Woodlynne School District Curriculum Guide

Transcription

1 Woodlynne School District Curriculum Guide Mathematics Grade 5 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 with consideration for the district s calendar. 1

2 Woodlynne School District Curriculum Guide Content Area: Mathematics Course Title: Grade 5 Math Grade Level: 5 Unit 1: Place Value, Multiplication and Expressions 4 weeks Unit 2: Divide Whole Numbers 3 weeks Unit 3: Add and Subtract Decimals 4 weeks Unit 4: Multiply Decimals 4 weeks Unit 5: Divide Decimals 3 weeks Unit 6: Adding and Subtracting Fractions 3 weeks 2

3 Unit 7: Multiply Fractions 3 weeks Unit 8: Dividing Fractions 3 weeks Unit 9: Algebra: Patterns and Graphing 3 weeks Unit 10: Convert Units of Measure 3 weeks Unit 11: Geometry and Volume 3 weeks Board Approved on: 9/9/14 3

4 Content Area Mathematics Unit 1 Overview Unit 1: Place Value, Multiplication, and Expressions 6 Lessons/ Four Weeks Target Course/Grade Level Grade 5 Math Unit Summary and Rationale Students will use operations and algebraic thinking to evaluate operations in base ten. Interdisciplinary Integration Language Arts: Journal writing, open-ended response questions; Consumer Economics: real-world problem-solving. Technology Integration SMART board, Document Camera, virtual manipulatives, Internet sites, EnVision Math Animated Software, calculator, i-ready 21 st Century Themes Global awareness, financial, economic, business and entrepreneurial literacy Practice Standards: MP.1: Make sense of problems and persevere in solving them. MP.8: Look for and express regularity in repeated reasoning. 21 st Century Skills Creativity/innovation, information literacy, critical thinking/problem solving, communication and collaboration, life and career skills, media literacy Learning Targets Math Domain Standards: 5. OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5. OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product 5. NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5. NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. 5. NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4

5 Unit Essential Questions How can you use place value, multiplication, and expressions to represent and solve problems? Unit Enduring Understandings Reading, writing and representing whole numbers through millions, using properties and multiplication to solve problems and using expressions to represent and solve problems are all used in problem solving. Goals/Objectives Students will be able to - Write and interpret numerical expressions Understand the place value system Perform operations with multi-level whole numbers and with decimals to hundredths. Recommended Learning Activities/Instructional Strategies Instructional Strategies Write the expression 6 x 14 on the board. Have students draw an array with 6 rows and 14 columns on grid paper to model this product. Encourage students to see that they can break apart the array into 10 columns and 4 columns to make the product easier to find. How is breaking apart the array helpful? Draw a 6 by 6 grid on the board, with columns and rows labeled as shown x Model how to name a fact, and write the product on the table. Then have students provide other examples. Ask students to name a related division sentence. 42 divided by 6 = 7 Have students use counters or draw pictures to help them understand related multiplication and division sentences. Continue until table is complete. 5 Evidence of Learning (Formative & Summative) Weekly quiz on place value, properties, powers of 10, and multiplication patterns. Unit test includes all skills on the quiz and multiply by one and two digit numbers, relate multiplication to division, numerical expressions, and grouping symbols. 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, EnVision Math Center and Manipulative Kit., & Terminology: base, distributive property, evaluate, exponent, inverse operation, numerical expression, order of operation, period 6

7 Content Area Mathematics Unit 2: Dividing Whole Numbers 4 Lessons/ Three Weeks Target Course/Grade Level Grade 5 Math Unit 2 Overview Unit Summary and Rationale Students will find whole number quotients and interpret a fraction as division of the numerator by the denominator. Interdisciplinary Integration Language Arts: Journal writing, open-ended response questions; Consumer Economics: real-world problem-solving. Technology Integration SMART board, Document Camera, virtual manipulatives, Internet sites, i-ready 21 st Century Themes Global awareness, financial, economic, business and entrepreneurial literacy 21 st Century Skills Creativity/innovation, information literacy, critical thinking/problem solving, communication and collaboration, life and career skills, media literacy Learning Targets Practice Standards: MP.1: Make sense of problems and persevere in solving them. MP.4: Model with mathematics. MP.7: Look for and make use of structure. Math Domain Standards: 5. NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5. NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Unit Essential Questions How can you divide whole numbers? Terminology: compatible numbers, estimate, inverse operations, remainder Unit Enduring Understandings Checking work, estimating for the reasonableness of quotients and identifying key words to know how to solve a problem are important strategies in evaluating problems. 7

