BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
Duration: ​
November
Topic 9: ​
Adding and Subtracting Fractions Learning Objectives: ●
Find equivalent fractions. ●
Write fractions in simplest form. ●
Write an explanation of how to estimate fractional parts. ●
Estimate sums and differences of fractions. ●
Determine common multiples and least common multiples and least common multiples of numbers. ●
Find common denominators for fractions with unlike denominators. ●
Add fractions with unlike denominators. ●
Subtract fractions with unlike denominators. ●
Solve problems involving addition and subtraction of fractions. ●
Draw a picture and write an equation to solve a problem. Topic 10: ​
Adding and Subtracting Mixed Numbers Learning Objective ●
Write improper fractions and mixed numbers and mixed numbers as improper fractions, and they place them on a number line. ●
Estimate sums and differences of fractions and mixed numbers by rounding to the nearest whole number. ●
Use models to add and subtract mixed numbers. BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
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Use models and computational procedures to add mixed numbers. ●
Use models and computational procedures to subtract mixed numbers. ●
Solve more complex problems involving the addition and subtraction of mixed numbers. Resource:​
Pearson Envision Math 2012 Duration: ​
November Essential Questions: Topic 9: ● What does it mean to add and subtract fractions with unlike denominators? ● What is a standard procedure for adding and subtracting fractions with unlike denominators? Topic 10: ● What does it mean to add and subtract mixed numbers? ● What is a standard procedure for adding and subtracting mixed numbers? Enduring Understandings: Topic 9: ●
The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number. BOE Approved 4/15​
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Cliffside Park Public Schools
5
A fraction is in simplest form when 1 is the only common factor of the numerator and denominator. A number line can be used to determine the nearest half or whole a fraction is closest to. All non­zero whole numbers have common multiples, including a least one. Sometimes the least common multiple of two numbers is one of the numbers Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions with unlike denominators. The product of the denominators of two fractions is a common denominator of both. Fraction sums and differences can be estimated by replacing fractions with the closest half or whole. Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand. Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation. Topic 10: ●
Fractional amounts greater than one can be represented using the whole number and a fraction. Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction equals one. Fractions greater than one can be named using a whole number and a fraction or an improper fraction. ●
Models can be used to show different ways of adding and subtracting mixed numbers. ●
There is more than one way to add or subtract mixed numbers. ●
Sums and differences of mixed numbers can be estimated by rounding each mixed number to the nearest whole number. ●
One way to add or subtract mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed. Relevant Standards: ​
(i.e., CCSS; NJCCCS; NGSS) BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
Topic 9: ​
5.NF.1, 5.NF.2 Topic 10: ​
5.NF.1, 5.NF.2 CCSS.MATH.PRACTICE.MP1​
Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2​
Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3​
Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4​
Model with mathematics.
CCSS.MATH.PRACTICE.MP5​
Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6​
Attend to precision.
CCSS.MATH.PRACTICE.MP7​
Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8​
Look for and express regularity in repeated reasoning. Interdisciplinary Connections Language Arts: ● Use reading comprehension strategies in math to repair comprehension of text by summarizing, using graphic and semantic organizers, questioning, and clarifying by checking other sources. Vocabulary: ● Have students use the Frayer Model to organize their understanding of the terms ​
common multiple ​
and ​
common denominator​
. Tell students to choose two numbers for ​
common multiple​
and fractions for ​
common denominator​
­ and to write those numbers below the model. Then have them list at least three examples and three non­examples of the term as applied to these two numbers. Science: ● Factoid:​
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There are more than 37,000 known species of spiders. Spiders are found worldwide and range in size from 0.02 to 3.5 inches. ● Directions:​
Have students research the size of several species of spiders. Then have students draw several parallel number lines 4.0 inches long. Mark tics at eighths. Graph the length 0 to 3.5 on the first number line to represent the known length of species of spiders. Finally, have students complete separate number lines for each of their researched spiders. BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
Factoid: ​
Bats are the only mammal that can truly fly. The smallest bat in the world is the bumblebee bat of Thailand with a wingspan of about 6 ½ inches. ● Directions:​
Have each student research the lengths of different species of bats. For each one, students should write the wingspan as a mixed number. Then students should create story problems that involve adding and subtracting these mixed numbers. ●
