Fourth Grade Unit 1: 9 weeksIn this unit students will: Read and write multi-digit whole numbers through the millions. Recognize numbers in standard, expanded, and word form. Round multi-digit numbers to any place. Compare rounded multi-digit numbers and express their relationship using >, <, or =. Estimate sum and/or difference of numbers, apply estimation to solve problems, and determine when it is necessary or appropriate to apply estimation

strategies. fluently solve multi-digit addition and subtraction problems using the standard algorithm solve multi-step problems using addition and subtraction solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money apply the perimeter formulas for rectangles in real world and mathematical problemsUnit Resources:Unit 1 Overview video Parent Letter (Spanish) Parent Standards Clarification Number Talks Vocabulary Cards Prerequisite Skills Assessment Sample Post Assessment Student Friendly Standards Concept Map

Topic 1: Whole Numbers, Place Value, and Rounding Big Ideas/Enduring Understandings: The value of a number is determined by the place of its digits. Using rounding is an appropriate estimation strategy for solving problems and estimating. Rounded numbers are approximate and not exact. Exact answers can be rounded to different place values. A number can be written using digits in standard form, word, or expanded form. Larger numbers can be compared using the place value of the digits within the numbers. The relationship between the two numbers can be expressed using

the symbols >, <, or =.Essential Questions: How does our base ten number system work? How does understanding the base ten number system help us add and subtract? How does the value of a digit change if its location is changed in a large number? What determines the value of a digit? How does estimation help us understand large numbers?Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Generalize place value understanding for multi-digit whole numbers.MGSE4.NBT.1 Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right. For example,

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recognize that 700 ÷ 70 = 10 by applying concepts of place value and division MGSE4.NBT.2 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. MGSE4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

Vertical Articulation Second Grade Place Value StandardUnderstand Place Value.MGSE2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

a. Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Third Grade Place Value StandardUse place value understanding and properties of operations to perform multi-digit arithmetic.MGSE3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

Fifth Grade Place Value StandardUnderstand the place value system. MGSE5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Instructional Strategies:Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: place value, greater than, less than, equal to, ‹, ›, =, comparisons/compare, round

NBT.1This standard calls for students to extend their understanding of place value related to multiplying and dividing by multiples of 10. In this standard, students should reason about the magnitude of digits in a number. Students should be given opportunities to reason and analyze the relationships of numbers that they are working with.

Example:How is the 2 in the number 582 similar to and different from the 2 in the number 528?Students should be familiar with and use place value as they work with numbers. Some activities that will help students develop understanding of this standard are: Investigate the product of 10 and any number, then justify why the number now has a 0 at the end. (7 × 10 = 70) because 70 represents 7 tens and no ones, 10 × 35 = 350 because the 3 in 350 represents 3 hundreds, which is 10 times as much as 3 tens, and the 5 represents 5 tens, which is 10 times as much as

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5 ones.) While students can easily see the pattern of adding a 0 at the end of a number when multiplying by 10, they need to be able to justify why this works. Investigate the pattern, 6, 60, 600, 6,000, 60,000, 600,000 by dividing each number by the previous number.

NBT.2This standard refers to various ways to write numbers. Students should have flexibility with the different number forms. Traditional expanded form is 285 = 200 + 80 + 5. Written form is two hundred eighty-five. However, students should have opportunities to explore the idea that 285 could also be 28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones.

Students should also be able to compare two multi-digit whole numbers using appropriate symbols.

The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For example, in comparing 34,570 and 34,192, a student might say, both numbers have the same value of 10,000s and the same value of 1000s however, the value in the 100s place is different so that is where I would compare the two numbers.

In second and third grades, students only worked with numbers to one thousand. It is important to provide multiple opportunities in the classroom setting and use real-world context for students to read and write multi-digit whole numbers.

Students need to have opportunities to compare numbers with the same number of digits, e.g., compare 5,478 and 4,892; numbers that have the same number in the leading digit position, e.g., compare 35,126 and 38,087, e.g., and numbers that have different numbers of digits, e.g., 549, 86, 1,246, and 12,199.

