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Grade 4 UNIT 1: Place Value, Rounding, and Algorithms for Addition and Subtraction Unit Instructional Days: 25

|Essential Question |Key Concepts |Cross Curricular Connections |

|How does understanding place value and units of measure help you to solve |Place Value of Multi-Digit Whole numbers |Religion: Use a parable, such as the Parable of the Talents, to |

|multi-digit and multi-step problems? |Comparing Multi-Digit Whole Numbers |use addition to count and explain its meaning. |

| |Rounding Multi-Digit Whole Number Addition* |Science: |

|Vocabuarly |Multi-Digit Whole Number Addition |1. Use the Internet to research hurricanes and/or tornadoes. |

|Ten thousands, hundred thousands |Multi-Digit Whole Number Subtraction |Compare and evaluate two recent hurricanes and/or tornadoes based |

|One millions, ten millions, hundred millions |Addition and Subtraction Word Problems** |on wind speed and/or rainfall. Create a bar graph with an |

|Algorithm | |appropriate number scale. Generate addition, subtraction, |

|Variable |*Assessments |multiplication and division word problems based on the data. |

|Sum Digit |*Mid-Module Assessment: After Section C | |

|Difference Standard format |(2 days, included in Unit Instructional Days) | |

|Rounding Expanded form |**End-of-Module Assessment: after Section F (2days, included in Unit | |

|Place value Word form |Instructional Days) | |

|Tape diagram =, | | |

|Number line | | |

|Number sentence | | |

|Bundling, making, renaming, changing, exchanging, regrouping, trading (e.g. | | |

|exchanging 10 ones for 1 ten) | | |

|Mathematical Practices |

|MP.1 Make sense of problems and persevere in solving them. Students use the place value chart to draw diagrams of the relationship between a digit’s value and what it would be one place to its right, for instance, by |

|representing 3 thousands as 30 hundreds. Students also use the place value chart to compare very large numbers. |

|MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their relationships as they use both special strategies and the standard addition algorithm to add and subtract multi-digit numbers. Students|

|also decontextualize when they represent problems symbolically and contextualize when they consider the value of the units used and understand the meaning of the quantities as they compute. |

|MP.3 Construct viable arguments and critique the reasoning of others. Students construct arguments as they use the place value chart and model single- and multi-step problems. Students also use the standard algorithm as a |

|general strategy to add and subtract multi-digit numbers when a special strategy is not suitable. |

|MP.5 Use appropriate tools strategically. Students decide on the appropriateness of using special strategies or the standard algorithm when adding and subtracting multi-digit numbers. |

|MP.6 Attend to precision. Students use the place value chart to represent digits and their values as they compose and decompose base ten units. |

|Unit Outcome (Focus) |

|In this 25-day Unit 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). |

UNIT 1 SECTION A: Place Value of Multi-Digit Whole Numbers Instructional Days: 4

|Essential Question |Key Objectives |

|How does understanding place value and units of measure help |Interpret a multiplication equation as a comparison. |

|you to solve multi-digit and multi-step problems? |Recognize a digit represents 10 times the value of what it represents in the place to its right. |

| |Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units. |

| |Read and write multi-digit numbers using base ten numerals, number names, and expanded form. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|The place value chart will be fundamental in Section A. |4.NBT.1 |Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the | |

|Building upon their previous knowledge of bundling, students |(DOK 1) |place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. |( |

|learn that 10 hundreds can be composed into 1 thousand and, | | | |

|therefore, 30 hundreds can be composed into 3 thousands because| |Read and write multi-digit whole numbers using base-ten numerals, number 5 names, and expanded form. Compare two | |

|a digit’s value is ten times what it would be one place to its |4.NBT.2 |multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of |( |

|right (4.NBT.1). Conversely, students learn to recognize that |(DOK 1) |comparisons. | |

|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 | |Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as | |

|can be decomposed into 10 hundreds, therefore 7 thousands can |4.OA.1 |many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as a multiplication |( |

|be decomposed into 70 hundreds. |(DOK2) |equations. | |

|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 | | | |

| | | | |

| | | | |

| | | | |

UNIT 1 SECTION B: Comparing Multi-Digit Whole Numbers Instructional Days: 2

|Essential Question |Key Objectives |

|How does understanding place value and units of |Compare numbers based on meanings of the digits, using >,, =, and < symbols to record the results of comparisons. |( |

|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. | | | |

UNIT 1 * SECTION C: Rounding Multi-Digit Whole Numbers Instructional Days: 4

|Essential Question |Key Objectives |

|How does understanding place value and units of |Round multi-digit numbers to the thousands place using the vertical number line. |

|measure help you to solve multi-digit and |Round multi-digit numbers to any place using the vertical number line. |

