Woodlynne School District Curriculum Guide Mathematics Grade 3 NOTE: The following pacing guide was developed during the creation of these curriculum units. The actual implementation of each unit may take more or less time. Time should also be dedicated to preparation for benchmark and State assessments, and analysis of student results on the same. A separate document is included at the end of this curriculum guide with suggestions and resources related to State Assessments. The material in this document should be integrated throughout the school year, and with an awareness of the State Testing Schedule. It is highly recommended that teachers meet throughout the school year to coordinate their efforts in implementing the curriculum and preparing students for benchmark and State Assessments in consideration of both the School and District calendars. 1
2
Woodlynne School District Curriculum Guide Content Area: Mathematics Course Title: Grade 3 Math Grade Level: 3 rd Grade Unit 1: Addition and Subtraction within 1,000 Three Weeks Unit 2: Represent and Interpret Data Three Weeks Unit 3: Understand Multiplication Three Weeks Unit 4: Multiplication Facts and Strategies Three Weeks Unit 5: Multiplication Facts Three Weeks Unit 6: Understand Division Three Weeks 3
Unit 7: Division Facts & Strategies Three Weeks Unit 8: Understand Fractions Three Weeks Unit 9: Compare Fractions Three Weeks Unit 10: Measurement Three Weeks Unit 11: Perimeter and Area Three Weeks Unit 12: Two-Dimensional Shapes Three Weeks Board Approved on: 9/9/14 4
Content Area Mathematics Unit 1: Addition and Subtraction within 1,000 Target Course/Grade Level Grade 3 Math Unit 1 Overview 4 Lessons/Three Weeks Unit Summary/Rationale Exploring number patterns helps students develop algebraic thinking skills. Identifying and describing number patterns are important skills that prepare students for the study of functions in later grades. Rounding is a way to find about how much or about how many. It involves finding the multiple of 10 or 100 that is closest to a given number. Estimating sums by using compatible numbers or by rounding is an important skill for checking the reasonableness of an answer or finding an estimated sum when an exact sum is not needed. Students develop a deeper understanding of the meaning of addition with 2 and 3 digit numbers by learning and using various mental math strategies to add. Associative Property of Addition will be used to help add more than two addends so students will learn that you can group addends in different ways. Estimating differences is an important skill for checking the reasonableness of an answer or finding an estimated difference when an exact difference is not needed. Interdisciplinary Connections - Science Technology Integration Computer, SMART Board, internet, ENVision Math Software 21 st Century Themes Financial, Economic, Business, Entrepreneurial Literacy 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Practice Standards: MP.6: Attend to precision. MP.7: Look for and make use of structure. Math Domain Standards: CC 3.0A.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. CC.3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. CC.3.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. CC.3.0A.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. 5
Unit Essential Questions How can you add and subtract whole numbers and decide if an answer is reasonable? How do you know when an estimate will be close to an exact answer? When do you regroup to add or subtract whole numbers? Unit Enduring Understandings Algebraic representation can be used to generalize patterns and relationships Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole Terminology: compatible numbers, estimate, pattern, associative property of addition, round commutative property of addition, Identify Property of Addition regroup. Goals/Objectives Students will be able to - Identify and describe whole number patterns and solve problems. Round 2 and 3 digit numbers to the nearest ten or hundred. Use compatible numbers and rounding to estimate sums. Recommended Learning Activities/Instructional Strategies Use an addition table to explore patterns that can be found in each row, column, and diagonal. Using a number line to round to the nearest ten. Use compatible numbers to estimate to find about how many or about how much. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Project: Inventing Toys The students will develop an understanding of multiplication and division and strategies for multiplication and division within 100. They will work with a partner in a pretend toy store. They have to order enough dolls to fill two shelves in the store. Each shelf is 72 inches long. How many cartons of dolls will fill the two shelves? Students must take into account the important facts that the dolls come in a box that is 8 inches wide as well. Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument 6
Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 7
Unit 2 Overview Content Area Mathematics Unit 2: Represent and Interpret Data 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit Summary/Rationale Using a graphic organizer to scaffold a problem helps students analyze the problem, understand what they need to find, identify the information they need to use, and develop a strategy to solve the problems. A picture graph is a good way to display data visually for the purpose of comparing data that can be counted and are multiples of number. The students will then take numerical data and put it in a visual form. It is important for students to be able to analyze and create a bar graph with a scale that has an interval greater than one. Line plots show the shape of data, so any clusters or gaps are clearly visible and to show frequencies for data items. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math Models/Software 21 st Century Themes Financial, Economic, Business, and Entrepreneurial Practice Standards: MP.1: Make sense of problems and persevere in solving them. MP.4: Model with Mathematics. 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Math Domain Standards: CC.3.MD.3: Draw a scaled picture graph and a scaled bar graph and a scaled bar graph to represent a data set with several categories. Solve oneand two-step how many more and how many less problems using information presented in scaled bar graphs. CC.3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units- whole numbers, halves, or quarters. Unit Essential Questions How can you represent and interpret data? How can you use the strategy of making a table to organize data and solve problems? How can you draw a bar graph to show data in a table or pictograph? Unit Enduring Understandings The message conveyed by the data depends on how the data is collected, represented, and summarized. The results of a statistical investigation can be used to support or refute an argument. 8
