Materials Bank
Mathematics G5 Q1
Unit: Core: Mathematics , Grade(s) 5th Grade
Mathematics G5 Q1
Duration: 10 Weeks
Unit
Scope and Sequence
DIGITAL / PRINT TEXT
Big Ideas:
PERFORMANCE TASKS
DIFFERENTIATION
Source: Math Expressions: Common Core
Text: Math Expressions Common Core Assessment
Source: Math Expressions: Common Core Assessment Guide
Assessment Guide
Differentiated Instruction Activities
Guide
Unit 1
Unit 1: Addition and Subtraction with Fractions
Performance Assessment
139, 145, 153, 159, 169, 175, 181
Pages: 26-28
Think Central Resources:www.thinkcentral.com
Unit 2
Below Level-Soar to Success, On Level-Mega Math, Challenge-
(Sections: 1.1-1.13)
Equivalent Fractions
Addition and Subtraction with Fractions
Unit 2: Addition and Subtraction with Decimals
(Sections 2.1-2.10)
Pages: 5, 15, 23, 33, 41, 49, 59, 65, 73, 79, 85, 91, 97, 109, 119, 131,
Destination Math
Performance Assessment
Pages: 40-42
Read and Write whole Numbers and Decimals
Addition and Subtraction
Round and Estimate with Decimals
VOCABULARY
denominator, fraction, numerator, unit fraction, equivalent fraction, multiplier, n-split, simplify, unsimplify, benchmark, common denominator, common factor, greater than (>), less
than (<), mixed number, add on, regroup, ungroup, line plot, benchmark, estimate, round, situation equation, solution equation, decimal, tenth, hundredth, thousandth, notation,
standard form, word form, expanded form, power of 10, equivalent decimal, meter (m), decimeter (dm), centimeter (cm), millimeter (mm), grouping, ungrouping, break apart
drawing, ungroup, commutative property of addition, associative property of addition, distributive property multiplication over addition, round, estimate
Source: Math Expressions: Common Core Assessment Guide
Formative Assessment: Check for Understanding embedded in each
lesson
ASSESSMENTS Unit 1 Quick Quiz 1 and 2, Unit 1 Assessment form A, Unit 1 Assessment form B
Unit 2 Quick Quiz 1, 2, and 3 Unit 2 Assessment form A, Unit 2 Assessment form B
ELA: Reading Standards for Informational Text
SEL - Relationship Skills: communication, social engagement,
ACADEMIC
Topic: Craft and Structure
CONNECTIONS
Standard Statement 4. Determine the meaning of words and phrases in a text relevant to
a Gr 5 topic or subject area.
working cooperatively, resolving conflicts, helping/seeking help; SelfManagement: goal setting, organizational skills; Responsible
Decision Making: problem-solving, evaluation, reflection
Unit 1: Math Literature Library: “Polar Bear Math: Learning About Fractions with Klondike and Snow”
ADDITIONAL
Unit 2: Math Literature Library: “Sold! A Mothematics Adventure”
RESOURCES
Technology: First In Math, Study Island, SchoolNet Short Cycle Assessments
ESL: ELL standards corresponding to Math Grade 5- Quarter 1 Scope and Sequence
Standard 2- Students will participate in grade-appropriate oral and written exchanges of information, ideas, and analyses, responding to peer,
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audience, or reader comments and
questions.
Standard 7- Students will adapt language choices to purpose, task, and audience when speaking and writing.
Standard 10- Students will make accurate use of standard English to communicate in grade-appropriate speech and writing
ACTIVITIES
Target Skill/ Target Strategy – Add and Subtract fractions of Unlike Denominators.
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Use mixing cups/bowls and flour/rice to show fractions of a whole number
Have students use mixing cups/bowls and ingredients to make equivalent fractions
Use pictures to show fractions of unlike denominators.
from different denominators.(i.e. 1/2 of a cup = 2/4 of a cup)
Use number lines to show the value of equivalent fractions with different
Use pictures to make equivalent fractions from different denominators.
denominators.
Use number lines to find the value of equivalent fractions with unlike denominators.
(i.e. number lines that by increments of 1/8’s and 1/4’s and find 4/8 = 2/4)
Target Skill/ Target Strategy – Decimals / base ten value system
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Use parts of shapes to express decimals.