8 Goals/Objectives Students will be able to - Perform operations with multi-digit whole numbers and with decimals to hundredths. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Recommended Learning Activities/Instructional Strategies Instructional Strategies On the board, write 75 divided by 5 and sketch a rectangle as shown: 75 divided by 5 = ( ) divided by To model 75 divided by 5, draw a rectangle. What is the next step? (Break 75 into multiples of 5 whose sum is 75) Distribute the 5 to 40 divided by 5 = 8 and 35 divided by 5 = 7 add 8 +7 to get the quotient of 15 Evidence of Learning (Formative & Summative) Weekly quiz on placing the first digit, dividing by onedigit divisor, two-digit divisor and adding partial quotients. Unit test includes all skills on the quiz and estimate and divide with two-digit divisors, interpret the remainder, and problem-solving division Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument Using 100 square flats, 10 square sticks and single square flats, Write 426 divided by 3. Students separate flats and sticks equally into three groups. There is one hundred flat left over. Regroup the 1 hundred as 10 tens. (There should be 142 in each group, therefore the quotient is 142. 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, EnVision Math Center and Manipulative Kit., & 8

9 Unit 3 Overview Content Area Mathematics Unit 3: Add and Subtract Decimals 6 Lessons/ Four Weeks Target Course/Grade Level Grade 5 Math Unit Summary and Rationale Students will demonstrate an understanding of decimal and whole number place value. Students will read, write, round, compare, add and subtract decimals. Interdisciplinary Integration Language Arts: Journal writing, open-ended response questions; Consumer Economics: real-world problem-solving. Integration SMART board, Document Camera, virtual manipulatives, i-ready 21 st Century Themes Global awareness, financial, economic, business and entrepreneurial literacy 21 st Century Skills Creativity/innovation, information literacy, critical thinking/problem solving, communication and collaboration, life and career skills, media literacy Learning Targets Practice Standards: MP.3: Construct viable arguments and critique the reasoning of others. MP.8: Look for and express regularity in repeated reasoning. Math Domain Standards: 5. NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5. NBT.3: Read, write, and compare decimals to thousandths. 5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). 5. NBT.3.b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 5. NBT.4: Use place value understanding to round decimals to any place. Unit Essential Questions How can you add and subtract decimals? Unit Enduring Understandings Understanding place value helps you add and subtract decimals. Various methods can be used to find decimal sums and differences. 9

10 Terminology: Sequence, term, thousandth, benchmark, estimate, hundredth, round, tenth Goals/Objectives Students will be able to - Understand the place value system Perform operations with multi-digit whole numbers and decimals to hundredths Recommended Learning Activities/Instructional Strategies Instructional Strategies On the board, write the addition problem shown below. Have students find the sum by recording the regroupings above the addends. Have students use base-ten blocks to model the addition problem. Provide an example with subtraction of decimals. Use base-ten blocks to model the subtraction problem. Give each student 10 index cards and have them write a decimal up to thousandths on each card. Have partners combine their cards, shuffle them and then divide them into two equal piles. Each student takes a pile and keeps the cards facedown. Partners turn over their top card at the same time and compare the decimals. The student with the greater decimal keeps the cards. If two cards are of equal value, then each partner turns over one more card and compares. The card with the greater value takes all four cards. Play continues until one player has all the cards. Evidence of Learning (Formative & Summative) Weekly quiz on place value of decimals, comparing and ordering decimals, rounding decimals. Unit test on all skills from quiz and estimating decimal sums and differences, adding and subtracting decimals, pattern with decimals, adding and subtracting money, and problem solving choose a method. 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, EnVision Math Center and Manipulative Kit., & 10