Terminology: frequency table, data, tally table, key picture graph, experiment, survey, bar graph, horizontal bar graph, scale, vertical bar graph, skip count. Goals/Objectives Students will be able to Recommended Learning Activities/Instructional Strategies Evidence of Learning (Formative & Summative) Organize data in tables and solve problems using the strategy make a table. Read and interpret data in a scaled picture graph. Use a tally table to organize data into a frequency table that uses numbers to record data instead of tallies. a. Have the students conduct a survey on a topic of favorite pets by organizing the data with a tally table. b. Create a frequency table based on the data collected with the tally table. Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Draw a scaled picture graph to show data in a table. Use a picture graph to interpret data that uses small pictures or symbols to show information. a. Students will conduct another survey as to favorite books to read. b. Create a pictograph using the data collected with a key and symbol. Use a bar graph to show data and a scale to help read the number of each bar represents for the data. 9
a. Have the students conduct a survey on favorite team sports. b. Construct a bar graph with a scale using the data collected. Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 10
Content Area Mathematics Unit 3: Understand Multiplication 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 3 Overview Unit Summary/Rationale Understanding equal groups and how they can be represented builds the foundation for understanding the operation of multiplication. Multiplication is a way of combing equal groups. A number line can be a useful tool to help students combine equal groups by skip counting. A number line helps to see the progression of multiplication as related to the number sequence. Modeling a problem in context by drawing a diagram helps students to decontextualize the problem and represent it symbolically. It is important for students to understand the array model for multiplication because it has many applications throughout mathematics. Using the strategy of Commutative Property of Multiplication, which states that the order in which you multiply factors doesn t affect the product, makes it easier to solve multiplication problems. Explore the patterns of multiplying numbers by 1 and 0 to understand the concept of properties: Identity Property of Multiplication and Zero Property of Multiplication. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math Models/Software 21 st Century Themes Financial, Economic, Business, Entrepreneurial Literacy 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Practice Standards: MP.1: Reason abstractly and quantitatively. MP.8: Look for and express regularity in repeated reasoning Math Domain Standards: CC.3.OA.1: Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. CC.3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.3.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. CC.3.OA.5: Apply properties of operations as strategies to multiply and divide. 1 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative 11
property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) Unit Essential Questions How can you use multiplication to find how many in all? Unit Enduring Understandings One representation may sometimes be more helpful than another; and, used together, multiple representations give a fuller understanding of a problem. Numeric fluency includes both the understanding of and the ability to appropriately use numbers. Computational fluency includes understanding the meaning and the appropriate use of numerical operations. Terminology: Equal groups, factor, multiply, product, array, equal groups, factor, multiply, product, array, commutative property of multiplication, identify property of multiplication, zero property of multiplication. Goals/Objectives Students will be able to - Model and skip count objects in equal groups to find how many there are. Write an addition sentence and a multiplication sentence for a model. Model and skip count on a number line to find how many there are. Recommended Learning Activities/Instructional Strategies Students will use counters to model equal groups and then skip count to find how many in all. Students will use drawing and repeated addition with counting blocks to find the number of apples needed in all. Students will a number line to identify the number of groups as the number of times to skip count, and the number in each group as the number to skip count by. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). 12
These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 13
Content Area Mathematics Unit 4: Multiplication Facts and Strategies 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 4 Overview Unit Summary/Rationale Presenting more than one way to multiply by 2 and 4 gives students a deeper understanding of multiplication. Students will then be able to explore the relationship of doubles. Presenting multiple strategies for multiplying 5 and 10 & 3 and 6 promotes a deeper understanding of multiplication. Models help students develop a better understanding of concepts such as an array to show why the Distributive Property works. The Associative Property of Multiplication is another strategy which states that the grouping of the factors doesn t change the product. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math Models/Software 21 st Century Themes Financial, Economic, Business, Entrepreneurial Literacy 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Practice Standards: MP.3: Construct viable arguments and critique the reasoning of others. MP.7: Look for and make use of structure. 14