Students also need to create numbers that meet specific criteria. For example, provide students with digit cards numbered 0 through 9. Ask students to select 4-6 cards; then, using all cards make the largest number possible number with the cards, the smallest number possible and then the closest number to 5000 that is greater than 5000 or less than 5000.

NBT.3This standard refers to place value understanding, which extends beyond an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have numerous experiences using a number line and a hundreds chart as tools to support their work with rounding.

Example:On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many total miles did they travel? Some typical estimation strategies for this problem:

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Example:Round 368 to the nearest hundred.

This will either be 300 or 400, since those are the two hundreds before and after 368.

Draw a number line, subdivide it as much as necessary, and determine whether 368 is closer to 300 or 400.

Since 368 is closer to 400, this number should be rounded to 400

When students are asked to round large numbers, they first need to identify which digit is in the appropriate place.

Example or reasoning:Round 76,398 to the nearest 1000.Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or 77,000.Step 2: I know that the halfway point between these two numbers is 76,500.Step 3: I see that 76,398 is between 76,000 and 76,500.Step 4: Therefore, the rounded number would be 76,000.

Rounding is not new in grade 4. Students need to build on the Grade 3 skill of rounding to the nearest 10 or 100 to include larger numbers and place value. What is new for Grade 4 is rounding to digits other than the leading digit, e.g., rounding 32,580 to the nearest hundred. This requires a deeper understanding than rounding to the nearest ten thousand because the digit in the hundreds place represents 900 and when rounded it becomes 1,000, not just zero. Using an open number line is crucial for developing this deep understanding.

Students should also begin to develop some rules for rounding, building off the basic strategy of; “Is 48 closer to 40 or 50?” Since 48 is only 2 away from 50 and 8 away from 40, 48 would round to 50. Number Lines are affective tools here. Then, students need to generalize the rule for much larger numbers and rounding to values that are not the leading digit.

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Engage NY Lessons are included in the activity file. Coming Soon…Common Misconceptions:NBT.2 There are several misconceptions students may have about writing numerals from verbal descriptions. Numbers like one thousand two causes problems for students. Many students will understand the 1000 and the 2 but instead of placing the 2 in the ones place, students will write the numbers as they can hear them, 10002 (ten thousand two). There are multiple strategies that can be used to assist with this concept, including place-value boxes and vertical-addition methods.

Students often assume that the first digit of a multi-digit number indicates the “greatness” of a number. The assumption is made that 954 is greater than 1002 because students are focusing on the first digit instead of the number as a whole.

Students need to be aware of the greatest place value. In this example, there is one number with the lead digit in the thousands and another numbers with its lead digit in the hundreds.

Development of a clear understanding of the value of the digits in a number is critical for the understanding of and using numbers in computations. Helping students build the understanding that 12345 means one ten thousand or 10,000, two thousands or 2000, three hundreds or 300, four tens or 40, and 5 ones or 5. Additionally, the answer is the sum of each of these values 10,000 + 2000 + 300 + 40 + 5.Differentiation:Increase the RigorNBT.1 What is the relationship between the digits in this number? (e.g. 777, etc.) How would adding a 0 to the end of a number affect the value of the digits? (e.g. 75 becoming 750) Ask students to show 523 in two different ways. Use base ten blocks or a place value chart to show examples. (see example to the right) How do you think place value connects to other math operations? (e.g. explore the relationship between place value and multiplication/division) Jill created a number using 15 base ten blocks. Using the same number of blocks, what other numbers could Jill make? How many different ways can you use base ten blocks to show 293?NBT.2 Using the digits 2, 9, and 4, create three different numbers and then order them greatest to least. Can you think of three numbers larger than 496? Justify your answer. When ordering the following numbers, what are three different numbers that could go in the blank? 45, 68, 80, ___, 113, 134 Enoch and Jasmine are comparing numbers. Enoch has 92 and Jasmine has 108. Enoch knows that you need to start at the left when comparing numbers. He

thinks that his number is bigger because it starts with a 9 and Jasmine’s number starts with a 1. Jasmine argues that her number is larger because she has more digits in her number. Who is correct and why? Use what you know about place value and the value of digits in explaining your answer.

Juan and Renaldo each have a 4-digit number that contains the digits 3, 7, 1, and 5. Juan’s number is larger. What could Juan and Renaldo’s numbers be? What are two other numbers they could be?

