4.2.4Ma


 * Grade: 4 Unit: 2 Week: 4 Content: Math Dates: 10/8-10/12 **


 * Theme Essential Question: ** How and when do we apply multiplication and division to solve mathematical problems?


 * Essential Questions: **
 * How can I use “breaking apart” numbers to develop strategies for multiplication?
 * How can I represent multiplication problems with pictures, diagrams, and models?
 * How can I use my knowledge of factors to build different arrays for a given number?


 * Standards **
 * ** 4.OA.3 ** Solve multistep word problems posed 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 letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and e estimation strategies including rounding.
 * ** 4.OA.4 ** Find all factor pairs for a whole number in a range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given 1 digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
 * ** 4.NBT.5 ** Multiply a whole number of up to four digits by a 1-digit whole number, and multiply two 2-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


 * Objectives **
 * I can “break apart” numbers to develop strategies for multiplication.
 * I can represent multiplication problems with pictures, diagrams, and models.
 * I can use my knowledge of factors to build different arrays for a given number.


 * Assessment **
 * Product **
 * Investigations session 1.5 (Students will solve the problem 18x7 using a model, demonstrating and explaining how they broke the numbers apart.)


 * Key Questions (match standards) **
 * Can students use “breaking apart” numbers to develop strategies for multiplication?
 * Can students represent multiplication problems with pictures, diagrams, and models?
 * Can students use knowledge of factors to build different arrays for a given number?


 * Observable Student Behaviors (Performance) **
 * The student will be able to compose and decompose numbers to solve multiplication problems.
 * The student will be able to represent the breaking apart of a multiplication problem into smaller parts using models and equations.
 * The student will use their knowledge of factors in their composition/decomposition of numbers.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ** Mathematical Practices **

Additive comparison Multiplicative comparison Algebraic equation Reasonableness *Multiply *Divide *Solve *Distinguish *Using drawing/equations ||
 * Vocabulary **
 * ** Math ** ||
 * Symbol

Gizmos: The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. Teacher Guide and Student Exploration Sheet Available
 * Suggested Activities **
 * **Odyssey Lesson:** Multiplication (Located in Assignmnet Archive Under District)
 * **Factor Trees** (Factoring Numbers)
 * __ Math Investigations – __ Unit 3 Multiple Towers and Division Stories: Lessons 1.1-1.5. These lessons focus on developing strategies for multiplying that involve breaking apart numbers; representing a multiplication problem with pictures, diagrams, models (arrays).
 * __ On Core Mathematics- __ Lesson 25 (Student book pg. 49-50) 4.NBT.5; Lesson 33 (Student book pgs. 65-66) 4.NBT.5


 * Homework **


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers || || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ||  ** Multicultural Concepts **


