Unit 3 Multiplication and Division


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1 WEEK DATES TEK DESCRIPTION 9 Oct F, 3.4E, 3.4D Unit 3 Multiplication and Division Unit 3 Multiplication and Division 4 district biweekly scanned tests 10 Oct G 2x1 digit multiplication Recall facts, model multiplication facts in multiple ways (see TEKS) 11 Nov C, 3.5D Multiplication as comparisons; relationship between multiplication and division using fact families 12 Nov H, 3.4I, 3.4J, Division pictorials, divisibility rules, 13 Nov K, 3.5B Multiplication and division problem solving Thanksgiving Week 14 Nov 30Dec4 3.5E Relationship tables 15 Dec C, 3.6D Area 16 Dec AB, 3.5A, 3.4K, 3.5B Problem Solving with all operations district biweekly scanned test not given this week due to Christmas activities; test to be given at the end of review week when we get back from Christmas break. Winter Break In this document, Readiness standards are green, Supporting standards are yellow, and Processing standards are blue. The process standards shown below must be incorporated into each skill taught in this unit so that students will acquire the depth and complexity required by the state Mathematical Process Standards 3.1(A) 3.1(B) 3.1(C) 3.1(D) 3.1(E) 3.1(F) 3.1(G) apply mathematics to problems arising in everyday life, society, and the workplace use a problem solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem solving process and the reasonableness of the solution select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate create and use representat ions to organize, record, and communica te mathematic al ideas analyze mathematical relationships to connect and communicate mathematical ideas display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
2 Week 9 Recall facts, model multiplication facts in multiple ways (see TEKS) TEK Student Expectation Supporting Information (Key: clarification, new, deleted) 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4F The student is expected to recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts. The recall of multiplication facts up to 10 by 10 with automaticity has moved from grade 4. Recalling with automaticity facts related to 11s and 12s is not included in the Revised TEKS (2012). 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4E The student is expected to represent multiplication facts by using a variety of approaches such as repeated addition, equalsized groups, arrays, area models, equal jumps on a number line, and skip counting. Specificity has been added about strategies that support the learning of multiplication facts: repeated addition, equalsized groups, arrays, area models, equal jumps on a number line, and skip counting. The learning of facts related to 11s and 12s is not included in the Revised TEKS (2012). 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4D The student is expected to determine the total number of objects when equallysized groups of objects are combined or arranged in arrays up to 10 by 10. Specificity has been added for the use of concrete models and objects. Arrays should reflect the combination of equallysized groups of objects. The learning of facts related to 11s and 12s is not included in the Revised TEKS (2012). Essential Questions What is multiplication? How can I find the answer when I don t know my facts? (array, area model, pictorial, skip counting, number line) What is an array? What is an area model? What are factors? Product? Multiple?
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4 Examples
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7 Examples /Product/ArraysArraysArrays
8 om/product/multiplication StrategiesAnchorChart
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10 Examples Resources Motivation Math TE: 3.4D/3.4E pgs , 3.4F pgs SE: 3.4D/3.4E pgs , 3.4F pgs Envision: Topic 4 Topic 5 Math Literature Amanda Bean s Amazing Dream Minnie s Diner Multiplying Menace The Best of Times Too Many Kangaroos
11 Week 10 2x1 digit multiplication district biweekly scanned test TEK Student Expectation Supporting Information (Key: clarification, new, deleted) 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4G The student is expected to use strategies and algorithms, including the standard algorithm, to multiply a twodigit number by a onedigit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties Specificity has been added with strategies and algorithms that may be used to record and solve multiplication problems of a twodigit by a onedigit number. Strategies and algorithms include mental math; partial products; the commutative, associative, and distributive properties; and the standard algorithm. For example, when prompted to multiply 97x3, a student may determine the product by multiplying 90x3 and 7x3 and adding 270 and 21 for an answer of 291. A student may also think of 97x3 as (1003) x3 and multiply 100x3 to get 300 and subtract 3x3 or 9 for an answer of 291. Essential Questions Why do we learn more than one way to multiply 2x1 digit numbers? What are the properties of multiplication? How can they help us solve problems?
