Table of Contents I. Unit Overview p. 3 - 22 II. MIF Lesson p. 23 - 25 III. MIF Pacing p. 26 - 29 IV. Pacing Calendar p. 30 - 32 V. Unit 2 Math Background p. 33 - 35 VI. PARCC Assessment Evidence/Clarification Statements p. 36 - 39 VII. Connections to the Mathematical Practices p. 40 - 41 VIII. Visual Vocabulary p. 42 - 46 IX. Potential Student Misconceptions p. 47 X. Teaching Multiple Representations p. 48 - 51 XI. Assessment Framework p. 52 - 53 XII. Performance Tasks p. 54 - 61 XIII. Additional Assessment Resources p. 62 Unit Overview Unit 2: Chapters 6-8 In this Unit Students will: Add and subtract unlike fractions, rename improper fractions and mixed numbers, rename whole numbers when adding and subtracting fractions, find a fraction of a set, display data involving fractions
18 19 20 21 Chapter 6 Test 22 Mini Assessment #6 23 12:30 Dismissal 24 25 26 No School 27 No School 28 No School 29 No School 30 No School 31 JANUARY Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 No School 3 Chapter 7 Pre-Test 4 5 6 7 8 9 10 11 12 13 14 15 16 No School 17 18 19 20 Authentic Assessment #5 21
Item 2; 6; 7 Write fractions in simplest form. 3B pp. 92-96 Lesson 14.3 3B Chapter 14 Lesson 3 Compare and order fractions. 3B pp. 97-106 Lesson 14.4 3B Chapter 14 Lesson 4 Items 1; 7; 10 Add two or three like fractions with sums of 1. 3B pp. 107-110 3B Chapter 14 Lesson 5 Items 1; 7; 11 Subtract a like fraction from another like fraction or one whole. 3B pp. 110-112 3B Chapter 14 Lesson 5 Item 8 Read, write and identify fractions of a set. 3B pp. 113-114 Lesson 14.5 3B Chapter 14 Lesson 6 Items 4; 9 Find the number of items in a fraction of a set. 3B pp. 115-116 Lesson 14.5 3B Chapter 14 Lesson 6 Chapter 7: Decimals and Chapter 8: Adding and Subtracting Decimals Transition Topic: Money and Decimals Grade 4 Chapter 7-8 Pre Test Items Grade 4 Chapter 7-8 Pre Test Item Objective Additional Support for the Objective: Grade 4 Reteach Additional Support for the Objective: Grade 4 Extra Practice Grade 4 Teacher Edition Support Use rounding to estimate sums and differences 3A pp. 31-34 Lesson 2.4 3A Chapter 2 Lesson 4 Chapter 7Items 2; 3 Identify numerator and denominator. 3B p. 84 Lesson 14.1 3B Chapter 14 Lesson 1 Chapter 7 Item 1 Use models to identify equivalent fractions. 3B p. 85-87 Lesson 14.2 3B Chapter 14 Lesson 3 Use a number line to identify equivalent fractions. 3B p. 88 Lesson 14.2 3B Chapter 14 Lesson 2 Chapter Use multiplication and division to find 3B p. 89-96 Lesson 14.3 3B Chapter 14 Lesson
Assessment Framework Unit 2 Assessment / Authentic Assessment Framework Assessment NJSLS Estimated Time Format Graded Pre Test 6 4.NF.1, 4.NF.3a-d, 4.NF.4a-c, 4.MD.1, 4.MD.4. 4.OA.2 30 minutes Individual Y Mini Assessment #4 4.NF.1-2 30 minutes Individual Y Test Prep 6 4.NF.1, 4.NF.3a-d, 4.NF.4a-c, 4.MD.1, 4.MD.4. 4.OA.2 1 Block Individual Y Authentic Assessment #5 Raising Money 4.NF.1-2 30 minutes Individual Y Doubling a Recipe 4.NF.1-4c, Individual Home Project Individual Optional Mini Assessment #5 4.NF.3 30 minutes Individual Y Pre Test 7 4.NF.1, 4.NF.3a, 4.NF.5, 4.NF.6, 4.NF.7, 4.OA.5, 4.MD.1, 5.NF.5 30 minutes Individual Y Chapter Test/Review 7 w/TP 4.NF.1, 4.NF.3a, 4.NF.5, 4.NF.6, 4.NF.7, 4.OA.5, 4.MD.1, 5.NF.5 1 Block Individual Y Authentic Assessment#6 Chocolate Bar Fractions 4.NF.2, 4.NF.4 30 minutes Individual Y Mini Assessment #6 4.NF.4 30 minutes Individual Y Chapter Test 4.NBT.1-2, 4.NBT.4, 4.NF.5, 4.MD1-2 1 Block Individual Y Authentic Assessment #7 Cynthia’s Perfect Punch 4.NF.b.3.c 30 minutes Individual Y Mini Assessment#7 4.NF.5-6 30 minutes Individual Y Mosaic Art 5.NF.5, 4.NF.5-7 1 Block or Home Project Individual Optional Mini Assessment #8 4.NF.7 30 minutes Individual Y