NBT.35

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If a number was rounded to 300, what could the number have been originally? If a number was rounded to 500, what would have been the lowest and highest values for the number if the number was rounded to the tens? What would

have been the lowest and highest values of the number if the number was rounded to hundreds? Explain your thinking. What are two different numbers you could round 4,596 to? Explain your thinking. Why is rounding important? When might it be valuable to round to the hundreds place, and when might it be valuable to round to the tens place? For example, when ordering new pencils,

round up to 400 because it’s okay to have a lot extra and they will get used, but if ordering bagged lunches for a field trip round to 380 because you wouldn’t want the food to go to waste.

When might you use rounding when adding and subtracting numbers? How about when working with fractions?

Acceleration Intervention Coming Soon…Evidence of Learning:By completion of this unit, students will be able to: Read multi-digit whole numbers. Write multi-digit-numbers. Recognize numbers in standard, expanded, and word form. Round multi-digit numbers to any place. Compare rounded multi-digit numbers and express their relationship using >, <, or =.Formative Assessments: Shared Assessments: See assessment folder for Topic 1.Adopted ResourcesMy Math:Chapter 1: Place Value 1.1 Place Value1.2 Read and Write Multi-Digit Numbers1.3 Compare Numbers1.4 Order Numbers1.5 Use Place Value to Round1.6 Problem-Solving Investigation

*These lessons are not to be completed in consecutive days as it is too much material. They are designed to help support you as you teach your standards.

Adopted Online Resourceshttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

http://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath

“Planely” a problem (NBT.1) Hot Dogs for a Picnic (NBT.2) Olympic Medal Count (NBT.2)

Think Math:Chapter 3: The Eraser Store3.5 Packaging Erasers In Tens Chapter 8: Decimals8.1 Using Place Value

Additional Resources: K-5 Math Teaching Resources http://www.k-5mathteachingresources.com/4th-grade-number-activities.html

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NBT.1Place Value ProblemsPlace Value ChartNBT.2Numeral, Word, and Expanded FormPlace Value TriangleNBT.3Round to the Nearest TenIllustrative Mathematics https://www.illustrativemathematics.org/content-standards/4/NBT/ANBT.1What’s My Number?NBT.2Ordering 4-Digit NumbersNBT.3Rounding to the Nearest 100 and 1000 (also incorporates standard NBT.1)Rounding on the Number LineRounding to the Nearest 1000Learn Zillion https://learnzillion.com/NBT.1Use a Place Value Chart and Arrow Cards to Understand Large NumbersModel Numbers Using Base-Ten BlocksUnderstand Relationships Between Digits and Their Place ValueDivide by Powers of TenNBT.2Read and Write Numbers in Numeric FormRead and Write Numbers in Word FormRead and Write Numbers in Expanded FormRead and Write Numbers with ZerosCompare Numbers Using the Symbols <, >, and =Creating Numbers Based on Given Conditions by Comparing DigitsNBT.3Locate Benchmark Numbers on a Number LineRound Numbers to the Leading Digit Using a Number LineRound Numbers to a Specified Place on a Number LineRound 9s Using Base-Ten BlocksRound in Real-Life Situations

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Study Jams provide short videos, lessons, and tutorials on specific math skills. http://studyjams.scholastic.com/studyjams/jams/math/index.htmNational Library of Virtual Manipulatives consists of web-based manipulatives. http://nlvm.usu.edu/en/nav/vlibrary.htmlEstimation 180 is a website of 180 days of estimation ideas that build number sense. http://www.estimation180.com/days.htmlGreg Tang Math Number Games http://www.gregtang.comInside Mathematics provides lessons: http://www.insidemathematics.orgFor additional assistance with this unit, please watch the unit webinarhttps://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspxSuggested ManipulativesBase ten blocksPlace value chartNumber lineExpanded-numbersHundreds chart

Vocabulary digitplace valueroundestimate

Suggested Literature Count to a MillionA Million Fish…More or LessThe Grapes of MathHow Much, How Many, How Far, How Heavy, How Long, How Tall is 1000?

