3Rd Gradeplace Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2

Unit of Study Place Value and Multi-Digit Arithmetic Topic: Understanding place value; Solving problems Grade: 3 involving measurement and estimation of units of Length of Unit: measure Focus of Learning Common Core Standards: Mathematical Practices: Number and Operations in Base Ten 1. Make sense of problems Use place value understanding and properties of operations to perform multi- and persevere in solving digit arithmetic. them. 3.NBT.1 Use place value understanding to round whole numbers to the nearest 2. Reason abstractly and 10 or 100. quantitatively. 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms 3. Construct viable arguments based on place value, properties of operations, and/or the relationship between addition and subtraction. and critique the reasoning 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the rage 10 – of others. 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of 4. Model with mathematics. operations. 5. Use appropriate tools Measurement and Data strategically. Solve problems involving measurement and estimation of intervals of time, 6. Attend to precision. liquid volumes, and masses of objects. 7. Look for and make use of 3.MD. 1 Tell and write time to the nearest minute and measure time intervals in structure. minutes. Solve word problems involving addition and subtraction of time 8. Look for and express intervals in minutes, e.g., by representing the problem on a number line regularity in repeated diagram. reasoning. 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 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. Enduring Understanding(s): Students will understand that… 1) The positions of digits in numbers determine what value they represent 2) Place value is used to compose and decompose numbers, for example 1,234 is 1,000 + 200 + 30 + 4 3) Composing and decomposing numbers using base-10 units can be helpful for computation 4) Numbers can be rounded up or down 5) Rounding is used as a way to estimate an answer and/or check the reasonableness of a result 6) Addition and subtraction are inverse operations 7) Addition and subtraction are used to represent and solve real-world situations Essential Questions: These questions will guide student inquiry. 1) What is place value and why is it important? 2) Why is there only one digit allowed in each place of a multi-digit number? 3) What does “base ten” mean? 4) What does “rounding” mean? 5) How can a number line help you round? 6) What is an interval? 7) How do you select an appropriate interval for a number line? 8) When might you round to the nearest 10? When might you round to the nearest 100? 9) In what kinds of situations is it appropriate to estimate? Why? 10) How is subtraction related to addition? 11) How is multiplication related to addition?

3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2 12) Why is it useful to tell and write time to the nearest minute? 13) When might you solve problems involving addition and subtraction of time intervals? 14) When might you measure and estimate liquid volumes and masses of objects in your everyday life? Student Performance Knowledge: Students will understand/know… Application: Students will be able to…  The position of digits in a number determine its  Label a place value chart to the 1,000s value  Compose and decompose numbers  Multi-digit numbers are composed of ones, tens,  Round whole numbers to the nearest 10 and/or to the hundreds, etc… nearest 100  As you move to the left on a place value chart, the  Represent numbers on a number line numbers get larger  Use a number line as a strategy to round numbers  Big numbers possess the same place-value structure  Add and subtract numbers within 1000 by as smaller numbers manipulating materials and/or drawing pictures  Rounding can be used to estimate and check  Add and subtract numbers within 1000 by using tape answers for reasonableness diagrams  Rounding is simplifying a number to its nearest  Represent numbers on a number line multiple of 10 or 100  Add and subtract numbers within 1000 by using  Rounding a number can be determined by its number lines position on a number line  Add and subtract numbers within 1000 by using the  Rounding gives an approximation algorithms  Addition and subtraction are inverse operations  Fluently add and subtract within 1000  Properties of addition and subtraction:  Choose an appropriate strategy for adding and a) Commutative property of addition: a + b = b subtracting based on the context of the problem + a  Tell and write time from a clock to the nearest minute b) Associative property of addition: (a + b) + c =  Solve word problems involving addition and a + (b + c) subtraction of time intervals in minutes c) Identity property: a + 0 = a and a – 0 = a  Use place value to compute multiples of 10 in the  Repeated grouping by 10 makes a new unit (i.e. range of 10 – 90 regrouping)  Multiply 1 digit whole numbers by multiple of tens  The algorithms for adding and subtracting numbers  Measure and estimate masses of objects using within 1000 standard metric units (grams, kilograms)  Various strategies for adding and subtracting,  Measure and estimate liquid volumes using standard including drawing pictures, manipulating materials, metric units (liters) using number lines, using tape diagrams, and using  Solve one-step word problems involving liquid the algorithms. volumes and masses  The large numbers on a clock (1 – 12) represent intervals of 5 minutes.  Minutes and hours are represented by the different hands on a clock.  There are 24 hours in a day and 60 minutes in an hour  Multiplication of one-digit numbers with multiples of 10 can be represented as groups of tens  The relative size of standard units of mass  The relative size of standard units of liquid volume Assessments (attached) Pre-Assessment:

Formative Interim Assessment:

Post Assessment (Culminating Task): NYS Common Core Mathematics Curriculum; Grade 3, Module 2, #1 – 5