11 Content Area Mathematics Unit 4: Multiply Decimals 6 Lessons/ Four Weeks Target Course/Grade Level Grade 5 Math Unit 4 Overview Unit Summary and Rationale Students will explain patterns in the number of zeros of a product and placement of the decimal point when multiplying or dividing by powers of 10. Students will multiply decimals to hundredths using various methods. Interdisciplinary Integration Language Arts: Journal writing, open-ended response questions; Consumer Economics: real-world problem-solving. Technology Integration SMART board, Document Camera, virtual manipulative, Internet sites, accelerated math, calculator, study island 21 st Century Themes 21 st Century Skills Global awareness, financial, economic, business Creativity/innovation, information literacy, critical thinking/problem solving, and entrepreneurial literacy communication and collaboration, life and career skills, media literacy Learning Targets Practice Standards: MP.7: Look for and make use of structure. MP.8: Look for and express regularity in repeated reasoning. Math Domain Standards: 5. NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 11

12 Unit Essential Questions How can you solve decimal multiplication problems? Unit Enduring Understandings Multiplying with whole numbers is similar to multiplying with decimals. Pattern, models and drawings help you solve decimal multiplication problems. Terminology: decimal, expanded form, hundredths,multiplication, ones, patterns, place value, product, tenths, thousandths Goals/Objectives Students will be able to - Understand the place value system Perform operations with multi-digit whole numbers and decimals to hundredths Recommended Learning Activities/Instructional Strategies Instructional Strategies A 10 x 10 grid can be used to model 1.0, where each square on the grid represents onehundredth. For example, 0.2 x 1.5. Two grids are used to model this problem. Use a blue crayon to shade 1.5 on the model. Use a red crayon to shade 0.2 of the blue hundredths. The result is 30 hundredths shaded purple. So, 0.2 x 1.5 = 0.30 Present the problem 4.92 x 1,000 to students along with the pattern shown below. Ask then to underline and count the number of zeros for each factor that is a power of 10. Explain to students that the number of zeros they underlined and the number of places the decimal point moves from the original factor or 4.92 is the same. Repeat with different examples. Evidence of Learning (Formative & Summative) Weekly Quiz on multiplication patterns, multiplying decimals and whole numbers, multiplying with expanded form, and multiplying money. Unit test on all of the skills from the quiz and zeros in the product. Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument 12

13 4.92 x 1 = x 10 = x 100 = x 1,000 = 4,920 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, EnVision Math Center and Manipulative Kit., & 13

14 Unit 5 Overview Content Area Mathematics Unit 5: Divide Decimals 4 Lessons/ Three Weeks Target Course/Grade Level Grade 5 Math Unit Summary and Rationale Students will add, subtract, multiply and divide decimals to hundredths using various strategies. Students will explain patterns in multiplying and dividing with powers of ten. Interdisciplinary Integration Language Arts: Journal writing, open-ended response questions; Consumer Economics: real-world problem-solving. Technology Integration SMART board, Document Camera, virtual manipulative, i-ready 21 st Century Themes Global awareness, financial, economic, business and entrepreneurial literacy 21 st Century Skills Creativity/innovation, information literacy, critical thinking/problem solving, communication and collaboration, life and career skills, media literacy Learning Targets Practice Standards: MP.4: Model with mathematics. MP.7: Look for and make use of structure. Math Domain Standards: 5. NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 5. NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Unit Essential Questions How can you solve decimal division problems? Unit Enduring Understandings Dividing with decimals is similar to dividing with whole numbers Patterns, models and drawings help you solve decimal division problems Terminology: compatible numbers, decimal, decimal point, dividend, division, divisor, estimate, hundredth, tenth 14

