2016-2017 Mathematics Curriculum Map Grade 5, Q2
Unifying Concept: Fractions, Measurement, Operations
Target Standards are emphasized every quarter and used in formal assessment to evaluate student mastery.
Highly-Leveraged Standards1
5.NBT.B.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.A.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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.A.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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 12.
Supporting Standards2
5.MD.B.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. For example, given different
measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in
all the beakers were redistributed equally.
Quarter 2
Additional Standards
Complementary Standards:
(Standards to be assessed in classroom
and/or future benchmarks)
5.NBT.A.1
5.NBT.A.2
5.NBT.B.5
5.NBT.B.6
5.OA.A.1
5.OA.A.2
5.MD.A.1
Standards for Mathematical Practice:
(quarterly focus)
Mathematically proficient students:
SMP 1. Make sense of problems and
persevere in solving them.
SMP 2. Reason abstractly and
quantitatively.
SMP 3. Construct viable arguments and
critique the reasoning of others.
SMP 4. Model with mathematics.
SMP 5. Use appropriate tools
strategically.
SMP 6. Attend to precision.
SMP 7. Look for and make use of
structure.
SMP 8. Look for and express regularity
in repeated reasoning.
Mathematical Practices Poster
1
Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality. This definition for highly-leveraged standards
was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA. http://www.millis.k12.ma.us/services/curriculum_assessment/brochures
Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade Level Focus documents. They should encompass
a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35% for Supporting Cluster Instruction. See the Grade Level Focus documents at: LINK
2
Supporting Standards are related standards that support the highly-leveraged standards in and across grade levels.
*Highly-Leveraged standards in bold and supporting standards are normal text.
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/19/2016 2:07 PM
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2016-2017 Mathematics Curriculum Map Grade 5, Q2
Adopted and Supplemental Texts
Big Ideas
Eureka Math/ Engage NY:
Module 2 (last 10 days )
Module 3
Module 4 (first 14 days)
Investigations: (Common Core Adaptations hyperlinked)
Unit 1, supplement 2.4A
Unit 4 (Investigations 1 – 3, NOT Investigation 4 supplement yet)
Unit 7 CC supplement pages C101 – C103
Unit 9 (ONLY Investigation 1, emphasis on supplements 1.5A & 1.6A)
Additional Resources:
Grade 5 Fluency Brochure
http://achievethecore.org/
http://illuminations.nctm.org/Search.aspx?view=search&type=ls_ac&st=n&gr=
3-5
http://maccss.ncdpi.wikispaces.net/Fifth+Grade
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
http://nlvm.usu.edu/en/nav/category_g_2_t_4.html
http://www.etown.k12.ky.us/uplimg/cms/gr5_math.pdf
http://www.insidemathematics.org/common-core-resources/mathematicalcontent-standards/standards-by-grade/5th-grade
http://www.k-5mathteachingresources.com/5th-grade-measurement-anddata.html
http://www.k-5mathteachingresources.com/5th-grade-number-activities.html
http://www.mathplayground.com/tb_fractions/thinking_blocks_fractions.html
http://www.pbslearningmedia.org/standards/1
https://learnzillion.com/
https://www.illustrativemathematics.org/content-standards/5/MD/A
https://www.illustrativemathematics.org/content-standards/5/NF/A
https://www.illustrativemathematics.org/content-standards/5/OA/A
https://www.ixl.com/math/grade-5
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-algebraicthinking
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurementtopic
https://www.youcubed.org/
www.visualfractions.com
Essential Concepts:
• Equivalent fractions can be created by multiplying the fraction a/b × n/n where
n/n=1. Fractions with unlike denominators can be added and subtracted by
creating and using equivalent fractions. This is determined by subdividing (i.e.,
further dividing a fractional part) the fraction of one using the denominator of
other (i. e. , a/b + c/d = (a×d)/(b×d) + (c×b)/(d×b) = (ad+bc)/bd ). Subdividing
is actually the process of multiplying a fractional part by a whole that will make
each fractional part smaller. (5.NF.A.1)
• Benchmark fractions and number sense can be used to determine if a solution
is reasonable. (5.NF.A.2)
•Students will understand how the operations of addition, subtraction,
multiplication, and division are all related and how those understandings extend
into decimal numbers to the hundredths. (5.NBT.B.7)
• Fractions are used to express measurements that fall between whole numbers.
Line plots are a way to display a set of data so we can organize and interpret the
data. (5.MD.B.2)
Essential Questions:
• Why is it important to estimate before solving fraction problems? (5.NF.A.2)
• How can you mentally estimate the sum or difference of fractions with unlike
denominators? (5.NF.A.2)
• Why does multiplying a fraction by n/n not change the value of the original
fraction? (5.NF.A.2)
• How can fraction models, benchmark fractions, and equivalent fractions be
used to solve addition and subtraction of fractions with unlike denominators?
How are these strategies the same and how are they different? (5.NF.A.2)
• What role does place value play in your
strategy? (5.NBT.B.7)
•How do the models and strategies used with whole number computation
compare with decimal computation? How does computing with decimal
numbers change estimation strategies? (5.NBT.B.7)
• How can we use line plots to display a data set of fraction measurements?