Use parts of shapes to express shapes and have students fill the appropriate decimal value
Use 10x10 grids to have a visual example of 10ths and 100ths
such as:http://www.mathinenglish.com/PWkS/grade4/understanding%20decimals.pdf
https://www.teachingchannel.org/videos/elementary-math-
Use 10 x 10 grids and have students add different variations of decimals to come up with one
lesson-plan Math.5.NBT.B.7
whole 100/100.
https://www.teachingchannel.org/videos/elementary-math-lesson-plan Math.5.NBT.B.7
Target Skill/ Target Strategy – Add- Subtract decimals up to the hundredth place.
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Use pictures or actual fruits and vegetables with coordinating prices using
Use pictures of fruits and vegetables with coordinating prices using dollars
dollars and cents to the hundredth place.
and cents to the hundredth place and put the fruits and vegetables in order
Use pictures or actual fruits and vegetables to and have students find how
from least to greatest.
many they could buy with $5.00.
Use pictures or actual fruits and vegetables to and have students find how
Have students use the visual fruits, vegetables, starches to choose the
many they could buy with $2.00, $5.00, and $10.00.
necessary ingredients necessary for a meal (sandwich, rice with chicken,
Have students use the visual fruits, vegetables, starches to choose the
salad,) and have them calculate the cost of the meal using prices to the
necessary ingredients necessary for breakfast, lunch, and dinner (sandwich,
nearest hundredth (ie $2.79).
rice with chicken, salad,) and have them calculate the costs of the meals,
using prices to the nearest hundredth (ie $2.79).
Standards Covered
Core: Mathematics
Grade 5 Introduction
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5: In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the
multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to
2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with
whole number and decimal operations; and (3) developing understanding of volume.
5.1: Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent
calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the
meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and
dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)
5.2: Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with
multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and
subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between
decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole
number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to
hundredths efficiently and accurately.
5.3: Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of
volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select
appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of
right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to
solve real world and mathematical problems.
CCSS.Math.Content.5.MD: Measurement and Data
CCSS.Math.Content.5.MD.A: Convert like measurement units within a given measurement system.
CCSS.Math.Content.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these
conversions in solving multi-step, real world problems.
CCSS.Math.Content.5.MD.B: Represent and interpret data.
CCSS.Math.Content.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.
CCSS.Math.Content.5.NBT: Number and Operations in Base Ten
CCSS.Math.Content.5.NBT.A: Understand the place value system.
CCSS.Math.Content.5.NBT.A.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.
CCSS.Math.Content.5.NBT.A.3: Read, write, and compare decimals to thousandths.
CCSS.Math.Content.5.NBT.A.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1
+ 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
CCSS.Math.Content.5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of
comparisons.
CCSS.Math.Content.5.NBT.A.4: Use place value understanding to round decimals to any place.
CCSS.Math.Content.5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths.
CCSS.Math.Content.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.
CCSS.Math.Content.5.NF: Number and Operations-Fractions
CCSS.Math.Content.5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions.
CCSS.Math.Content.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, / + / = ( + )/.)
CCSS.Math.Content.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 < 1/2.
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.
Materials
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For a closer look at the materials list below, log onto https://cleveland.schoolnet.com
Lessons:
1. Eggsactly Equivalent
2. Sports Math
3. Fraction Feud: Comparing and Ordering Fractions
4. Converting Fractions to Decimals by Dividing
Additional Properties
Author: CMSD
Publisher: Cleveland Metro SD
Cost/Fee: No
Restricted Use: No
Rights: All Rights Reserved
Keywords:
Created by: DORSEY, KAREN (4/21/2015 1:45 PM)
Last modified by: Thompson, Karen (8/12/2015 3:33 PM)
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Materials Bank
Mathematics G5 Q2
Unit: Core: Mathematics , Grade(s) 5th Grade
Mathematics G5 Q2
Duration: 10 Weeks
Unit
Scope and Sequence
DIGITAL / PRINT TEXT
PERFORMANCE TASKS
DIFFERENTIATION
Big Ideas:
Source: Math Expressions: Common Core Assessment Guide
Source: Math Expressions: Common Core Assessment Guide
Text: Math Expressions Common Core Assessment Guide