Math Domain Standards: CC.3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.3.OA.5: Apply properties of operations as strategies to multiply and divide. 2 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) CC.3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. CC.3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. CC.3.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. Unit Essential Questions What strategies can you use to multiply? How do operations affect numbers? How do mathematical ideas interconnect and build on one another to produce a coherent whole? Unit Enduring Understandings Computational fluency includes understanding the meaning and the appropriate use of numerical operations. A quantity can be represented numerically in various ways. Problem solving depends upon choosing wise ways. In many cases, there are multiple algorithms for finding a mathematical solution, and those algorithms are frequently associated with different cultures. Terminology: multiple, Distributive Property, Associative Property of Multiplication, factor, product, addend, sum, Commutative Property of Multiplication, even, odd, subtraction 15
Goals/Objectives Students will be able to - Draw a picture, count by 2 s, or use doubles to multiply with the factors 2 and 4. Use skip counting, a number line, or a bar model to multiply with the factors 5 and 10. Draw a picture, use 5s facts and addition, doubles, or a multiplication table to multiply with the factors 3 and 6. Recommended Learning Activities/Instructional Strategies Students will use counters to discover equal groups a a. That the first factor represents the number of equal groups. b. The second factor represents the number in each group c. Demonstrate how to use doubles to find the products within the four times tables. Students will use the game of leap frog with a number line on the floor to skip count by fives to obtain the products to the five times tables. They will also use doubling of the multiples of five to obtain the products to the ten times table. Students will use 24 tiles to make two arrays with 3 rows of 4 tiles each. a. Combine the arrays to show 6 and 4. b. This will show that the number of tiles doubled to introduce the concept of doubling with the three times tables to find the products of the six times tables. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models,Real World Videos, EnVision Math Center and Manipulative Kit. 16
17
Unit 5 Overview Content Area Mathematics Unit 5: Use Multiplication Facts 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit Summary/Rationale Working with arithmetic patterns helps students develop algebraic thinking skills and prepares them for their future studies of algebra. Finding unknown factors is a prerequisite skill for division and introduces students to algebra. An area model helps students visualize multiplication and how the Distributive Property can be used to multiply with greater numbers. Students can develop a deeper understanding of the meaning of multiplication by using various strategies such as the role of 10 in the base-ten number system, place value, and the Associative Property of Multiplication. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/Software 21 st Century Themes Financial, Economic, Business Practice Standards: MP.1: Make sense of problems and persevere in solving them. MP.5: Use appropriate tools strategically. 21 st Century Skills Financial, Economic, Business, Entrepreneurial Literacy, Critical Thinking, Problem Solving Learning Targets Math Domain Standards: CC.3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. CC.3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = 3, 6 6 =? CC.3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10 90 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. 18
Unit Essential Questions How can you use multiplication facts, place value, and properties to solve multiplication problems? Unit Enduring Understandings Strong visual images of multiplication help develop various strategies for solving multiplication problems. Relationships exist among factors. The distributive property of multiplication, commutative property of multiplication, identity, and zero property are utilized to simplify/solve real-world problems. Basic multiplication facts with 3, 4, 6, 7, 8, 10 11, or 12 as a factor can be found by breaking apart the unknown fact into known facts. The answers to the known facts are added to get the final product. Patterns and known multiplication facts can be used to find unknown multiplication facts. Terminology: pattern, equation, array, Commutative Property of Multiplication, factor, product, Distributive Property, multiple, place value, tens, hundreds, ones Goals/Objectives Students will be able to - Identify and describe a number pattern shown in a function table. Use an array or a multiplication table to find an unknown factor. Recommended Learning Activities/Instructional Strategies Students will plan a camping trip where each camper will need a flashlight a. One flashlight uses 4 batteries and 8 flashlights are needed how many batteries are needed? b. Create a table to discover the pattern and operation to figure out the pattern in the rows of the table. Students are planning a picnic with 24 people. a. Invitations come in packs of 8 how many packs of invitations do they need to buy? b. Create an equation using a symbol such as n for the unknown factor. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument 19
Solve multiplication problems by using the strategy draw a diagram. c. Use 24 tiles to display with 8 tiles in each row; count the number of rows which will be the unknown factor. Present the following problem: 5 x 20; rewrite the factor 20 using addends of 10: 10 + 10 a. Have students model the multiplication problem using grid paper to make a 5 x20 rectangle b. The rectangle should be broken apart into two smaller rectangles, each representing 5 by 10. c. Have the students find the products of each rectangle, then add the products to find the total product. Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models,Real World Videos, EnVision Math Center and Manipulative Kit. 20