Task DescriptionsScaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Task Name Task Type/Grouping Strategy

Content Addressed Standard(s) Description of Task

What Comes Next ? Scaffolding TaskPartner/Small Group Task Relative size of numbers MGSE4.NBT. 1 Students work with base ten materials to

experience that a place value in a number is ten times more than the digit to its right.

Relative Value of Places Constructing TaskPartner/ Small Group Task Relative size of numbers MGSE4.NBT.2

MGSE4.NBT.1

Students work with dotty array pieces to understand patterns within the base ten number system. Students solve place value problems to show understanding of the patterns learned.

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Number Scramble Practice TaskIndividual/Partner Task

Making and Naming Large Numbers MGSE4.NBT.2

Students create numbers given specific directions and write those numbers in standard, word and expanded form.

Ordering and Comparing Numbers

Practice TaskIndividual/Partner Task Ordering Larger Numbers MGSE4.NBT.2

Students order and compare numbers through a dice game played with a partner.

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Fourth Grade Unit 1: Topic 2: Addition and SubtractionBig Ideas/Enduring Understandings: Fluently add and subtract multi-digit whole numbers using the standard algorithm and strategies based on place value, properties of operations, and/or

the relationship between addition and subtraction. Some word problems may require multiple steps and more than one operation to find the solution.Essential Questions: How do I use the standard addition and subtraction algorithms to solve computation problems? What strategies can I use to help me make sense of a written algorithm? How do addition, subtraction, and estimation help us solve real world problems? How can we organize our work when solving a multi-step word problem?Content Standards:Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Use place value understanding and properties of operations to perform multi-digit arithmetic.MGSE4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Use the four operations with whole numbers to solve problems.MGSE4.OA.3 Solve multistep word problems with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Vertical ArticulationThird Grade Addition and Subtraction StandardsMGSE3.NBT.2 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.MGSE3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Fifth Grade Addition and Subtraction StandardsMGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.MGSE5.NF.2 Solve word problems involving addition and subtraction of fractions, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7, by observing that 3/7 < ½.

Instructional Strategies:10

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NBT.4Students build on their understanding of addition and subtraction, their use of place value and their flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place value in describing and justifying the processes they use to add and subtract.

This standard refers to fluency, which means accuracy and efficiency (using a reasonable amount of steps and time), and flexibility (using a variety of strategies such as the distributive property, decomposing and recomposing numbers, etc.).

This is the first-grade level in which students are expected to be proficient at using the standard algorithm to add and subtract. However, other previously learned strategies are still appropriate for students to use.

When students begin using the standard algorithm their explanation may be quite lengthy. After much practice with using place value to justify their steps, they will develop fluency with the algorithm. Students should be able to explain why the algorithm works.

Addition Example: 3892+1567

Student explanation for this problem:1. Two ones plus seven ones is nine ones.2. Nine tens plus six tens is 15 tens.3. I am going to write down five tens and think of the 10 tens as one more hundred.(notates with a 1 above the hundreds column)4. Eight hundreds plus five hundreds plus the extra hundred from adding the tens is 14 hundreds.5. I am going to write the four hundreds and think of the 10 hundreds as one more 1000. (notates with a 1 above the thousands column)6. Three thousands plus one thousand plus the extra thousand from the hundreds is five thousand.

Subtraction Example: 3546- 928

Student explanation for this problem:1. There are not enough ones to take 8 ones from 6 ones so I have to use one ten as 10 ones. Now I have 3 tens and 16 ones. (Marks through the 4 and

notates with a 3 above the 4 and writes a 1 above the ones column to be represented as 16 ones.)2. Sixteen ones minus 8 ones is 8 ones. (Writes an 8 in the ones column of answer.)3. Three tens minus 2 tens is one ten. (Writes a 1 in the tens column of answer.)4. There are not enough hundreds to take 9 hundreds from 5 hundreds so I have to use one thousand as 10 hundreds. (Marks through the 3 and notates

with a 2 above it.) (Writes down a 1 above the hundreds column.) Now I have 2 thousand and 15 hundreds.

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5. Fifteen hundreds minus 9 hundreds is 6 hundreds. (Writes a 6 in the hundreds column of the answer).6. I have 2 thousands left since I did not have to take away any thousands. (Writes 2 in the thousands place of answer.)