Unit 3
Differentiated Instruction Activities
Unit 3: Multiplication with Fractions (Sections 3.1-3.14)
Performance Assessment
Pages: 193, 199, 207, 217, 233, 241, 247, 253, 261, 267, 275, 281,
Multiplication with Fractions
Multiplication Links
Division with Fractions
Unit 4: Multiplication with Whole Numbers & Decimals
(Sections: 4.1-4.12)
287, 303, 309, 315, 323, 327, 335, 345, 351, 359,367, 373 and 379
Pages: 54-56
Think Central Resources:www.thinkcentral.com
Unit 4
Below Level-Soar to Success, On Level-Mega Math, Challenge-
Performance Assessment
Destination Math
Pages: 67-69
Multiplication with Whole Numbers
Multiplication with Decimals Numbers
VOCABULARY
comparison bars, multiplicative comparison, factor product, area model for multiplication, fraction-bar model for multiplication, multiply and simplify method, simplify and multiply method, unit fraction method,
associative property, commutative property, distributive property, decimal fraction, dividend, divisor, quotient, shift, base, exponent, exponential form, power of 10, even, odd, partial products, place value sections,
expanded notation, new groups below, place value rows, short cut, commutative property of multiplication, associative property of multiplication, distributive property of multiplication over addition
Source: Math Expressions: Common Core Assessment Guide
Formative Assessment: Check for Understanding embedded in each
lesson
ASSESSMENTS Unit 3 Quick Quiz 1,2 and 3 Unit 3 Assessment form A, Unit 3 Assessment form B
Unit 4 Quick Quiz 1 and 2 Unit 4 Assessment form A, Unit 4 Assessment form B
ELA: Reading Standards for Informational Text
SEL - Relationship Skills: communication, social engagement, working
ACADEMIC
cooperatively, resolving conflicts, helping/seeking help; Self-
Topic: Craft and Structure
Management: goal setting, organizational skills; Responsible
CONNECTIONS
Standard Statement 4. Determine the meaning of words and phrases in a text relevant to a Gr 5 topic or subject area.
Decision Making: problem-solving, evaluation, reflection
Unit 3: Math Literature Library: “Go, Fractions!”
ADDITIONAL
Unit 4: Math Literature Library: “The Amazing Impossible Erie Canal”
RESOURCES
Technology: First In Math, Study Island, SchoolNet Short Cycle Assessments
ESL: ELL standards corresponding to Math Grade 5- Quarter 2 Scope and Sequence
Standard 3- Students will speak and write about grade-appropriate complex literary and informational texts and topics
Standard 7- Students will adapt language choices to purpose, task, and audience when speaking and writing.
Standard 10- Students will make accurate use of standard English to communicate in grade-appropriate speech and writing
Activities: Target Skill/ Target Strategy –Represent and Interpret Data including Fractions
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Use mixing cups/bowls and flour/rice to show different values. Have students put the
Have students use mixing cups/bowls and ingredients to show fractions of different values
mixing cups in order from least to greatest.
and put the values in a line plot placing each bowl in the appropriate place.
Use the colors of student clothing to make visual fractions expressing how many students
Use the colors of student clothing to make visual fractions expressing how many students
are wearing a specific color out of the total students. (i.e. There 6 students out of 25 that
are wearing a specific color out of the total students. (i.e. There 6 students out of 25 that
have on a white shirt so the fraction for white shirts is 6 / 25.)
have on a white shirt so the fraction for white shirts is 6 / 25.) Have students use the data to
make a line plot or other graph expressing the fractions.
Have students wearing a specific color stand on one side of the room to show the number
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of students wearing that color is the numerator and the rest of the class is the
Graph the fractions on a number line or another graph to show the value of each of the
denominator.
fractions of students wearing each color of shirts.
Activities: Target Skill/ Target Strategy – Place Value / Rounding
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Give students signs or index cards with place values on them and put students in order of
Give students signs or index cards with place values on them and have students come up
place value (ie student with card reading “millions” stands at far left facing class, followed
to the front of the class in random order and have the class put each student holding the
by student with “hundred thousand,” etc all the way to the thousandth place)
place value sign in correct order of place value (ie student card reading “millions” stands at
Use 100 x 100, 10 x 10 or 10 block grid filled to different denominations to show which
far left facing class, followed by student with “hundred thousand,” etc all the way to the
number should be rounded to the nearest 10, 100, or 1,000.
thousandth place).
Use 100 x 100, 10 x 10 or 10 block grid filled to different denominations to show which
Explain that 100 x 100, 10 x 10, or 10 block grids can also be used as a way to visualize
decimals. (1,000 pieces = 1 whole, 100 pieces = 1 whole or 10 pieces = 1 whole).
number should be rounded to the nearest 10, 100, or 1,000 and have students tell
which grids should be rounded up or down.