Content Area Mathematics Unit 6: Understand Division 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 6 Overview Unit Summary/Rationale Division is an operation by which you separate into equal groups or find the number of equal groups. Division is the inverse of multiplication, where equal groups are put together to find a total. Division can have two meanings: partitive (sharing) and quotative (measurement). It important that students explore both types. Knowing various ways to think about and visualize the process of division gives students a deep understanding of the operation and its related symbolism. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/ Software 21 st Century Themes Financial, Economic, Business Practice Standards: MP.2: Reason abstractly and quantitatively. MP.8: Look for and express regularity in repeated reasoning 21 st Century Skills- Financial, Economic, Business, Entrepreneurial Literacy, Critical Thinking, Problem Solving Learning Targets 21
Domain Standards: CC.3.OA.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8. CC.3.OA.6: Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. CC.3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. CC.3.OA.5: Apply properties of operations as strategies to multiply and divide. 3 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) Unit Essential Questions Unit Enduring Understandings How can you use division to find how many in each group or how many equal groups? The use of representations can be used to provide meaning for multiplication and division of whole numbers (e.g. Equal-sized groups, arrays, area models, and equal jumps on number lines for multiplication, and successive subtraction, partitioning, and sharing for division). Comparing a variety of solution strategies will help to demonstrate multiplication and division as inverse operations. Terminology: divide, equal groups, dividend, divisor, quotient, array 22
Goals/Objectives Students will be able to - Solve division problems by using the strategy act it out. Recommended Learning Activities/Instructional Strategies Using the problem-solving graphic organizer, have students work in groups to solve the following problem step by step. a. Pam bought 20 party favors. There are 5 favors in each pack how many packs of party favors did Pam buy? b. Use counters to display the 20 favors to take out 5 equal groups at a time to determine how many packs to buy. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Use models to explore the meaning of partitive (sharing) division. Each group 12 counters and 3 paper plates. Ask the students to make 3 equal groups from the 12 counters. a. Have students count out one counter for each plate and continue until all the counters have been placed on plates. b. Then have students count the number of counters on each plate to find how many are in each group. c. Repeat the activity having the students make 2 equal groups from the 12 counters. Use models to explore the meaning of quotative (measurement) division. Give each group 15 tiles; have students make stacks of 3 tiles each; discuss how many equal stacks of 3 tiles they can make. a. Ask students to separate the tiles into stacks of 5 tiles each, and find how many stacks they can make; discuss how their answer for the number of 3 tiles can help them 23
predict how many stacks of 5 tiles there will be. b. Have the students complete the activity and discuss their results. Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 24
Content Area Mathematics Unit 7: Division Fact and Strategies 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 7: Overview Unit Summary/Rationale Presenting both partitive and quotative division problems in context using 2 as a factor gives students a deeper understanding of the concept of division. Students can develop a deeper understanding of the meaning of division and its relationship to other operations by learning and using various methods to divide by 5. Teaching students several ways to think of and visualize the process of division gives them a deeper meaning of the operation and its associated symbolism. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/Software 21 st Century Themes Financial, Economic, Business Practice Standards MP.3: Construct viable arguments and critique the reasoning of others. MP.7: Look for and make use of structure. 21 st Century Skills Financial, Economic, Business, Entrepreneurial Literacy, Critical Thinking, Problem Solving Learning Targets s Math Domain Standards: CC.3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. CC.3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. Unit Essential Questions What strategies can you use to divide? Unit Enduring Understandings The use of representations can be used to provide meaning for multiplication and division of whole numbers (e.g. Equal-sized groups, arrays, area models, and equal jumps on number lines for multiplication, and successive subtraction, partitioning, and sharing for division). Comparing a variety of solution strategies will help to demonstrate multiplication and division as inverse operations. 25
Terminology: order of operations, divide, dividend, divisor, factor, inverse operations, product, quotient, related facts Goals/Objectives Students will be able to - Use models to represent division by 2 Recommended Learning Activities/Instructional Strategies Have students work in pairs to divide 18 counters into 2 equal groups. a. Have them record their results as equal groups of b. Then ask students to write the division equation for the model. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Online Assessment - Summative Use repeated subtraction, a number line, or a multiplication table to divide by 10 Count by 5s, count back on a number line, or use 10s facts and doubles to divide by 5 Write the following numbers on the board: 15, 25, 40. a. Have students work together to find how many groups of 5 there are in each number. b. Have students take turns putting up one hand at a time and counting by 5s. Students stop when they reach the number and then count how many hands are up. c. Have students write the division equation for each problem they model. (EX: 15/5 = 3, 25/5 =5) 26 Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit.