15 Goals/Objectives Students will be able to - Understand the place value system Perform operations with multi-digit whole numbers and with decimals to hundredths Recommended Learning Activities/Instructional Strategies Instructional Strategies Give each pair of Students 1 flat, and explain that it represents one whole. Have students exchange 1 flat for 10 longs and explain that each long represents one tenth of a whole. Write one tenth = 0.1 on the board so students recall how to use a decimal point correctly. Write these division problems on the board: 1/1 = 1 1/2 = 0.5 1/5 = 0.2 1/10 = 0.1 (use the division sign) Have students model each problem by separating 10 longs into equal groups. The number of longs in each group is the quotient. Work with students to count the longs in each group by tenths. For example, students should count 2 longs as one-tenth, two-tenths. Have volunteers come to the board to write the solution for each problem. Show students 1 whole by displaying 1 flat on a piece of paper. Label it 1.0. Provide students with 10 longs. Allow students time to line up longs on top of the flat to determine how many longs are equivalent to 1 whole. How many longs are needed to make 1 whole? (ten) What part of the whole does one long represent? (one tenth) Display one long and label it 0.1. Have a volunteer model 0.5 using 5 longs. Have students repeat this activity modeling numbers from 0.1 through 2.0. Provide assistance to individual students as needed Evidence of Learning (Formative & Summative) Weekly Quiz on division patterns with decimals, dividing decimals by whole numbers, and estimating quotients. Unit test on all of the skills from the quiz and dividing decimals, writing zeros in the dividend, and problemsolving with decimal operations. Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument 15

16 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, EnVision Math Center and Manipulative Kit., & 16

17 Content Area Mathematics Unit 6 Overview Unit 6: Add and Subtract Fractions with Unlike Denominators 4 Lessons/ Three Weeks Target Course/Grade Level Grade 5 Math Unit Summary and Rationale Students will be able to develop fluency with addition and subtraction of fractions. Interdisciplinary Integration Language Arts: journal writing; open-ended extended response questions; Consumer Economics: real world problem solving Technology Integration SMART board, projector, virtual manipulatives, and i-ready 21 st Century Themes Global Awareness, Financial Economic, Business and Entrepreneurial Literacy, Environmental Literacy 21 st Century Skills Critical Thinking/Problem Solving, Communication & Collaboration, Life & Career Skills Learning Targets Practice Standards: MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. Math Domain Standards: 5. NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 5. NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Unit Essential Questions How can you add and subtract fractions with unlike denominators? How can the ability to recognize the meanings of operations and how they relate to one another help solve real world mathematical problems? Unit Enduring Understandings Models are used to help to find sums and differences of fractions. The least common denominator is used when adding and subtracting fractions. Understanding of the number system helps to solve real world problems. Computational fluency requires efficient, accurate, and flexible methods for computing. Terminology: common denominator, common multiple, equivalent fractions, mixed number, simplest form 17

18 Goals/Objectives Students will be able to - Use equivalent fractions as a strategy to add and subtract fractions. Recommended Learning Activities/Instructional Strategies Instructional Strategies Think Pair Share Activity: Number Line Activity Use a number line to model like fraction sums. Write 8/10 + 6/10 on the board and have pair of students sketch a number line from 0 to 2 by fifths. Have students describe two different ways the number line can be used to find 8/10 + 6/10. Ask what operation is used to write equivalent fractions for tenths to fractions in fifths. (division) Ask what operation is used to write equivalent fractions for fifths to fractions in tenths. (multiplication) Show process of adding unlike fractions using number line with: unlike.html Think Pair Share Activity: Fraction Strips Activity Use fraction strips to model like fraction sums and differences. Distribute fraction strips for sixths to each pair of students. Write 2/6 + 3/6 on the board. Have students use fraction strips to follow along as you add and name the sum 5/6. Explain how paper and pencil are used to find the sum of two fractions that have the same denominator. (common denominator) Write 5/6 4/6 on the board. Have the students use fraction strips to follow along as you subtract and name the difference. (1/6) Explain how you record the difference by writing the numerators over the common denominator. Then put ½ + ¼ and 6/10 2/5 on the board. Ask the students to add or subtract the fractions and model it using 18 Evidence of Learning (Formative & Summative) Weekly quiz on adding and subtracting fractions Chapter test on adding and subtracting fractions Constructed Response Performance Task with grading rubric Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument

19 their fraction bars. Ask the pairs to explain to their classmates how they obtained their answer. (obtain a common denominator) Fraction Song Print out lyrics to fractions song for each student. Let them listen to the song them replay the song and have the students sing along. The tune is to Jingle Bells. Song and lyrics located at: all/35how_easy_is_that.html Think Pair Share Activity: Pattern Blocks Use pattern blocks to model subtraction of fractions. Model the two fractions with common denominators to be subtracted with pattern blocks. Name the fraction for the difference. Have the students summarize with a partner how to subtract fractions with the same denominator. Be sure to point out that when subtracting fractions that have the same denominator, just subtract the numerators and keep the same denominator. Ask the children how they would use pattern blocks to solve 2/3 1/6. After a few minutes, have the children share their approaches. Model both fractions with pattern blocks. Lay the blocks representing the smaller fraction on top of the blocks representing the larger fraction. Explain that the part of the larger fraction that remains uncovered is the difference. Another method to model is the take away method. Here, you need to model the larger fraction with pattern blocks. Then take away the blocks representing the smaller fraction, trading for pattern blocks of the proper 19

20 size if necessary. The remaining pattern blocks represent the difference. Have the students summarize with a partner how to subtract fractions with different denominators. Continue to have students to work in partners to solve fraction subtraction problems. 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, EnVision Math Center and Manipulative Kit., & 20

21 Content Area Mathematics Unit 7: Multiplying Fractions 4 Lessons/ Three Weeks Target Course/Grade Level Grade 5 Math Unit 7 Overview Unit Summary and Rationale Students will be able to develop fluency with multiplying fractions. Interdisciplinary Integration Language Arts: journal writing; open-ended extended response questions; Consumer Economics: real world problem solving Technology Integration i-ready Math, SMART board, projector, virtual manipulatives, and Internet 21 st Century Themes Global Awareness, Financial Economic, Business and Entrepreneurial Literacy, Environmental Literacy 21 st Century Skills Critical Thinking/Problem Solving, Communication & Collaboration, Life & Career Skills Learning Targets Practice Standards: MP.3: Construct viable arguments and critique the reasoning of others. MP.5: Use appropriate tools strategically. Math Domain Standards: 5. NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5. NF.4.a: Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. 5. NF.4.b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.NF.5: Interpret multiplication as scaling (resizing), by: 5. NF.5.a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5. NF.5.b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 21

22 Unit Essential Questions How do you multiply fractions? How can you use a model to show the multiplication of fractions? How does the size of the product compare to the size of one factor when multiplying fractions? How can the ability to recognize the meanings of operations and how they relate to one another help solve real world mathematical problems? Unit Enduring Understandings Models can be used to represent the product of fractions. The magnitude of numbers affects the outcome of operations on them. Understanding of the number system helps to solve real world problems. Computational fluency requires efficient, accurate, and flexible methods for computing. Terminology: denominator, equivalent fractions, mixed number, numerator, product, simplest form 22

23 Goals/Objectives Students will be able to - Apply and extend previous understanding of multiplication of whole numbers to multiplying fractions. Recommended Learning Activities/Instructional Strategies Instructional Strategies Think Pair Share Activity: Model Concept Demonstrate how to use an area model to show the product of ¼ x ½ by folding and shading paper. Explain each step in the process and how you obtain a product of 1/8. Then have the students model the same problem. Have them wire the answer and share their responses with the group. Repeat with other problems asking each pair to answer: Into how many equal parts will we fold the paper vertically? How many parts will we shade to represent each factor? In to how many equal parts will we fold the paper horizontally? How many equal parts are there in the whole paper now? Play an I Have, Who Has game. I Have... Who Has? games can be created for virtually any topic and used as both a whole class practice or a center activity for small groups. Create cards with fraction multiplication problems on them. On the top of the card write: I have then the answer to a fraction multiplication problem. Below the problem, write Who has. Underneath this, write out a fraction multiplication problem. How to Play: Shuffle the cards and distribute one card to each student. If any cards are left over distribute these to random students. The first student begins with "I have... Who has" while the others listen for the question and try to find the answer that on their card. The student with the correct answer reads the I have portion and begins the next round by reading the Who 23 Evidence of Learning (Formative & Summative) Grade Level quiz on multiplying fractions Grade Level chapter test on multiplying fractions Constructed Response Performance Task with grading rubric Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument

24 has on the same card. Play continues until the last card is read. As students develop confidence with the game a stop watch can be used to time a round. Record the time on the board so that students try each game to beat their current best time. When using the cards as a math center activity one student deals out the cards to all players. Players arrange the cards face-up in front of them. Play continues as in the class game. Whoever has the card that answers the question reads that answer and then reads the question on their card. Students turn over the cards after reading them. The first person to turn over all of his/her cards wins the game. Cards can be shuffled and the game repeated. Recipe Activity Provide a recipe for a healthy trail mix that serves 10 people which involves fractions. Ask the students what you should do if you need to serve 20 people, 10 people, 5 people, etc. Students should respond with multiply or divide the ingredients. Distribute the recipe and ask the students to halve the amount to make enough for 5 people by multiplying each ingredient by 1/2. After students answers are checked, have stations set up so groups of 4 or 5 students can actually create the trail mixture by measuring ingredients using measuring cups and measuring spoons for their group to enjoy. 24

25 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, EnVision Math Center and Manipulative Kit., & 25

26 Content Area Mathematics Unit 8: Dividing Fractions 4 Lessons/Three Weeks Target Course/Grade Level Grade 5 Math Unit 8 Overview Unit Summary and Rationale Students will be able to develop fluency with multiplying fractions. Interdisciplinary Integration Language Arts: journal writing; open-ended extended response questions; Consumer Economics: real world problem solving Technology Integration Accelerated Math, SMART board, Document Camera, virtual manipulatives, and Internet, i-ready 21 st Century Themes Global Awareness, Financial Economic, Business and Entrepreneurial Literacy, Environmental Literacy 21 st Century Skills Critical Thinking/Problem Solving, Communication & Collaboration, Life & Career Skills Learning Targets Practice Standards: MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. Math Domain Standards: 5. NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5. NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 5. NF.7.a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 5. NF.7.b: Interpret division of a whole number by a unit fraction, and compute such quotients. 5. NF.7.c: Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Unit Essential Questions How do you divide fractions? How can you use a model to show the division of fractions? How does the size of the quotient compare to the size of the original number? Unit Enduring Understandings Models can be used to represent the quotient of fractions. The magnitude of numbers affects the outcome of operations on them. Understanding of the number system helps to solve real world problems. Computational fluency requires efficient, accurate, and flexible methods for computing. 26

27 How can the ability to recognize the meanings of operations and how they relate to one another help solve real world mathematical problems? Terminology: dividend, equation, fraction, quotient, whole number 27

28 Goals/Objectives Students will be able to - Apply and extend previous understanding of multiplication and division of whole number to dividing fractions. Recommended Learning Activities/Instructional Strategies Instructional Strategies Fraction Dominos - To make the game: divide 28 index cards in half by drawing a line down the center of each card. Write fractions, mixed numbers, and whole numbers on the cards. For example, one card might show 1/2 on one side and 1 1/3 on the other side. Be sure to include matches. If you make a card that says 1/3 and 4/5, you should also make cards that say 1/3 and 6/9 or 4/5 and 8/12. You may also wish to make doubles (1/3 and 1/3 on a card). Follow the general directions for playing dominos with the exception that players will divide the numbers on the domino they place on the table. For example, if your turn starts with a domino that says 1/3 and 1/3 on the table, you may lay down a domino with 1/3 and 1. However, before you can play, you will divide 1/3 by 1. If you get the correct answer, you may lay down the domino. Picture This Activity - Copy one expression from below onto each index card. Shuffle the cards and lay them face down. Turn over the first card. All group members then use the grid paper to draw a picture for the division problem. Draw either a Geo-board picture of the problem or try to find a unique way to draw the quotient. When you have drawn a picture of the problem, find each quotient. When all group members are done, compare drawings and answers. Discuss which drawing was the most unique and which drawing was the easiest to understand. Play several rounds or play until all the cards have been used. Share with the entire class some of your group's unique ideas. Expressions to be included on index cards: 1/2 28 Evidence of Learning (Formative & Summative) Weekly quiz on dividing fractions Unit chapter test on dividing fractions Constructed Response Performance Task with grading rubric Alternative or project-based assessments will be evaluated using a teacher-selected or created rubric or other instrument

