Place Value, Rounding, and Algorithms for Addition and Subtraction
In this 25-day Grade 4 module, 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 is fundamental to 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 10 times what it would be one place to its right (4.NBT.1). 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. One thousand can be decomposed into 10 hundreds, therefore 7 thousands can be decomposed into 70 hundreds.
Similarly, multiplying by 10 shifts digits one place to the left, and dividing by 10 shifts digits one place to the right.
3,000 = 10 × 300 3,000 ÷ 10 = 300
In Topic B, students use place value as a basis for comparing whole numbers. Although this is not a new concept, it becomes more complex as the numbers become larger. For example, it becomes clear that 34,156 is 3 thousands greater than 31,156.
34,156 > 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 three-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 apply their algorithmic knowledge to solve word problems. Students also 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. A cow produces 17,279 gallons of milk a year. How much more milk does a goat need to produce to make the same amount of milk as a cow?
17,279 - 5,212 = _____
A goat needs to produce _______ more gallons of milk a year.
The Mid-Module Assessment follows Topic C. The End-of-Module Assessment follows Topic F.
¹Grade 4 expectations in the NBT standards domain are limited to whole numbers less than or equal to 1,000,000.Read More
- Fluency Practice
- Application Problem
- Concept Development
- Student Debrief
- Lesson 1: Objective: Interpret a multiplication equation as a comparison.
- Lesson 2: Objective: Recognize a digit represents 10 times the value of what it represents in the place to its right.
- Lesson 3: Objective: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units.
- Lesson 4: Objective: Read and write multi-digit numbers using base ten numerals, number names, and expanded form.
- Standards 4.NBT.2
- Standards 4.NBT.3
- Lesson 7: Objective: Round multi-digit numbers to the thousands place using the vertical number line.
- Lesson 8: Objectives: Round multi-digit numbers to any place using the vertical number line.
- Lesson 9: Objective: Use place value understanding to round multi-digit numbers to any place value.
- Lesson 10: Objective: Use place value understanding to round multi-digit numbers to any place value using real world applications.
- Lesson 11: Objective: Use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm and apply the algorithm to solve word problems using tape diagrams.
- Lesson 12: Objective: Solve multi-step word problems using the standard addition algorithm modeled with tape diagrams and assess the reasonableness of answers using rounding.
- Lesson 13: Objective: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams.
- Lesson 14: Objective: Use place value understanding to decompose to smaller units up to 3 times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.
- Lesson 15: Objective: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.
- Lesson 16: Objective: Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using rounding.
- Lesson 17: Objective: Solve additive compare word problems modeled with tape diagrams.
- Lesson 18: Objective: Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding.
- Lesson 19: Objective: Create and solve multi-step word problems from given tape diagrams and equations.