Mathematical Practice: 1, 3, 6 Type: Individual or Individual w/Interview SOLUTION: See below Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Level 1: No Command Students used representation to find equivalents fractional benchmarks. Students were able to use benchmarks to help estimate the size of the number and compare fractions to see if they were equal. Students were able to develop and use benchmarks that relates to different forms of representation of rational numbers (for example, 25 out of 100 is the same as ¼). By doing so, students were able to determine that two out of the three fractions were equal and 30/100 would give the band club less money. Students showed their work and gave a clear explanation of the answer to their problem. Students did not use benchmarks to solve the problem, however, they were able to determine that two out of the three fractions were equal and 30/100 would give the band club less money. Students showed their work and gave a clear explanation of the answer to their problem. Students attempted to compare the fractions using representation; however, their answer did not come up with the correct solution. An understanding of using benchmark fractions was not evident in their work. Does not address task, unresponsive, unrelated or inappropriate. Response includes an efficient and logical progression of steps. Compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators, comparing to a benchmark fraction and generating equivalent fractions Demonstrates the use of conceptual Response includes a logical progression of steps Compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators, comparing to a benchmark fraction and generating equivalent fractions Demonstrates the Response includes a logical but incomplete progression of steps. Minor calculation errors. Given a visual model and/or manipulatives, compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators and comparing to a benchmark fraction. Response includes an incomplete or Illogical progression of steps. Given a visual model and/or manipulatives, compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators The student shows no work or justification
understanding of fractional equivalence and ordering when solving simple word problems requiring fraction comparison. use of conceptual understanding of fractional equivalence and ordering when solving simple word problems requiring fraction comparison. and comparing to a benchmark fraction. Name:_______________________________________ John is giving out chocolate to his friends. If he wants to give each friend of a chocolate bar and he has 13 friends, how many chocolate bars will he need to buy? Use words, a model, or an equation to justify your answer
Since addition is commutative and associative, we can add the numbers in any order we wish. Let's add the whole numbers together and the fractions together. 4++3+=4+3++ 4+3++=7+5+=7+ Next we can re-write as a mixed number... 7+=7+=7++=7+1+ and add the whole numbers once again. 7+1+=8+ Since =, we can write the sum as 8. So we see that this recipe makes 8 gallons of punch. Level 5: Distinguished Command Level 4: Strong Command Level 3: Moderate Command Level 2: Partial Command Level 1: No Command Student correctly answers both questions and clearly constructs and communicates a complete response based on explanations/reasoning using : Properties of Operations Relationship between addition and subtraction Equivalent Fractions using mixed numbers Response includes an efficient and logical progression of steps. Student correctly answers both questions and clearly constructs and communicates a complete response based on explanations/reasoning using : Properties of Operations Relationship between addition and subtraction Equivalent Fractions using mixed numbers Response includes a logical progression of steps. Student correctly answers one question and clearly constructs and communicates a complete response based on explanations/reasoning using : Properties of Operations Relationship between addition and subtraction Equivalent Fractions using mixed numbers Response includes a logical but incomplete progression of steps. Student correctly answers one question and clearly constructs and communicates a complete response based on explanations/reasoning using : Properties of Operations Relationship between addition and subtraction Equivalent Fractions using mixed numbers Response includes a illogical or incomplete progression of steps. The student shows no work or