Goals/Objectives Students will be able to - Explore and identify equal parts of a whole Divide models to make equal shares Use a fraction to name one part of a whole that is divided into equal parts Recommended Learning Activities/Instructional Strategies Direct students attention to a number line. a. Why is the number line being divided into four equal lengths? b. How do you know where to draw a point for ¾? c. Have students describe how they would make a number line for this situation if one were not provided for them. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Have students draw several 4-by-4 squares on grid paper. a. Have them find as many ways as they can to divide the squares into 4 equal parts that are shaped differently. b. Have student share their drawings and strategies. Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources - Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 27
Content Area Mathematics Unit 8: Understand Fractions 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 8 Overview Unit Summary/Rationale Gaining experience in making equal shares gives students an important foundation in partitioning. This skill will be applied as students advance in their study of fractions. The denominator represents the number of equal parts that the whole is divided into. Students apply that knowledge to fractions where the numerator is greater that the denominator. This type of fraction gives students an opportunity to develop quantitative reasoning. Visualizing a problem with objects or pictures can make a solution to a problem more evident. Drawing a diagram is similar to making a picture. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/Software 21 st Century Themes Financial, Economic, Business 21 st Century Skills Financial, Economic, Business, Entrepreneurial Literacy, Critical Thinking, Problem Solving Learning Targets Practice Standards: MP.2: Reason abstractly and quantitatively MP.4: Model with mathematics Math Domain Standards: CC.3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. CC.3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/ b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 28
CC.3.NF.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Unit Essential Questions What are equal parts of a whole? Why do you need to know how to make equal shares? What do the top and bottom numbers of a fraction tell? Unit Enduring Understandings One representation may sometimes be more helpful than another; and, used together, multiple representations give a fuller understanding of a problem. Numeric fluency includes both the understanding of and the ability to appropriately use numbers. Computational fluency includes understanding the meaning and the appropriate use of numerical operations. Terminology: eights, equal parts fourths, halves, sixths, thirds, whole, fraction, unit fraction, denominator, numerator, fraction greater than 1 29
Content Area Mathematics Unit 9: Compare Fractions 4 Lessons/Three Weeks Target Course/Grade Level Grade 3 Math Unit 9 Overview Unit Summary/Rationale Children need lots of informal experiences with fractions before proceeding to formal fraction operations because they need to build up some fraction sense. Informal, visual, and hands-on approaches to comparing fractions set the stage for the formal algorithm. Students who employ these practices search for visual or symbolic clues, explore patterns, and seek alternative strategies to solve problems. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/ Software 21 st Century Themes Financial, Economic, Business, Entrepreneurial Literacy Practice Standards: MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Math Domain Standards: CC.3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. CC.3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. 30
Unit Essential Questions How can you compare fractions? Unit Enduring Understandings Computational fluency includes understanding the meaning and the appropriate use of numerical operations. A quantity can be represented numerically in various ways. Problem solving depends upon choosing wise ways. In many cases, there are multiple algorithms for finding a mathematical solution, and those algorithms are frequently associated with different Terminology: equivalent, equivalent fractions, compare, equal to, greater than, less than, denominator, numerator, order Goals/Objectives Students will be able to - Solve comparison problems by using the strategy act it out. Compare fractions with the same denominator by using models and reasoning strategies Compare fractions with the same numerator by using models and reasoning strategies. Recommended Learning Activities/Instructional Strategies Have students work in pairs and put the fraction strips together in order from largest pieces to smallest pieces. a. Tell students to align a ruler with the right edge of ½ and look for pieces in different rows that match or are the same size as ½. b. What fractions are the same size as 1/2? (2/4, 3/6, 4/8, 5/10, 6/12) c. Show students how to write an equivalent chain using equal signs. Equivalent chain: 1/2=2/4=3/6=4/8=5/10=6/12 Discuss the word compare. Help students recall that when you compare two numbers, you find which is greater or lesser. Review the symbols for equal to (=), greater than (>), less than (<). a. List pairs of whole numbers on the board, and have volunteers write the correct symbol between the numbers. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument 31