Explain that 100 x 100 grid can also be used as a way to visualize a thousandth. (1,000
pieces = 1 whole). Have students explain which grids should be rounded up or down to the
nearest whole number.
Target Skill/ Target Strategy – Read, Write Decimals using Expanded form/notation
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Have students complete audio/visual interactive activity on expanded form (notation).
Have students complete audio/visual interactive activity on expanded form (notation),
http://studyjams.scholastic.com/studyjams/jams/math/numbers/expanded-notation.htm
and also complete “Try It” section.
Give students note cards that have individual numbers describing place values such as
http://studyjams.scholastic.com/studyjams/jams/math/numbers/expanded-notation.htm
“4,000,” “60,” and “.005” and have students find the value of all the cards added together.
Give students 2 sets of note cards that have individual numbers describing place values
such as “4,000,” “60,” and “.005” and have students add 2 sets together to find the value
of all the cards added together.
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Standards Covered
Core: Mathematics
CCSS.Math.Content.5.MD: Measurement and Data
CCSS.Math.Content.5.MD.B: Represent and interpret data.
CCSS.Math.Content.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.
CCSS.Math.Content.5.NBT: Number and Operations in Base Ten
CCSS.Math.Content.5.NBT.A: Understand the place value system.
CCSS.Math.Content.5.NBT.A.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.
CCSS.Math.Content.5.NBT.A.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 10.
CCSS.Math.Content.5.NBT.A.3: Read, write, and compare decimals to thousandths.
CCSS.Math.Content.5.NBT.A.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
CCSS.Math.Content.5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
CCSS.Math.Content.5.NBT.A.4: Use place value understanding to round decimals to any place.
CCSS.Math.Content.5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths.
CCSS.Math.Content.5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm.
CCSS.Math.Content.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.
CCSS.Math.Content.5.NF: Number and Operations-Fractions
CCSS.Math.Content.5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions.
CCSS.Math.Content.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, / + / = ( + )/.)
CCSS.Math.Content.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 < 1/2.
CCSS.Math.Content.5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
CCSS.Math.Content.5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (/ = ÷ ). 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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared
equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers
does your answer lie?
CCSS.Math.Content.5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.Math.Content.5.NF.B.4a: Interpret the product (/) × as a parts of a partition of into equal parts; equivalently, as the result of a sequence of operations × ÷ . For example, use a visual fraction model to
show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (/) × (/) = /.)
CCSS.Math.Content.5.NF.B.4b: 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.
CCSS.Math.Content.5.NF.B.5: Interpret multiplication as scaling (resizing), by:
CCSS.Math.Content.5.NF.B.5a: 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.
CCSS.Math.Content.5.NF.B.5b: 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 / = (×)/(×) to the
effect of multiplying / by 1.
CCSS.Math.Content.5.NF.B.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.
CCSS.Math.Content.5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can develop
strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
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.
Additional Properties
Author: CMSD
Publisher: Cleveland Metro SD
Cost/Fee: No
Restricted Use: No
Rights: All Rights Reserved
Keywords:
Created by: DORSEY, KAREN (4/21/2015 1:53 PM)
Last modified by: Thompson, Karen (8/12/2015 3:29 PM)
For additional instructional materials in Classrooms, visit https://cleveland.schoolnet.com
Generated 10/2/2016
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Mathematics G5 Q3
Unit: Core: Mathematics , Grade(s) 5th Grade
Mathematics G5 Q3
Duration: 10 Weeks
Unit
Scope and Sequence
DIGITAL /
PRINT TEXT
PERFORMANCE TASKS
DIFFERENTIATION
Big Ideas:
Source: Math Expressions: Common Core Assessment Guide
Source: Math Expressions: Common Core Assessment Guide
Text: Math
Unit 5
Differentiated Instruction Activities
Performance Assessment
Pages: 395, 401, 407, 415, 421, 429, 439, 447, 453, 461, 465, 479,
Expressions
Common Core
487, 493, 501, 509, 517, 525, 533, 539, 545 and 551
Assessment Guide Pages: 80-82
Think Central Resources:www.thinkcentral.com
Unit 6
Unit 5: Division
with Whole
Below Level-Soar to Success, On Level-Mega Math, Challenge-
Performance Assessment
Numbers
Destination Math
(Sections 5.1-5.11) Pages: 94-96