Note: Students should know that it is mathematically possible to subtract a larger number from a smaller number but that their work with whole numbers does not allow this as the difference would result in a negative number.

In terms of adding and subtracting multi-digit whole numbers using the standard algorithm, it is crucial that students understand, can think about, and explain the standard algorithm instead of following a sequence of directions or procedures that they don’t understand. Both Grade 2 and Grade 3 spent time working on developing strategies for addition and subtraction, so students should be ready to bridge the gap to the standard algorithm with understanding. The goal for Grade 4 students is for them to understand all the steps in the algorithm, and be able to explain the meaning of each digit. For example, a 1 can represent one, ten, one hundred, and so on. For multi-digit addition and subtraction in Grade 4, the goal is also fluency, which means students must be able to carry out the calculations efficiently and accurately. Holding students accountable to correct vocabulary using the Standards for Mathematical Practices is also very important as they move to the standard algorithm. It is not appropriate for students to say, “I carried the one” when it is actually a ten.

Start with a student’s understanding of a certain strategy, and then make intentional, clear-cut connections for the student to the standard algorithm. This allows the student to gain understanding of the algorithm rather than just memorize certain steps to follow.

Sometimes students benefit from 'being the teacher' to an imaginary student who is having difficulties applying standard algorithms in addition and subtraction situations. To promote understanding, use examples of student work that have been done incorrectly and ask students to provide feedback about the student work.

It is very important for some students to talk through their understanding of connections between different strategies and standard addition and subtractions algorithms. Give students many opportunities to talk with classmates about how they could explain standard algorithms. Think-Pair-Share is a good protocol for all students.

OA.3The focus in this standard is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. Students need many opportunities solving multistep story problems using addition and subtraction (unit 1).

Example: On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many miles did they travel total? Some typical estimation strategies for this problem:

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The assessment of estimation strategies should only have one reasonable answer (500 or 530), or a range (between 500 and 550). Problems will be structured so that all acceptable estimation strategies will arrive at a reasonable answer.

Estimation skills include identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or determining the reasonableness of situations using various estimation strategies. Estimation strategies include, but are not limited to: front-end estimation with adjusting (using the highest place value and estimating from the front end, making adjustments to the estimate by taking into

account the remaining amounts), clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an

estimate), rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original

values), using friendly or compatible numbers such as factors (students seek to fit numbers together - e.g., rounding to factors and grouping numbers together

that have round sums like 100 or 1000), using benchmark numbers that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate).

An interactive whiteboard, document camera, drawings, words, numbers, and/or objects may be used to help solve story problems.

Students need many opportunities solving multistep story problems using addition and subtraction and ALL situations shown in the table on the following page.

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Engage NY Lessons are included in the activity file. Coming Soon…Common Misconceptions:

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NBT.4 Often students mix up when to “carry” and when to “borrow”. Also students often do not notice the need of borrowing and just take the smaller digit from the larger one. Emphasize place value and the meaning of the digits.If students are having difficulty with linking up similar place values in numbers as they are adding and subtracting, it is sometimes helpful to have them write their calculations on the grid paper. This assists the student with lining up the numbers more accurately.

If students are having a difficult time with a standard addition algorithm, a possible modification to the algorithm might be helpful. Instead of the “shorthand” of “carrying,” students could add by place value, moving left to right placing the answers down below the “equals” line. For example:

249 + 372

500 (Start with 200 + 300 to get the 500 110 then 40 + 70 to get 110 11 and 9 + 2 to get 11.) 621

Differentiation:Increase the RigorNBT.4 What two addends could equal a sum of 146? (e.g. 67, 298, 1,130, etc.) What two numbers could you subtract to make a difference of 94? What could the two numbers be when regrouping is required? What could the two

numbers be if no regrouping is required? How many different ways can you solve 39+84? 73-25? What is similar/different between these strategies and the standard algorithm? Do you think the standard algorithm is more efficient than other strategies? Why or why not? What is the relationship between the standard algorithm and place value? Using two 3-digit numbers, create two different addition equations with a sum between 300 and 400. Using the digits 3, 5, 1, 8, 2 and 6, create a subtraction equation with the largest possible difference.OA.3 There are 583 students in Suzy’s school. 99 third grade students left the school on a field trip. There are about 20 students in each class. How many

classrooms are being used today? Explain your answer. Write an addition problem that has an answer of 548. Write a subtraction problem that has an answer of 376.