3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2 3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2 Learning Experiences (Lesson Plans Attached) Days Lesson Sequence Materials Lesson 1: Understanding Place Value Students will know:  The position of digits in a number determine its value  Multi-digit numbers are composed of ones, tens, hundreds, etc…  As you move to the left on a place value chart, the numbers get larger  Big numbers possess the same place-value structure as smaller numbers Students will be able to:  Label a place value chart to the 1,000s  Compose and decompose numbers Lesson 2: Rounding Whole Numbers Students will know:  Rounding can be used to estimate and check answers for reasonableness  Rounding is simplifying a number to its nearest multiple of 10 or 100  Rounding a number can be determined by its position on a number line  Rounding gives an approximation Students will be able to:  Round whole numbers to the nearest 10 and/or to the nearest 100  Represent numbers on a number line  Use a number line as a strategy to round numbers Lesson 3: Adding and Subtracting Using Manipulatives and Drawings Students will know:  Addition and subtraction are inverse operations  Properties of addition and subtraction: a. Commutative property of addition: a + b = b + a b. Associative property of addition: (a + b) + c = a + (b + c) c. Identity property: a + 0 = a and a – 0 = a  Repeated grouping by 10 makes a new unit (i.e. regrouping) Students will be able to:  Add and subtract numbers within 1000 by manipulating materials and/or drawing pictures Lesson 4: Adding and Subtracting Using Tape Diagrams Students will know:  Addition and subtraction are inverse operations  Properties of addition and subtraction: a. Commutative property of addition: a + b = b + a b. Associative property of addition: (a + b) + c = a + (b + c) c. Identity property: a + 0 = a and a – 0 = a  Repeated grouping by 10 makes a new unit (i.e. regrouping) Students will be able to:  Add and subtract numbers within 1000 by using tape diagrams Lesson 5: Adding and Subtracting Using The Number Line Students will know:  Addition and subtraction are inverse operations  Properties of addition and subtraction: a. Commutative property of addition: a + b = b + a b. Associative property of addition: (a + b) + c = a + (b + c) c. Identity property: a + 0 = a and a – 0 = a 3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2  Repeated grouping by 10 makes a new unit (i.e. regrouping) Students will be able to:  Represent numbers on a number line  Add and subtract numbers within 1000 by using number lines

Lesson 6: Adding and Subtracting Using Algorithms Students will know:  Addition and subtraction are inverse operations  Properties of addition and subtraction: a. Commutative property of addition: a + b = b + a b. Associative property of addition: (a + b) + c = a + (b + c) c. Identity property: a + 0 = a and a – 0 = a  Repeated grouping by 10 makes a new unit (i.e. regrouping)  The algorithms for adding and subtracting numbers within 1000 Students will be able to:  Add and subtract numbers within 1000 by using the algorithms Lesson 7: “Putting it All Together” with Addition and Subtraction Students will know:  Addition and subtraction are inverse operations  Properties of addition and subtraction: a. Commutative property of addition: a + b = b + a b. Associative property of addition: (a + b) + c = a + (b + c) c. Identity property: a + 0 = a and a – 0 = a  Repeated grouping by 10 makes a new unit (i.e. regrouping)  Various strategies for adding and subtracting, including drawing pictures, manipulating materials, using number lines, using tape diagrams, and using the algorithms. Students will be able to:  Fluently add and subtract within 1000  Choose an appropriate strategy for adding and subtracting based on the context of the problem Lesson 8: Telling and Writing Time Students will know:  The large numbers on a clock (1 – 12) represent intervals of 5 minutes.  Minutes and hours are represented by the different hands on a clock.  There are 24 hours in a day and 60 minutes in an hour Students will be able to:  Tell and write time from a clock to the nearest minute  Solve word problems involving addition and subtraction of time intervals in minutes Lesson 9: Multiplication with Multiples of Tens Students will know:  Multiplication of one-digit numbers with multiples of 10 can be represented as groups of tens Students will be able to:  Use place value to compute multiples of 10 in the range of 10 – 90  Multiply 1 digit whole numbers by multiple of tens Lesson 10: Measure and Estimate Mass Students will know:  The relative size of standard units of mass 3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2 Students will be able to:  Measure and estimate masses of objects using standard metric units (grams, kilograms) Lesson 11: Measure and Estimate Volume Students will know:  The relative size of standard units of liquid Students will be able to:  Measure and estimate liquid volumes using standard metric units (liters) Lesson 12: Problem Solving with Mass and Volume Students will know:  The relative size of standard units of mass  The relative size of standard units of liquid Students will be able to:  Measure and estimate masses of objects using standard metric units (grams, kilograms)  Measure and estimate liquid volumes using standard metric units (liters)  Solve one-step word problems involving liquid volumes and masses End-of-Unit Culminating Task NYS Common Core Students will propose and justify solutions Mathematics Curriculum; Grade 3, Module 2, #1 – 5 Resources Online Text Illustrative Mathematics http://www.illustrativemathematics.org/ Shoseki, Tokyo. Mathematics International: Grade 3. Inside Mathematics/MARS tasks http://www.insidemathematics.org/ ; 2012 (Japanese Text) http://map.mathshell.org/materials/index.php

National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html Van de Walle, John, and LouAnn Lovin. Teaching Student-Centered Mathematics: Progressions for the Common Core State Standards in Grades 3-5. Vol. Mathematics 2. Boston: Pearson, 2006. http://ime.math.arizona.edu/progressions/

Smarter Balanced Assessment Consortium http://www.smarterbalanced.org/smarter-balanced- assessments/#item

EngageNY http://www.engageny.org/ela-math-landing http://www.engageny.org/resource/grade-3- mathematics-module-2

Georgia Department of Education https://www.georgiastandards.org/Common- Core/Pages/Math-K-5.aspx

3rd Grade Place Value and Multi-Digit Arithmetic 3.NBT.1,2,3 and 3.MD.1,2