LEVELED READERS: ● The Mighty Mekong ​
(WorldScapes Readers) ● Cruising the Caribbean​
(WorldScapes Readers) Tier 2 Vocabulary: ​
simplest form, proper fraction, improper fraction, mixed number Tier 3 Vocabulary: ​
equivalent fraction, benchmark fraction, common multiples, Least Common Multiple (LCM), common denominator, Least Common Denominator (LCD) Core Instructional Materials/Resources/Digital Tools:
i.e., specific textbooks, classroom resources, digital tools, links to websites and videos
enVision Math: Common Core, ​
Pearson Education, Inc. 2012. Hyde, Arthur. ​
Comprehending Math,: Adapting Reading Strategies to Teach Mathematics, K­6.​
2006 Murray, Miki. ​
The Differentiated Math Classroom: A Guide for Teachers, K­8. ​
2007. Math Process Standards Series. ​
2007. Heinemann. O’Connell, Susan. ​
Now I Get It: Strategies for Building confident and Competent Mathematicians, K­6. ​
2005. Websites: ● www.mathblaster.com ● www.Brainpopjr.com BOE Approved 4/15​
GRADE:
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Cliffside Park Public Schools
5
www.atmath.com www.funbrain.com www.multiplication.com www.scholastic.com www.elearning4kids.com www.enchantedlearning.com www.mathcats.com www.abcya.com www.aplusmath.com www.exchange.smarttech.com www.superteacherworksheets.com www.edhelper.com www.abcteach.com www.studyisland.com www.softschools.com SmartBoard
st ​
21​
Century Themes and Skills:
(CRP Standards)
12 Career Ready Practices follow the link below.
http://www.state.nj.us/education/cccs/2014/career/CareerReadyPractices.pdf CRP2. Apply appropriate academic and technical skills.
CRP4. Communicate clearly and effectively and with reason.
CRP5. Consider the environmental, social and economic impacts of decisions.
RP8. Utilize critical thinking to make sense of problems and persevere in solving them.
CRP11. Use technology to enhance productivity.
8.1 Educational Technology
http://www.state.nj.us/education/cccs/2014/tech/8.pdf
BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
8.1.5.A.1​
Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems. 8.1.5.A.2​
Format a document using a word processing application to enhance text and include graphics, symbols and/ or pictures. 8.1.5.A.3​
Use a graphic organizer to organize information about problem or issue. 8.1.5.A.4​
Graph data using a spreadsheet, analyze and produce a report that explains the analysis of the data 8.1.5.A.5​
Create and use a database to answer basic questions. 8.1.5.A.6​
Export data from a database into a spreadsheet; analyze and produce a report that explains the analysis of the data. 8.2 Technology Education, Engineering,
Design, and Computation
8.2.5.A.1​
Compare and contrast how products made in nature differ from products that are human made in how they are produced and used. 8.2.5.A.2​
Investigate and present factors that influence the development and function of a product and a system. 8.2.5.A.3​
Investigate and present factors that influence the development and function of products and systems, e.g., resources, criteria and constraints 8.2.5.A.4​
Compare and contrast how technologies have changed over time due to human needs and economic, political and/or cultural influences. 8.2.5.A.5​
Identify how improvement in the understanding of materials science impacts technologies. Assessments and Performance Tasks:
Locally developed assessments should be referenced here, example of assessments will need to be
provided during a QSAC visit.
Cliffside Park Public Schools
BOE Approved 4/15​
GRADE:
5
Activities: ●
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Flexible Grouping Iiad use Study Island Math Journals Writing real­world word problems Spiraling (Pearson Daily Common Core or other daily review) Problem of the day SmartBoards Pearson Interactive Software Assessment: ●
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Topic 9 Test Topic 10 Test Renaissance Study Island Benchmark Tests Quick Checks Problem of the Day Addition/ Subtraction/Multiplication/Division Time Test Formative: conversation, observation, journal writing, self­assessment and daily work/homework Summative: Chapter Tests/Quizzes, Minute Math Book Performance­based: Hands­on Activities SmartBoard Activities Cliffside Park Public Schools
BOE Approved 4/15​
GRADE:
5
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Exit Slips Differentiation/Accommodations/Modifications Gifted and Talented
Extension Activities
Conduct research and provide presentation of cultural topics. Design surveys to generate and analyze data to be used in discussion English Language Learners
Modifications for Classroom Manipulatives Visual Models Concrete Objects Debate topics of interest / cultural importance. Leading Questions Authentic listening and reading sources Act Out that provide data and support for speaking and writing prompts. Tools (rulers, measuring cups, scales, etc.) Exploration of art and/or artists to understand society and history. Pattern Blocks Implement RAFT Activities as they Cooperative Learning: Team pertain to the types / modes of Assisted Individualization (TAI) communication (role, audience, format, topic). Students with Disabilities
Students at Risk of School Failure
Modifications for Classroom Modifications for Classroom Review, restate, and repeat directions. Pair visual prompts with verbal presentations
Break assignments into segments of shorter tasks. Ask students to restate information, directions, and assignments.