|multi-step problems? |Use place value understanding to round multi-digit numbers to any place value. |

| |Use place value understanding to round multi-digit numbers to any place value using real world applications. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Comparison leads directly into rounding, where |4.NBT.3 |Use place value understanding to round multi-digit whole numbers to any place. | ( |

|their skill with isolating units is applied and |(DOK2) | | |

|extended. Rounding to the nearest ten and | | | |

|hundred was mastered with 3 digit numbers in | | | |

|Grade 3. Now Grade 4 students moving into | | | |

|Section 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. Section C also includes| | | |

|word problems where students apply rounding to | | | |

|real life situations. | | | |

UNIT 1 SECTION D: Multi-Digit Whole Number Addition Instructional Days: 2

|Essential Question |Key Objectives |

|How does understanding place value and units of |Use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm and apply the algorithm to solve word |

|measure help you to solve multi-digit and multi-step|problems using tape diagrams. |

|problems? |Solve multi-step word problems using the standard addition algorithm modeled with tape diagrams and assess the reasonableness of answers using rounding. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Grade 4, students become fluent with the standard| | | |

|algorithms for addition and subtraction. In Section |4.OA.3 |Use the four operations with whole numbers to solve problems. |( |

|D students focus on single like-unit calculations |(DOK 2) |Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including | |

|(ones with ones, thousands with thousands, etc.) at | |problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the | |

|times requiring the composition of greater units | |unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including | |

|when adding (10 hundreds are composed into 1 | |rounding. | |

|thousand) (4.NBT.4). Throughout these lessons, | | | |

|students will apply their algorithmic knowledge to | |Fluently add and subtract multi-digit whole numbers using the standard algorithm. | |

|solve word problems. Also, students use a variable |4.NBT.4 | |( |

|to represent the unknown quantity. |(DOK1) | | |

| |( | | |

| | |Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to | |

| |4.NBT.1 |its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. | |

| |(DOK1) | |( |

| | |Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit | |

| | |numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | |

| |4.NBT.2 | |( |

| |(DOK1) | | |

UNIT 1 SECTION E: Multi-Digit Whole Number Subtraction Instructional Days: 4

|Essential Question |Key Objectives |

|How does understanding place value and units of |Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems |

|measure help you to solve multi-digit and |using tape diagrams. |

|multi-step problems? |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. |

| |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. |

| |Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams and assess the reasonableness of answers using |

| |rounding. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Grade 4, students become fluent with the |4.OA.3 |Use the four operations with whole numbers to solve problems. | ( |

|standard algorithms for subtraction. In Section |(DOK 2) |Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including | |

|E students focus on single like-unit | |problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the | |

|calculations (ones with ones, thousands with | |unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | |

|thousands, etc.) at times requiring the | | |( |

|decomposition into smaller units when | |Fluently add and subtract multi-digit whole numbers using the standard algorithm. | |

|subtracting (1 thousand is decomposed into 10 | | |( |

|hundreds) (4.NBT.4). Throughout these topics, |4.NBT.4 | | |

|students will apply their algorithmic knowledge |(DOK1) | |( |

|to solve word problems. Also, students use a |( |Use place value understanding to round whole numbers to the nearest 10 or 100. | |

|variable to represent the unknown quantity. | | | |

| |4.NBT.1 | | |

| |(DOK1) |Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the| |

| | |relationship between addition and subtraction. | |

| |4.NBT.2 | | |

| |(DOK1) | | |

UNIT 1 **SECTION F: Addition and Subtraction Word Problems Instructional Days: 3

|Essential Question |Key Objectives |

|How does understanding place value and units of |Solve additive compare word problems modeled with tape diagrams. |

|measure help you to solve multi-digit and |Solve multi-step word problems modeled with tape diagrams and assess the reasonableness of answers using rounding. |

|multi-step problems? |Create and solve multi-step word problems from given tape diagrams and equations. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|The Unit culminates with multi-step word problems |4.OA.3 |Use the four operations with whole numbers to solve problems. | |

|in Section F (4.OA.3). Tape diagrams are used |(DOK 2) |Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including |( |

|throughout the Section to model additive compare | |problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown | |

|problems like the one exemplified below. These | |quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | |

|diagrams facilitate deeper comprehension and serve| | | |

|as a way to support the reasonableness of an | |Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its | |

|answer. | |right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. | |

|A goat produces 5,212 gallons of milk a year. The |4.NBT.1 | |( |

|cow produces 17,279 gallons a year. How much more |(DOK1) |Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers| |

|milk does the goat need to produce to make the | |based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | |

|same amount of milk as a cow? | | | |

|[pic] |4.NBT.2 |Fluently add and subtract multi-digit whole numbers using the standard algorithm. |( |