Division with
Whole
Numbers
Division with
Decimals
Numbers
Unit 6 Operations
and World
Problems
(Sections: 6.16.11)
Equations and
Problem
Solving
Comparison
Word Problems
Problems with
More Than One
Step
VOCABULARY
digit-by-digit method, dividend, divisor, expanded notation method, place value sections method, quotient, remainder, overestimate, underestimate, situation equation, solution equation, break apart drawing,
rectangle model, benchmark, comparison, leading language, misleading language, scaling, additive, multiplicative, parentheses, equation
Source: Math Expressions: Common Core Assessment Guide
Formative Assessment: Check for Understanding embedded in each lesson
ASSESSMENTS Unit 5 Quick Quiz 1 and 2 Unit 5 Assessment form A, Unit 5 Assessment form B
Unit 6 Quick Quiz 1, 2 and 3 Unit 6 Assessment form A, Unit 6 Assessment form B
ELA: Reading Standards for Informational Text
SEL - Relationship Skills: communication, social engagement, working cooperatively, resolving conflicts,
ACADEMIC
Topic: Craft and Structure
CONNECTIONS
Standard Statement 4. Determine the meaning of words and phrases in a text relevant to a Responsible Decision Making: problem-solving, evaluation, reflection
helping/seeking help; Self-Management: goal setting, organizational skills;
Gr 5 topic or subject area.
Unit 5: Math Literature Library: “A Remainder of One”
ADDITIONAL
Unit 6: Math Literature Library: “O, Say Can You See?”
RESOURCES
Technology: First In Math, Study Island, SchoolNet Short Cycle Assessments
For additional instructional materials in Classrooms, visit https://cleveland.schoolnet.com
Generated 10/2/2016
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ESL: ELL standards corresponding to Math Grade 5- Quarter 3 Scope and Sequence
Standard 1- Students will construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing.
Standard 7- Students will adapt language choices to purpose, task, and audience when speaking and writing.
Standard 9- Students will create clear and coherent grade-appropriate speech and text.
Activities:
Target Skill/ Target Strategy –Order of Operations/ Algebraic Thinking
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
After reviewing the order of
After reviewing the order of
operations give students index
operations give students index
cards with the steps on them have
cards with the steps on them have
students arrange them in the
students arrange them in the
correct order.
Watch video to give students a
musical and visual remembrance of
the concept.Flocabulary- PEMDAS
correct order, after completion take
one of the index cards away and
have students tell you which step is
missing.
Watch video to give students a
musical and visual remembrance of
Show students examples of what
the concept.Flocabulary- PEMDAS
can happen if you do things in the
and have students complete
wrong order to emphasize the
challenge questions going with the
necessity to completing parts of the
video.
problems in order (i.e. buying
something from the store, tying your
shoe or going to classes at the
wrong time.).
Show students examples of what
can happen if you do things in the
wrong order to emphasize the
necessity to completing parts of the
problems in order (i.e. buying
something from the store, tying
your shoe or going to classes at
the wrong time.). Have students
complete order of operations
problems in the wrong order to see
that the answers are completely
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different than when it is done in the
correct order.
Target Skill/ Target Strategy – Solve Real- World Word Problems
Involving Multiplication of Fractions
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Spend extra time going over
Have students make lists of words that
vocabulary necessary in word
have a one meaning in normal speech
problems. Specifically polysemous
but have a different meaning when it
words (words that have same spelling
comes to math.
and pronunciation but mean something
else in the context of math). Math terms
like “mean, “operation,” and
Have students makes their own short
“expression,” can be very confusing to
word problems using keywords or
ELL students.
phrases that give clues to the
Make a list of keywords or phrases in
operation.
mathematical word problems such as
problems in the wrong order to see that
“more than,” “of,” “shared equally,” that
the answers are completely different
show which operation to use in solving
than when it is done in the correct
the problem and have students highlight
order.
the keywords / phrases in word
problems.
Give students visuals to demonstrate
Give students visuals to demonstrate
such as video
such as video
https://www.khanacademy.org/math/cc-
https://www.khanacademy.org/math/cc-
fifth-grade-math/cc-5th-fractions-
fifth-grade-math/cc-5th-fractions-
topic/cc-5th-multiplying-
topic/cc-5th-multiplying-
fractions/v/visualizing-fraction-products
fractions/v/visualizing-fraction-products
Have students complete “practice this”
section.