(5.MD.B.2)
https://smart.wikispaces.hcpss.org/file/view/grade5_fluency_brochure.pd
f/519695646/grade5_fluency_brochure.pdf
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/19/2016 2:07 PM
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2016-2017 Mathematics Curriculum Map Grade 5, Q2
Vocabulary
Fractions
benchmark
between
denominator
equal (=)
equivalence
equivalent
fraction
fraction > 1
fraction = 1
fractional unit
greater than (>)
less than (<)
less than half
more than half
numerator
whole
Additional Resource: http://www.graniteschools.org/mathvocabulary/
Measurement and Data
Operations
benchmark
benchmark
between
braces
centimeter (cm)
brackets
cup (c)
equal (=)
data
equation
experiment
number sentence
foot (ft)
operation
gallon (gal)
order
gram (g)
order of operations
greater than (>)
parentheses
hour (h)
inch (in)
less than (<)
line plot
liter
kilogram (kg)
kilometer (km)
median
meter (m)
mile (mi)
milliliter (ml)
minute (min)
ounce (oz)
pint (pt)
pound (lb)
quart (qt)
range
Interdisciplinary Connections
Multicultural Math Connections:
Literacy Connections:
Teaching Mathematics through Multicultural Literature
Integrating Mathematics of Worldwide Cultures into K-12 Instruction
A Course in Multicultural Mathematics
How Do I Teach Mathematics in a Culturally Responsive Way?
Reading:
Adding Fractions, Jerry Pallotta
Eating Fractions, Bruce McMillan
Fractions in Disguise, Edward Einhorn
Math for Kids: & Other People Too, Theoni Pappas
Pizza Fractions, Jerry Pallotta
http://everydaymath.uchicago.edu/teachers/5th-grade/literature-list/
Math Solutions Bibliography
Multicultural Mathematics Lessons
Multi-Cultural Multiplication
Critical Multicultural Pavilion: Links to Other Sites for Multicultural Education
and Math
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/19/2016 2:07 PM
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2016-2017 Mathematics Curriculum Map Grade 5, Q2
Mathematics Activities from Diverse Cultures
Multicultural Mathematics: A More Inclusive Mathematics. ERIC Digest.
(Radical Math – multicultural math journal ariticles)
http://radicalmath.org/browse_category.php?cat=data
http://radicalmath.org/browse_category.php?cat=Data Analysis
http://radicalmath.org/browse_category.php?cat=Equivalent Fractions
http://radicalmath.org/browse_category.php?cat=Fractions
http://radicalmath.org/browse_category.php?cat=Graph
http://radicalmath.org/browse_category.php?cat=mean
http://radicalmath.org/browse_category.php?cat=measurement
http://radicalmath.org/browse_category.php?cat=Percents
http://users.wfu.edu/mccoy/mgames.pdf
http://www.edchange.org/multicultural/sites/math.html
https://www.deltacollege.edu/dept/basicmath/Multicultural_Math.htm
Math Picture Books
Math Related Children’s Books
Writing:
Howard County: Math Journals
K-5 Math Teaching Resources: Math Journals
Writing in Math Article
Writing in Math Class? Absolutely! Article
http://mathsolutions.com/wpcontent/uploads/1995_Writing_in_Elem_Grades.pdf
Books:
Zaslavsky, Claudia, Multicultural Math: Hands-On Math Activities from
Around the World. New York: Scholastic Professional Books, 1994.
LHS GEMS, Lawrence Hall of Science, Math Around the World: Great
Explorations in Math and Science, A Teacher’s Guide. Berkeley: University of
California. No date.
Germain-McCarthy, Yvelyne, and Owens, Katharine, Mathematics and MultiEthnic Students: Exemplary Practices. New York: Eye on Education, 2005.
Assessment Guides and Resources
Performance Level Descriptors
http://www.azed.gov/assessment/files/2015/12/math-pld-grade-5.pdf
Assessment Resources
http://www.azed.gov/assessment/azmeritsupportmaterials/
The Mathematics Common Core Toolbox
Inside Mathematics: Tools for Educators
http://map.mathshell.org/materials/index.php
Achieve the Core
Howard County: Grade 5 Common Core Curriculum
Balsz, AZ District Formal Exit Ticket Assessments
Assessment Tasks
5.NF.A.1 https://hcpss.instructure.com/courses/108/pages/5-dot-nf-dot-1assessment-tasks
5.NF.A.2 https://hcpss.instructure.com/courses/108/pages/5-dot-nf-dot-2assessment-tasks
5.MD.B.2 https://hcpss.instructure.com/courses/108/pages/5-dot-md-dot-2assessment-tasks
5.NBT.7 https://hcpss.instructure.com/courses/108/pages/5-dot-nbt-dot-7TUSD Department of Curriculum and Instruction
Curriculum 3.0
Instructional Resources
DOK Levels
http://www.azed.gov/assessment/files/2014/11/dok-levels.pdf
DOK Stems
http://www.azed.gov/assessment/files/2014/11/dok-question-stems.pdf
Hess’s Matrix
http://static.pdesas.org/content/documents/M2-Activity_2_Handout.pdf
Bloom’s Taxonomy
http://www.bloomstaxonomy.org/Blooms%20Taxonomy%20questions.pdf
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2016-2017 Mathematics Curriculum Map Grade 5, Q2
assessment-tasks
TUSD Department of Curriculum and Instruction
Curriculum 3.0
Revised 5/19/2016 2:07 PM
Page 5