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13 Examples Partial Products Blog Associative Property Blog
14 Resources Motivation Math TE: SE: Envision: Topic 9 Math Literature
15 Week 11 Multiplication Comparisons and X Relationships TEK Student Expectation Supporting Information (Key: clarification, new, deleted) 3.5 Algebraic reasoning. The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to: 3.5 Algebraic reasoning. The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to: 3.5C describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as D The student is expected to determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product. With the current SEs related to multiplication, discussions have focused on multiplication as repeated addition, so 3x24 is often described as 3 groups of 24. With the revised SE, students also focus on the numerical relationship between 24 and the product 3x24. The product of 3x24 will be 3 times as much as 24. This lays the foundation for future work in grade 5 with fraction multiplication and determining part of a number. If the multiplication or division equation relates whole numbers from fact families up to 10x10, students may apply their knowledge of facts and the relationship between multiplication and division to determine the unknown number. Students may be expected to use the relationship between multiplication and division for a problem such as 12=[] 6. The student knows that if 12=[] 6 then 12x6=[], so []=72. Students may also be expected to solve problems where they state that the value 4 makes 3x[]=12 a true equation. Essential Questions Why is multiplication a comparison? What does the product tell you? Which factor tells the number of times you are increasing the size of the group? How would the meaning of the comparison change if the order of the factors was changed? In the equation 8 x 9 = 72, the symbol is read as times. How does this relate to this meaning of multiplication? What is an unknown number? How do you solve for an unknown number? How is a fact family used to help you know multiplication facts and division facts? How is multiplication related to division?
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17 Examples
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19 Examples Resources Motivation Math TE: 3.5C pgs ; 3.5D pgs SE: 3.5C pgs ; 3.5D pgs Envision: 3.5D Topic Math Literature
20 Week 12 Division pictorials, divisibility rules, relationship between multiplication and division using fact families district biweekly scanned test TEK Student Expectation Supporting Information (Key: clarification, new, deleted) Specificity has been added on how to use models to solve division problems. 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4H The student is expected to determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally. 3.4J The student is expected to determine a quotient using the relationship between multiplication and division. 3.4I The student is expected to determine if a number is even or odd using divisibility rules. Students are expected to think with both forms of division: partitioning into equal shares (determining the number of groups with a given number of objects in each group) and sharing equally (determining the number of items in each group when the objects are shared equally among a given number). When paired with revised SEs 3(1)(D) and 3(1)(E), students may be asked to use number sentences to record the solutions. The identification of the relationship between multiplication and division, as seen in fact families, lays the foundation for determining a quotient based on this relationship. Specificity has been added to identify the purpose of the relationship between multiplication and division to determining a quotient. For example, the quotient of 40 8 can be found by determining what factor makes 40 when multiplied by 8. To determine if a number is even, one may apply the divisibility rule for 2: A number is divisible by 2 if the ones digit is even (0, 2, 4, 6, or 8). Essential Questions What is division? What is a quotient? Divisor? Dividend? What is the divisor in division related to in multiplication? What is the dividend in division related to in multiplication? How are the product and quotient related? What is an example of an inverse operation? How is division related to multiplication? What does it meant to divide something into equal shares or equal groups? What are equal parts? When might you need to divide something into equal groups or have an equal number in each group? What is divisibility? Are even or odd numbers divisible by 2? Why?
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22 Examples
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24 Examples
25 onal.blogspot.com/2012/ 04/bonusmultiplicationdivisionfact.html
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27 Examples Resources Motivation Math TE: 3.4H pg ; 3.4J pg ; 3.4I pg SE: 3.4H pg ; 3.4J pg ; 3.4I pg Envision 3.4H Topic 0601, J Topic 7 3.4I Topic Math Literature
28 Week 13 Multiplication and division problem solving TEK Student Expectation Supporting Information (Key: clarification, new, deleted) The Revised SE 3(4)(K) builds to the Revised SE 3(5)(B). The focus of 3(4)(K) is on developing numberbased strategies to solve multiplication and division problems within Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. 3.4K The student is expected to solve onestep and twostep problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts. The use of models in the current SE includes the use of objects. With revised SE 3(4)(K), the dividend must be less than 100. Strategies to solve division problems other than concrete models, or objects, are included: pictorial models, including arrays, area models, and equal groups; properties of operations; and recall of facts. 3.5 Algebraic Reasoning The student applies mathematical process standards to analyze and create patterns and relationships. 3.5B The student is expected to represent and solve one and twostep multiplication and division problems within 100 using arrays, strip diagrams, and equations. The Revised SE 3(5)(B) is an extension of the Revised SE 3(4)(K). The focus of 3(5)(B) is on developing representations that build to numeric equations for multiplication and division situations by connecting arrays to strip diagrams. Essential Questions What is the question asking? What do you already know? What do you still need to find? Which operation will you use? How do you know? Is this a one or two step problem? Is your answer reasonable? How do you know? How could you solve this using a strip diagram?