Target Skill/ Target Strategy – Comparing Decimals to the Thousandth Place.
TASKS/ Activities Level 1/2
Be sure to caution students that the placement of zeroes can
Tasks /Activities Level 2/3
Have students write sentences explaining how placement of
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change the value of a number (i.e. a zero at the end of a
zeroes can change the value in decimals.
decimal vs. a zero added to the middle of the decimal.). .
Make simple place value charts to help students remember
Make simple place value charts to help students remember
that the value of digits are relative to their place value. Give
that the value of digits are relative to their place value.
students number and have the students put the numbers in
Use visual examples such as
the appropriate spots on the place value chart.
http://www.mathgoodies.com/lessons/decimals/compare.html
Use visual examples such as
http://www.mathgoodies.com/lessons/decimals/compare.html
and complete all activities.
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Standards Covered
Core: Mathematics
CCSS.Math.Content.5.NBT: Number and Operations in Base Ten
CCSS.Math.Content.5.NBT.A: Understand the place value system.
CCSS.Math.Content.5.NBT.A.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 10.
CCSS.Math.Content.5.NBT.A.3: Read, write, and compare decimals to thousandths.
CCSS.Math.Content.5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
CCSS.Math.Content.5.NBT.A.4: Use place value understanding to round decimals to any place.
CCSS.Math.Content.5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths.
CCSS.Math.Content.5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm.
CCSS.Math.Content.5.NBT.B.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.
CCSS.Math.Content.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.
CCSS.Math.Content.5.NF: Number and Operations-Fractions
CCSS.Math.Content.5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions.
CCSS.Math.Content.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, / + / = ( + )/.)
CCSS.Math.Content.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 < 1/2.
CCSS.Math.Content.5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
CCSS.Math.Content.5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (/ = ÷ ). 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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3
wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between
what two whole numbers does your answer lie?
CCSS.Math.Content.5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.Math.Content.5.NF.B.4a: Interpret the product (/) × as a parts of a partition of into equal parts; equivalently, as the result of a sequence of operations × ÷ . For example, use a visual fraction
model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (/) × (/) = /.)
CCSS.Math.Content.5.NF.B.4b: 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.
CCSS.Math.Content.5.NF.B.5: Interpret multiplication as scaling (resizing), by:
CCSS.Math.Content.5.NF.B.5a: 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.
CCSS.Math.Content.5.NF.B.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.
CCSS.Math.Content.5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can
develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
CCSS.Math.Content.5.NF.B.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to
show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
CCSS.Math.Content.5.NF.B.7b: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show
the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
CCSS.Math.Content.5.NF.B.7c: 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. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
CCSS.Math.Content.5.OA: Operations and Algebraic Thinking
CCSS.Math.Content.5.OA.A: Write and interpret numerical expressions.
CCSS.Math.Content.5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
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.
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Materials Bank
Mathematics G5 Q4
Unit: Core: Mathematics , Grade(s) 5th Grade
Mathematics G5 Q4
Duration: 10 Weeks
Unit
Scope and Sequence
DIGITAL / PRINT TEXT
PERFORMANCE TASKS
DIFFERENTIATION
Big Ideas:
Source: Math Expressions: Common Core Assessment Guide
Source: Math Expressions: Common Core Assessment Guide
Text: Math Expressions Common Core Assessment Guide
Unit 7
Differentiated Instruction Activities
Unit 7: Algebraic Reasoning and Expressions (Sections: 7.1-7.7)
Performance Assessment
Pages: 561, 567, 573, 581, 591. 597, 603, 615, 621, 627, 633, 639,
Algebraic Reasoning and Expressions
Patterns and Graphs
Unit 8: Measurement and Geometry (Sections: 8.1-8.17)
Measurement and Data
Area and volume
645, 651, 661, 669, 675, 681, 687, 693, 703, 711, 719 and 725
Pages: 107-109
Think Central Resources: www.thinkcentral.com
Unit 8
Below Level-Soar to Success, On Level-Mega Math, Challenge-
Performance Assessment
Destination Math
Pages: 121-123
Classify Geometric Figures
VOCABULARY