|The goat needs to produce _______ more gallons of |(DOK1) | | |

|milk a year. | | | |

| | | | |

| |4.NBT.4 | |( |

| |(DOK1) | | |

|Possible Activities |

|MEASUREMENT TABLES: Show students various objects (pencil, long stick, jug of marbles for weight or capacity, etc.). Have students write down the objects and their estimated guess for the object’s |

|measurement. Have them come up one by one to measure the objects, and record their measurements. Once they have recorded their data have them convert the units. Additional practice and games can be found |

|online (see below) |

|Ex: 3 feet = 1 yard = 36 inches. Try to stay to the nearest whole number for this activity. |

|Practice with conversions can be found at . Click on Conversions on the right. |

|Interactive conversion student game visit . Click on Math Games and select Measuring on the top menu. |

| |

|CONVERSION WORD PROBLEMS WITH DISPLAYS: Students can practice solving conversion word problems and display answers using a number line diagram that features a measurement scale. |

|Resources |

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|ROUNDING: Check out these great Rounding Graphs and Tutorials for students found at . Click on Math Charts and select Enter Here then Rounding Numbers examples at the bottom |

|of the page. |

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|Online video lesson and practice questions that address standard specific activities ( Solving multi-step word problems 4.OA.3): |

| |

|Free App: |

|Teaching Number Lines: Little Monkey Apps Number Lines aims to help students to visualize numbers for rote counting and ordering and to see the physical position of a number linking patterns and |

|relationships. Unlike counters, which model counting, a number line also models measurement, which is why the number line begins with zero as you would see on a ruler. Students are also exposed to |

|different vocabulary for addition and subtraction, such as step forward or jump back to physically suggest the movement of the frog along the number line. |

| |

|Possible Activities |

|PLACE VALUE PUZZLES: (group activity) This activity reinforces place value. Teacher writes dashes for an unknown number: ___ ___ ___ ___ ___. The teacher follows the dashes with clues: Clue 1: The digit in|

|the thousand place is the quotient of 36 and 6. The digit in the ones place is three squared etc. Extend: Ask students to create the puzzles for other students. Game sheets can be created or downloaded from|

| . Click on Math Games/Activities. |

|CROSS-OUT SINGLES ACTIVITY (group activity) Materials: Bank paper and 2 dice. This game reinforces addition. Have students draw a 3 x 3 rectangular array on a piece of paper. Roll the dice and call out the |

|sum/number. Have students write the sum in one of the nine squares. Roll the dice nine times total. After all nine squares are filled in; have the students calculate the sum of each column, row, and |

|diagonal. They now have 8 numbers. Have them cross out the “singles” (numbers that do not have a partner). Three matching numbers are crossed out as they all have a partner. Students then calculate the sum |

|of the remaining numbers. The student who has the highest (or lowest) number wins the game. Extend: Find ways to produce a zero score. Using the numbers 1 to 9 each once, what is the highest score possible?|

|Discuss strategies for how to place numbers. Game sheets can be created or downloaded from . Click on Math Games/Activities. |

|GET TO ZERO: (2 player game) Have each student start with the number 999 written on the top of a piece of paper. Students take turns rolling three dice. The student arranges the dice in any order and |

|subtracts that number from 999. For example, if students roll a 3, 5, and 6 they could subtract 536, 635, etc. from 999. Each student should “do the math” to check each other’s work. The students take |

|turns, rolling the dice and subtracting. At any time they can choose to roll only one or two dice instead of all three dice. The first student to get to zero (exactly) wins the game. If they cannot subtract|

|the number rolled, they skip their turn. Game sheets can be created or downloaded from . Click on Math Games/Activities. |

|CROSSWORD PUZZLE: Reinforce addition/subtraction within 10,000. Crosswords can be created or downloaded. Downloadable crossword puzzles at . Click on the link Cross Words and select Grade |

|Levels 3 and 4 for games. |

|ROUNDING ACTIVITY: (2 player game) This card game reinforces rounding. Each student has a half a deck of cards (face cards removed). The students flip over three cards in order and round the number to the |

|nearest hundred. The student with the highest number wins the two groups of cards. The players continue until all cards are gone from one student. |

|Resources |

|PRACTICE WORKSHEETS (AND ANSWERS): (math facts; multi-digit addition and subtraction; rounding; place value practice). |

|EXTRA MATH FACTS PRACTICE: |

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|math/addition.html |

|ROUNDING LINK: Check out these great Rounding Graphs and Tutorials for students found at . Click on Math Charts then Enter Here and select the Rounding Examples. |

|Online video lesson and practice questions to address standard specific needs (Use place value chart and arrow cards to understand large numbers 4.NBT.1): |

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|Online video lesson and practice questions to address standard specific needs ( Reading, writing, and comparing multi-digit whole numbers 4.NBT. 2): |

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