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31 Examples Pearson has great examples of using strip diagrams at the beginning of the student edition. Resources Motivation Math TE: 3.4K pg ; 3.5B pg SE: 3.4K pg ; 3.5B pg Envision Topic 10 Math Literature
32 Week 14 Relationship Tables district biweekly scanned test TEK Student Expectation Supporting Information (Key: clarification, new, deleted) When paired with revised SE 3(1)(A), the expectation is that students apply this skill in a problem arising in everyday life, society, and the workplace. 3.5 Geometry and measurement. The student applies mathematical process standards to analyze attributes of twodimensional geometric figures to develop generalizations about their properties. Essential Questions 3.5E The student is expected to represent realworld relationships using number pairs in a table and verbal descriptions. When paired with revised SE 3(1)(D), the expectation is that students extend the relationship represented in a table to explore and communicate the implications of the relationship. The revised SE restates generate as represent, a more appropriate verb to use when multiple representations such as tables are used to represent a realworld relationship. It also restates identify and describe patterns in a table with represent realworld relationships using... verbal descriptions. The revised SE 3(5)(E) builds to the revised SE 4(5)(B). Realworld relationships include situations such as the following: 1 insect has 6 legs, 2 insects have 12 legs, and so forth. What is the relationship between the numbers? Are the numbers getting smaller or larger? What rule is used in the table? How do you know? How can a table help you solve a problem?
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34 Examples Resources Motivation Math TE: pg SE: pg Envision Topic 1004, Math Literature
35 Week 15 Area TEK Student Expectation Supporting Information (Key: clarification, new, deleted) The revised SE limits the twodimensional surfaces to rectangles with whole number side lengths. 3.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of twodimensional geometric figures to develop generalizations about their properties. 3.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of twodimensional geometric figures to develop generalizations about their properties. 3.6C The student is expected to determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row. 3.6D The student is expected to decompose composite figures formed by rectangles into nonoverlapping rectangles to determine the area of the original figure using the additive property of area Students may use concrete or pictorial models of square units to represent the number of rows and the number of unit squares in each row. Units of area may be square inches or square centimeters. Students are expected to use multiplication to determine the area of a rectangle instead of counting squares. Composite figures should be comprised of no more than three rectangles, including squares as special cases of rectangles. Essential Questions What is area? How is that related to area models? How is multiplication used when calculating area? What units are used to measure area? If you decompose a shape into smaller rectangles, describe one way that you might determine a missing dimension? Why do we need to find area? Why would you need to decompose figures to find area?
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37 Examples Joseph and his sister covered their playroom floor with alphabet tiles. Which statement shows the number of tiles Joseph and his sister would need to cover the form? A. They would need 24 tiles because 4 x 6 = 24. B. They would need 10 tiles because = 10. C. They would need 2 tiles because 6 4 = 2. D. They would need 18 tiles because 3 x 6 =18.
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39 Examples Resources Motivation Math TE 3.6CD pg SE 3.6CD pg Envision Topic 13 Math Literature
40 Week 16 Problem Solving with All Operations district biweekly scanned test not given this week due to Christmas activities; test to be given at the end of review week when we get back from Christmas break. Review all addition, subtraction, multiplication, and division problem solving TEKS including: 3.4AB, 3.5AB, 3.4K Solve multi step problems with all of these TEKS. Make sure to use Motivation Math and other problem solving resources. Use problem solving format. Essential Questions What is the question asking? What do you already know? What do you still need to find? Which operation will you use? How do you know? Is this a one or two step problem? Is your answer reasonable? How do you know? How could you solve this using a strip diagram?
2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1
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