# Parent Packet. HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1

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1 Parent Packet HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE School Year

2 Grade 4 Module 1 Place Value, Rounding, and Algorithms for Addition and Subtraction 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).

3 Topic A Place Value of Multi Digit Whole Numbers In Topic A, students build the place value chart to 1 million and learn the relationship between each place value as 10 times the value of the place to the right. Students manipulate numbers to see this relationship, such as 30 hundreds composed as 3 thousands. They decompose numbers to see that 7 thousands is the same as 70 hundreds. As students build the place value chart into thousands and up to 1 million, the sequence of three digits is emphasized. They become familiar with the base thousand unit names up to 1 billion. Students fluently write numbers in multiple formats: as digits, in unit form, as words, and in expanded form up to 1 million. Topic B Comparing Multi Digit Whole Numbers In Topic B, students use place value to compare whole numbers. Initially using the place value chart, students compare the value of each digit to surmise which number is of greater value. Moving away from dependency on models and towards fluency with numbers, students compare numbers by observing across the entire number and noticing value differences. For example, in comparing 12,566 to 19,534, it is evident 19 thousands is greater than 12 thousands because of the value of the digits in the thousands unit. Additionally, students continue with number fluency by finding what is 1, 10, or 100 thousand more or less than a given number. Topic C Rounding Multi Digit Whole Numbers In Topic C, students round to any place using the vertical number line and approximation. The vertical number line allows students to line up place values of the numbers they are comparing. In Grade 3, students rounded to the nearest 10 or 100 using place value understanding. Now, they extend this understanding rounding to the nearest thousand, ten thousand, and hundred

5 Students use the algorithm to subtract numbers from 1 million allowing for multiple decompositions (4.NBT.4). The topic concludes with practicing the standard algorithm for subtraction in the context of two-step word problems where students have to assess the reasonableness of their answers by rounding (4.OA.3). When using tape diagrams to model word problems, students use a variable to represent the unknown quantity. Topic F Addition and Subtraction Word Problems Module 1 culminates with multi-step addition and subtraction word problems in Topic F (4.OA.3). In these lessons, the format for the Concept Development is different from the traditional vignette. Instead of following instruction, the Problem Set facilitates the problems and discussion of the Concept Development. Throughout the module, tape diagrams are used to model word problems, and students continue to use tape diagrams to solve additive comparative word problems. Students also continue using a variable to represent an unknown quantity. To culminate the module, students are given tape diagrams or equations and are encouraged to use creativity and the mathematics learned during this module to write their own word problems to solve using place value understanding and the algorithms for addition and subtraction. The module facilitates deeper comprehension and supports determining the reasonableness of an answer. Solving multi-step word problems using multiplication and division are addressed in later modules.

6 Grade 4 Module 1 Place Value, Rounding, and Algorithms for Addition and Subtraction OVERVIEW 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. 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). 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. 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, = 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 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). Throughout these topics, students will apply their algorithmic knowledge to solve word problems. Also, students use a variable to represent the unknown quantity.

7 The module culminates with multi-step word problems in Topic F. 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. **The sample questions/responses contained in this manual are straight from They are provided to give some insight into the kinds of skills expected of students as the lesson is taught.

8 Terminology New or Recently Introduced Terms Ten thousands, hundred thousands (as places on the place value chart) One millions, ten millions, hundred millions (as places on the place value chart) Algorithm Variable Familiar Terms and Symbols Sum (answer to an addition problem) Difference (answer to a subtraction problem) Rounding (approximating the value of a given number) Place value (the numerical value that a digit has by virtue of its position in a number) Digit (a numeral between 0 and 9) Standard form (a number written in the format: 135) Expanded form (e.g., = 135) Word form (e.g., one hundred thirty-five) Tape diagram (bar diagram) Number line (a line marked with numbers at evenly spaced intervals) Bundling, making, renaming, changing, exchanging, regrouping, trading (e.g. exchanging 10 ones for 1 ten) Unbundling, breaking, renaming, changing, regrouping, trading (e.g. exchanging 1 ten for 10 ones) =, <, > (equal, less than, greater than) Number sentence (e.g., = 7) Suggested Tools and Representations Place value charts Place value cards (including 7 place values) Number lines

9 Place value charts: Place value charts allow for students to determine the value of each digit of a number (ones, tens, hundreds, etc.) by relating its position to its value. Place value charts may also be used with number disks/dots to address the same idea. Place value cards: Place value cards allow for students to determine the value of each digit of a number (ones, tens, hundreds, etc.) by writing out its value in standard form (ie: 700 or 6). The cards may be proportionately sized to allow for the cards to be place on top of one another to show that the value of each individual digit builds up to the value of the whole number (ie: 700 or 7 hundreds + 6 or 6 ones = 706). Number Line: The number line is used to develop a deeper understanding of whole number units, fraction units, measurement units, decimals, and negative numbers. Throughout Grades K-5, the number line models measuring units. Vertical number lines are used to aid in rounding/estimation.

10 Tape Diagram: Tape diagrams, also called bar models, are pictorial representations of relationships between quantities used to solve word problems. At the heart of a tape diagram is the idea of forming units. In fact, forming units to solve word problems is one of the most powerful examples of the unit theme and is particularly helpful for understanding fraction arithmetic. The tape diagram provides an essential bridge to algebra and is often called pictorial algebra. There are two basic forms of the tape diagram model. The first form is sometimes called the part-whole model; it uses bar segments placed end-to-end (Grade 3 Example), while the second form, sometimes called the comparison model, uses two or more bars stacked in rows that are typically left justified. (Grade 5 Example).

11 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.

12 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.

13 Lesson 5 Objective: Compare numbers based on meanings of the digits, using >,<, or = to record the comparison. Lesson 6 Objective: Find 1, 10, and 100 thousand more and less than a given number.

14 Lesson 7 Objective: Round multi-digit numbers to the thousands place using the vertical number line. Lesson 8 Objective: Round multi-digit numbers to any place using the vertical number line.

15 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.

16 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.

17 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.

18 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.

19 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.

20 Lesson 19 Objective: Create and solve multi-step word problems from given tape diagrams and equations.

21 Technology Resources -This site provides an extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics. fun games to help kids master the common core standards. common core educational math games and videos. math video tutorials. practice common core interactive math skills practice. common core interactive math skill practice/ games, worksheets and tutorials. common core interactive practice, video lessons and worksheets animated tutorials of curriculum content that engages students. Can use a limited free version or buy a subscription.

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