Acceleration Intervention Coming Soon…Evidence of LearningBy completion of this lesson, students will be able to: Estimate sum and/or difference of numbers apply estimation to solve problems and determine when it is necessary or appropriate to apply estimation

strategies.15

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Fluently add and subtract multi-digit whole numbers using the standard algorithm and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Solve multistep word problems with addition and subtraction Formative Assessments: Shared Assessments: See assessment folder for Topic 2.Adopted ResourcesMy MathChapter 2: Add and Subtract Whole Numbers2.2 Addition and Subtraction Patterns2.3 Add and Subtract Mentally2.4 Estimate Sums and Differences2.5 Add Whole Numbers2.6 Subtract Whole Numbers2.7 Subtract Across Zeros2.8 Problem-Solving Investigation2.9 Multi-Step Word Problems

Adopted Online Resourceshttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

http://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath

Hanging Airplanes (OA.3 & NBT.4) Insects on Tiles (NBT.4) A Gift for Grandma (NBT.4) A Party (NBT.4) Apple Pies (NBT.4) Soup, Fruit, and Juice Cans (OA.3 & NBT.4) Hot Dogs for a Picnic (OA.3)

Think MathChapter 1: Magic Squares1.1 Introducing Magic Squares1.2 Adding Magic Squares1.3 Subtracting Magic SquaresChapter 15: Estimation15.1 Estimation Strategies

Additional Web Resources:K-5 Math Teaching Resources http://www.k-5mathteachingresources.com/4th-grade-number-activities.htmlNBT.4Adding and Subtracting Multi-Digit NumbersAddition and Subtraction Number StoriesOA.3Multistep Word ProblemsIllustrative Mathematics https://www.illustrativemathematics.org/content-standards/4/NBT/AOA.3Carnival TicketsLearn Zillion https://learnzillion.com/NBT.4Add Using the Standard Addition AlgorithmSubtract Using the Standard Subtraction Algorithm

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OA.3Estimate to Assess Whether an Answer is ReasonableSolve Word Problems Using ObjectsSolve Word Problems Using DrawingsSolve Word Problems by Writing an EquationSolve Multi-Step Word Problems by Writing Two EquationsStudy Jams provide short videos, lessons, and tutorials on specific math skills. http://studyjams.scholastic.com/studyjams/jams/math/index.htmEstimation 180 is a website of 180 days of estimation ideas that build number sense. http://www.estimation180.com/days.htmlGreg Tang Math Number Games http://www.gregtang.comInside Mathematics provides lessons: http://www.insidemathematics.orgSuggested ManipulativesBase ten blocksPlace value chartOpen number linesGrid Paper (to assist with lining up numbers)

Vocabularyalgorithmsumdifferenceaddends

Suggested LiteratureThe Action SubtractionOliver’s PartySubtraction ActionMath FablesGreat Estimations

Task DescriptionsScaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Task Name Task Type/Grouping Strategy

Content Addressed Standard(s) Description of Task

Super Bowl Numbers 3 Act TaskIndividual/Partner Task

Comparing Multi-digit Numbers, Adding Multi-

digit Numbers

MGSE4.NBT.2MGSE4.NBT.4

Students make connections between the base ten number system and the Roman Numeral number system.

NFL Salaries 3 Act TaskIndividual/Partner Task

Comparing Multi-digit Numbers, Adding Multi-

MGSE4.OA.3 MGSE4.NBT.4

Students compare salaries of football players to discuss why certain players are paid a particular

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digit Numbers amount of money.

Estimation as a Check Constructing TaskIndividual/ Partner Task

Rounding, Adding, Subtracting multi-digit

numbers

MGSE4.NBT.3MGSE4.NBT.4

Students find estimated solutions to problems.

Making Sense of the Algorithm

Constructing TaskIndividual/Partner Task

Fluently subtracting multi-digit numbers MGSE4.NBT.4

Students write about strategies that are used for given problems in the task, leading to a discussion of procedures within the subtraction standard algorithm.

