT.4). Throughout these topics, students will apply their algorithmic knowledge to solve word problems.  Also, students use a variable to represent the unknown quantity.

The module culminates with multi-step word problems in Topic F (4.OA.3). Tape diagrams are used throughout the topic to model additive compare problems like the one exemplified below.  These diagrams facilitate deeper comprehension and serve as a way to support the reasonableness of an answer.

A goat produces 5,212 gallons of milk a year. The cow produces 17,279 gallons a year. How much more milk does the goat need to produce to make the same amount of milk as a cow?

17,279 - 5,212 = _____

The goat needs to produce _______ more gallons of milk a year.

The mid-module assessment will follow Topic C. The end-of-module assessment follows Topic F.

[1] Grade 4 expectations in the NBT standards domain, however, are limited to whole numbers less than or equal to 1,000,000.

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