Reduce number of concepts presented. Repetition and and practice
Modify homework, classwork, and tests. Add time as needed. Pair visual prompts with verbal presentations
Ask students to restate information, directions, and assignments.
Model skills / techniques to be mastered. Extended time to complete class work Provide copy of classnotes Preferential seating to be mutually determined by the student and teacher Cliffside Park Public Schools
BOE Approved 4/15​
GRADE:
5
Anchor Activities Use of Higher Level Questioning Techniques
Provide assessments at a higher level of thinking
– heterogenEous groups helping each other Explicit Systematic Instruction​
: teacher demonstration, thinking aloud, about decision­making, opportunities for student questions and answers Repetition and and practice
Model skills / techniques to be mastered. Extended time to complete class work Provide copy of classnotes Pair visual prompts with verbal presentations Ask students to restate information, directions, and assignments. Preferential seating to be mutually determined by the student and teacher Student may request to use a computer to complete assignments. Repetition and and practice
Model skills / techniques to be mastered. Establish expectations for correct spelling on assignments. Modifications for Homework/Assignments
Modified Assignments
Establish expectations for correct spelling on assignments. Extra textbooks for home. Student may request books on tape / CD / digital media, as available and appropriate. Assign a peer helper in the class setting Student may request to use a computer to complete assignments. Establish expectations for correct spelling on assignments. Extra textbooks for home. Student may request books on tape / CD / digital media, as available and appropriate. Assign a peer helper in the class setting Provide oral reminders and check student work during independent work time
Assist student with long and short term planning of assignments
Encourage student to proofread assignments and tests Provide regular parent/ school communication
Cliffside Park Public Schools
BOE Approved 4/15​
GRADE:
5
Native Language Translation (peer, online assistive technology, translation device, bilingual dictionary)
Provide oral reminders and check student work during independent work Teachers will check/sign student agenda daily
time Extended time for assignment completion as needed
Assist student with long and short term planning of assignments
Highlight key vocabulary
Encourage student to proofread assignments and tests Use graphic organizers
Provide regular parent/ school communication
Teachers will check/sign student agenda daily
Student requires use of other assistive technology device Modifications for Homework and Assignments Extended time to complete assignments.
Student requires more complex assignments to be broken up and explained in smaller units, with work to be submitted in phases. Student requires use of other assistive technology device Modifications for Homework and Assignments Extended time to complete assignments.
Student requires more complex assignments to be broken up and explained in smaller units, with work to be submitted in phases. Provide the student with clearly stated (written) expectations and grading criteria for assignments. Implement RAFT activities as they pertain to the types / modes of communication (role, audience, format, topic). Modifications for Assessments Extended time on classroom tests and quizzes.
Student may take/complete tests in an BOE Approved 4/15​
GRADE:
Cliffside Park Public Schools
5
Provide the student with clearly stated (written) expectations and grading criteria for assignments. Implement RAFT activities as they pertain to the types / modes of communication (role, audience, format, topic). Modifications for Assessments Extended time on classroom tests and quizzes.
Student may take/complete tests in an alternate setting as needed.
Restate, reread, and clarify directions/questions
Distribute study guide for classroom tests.
Establish procedures for accommodations / modifications for assessments. SOURCES​
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Pearson Envision Math 2012; 2014 21st Century CCCS; 2014 Technology CCCS; Math CCSS ​
Common Core State Standards​
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CCSS.MATH.PRACTICE​
S; Career Ready Practices 2014 alternate setting as needed. Restate, reread, and clarify directions/questions Distribute study guide for classroom tests. Establish procedures for accommodations / modifications for assessments.