1
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
Subject(s)
Grade/Course
Unit of Study
Unit Type(s)
Pacing
Mathematics
4
Fractions and Decimals
❑ Topical
X Skills-based
6 weeks
❑ Thematic
Priority Common Core State Standards
Supporting Standards
Priority Pennsylvania Core Standards Numeration CC.2.1.4.C.2 Build fractions from unit fractions by Applying and extending previous understandings of operations on whole numbers. M04.A-­‐F.2.1.1: Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).. M04.A-­‐F.2.1.2: Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12. M04.A-­‐F.2.1.3: Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).. M04.A-­‐F.2.1.4: Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).. M04.A-­‐F.2.1.5: Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4. M04.A-­‐F.2.1.6: Multiply a whole number by a non-­‐unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6. M04.A-­‐F.2.1.7: Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100). CC.2.1.4.C.3 CONNECT decimal notation to fractions, and COMPARE decimal fractions (base 10 denominator, e.g., 19/100). M04.A-­‐F.3.1.1: Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
2
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
M04.A-­‐F.3.1.2: Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.. M04.A-­‐F.3.1.3: Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions Supporting Standards CC.2.1.4.C.1 Extend the understanding of fractions to show equivalence and ordering. M04.A-­‐F.1.1.1 M04.A-­‐F.1.1.2 “UNWRAPPED” Priority Standards
Supporting Standards
Priority Pennsylvania Core Standards Numeration CC.2.1.4.C.2 BUILD fractions from unit fractions by APPLYING and EXTENDING previous understandings of operations on whole numbers. M04.A-­‐F.2.1.1: ADD and SUBTRACT fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).. M04.A-­‐F.2.1.2: DECOMPOSE a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12. M04.A-­‐F.2.1.3: ADD and SUBTRACT mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).. M04.A-­‐F.2.1.4: SOLVE word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).. M04.A-­‐F.2.1.5: MULTIPLY a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4. M04.A-­‐F.2.1.6: MULTIPLY a whole number by a non-­‐unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6. M04.A-­‐F.2.1.7: SOLVE word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
CC.2.1.4.C.3 CONNECT decimal notation to fractions, and COMPARE decimal fractions (base 10 denominator, e.g., 19/100). M04.A-­‐F.3.1.1: ADD two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100. M04.A-­‐F.3.1.2: USE decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa. M04.A-­‐F.3.1.3: COMPARE two decimals to hundredths using the symbols >, =, or <, and justify the conclusions Supporting Standards CC.2.1.4.C.1 Extend the understanding of fractions to show equivalence and ordering. M04.A-­‐F.1.1.1 M04.A-­‐F.1.1.2 “Unwrapped” Concepts
(students need to know)
Build Apply Extend Add Subtract Decompose Add Subtract Solve “Unwrapped” Skills
(students need to be able to do)
Fractions Operations on whole numbers Operations on whole numbers fractions with a common denominator fractions with a common denominator a fraction or a mixed number into a sum of fractions with the same denominator mixed numbers with a common denominator mixed numbers with a common denominator word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Bloom’s
Taxonomy
Levels
2, 4 4 4,6 4
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
Multiply Multiply Solve Connect Compare
a whole number by a unit fraction a whole number by a non-­‐unit fraction word problems involving multiplication of a whole number by a fraction Decimal notation to fractions Decimal fractions
Essential Questions
4,6 4
Corresponding Big Ideas
1. How can you show that two fractions are equivalent? 2. How can you compare two unlike fractions? 3. How can you add or subtract like fractions 4. What is another way to represent an improper fraction using multiplication? 5. What is a decimal?
1. Fractions can be equivalent even though they have different numbers. 2. Fractions can be compared by finding common numerators and denominators. 3. Fractions can be added or subtracted by joining or separating the parts. 4. An improper fraction can be written as a multiplication equation. 5. A decimal is a fractional number and is indicated by digits after a period which is called a decimal point.
Standardized Assessment Correlations
(State, College and Career)
Note to Curriculum Designers: Review grade-or course-specific state standardized
assessments for the types of questions directly related to the “unwrapped” Priority
Standards concepts and skills in focus for this unit of study. Identify the vocabulary used
and frequency of these questions. Compare/contrast this information with the
“unwrapped” concepts and skills listed above to determine how closely the two are
aligned.
Unit Assessments
Pre-Assessment
After creating the Unit Post-Assessment,
decide whether the pre-assessment will
be aligned (directly matched to post-
Informal Progress Monitoring Checks
Create short, ungraded “checks for student
understanding” for the educator to
administer throughout the unit of study that
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
assessment but with fewer questions) or
are directly aligned to the postmirrored (exact number and type of
assessment questions (selected-, short-,
questions as post-assessment).
extended-response, and/or performancebased) and that coincide with learning
progressions—the “building block chunks”
of instruction.
Post-Assessment
See Unit Assessment Planner
Scoring Guides and Answer Keys
See Unit Assessment Planner
Engaging Learning Experiences
Learning Activities Using
Text or Program
Referring to selected texts from a
variety of sources listed in the
Instructional Resources and
Materials—Physical and
Technology-Based section,
identify specific learning activities to
use while teaching students the
“unwrapped” Priority Standards
concepts and skills, supporting
standards, interdisciplinary
connections, unit vocabulary terms,
and extension/enrichment activities.
Authentic Performance Tasks
See Engaging Learning Experiences Planner
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
6
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
Research-Based Effective
Teaching Strategies
ü Check all those that apply to the unit:
❑ Identifying Similarities and Differences
❑ Summarizing and Note Taking
❑ Reinforcing Effort, Providing Recognition
❑ Homework and Practice
❑ Nonlinguistic Representations
❑ Cooperative Learning
❑ Setting Objectives, Providing Feedback
❑ Generating and Testing Hypotheses
❑ Cues, Questions, and Advance Organizers
❑ Interdisciplinary Non-Fiction Writing
Differentiation
Strategies
(Additional
Supports +
Enrichment)
See Details to
Accompany Unit
Planning Organizer
Intervention
Strategies
(Tiers 1, 2, 3)
See Details to
Accompany Unit
Planning Organizer
21st Century Learning Skills
ü Check all those that apply to the unit:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
❑ Critical thinking and Problem Solving
❑ Flexibility and Adaptability
❑ Effective Oral and Written Communication
❑ Accessing and Analyzing Information
❑ Other
Specially Designed
Instruction for
Special Education
Students
See Details to
Accompany Unit
Planning Organizer
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Strategies for
English Language
Learners
See Details to
Accompany Unit
Planning Organizer
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The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
Instructional Resources and Materials
Physical
Identify a variety of tangible resources that
include selected texts and hands-on
manipulatives, maps, charts, diagrams, realia,
multimedia, etc., to use while teaching
students the “unwrapped” Priority Standards
concepts and skills, supporting standards,
interdisciplinary connections, unit vocabulary
terms, and extension/enrichment activities.
Unit Vocabulary Terms
“Unwrapped”
Priority
Standards
Concepts
Technology-Based
Locate Internet sites and software that
correspond with the “unwrapped” Priority
Standards concepts and skills, supporting
standards, interdisciplinary connections, unit
vocabulary terms, and extension/enrichment
activities.
Enrichment / Extension
Supporting
Standards
Concepts and
Other UnitSpecific Terms
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Interdisciplinary
Connections