 * __ Resources __**
 * Professional Texts **
 * __ Math Investigations __

** Literary Texts **

** Informational Texts **

** Art, Music, and Media **


 * Manipulatives **


 * Games **

** Videos **

** Sight Words **

Judging Reasonable Answers Students will estimate to judge if answers are reasonable in addition, subtraction, division, and multiplication problems. Problem Solving Strategies: inverse operations Solve problems using inverse operations. Problem Solving Strategies: patterns and tables Solve problems by extending the pattern, finding the rule and using tables Measures of Central Tendency Describe the distribution of data using mean, median, range and mode. Include minimum and maximum values (outliers) Place Value Build understanding of place value (hundredths through millions place) Multiplication Multiplication by one- digit and two-digit numbers (larger numbers with calculator). Area Develop strategies to determine the area of rectangles and plane figures. Measures of Central Tendency Describe the distribution of data using mean, median, range and mode. Include minimum and maximum values (outliers). @http://exchange.smarttech.com/details.html?id=03df2f2d-87a3-4c20-9323-b4215a936429 Algebra lesson focusing on balancing equations with shapes @http://exchange.smarttech.com/details.html?id=b64f3702-174c-49de-ae5e-db66d8bc5ecd This lesson activity can be used to introduce or review identifying and classifying factors and multiples @http://exchange.smarttech.com/details.html?id=7ccf863a-8b65-42f3-91d2-b20b42919a2a Brief introduction/review of prime and composite numbers with interactive activities. @http://exchange.smarttech.com/details.html?id=d845e1bc-9966-4592-90e0-f554ca15534f Walk students through finding the greatest factor and least common multiples @http://exchange.smarttech.com/details.html?id=dd36fd45-bc70-47ac-9c20-c841c1dd5b3e Introductory lesson on the concept of Greatest Common Factor and three ways to find the GCF @http://exchange.smarttech.com/details.html?id=4340b8d7-d749-4a91-97e0-5819c6d6345a Use the Senteo interactive response system to calculate factors. @http://exchange.smarttech.com/details.html?id=5691d2ef-c5c5-42af-9ff8-192a08933d8a This is an alternative approach to finding the greatest common factor of two numbers. It involves the use of a Venn Diagram to sort the common prime factors to find the greatest common factor. @http://exchange.smarttech.com/details.html?id=fd066bbc-1fec-46f3-92ed-f345e03ba390 Students use arrays to identify prime and composite numbers @http://exchange.smarttech.com/details.html?id=6c9f18fd-9a56-4397-b9ad-f2b51745ae79 Students will identify prime and composite number from 2-100. @http://exchange.smarttech.com/details.html?id=d51a73a0-a364-4f53-aa41-b8b88e16b853 A vocabulary review for factorization, including sorting activities for prime vs. compositie numbers @http://exchange.smarttech.com/details.html?id=a597d8d4-a459-42cb-b86c-b0c33a2c1ef2 This lesson practices using the lattice method to multiply multi-digit numbers @http://exchange.smarttech.com/details.html?id=085a20a6-9358-4a7d-ba70-8f7865a35cbe Introduction to 2Digit by 1Digit Multiplication @http://exchange.smarttech.com/details.html?id=5d3bff3a-4dee-4e87-a503-ffe1cb03d916 This lesson is Halloween themed and is an introduction to 2 digit by 1 digit multiplication. It includes problems with carrying and some without. @http://exchange.smarttech.com/details.html?id=82aa1640-70e3-47d4-bf5e-e8ff040876d3 Practice Notebook file for 2 digit Multiplication. 3rd or 4th Grade Level. @http://exchange.smarttech.com/details.html?id=643b730b-e0f5-40eb-b267-039fb8787486 This reviews the steps of double digit by double digit multiplication and has 10 questions under the frogs and answers to the questions under the bees. It also has a review of the steps of long division and a tile activity @http://exchange.smarttech.com/details.html?id=be22759e-bfcd-4280-815e-493a369a61b2 Students will create arrays and identify factor pairs for given numbers @http://exchange.smarttech.com/details.html?id=ccfe8fc7-8f8f-4143-b9cd-e0411cce7b43 Guides students through different methods for multiplying multiples of 10 and 100. @http://exchange.smarttech.com/details.html?id=ef64a46f-17e0-41cd-9530-6696001513fa Students solve a multiplication problem (using facts 2 through 12) in each pane of a stained-glass-like window. Students then color each pane based on whether the answer is even or odd, revealing a hidden picture. Animated buttons allow the student/teacher to view answers and to clear the coloring
 * SMART Board Lessons, Promethean Lessons **
 * ** AEGOM Lesson: G4M008 **
 * ** AEGOM Quiz: G4M008 **
 * ** AEGOM Lesson: G4M009 **
 * ** AEGOM Quiz: G4M009 **
 * ** AEGOM Lesson: G4M010 **
 * ** AEGOM Quiz: G4M010 **
 * ** AEGOM Lesson: G4M023 **
 * ** AEGOM Quiz: G4M023 **
 * ** AEGOM Lesson: G4M001 **
 * ** AEGOM Quiz: G4M001 **
 * ** AEGOM Lesson: G4M003 **
 * ** AEGOM Quiz: G4M003 **
 * ** AEGOM Lesson: G4M021 **
 * ** AEGOM Quiz: G4M021 **
 * ** AEGOM Lesson: G4M023 **
 * ** AEGOM Quiz: G4M023 **
 * **Balance Equations**
 * **Fun With Factors!**
 * **Prime and Composite**
 * **Greatest Factor Least Common Multiple**
 * **Greatest Common Factor**
 * **Factors (Question set)**
 * **Finding Greatest Common Factor using Venn Diagrams**
 * **Prime and Composite Numbers**
 * **Prime and Composite Numbers**
 * **Intro to Factorization (Prime vs. Composite)**
 * **Multiplication**
 * **Multiplication Cover Up!**
 * **Practice your multiplication facts**
 * **2 digit Multiplication**
 * **Multiplication and Division Review**
 * **Arrays**
 * **Extended Facts**
 * **Multiplication Coloring Book – Guitar**