29 1/6, 3/4 1/12, 2 1/3, 5/6 1/12, 1/2 1/10, 1 1/8, 2/3 1/9, 3/8 1/16, 5/7 1/14, 4/5 1/15 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, EnVision Math Center and Manipulative Kit., & 29

30 Content Area Mathematics Unit 9 Overview Unit 9: Algebra: Patterns and Graphing 4 Lessons/Three Weeks Target Course/Grade Level Grade 5 Math Unit Summary and Rationale Students will understand how to describe, extend, and create a wide variety of patterns and functional relationships. Students will understand how to collect, organize, and display relevant data to answer questions. Interdisciplinary Integration Language Arts: journal writing; open-ended extended response questions; Consumer Economics: real world problem solving Technology Integration i-ready, SMART board, projector, virtual manipulatives, and Internet 21 st Century Themes Global Awareness, Financial Economic, Business and Entrepreneurial Literacy, Environmental Literacy 21 st Century Skills Critical Thinking/Problem Solving, Communication & Collaboration, Life & Career Skills Learning Targets Practice Standards: MP.4: Model with mathematics. MP.8: Look for and express regularity in repeated reasoning. Math Domain Standards: 5. OA.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. 5. MD.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. 5. G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 5. G.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 30

31 Unit Essential Questions Why is it important to look for a pattern? What can we learn from looking at patterns? What are data sets, how are they graphed, and what can we learn from them? Unit Enduring Understandings Patterns and relationships can be used to describe and quantify physical relationships. Patterns and relationships can be represented graphically, numerically, symbolically or verbally. Data analysis is formulating questions that can be addressed, explored, and synthesized with relevant information. Terminology: interval, line graph, ordered pair, origin, scale, x-axis, x-coordinate, y-axis, y-coordinate 31

32 Goals/Objectives Students will be able to - Analyze patterns and relationships. Recommended Learning Activities/Instructional Strategies Instructional Strategies Treasures Activity Give each student in a pair a copy of a quadrant I grid. Have one student hid their grid from their partner while he or she colors two consecutive squares on their own grid. Have students color two more pairs of squares. The colored areas are treasures. The other student leaves his or her sheet blank until the game begins. Once the treasurers are hidden, the game can begin. The student that did not color his or her grid calls out ordered pairs. If the ordered pair lies on the border of a colored treasure square, the partner should say, You found a treasure. That student then plots that point on his or her grid. When a player finds all the points forming the treasure, that player gets the treasure. The winner of the game is the first student to get all three of his or her partner s treasures. Evidence of Learning (Formative & Summative) Weekly quiz on line plots, ordered pairs, and graphing data Unit chapter test on including all skills on the quiz and line graphs, numerical patterns, as well as analyzing relationships Constructed Response Performance Task with grading rubric Student Height Data Activity Prior to using this activity, measure each student s height in inches using mixed numbers. Compile the data and hand it out to the students. Ask the students to represent the data on a line plot. (You may need to provide assistance setting up the increments.) Ask questions along the way such as: How can a line plot help you organize this information? How many Xs should there be in your line plot? For which amount does your line plot show the greatest number of occurrences? How would you use this information to find the mean or average or the data? 32

33 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, EnVision Math Center and Manipulative Kit., & 33