Fourth Grade Unit 1: Topic 3: Measurement Word Problems and Perimeter

184th Grade Unit 1 4/16/2016

Big Ideas/Enduring Understandings: Perimeter is the linear measurement of a boundary. Perimeter can be measured using the formulas 2 l + 2 w and 2 (l + w). Addition and subtraction can be used to solve word problems that involve measurement concepts.Essential Questions: How do I calculate the perimeter of a rectangle? How can I use addition and subtraction to solve word problems that involve measurement concepts?Content StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.MGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.MGSE4.MD.3 Apply the perimeter formulas for rectangles in real world and mathematical problems.

Vertical Articulation Third Grade StandardGeometric Measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. MGSE3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.MGSE3.MD.1 Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, drawing a pictorial representation on a clock face, etc. MGSE3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).17 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem

Fifth Grade StandardSolve problems involving the four operations, and identify and explain patterns in arithmetic.MGSE5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Convert like measurement units within a given measurement system. MGSE5.MD.1 Convert among different-sized standard measurement units (mass, weight, length, time, etc.) within a given measurement system (customary and metric) (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real world problems.

194th Grade Unit 1 4/16/2016

Instructional StrategiesMD.2This standard includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents).

Students should have ample opportunities to use number line diagrams to solve word problems.

Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What was the total number of minutes Mason ran?

Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave the clerk a $5.00 bill, how much change will she get back?

Number line diagrams that feature a measurement scale can represent measurement quantities. Examples include: ruler, diagram marking off distance along a road with cities at various points, a timetable showing hours throughout the day, or a volume measure on the side of a container.

Example:At 7:00 a.m. Candace wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed and 17 minutes to eat breakfast. How many minutes does she have until the bus comes at 8:00 a.m.? Use the number line to help solve the problem.

Candace is finished at 7:34. If the bus comes at 8:00, I can count on to from 7:34 to 8:00 to find how many minutes it takes for the bus to arrive. From 7:34 to 7:35 is one minute. From 7:35 to 7:40 is 5 minutes and from 7:40 to 8:00 is 20 minutes. 1 minute + 5 minutes + 20 minutes = 26 minutes until the bus arrives.

MD.3 (Perimeter)Students developed understanding of perimeter in 3rd grade by using visual models. While students are expected to use formulas to calculate perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work.The formula for perimeter can be 2𝑙 + 2𝑤 𝑜𝑟 2(𝑙 + 𝑤) and the answer will be in linear units.

This standard calls for students to generalize their understanding of perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization.

204th Grade Unit 1 4/16/2016

Example:Find the perimeter of the square:

5 inches

Since a square has four sides that are equal in length, each side must measure 5 inches. Using the perimeter formulas:2 l + 2 w = (2 x 5) + (2 x 5) = 10 + 10 = 20 inches

2 (l + w) = 2 (2 x 5) = 2 (10) = 20 inches

The perimeter of the square is 20 inches.

Engage NY Lessons are included in the activity file. Coming Soon…Common MisconceptionsStudents may confuse perimeter and area when they measure the sides of a rectangle and then multiply. They think the attribute they find is length, which is perimeter. Pose problems situations that require students to explain whether they are to find the perimeter or area.

Differentiation:Increase the RigorMD.2 If I saw a movie that was 2 hours and 37 minutes long, what time could I have entered the theatre and what time could I have left the theatre? Julianna bought a bag of candy at the movie theatre. She spent less than 75/100 of a dollar but more than 5/10 of a dollar. How much money could Julianna

have spent on candy? Give your answer in decimal form. What is another possible answer? Malachi rode his bike 268 meters to his friend’s house. He then rode his bike half a kilometer to the park. How many total meters has Malachi ridden on his

bike? Represent your answer using a model, drawing, or other representation. 1,000 pounds is the answer, what could be a story problem for this answer? At the fair, the puppet show started at 8:38am and ended at 10:45am. Storytime was ¾ hour longer than the puppet show. How long was story time? Four jugs have water in them: Jug A has 36.5 quarts, Jug B has 144 cups and Jug C has 8 ¾ gallons. Order the jugs from least to greatest MD.3 How could you go about finding the area of your rectangular classroom? What information do you need and what steps would you take to solve? A rectangular figure has a perimeter of 35cm. What could the lengths of the sides be? Give two possibilities. The floorplan of a building has an area 1200 square feet. How many rooms could the building have, and what would the area of each room be?