@http://illuminations.nctm.org/LessonDetail.aspx?ID=L317 This lesson builds on the previous lesson and encourages students to explore another model for multiplication, the familiar set model. Students find products using equal sets and present results in the form of a table. The students apply their knowledge about multiplication in the creation of pictographs. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L528 Students examine the role of commutativity and the multiplicative identity, play a multiplication game, and explore products where one of the factors is 6. They also create a "My Personal Multiplication Chart" to record products @http://illuminations.nctm.org/LessonDetail.aspx?ID=L316 In this lesson, students generate products using the number line model. This model highlights the measurement aspect of multiplication and is a distinctly different representation of the operation. The order (commutative) property of multiplication is also introduced. Students are encouraged to predict products and to answer puzzles involving multiplication. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L329 By playing card games and using the The Product Game applet, students practice the multiplication facts. As students continue to master their facts, the teacher closely monitors their progress @http://illuminations.nctm.org/LessonDetail.aspx?ID=L529 Students create multiplication stories where one factor is 6 or 7, and play a multiplication game to help them master their multiplication facts. @http://illuminations.nctm.org/Lessons/Architect/Architect-AS-ProbSolvTasks.pdf This reproducible activity, from an Illuminations lesson, leads students through a series of exercises and questions pertaining to the construction of an originally-designed clubhouse. They are asked to consider how much paint they will need to cover the walls, what they will need to do to make a mosaic floor pattern, what materials they will need for the roof and more. @http://www.teachersdomain.org/resource/vtl07.math.algebra.var.lpfunction/ In this //Cyberchase// activity, students watch a video clip in which Hacker creates a cyberfrog with numeric buttons that produce different numbers of hops. The relationship between input and output values is used to teach students how to use algebraic expressions and, subsequently, equations. @http://www.teachersdomain.org/resource/vtl07.math.algebra.pat.arrange1/ In this video segment from //Cyberchase,// Matt and Digit need to set up tables so that 20 workers will each have a spot at a table in order to assemble their circuit boards. Matt and Digit want to know the number of tables they need so that they can transport them all at once. Matt decides to use small shingles to represent the tables and washers to represent workers. He tests his ideas by positioning the washers around the shingles. Check out "Arrangement 2" and "Arrangement 3" to view Matt's other attempts to solve the problem. @http://www.teachersdomain.org/resource/vtl07.math.algebra.pat.arrange2/ In this video segment from //Cyberchase,// Matt and Digit need to set up tables so that 20 workers will each have their own spot at a table as they assemble circuit boards. After arranging workers around five tables (in video segment "Arrangement 1"), Matt finds that there are still six workers without seats. He must go back to the drawing board to figure out how many more tables he needs to seat every worker. Check out "Arrangement 3" to see how Matt finally solves the problem. @http://www.teachersdomain.org/resource/vtl07.math.algebra.pat.arrange3/ In this video segment from //Cyberchase//, Matt and Digit need to set up tables so that 20 workers will each have their own spot at a table as they assemble circuit boards. They only have five tables, and they found out that when the tables were put together in video segment "Arrangement 1" there were not enough seats for all the workers. Since he cannot add any more tables, Matt realizes that perhaps changing the positioning of the tables will provide the extra seats they need. Check out "Arrangement 2" to watch one of Matt's other attempts to accommodate the 20 workers @http://illuminations.nctm.org/LessonDetail.aspx?ID=U162 A number-line model is an effective tool for helping students to understand the process of multiplication and to learn multiplication facts. In this unit, students begin with a number-line model and extend it to investigate linear relationships with the Distance, Speed, and Time Simulation from NCTM's E-Examples. Students then progress to plotting points and graphing linear functions while continually learning and reinfocing basic multiplication facts. @http://illuminations.nctm.org/LessonDetail.aspx?ID=U109 In this unit, students explore several meanings and representations of multiplication (number line, equal sets, arrays, and balanced equations). They also learn about the order (commutative) property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. In addition, students write story problems in which the operation of multiplication is required. Opportunities to connect with literature are presented in several of the lessons. A [|bibliography] of children's literature with a multiplication focus is provided.
 * Other Activities, etc. **
 * ** Exploring Equal Sets **
 * ** Finding Products **
 * ** Hopping on the Number Line **
 * ** Keeping It All Together **
 * ** Multiplication Stories **
 * ** Problem-Solving Tasks **
 * ** From Patterns of Input and Output to Algebraic Equations **
 * ** Arrangement 1 **
 * ** Arrangement 2 **
 * ** Arrangement 3 **
 * ** Running Races Unit **
 * ** All About Multiplication Unit **


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