Diverse Learners (ELL, Special Ed, Gifted & Talented) Differentiation strategies may include, but are not limited to, learning centers and cooperative learning activities in either heterogeneous or homogeneous groups, depending on the learning objectives and the number of students that need further support and scaffolding, versus those that need more challenge and enrichment. Modifications may also be made as they relate to the special needs of students in accordance with their Individualized Education Programs (IEPs) or 504 plans, or English Language Learners (ELL). These may include, but are not limited to, extended time, copies of class notes, refocusing strategies, preferred seating, study guides, and/or suggestions from special education or ELL teachers. Resources - Resources -Envision Math Teacher Edition, EnVision Student Practice Editions, EnVison Math Enrichment Edition, EnVision Animated Math Models, Real World Videos, EnVision Math Center and Manipulative Kit. 32
Unit 10 Overview Content Area Mathematics Unit 10: Time, Length, Liquid, Volume, and Mass Target Course/Grade Level Grade 3 Math 4 Lessons/Three Weeks Unit Summary/Rationale Many students do not have a deep understanding of measurement concepts. Students will naturally engage in a hands-on approach of exploring measurement. Engaging in measurement requires students to reason abstractly and quantitatively. Each measurement attribute (e.g. time, length, mass, etc.) has its own units for obtaining and recording a quantitative measurement. Students need to evaluate measures to determine if they make sense. Interdisciplinary Connections Science Technology Integration computer, SMART Board, EnVision Animated Math/Software 21 st Century Themes Financial, Economic, Business, Entrepreneurial Literacy 21 st Century Skills Communication & Collaboration, Critical Thinking/Problem Solving, Creativity/Innovation Learning Targets Practice Standards: MP.4: Model with mathematics MP.5: Use appropriate tools strategically. Math Domain Standards: CC.3.MD.1: Tell and write time to the nearest minute and measure 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. CC.3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. CC.3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 4 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. 4 33
Unit Essential Questions How can you tell time to the nearest minute? How can you tell time and use measurement to describe the size of something? How can you measure elapsed time in minutes? Unit Enduring Understandings Measurement describes the attributes of objects and events. Standard units of measure enable people to interpret results or data. All measurements have some degree of uncertainty. Terminology: minute, A.M., midnight, noon, P.M., elapsed time, inch, liquid, volume, liter (L), gram (g), kilogram (kg), mass Goals/Objectives Students will be able to - Read, write, and tell time on analog and digital clocks to the nearest minute. Measure length to the nearest half or fourth inch and use measurement data to make a line plot. Estimate and measure liquid volume. Estimate and measure mass in grams and kilograms. Add, subtract, multiply, or divide to solve problems involving liquid volumes or masses. Recommended Learning Activities/Instructional Strategies Have students show 9:00 on their clocks. a. Have them move the minute hand halfway around the clock to the 6 while they count aloud by fives as the minute hand points to each number. Ask students to tell how many minutes pass as the minute hand moves from the 12 to the 6. Have students estimate the mass of coins in grams: dime, nickel, penny, quarter. a) Have students record their estimates for the mass of each coin in a table. b) Have students use the pan balance and gram masses to measure the mass of each coin. c) Have students record their measurement of the mass of each coin. d) Students should compare their measurements with their estimates and describe whether any of their findings were unexpected. Evidence of Learning (Formative & Summative) Lesson Quick Check Formative Mid-Chapter Checkpoint Formative Chapter Review/Test Summative Performance Assessment Summative Chapter Test Summative 34