214th Grade Unit 1 4/16/2016

A construction worker laid 54 square feet of hardwood in the rectangular family room of a new house. What could possible perimeters of the room be? The areas of two shapes are each 40 square inches, but the perimeters are very different. Sketch the two shapes and calculate the perimeters. Imagine a rectangle with an area of 28 square centimeters. If the length of the rectangle is 3 centimeters shorter than the width, find the dimensions of the

rectangle. A rectangle has a length of 3 cm and a width of 2 cm, with an area of 6 sq.cm. Double the length and width. What is the area of this rectangle? How does that

affect the area? Try doubling the side lengths again and describe the pattern you see.

Acceleration Intervention Coming Soon…Evidence of LearningBy completion of this lesson, students will be able to: Understand the concept of perimeter and can apply it to real-world situations Calculates the perimeter of rectangles Solves word problems that involve concepts of measurement with addition and subtractionFormative Assessments: Shared Assessments: See assessment folder for Topic 3.Adopted ResourcesMy Math:Chapter 1313.1 Measure Perimeter13.2 Problem Solving

Adopted Online Resourceshttp://connected.mcgraw-hill.com/connected/login.doTeacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

http://www.exemplarslibrary.com/User: Cobb EmailPassword: cobbmath

Fence Painting (MD.2) Horseback Riding (MD.2) Pizza Time (MD.2) Snack Shopping (MD.2) Coins in Grandpa’s Pocket (MD.2) Flowerpots for Sale (MD.2) Maria’s Money (MD.2)

Think MathChapter 5: Area and Perimeter5.6 Introducing Perimeter

Additional Web ResourcesK-5 Math Teaching Resources http://www.k-5mathteachingresources.com/4th-grade-number-activities.htmlMD.2

224th Grade Unit 1 4/16/2016

Measurement Word ProblemsElapsed Time Ruler24-Hour Number LineMD.3Fencing a GardenIllustrative Mathematics https://www.illustrativemathematics.org/content-standards/4/NBT/AMD.2Margie Buys ApplesLearn Zillion https://learnzillion.com/MD.2Represent Quantities of Time Using DiagramsRepresent Liquid Volume Measurement Quantities Using DiagramsRepresent Weight Measurement Quantities Using DiagramsRepresent Quantities of Money By Using DiagramsMD.3Finding Perimeter Using the Standard FormulaFind Missing Side Lengths Using the Formula for PerimeterSuggested Manipulativesbase ten blocks grid papergeoboards pentominos color tiles

Vocabulary perimeterequationexpression sum

Suggested Literature Perimeter, Area, and Volume: A Monster Book of DimensionsSpaghetti and Meatballs for All!Bigger, Better, Best!Racing Around

Task Descriptions:Scaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solving Practice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation. Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Task Name Task Type/Grouping Content Addressed Standard(s) Task Description

234th Grade Unit 1 4/16/2016

Strategy

Nice Numbers Constructing TaskPartner/Small group Task

Rounding, Four Operations

MGSE4.OA.3 MGSE4.NBT.3MGSE4.NBT.4MGSE4.MD.2

Students apply rounding concepts to find estimated solutions to word problems.

Reality Checking Constructing TaskIndividual/ Partner Task

Ordering, Adding, Subtracting and Rounding

multi-digit numbers

MGSE4.NBT.2 MGSE4.NBT.4MGSE4.NBT.3MGSE4.MD.2

Students apply knowledge of the addition and subtraction standard algorithm in order to balance a mock check registry.

It’s in the Number Culminating TaskIndividual Task

Calculation and Estimation with Whole

Numbers

MGSE4.OA.3MGSE4.NBT.2MGSE4.NBT.3MGSE4.MD.2

Students gather data about populations in the U.S. to draw conclusions about why people choose to live in certain regions of the country.

244th Grade Unit 1 4/16/2016