expression, order of operations, simplify, evaluate, variable, numerical pattern, term, coordinate plane, ordered pair, origin, x-coordinate, y-coordinate, x-axis, y-axis, meter, millimeter, centimeter, decimeter,
dekameter, hectometer, kilometer, liter, milliliter, centiliter, deciliter, dekaliter, hectoliter, kiloliter, mass, gram, milligram, centigram, decigram, dekagram, hectogram, kilogram, mile (mi), ton, frequency, table, line
plot, perimeter, area, square centimeter, square unit, face, edge, rectangular prism, cube, unit cube, volume, cubic unit, rectangular prism, volume, cubic unit, one-dimensional, two-dimensional, threedimensional, composite, acute angle, adjacent angle, adjacent sides, congruent, counterexample, line of symmetry, opposite angles, opposite sides, parallel, parallelogram, perpendicular, quadrilateral, rectangle,
rhombus, right angle , square, trapezoid, acute angle, acute triangle, adjacent sides, congruent angles, congruent sides, equilateral triangle, isosceles triangle, obtuse angle, obtuse triangle, perpendicular sides,
right angle, right triangle, scalene triangle, closed, concave, convex, open, polygon, reflex angle, regular polygon
Formative Assessment: Check for Understanding embedded in each
Source: Math Expressions: Common Core Assessment Guide
lesson
ASSESSMENTS Unit 7 Quick Quiz 1 and 2 Unit 7 Assessment form A, Unit 7 Assessment form B
Unit 8 Quick Quiz 1, 2 and 3 Unit 8 Assessment form A, Unit 7 Assessment form B
ELA: Reading Standards for Informational Text
SEL - Relationship Skills: communication, social engagement, working
ACADEMIC
Topic: Craft and Structure
CONNECTIONS
Standard Statement 4. Determine the meaning of words and phrases in a text relevant to a Gr 5 topic or subject area.
cooperatively, resolving conflicts, helping/seeking help; SelfManagement: goal setting, organizational skills; Responsible
Decision Making: problem-solving, evaluation, reflection
Unit 7: Math Literature Library: “The Fly on the Ceiling”
ADDITIONAL
Unit 8: Math Literature Library: “The Math Chef: Over 60 Math Activities and Recipes for Kids”
RESOURCES
Technology: First In Math, Study Island, SchoolNet Short Cycle Assessments
ESL: ELL standards corresponding to Math Grade 5- Quarter 4 Scope and Sequence
Standard 1- Students will construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing.
Standard 7- Students will adapt language choices to purpose, task, and audience when speaking and writing.
Standard 9- Students will create clear and coherent grade-appropriate speech and text.
Activities:
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Target Skill/ Target Strategy –Convert Different Units across a Measurement System
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Have students measure items on
Have students measure items on
their desks in centimeters and
their desks in centimeters and
convert it to millimeters.
convert it to meters and millimeters.
Measure students’ weights in
.Measure students’ weights in
pounds and convert them to
pounds and convert them to
ounces.
ounces, and tons.
Measure students’ heights in
Measure students’ heights in
centimeters and make a class chart
centimeters and make a class
that shows all conversions from
chart that shows all conversions
millimeters to kilometers.
from millimeters to kilometers, and
have students go up and explain
and say number for all the
conversions from millimeters all the
way up to kilometers.
Target Skill/ Target Strategy – Volume of Rectangular Prisms
TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Show a visual example of finding volume of rectangular prisms such as
Show a visual example of finding volume of rectangular prisms such as
https://www.khanacademy.org/math/pre-algebra/measurement/volume-
https://www.khanacademy.org/math/pre-algebra/measurement/volume-
introduction-rectangular/v/volume-of-a-rectangular-prism-or-box-examples.
introduction-rectangular/v/volume-of-a-rectangular-prism-or-box-examples.
Have students bring shoe boxes or other small boxes and measure the length,
Students will also complete the “Practice This Concept” section.
width, and height in order to find the volume of the boxes.
.Have students bring shoe boxes or other small boxes and measure the length,
Have students complete interactive online activity on volume:
width, and height in order to find the volume of the boxes. Also have students
http://studyjams.scholastic.com/studyjams/jams/math/measurement/volume.htm
figure out which students have the largest and smallest boxes based off volume.
Have students complete interactive online activity on volume:
http://studyjams.scholastic.com/studyjams/jams/math/measurement/volume.htm
and complete “Test Yourself” section.
Target Skill/ Target Strategy – Graph Points on a Coordinate Plane.
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TASKS/ Activities Level 1/2
Tasks /Activities Level 2/3
Be sure to caution students that the x-axis is always first when
Have students write sentences explaining what problems may occur if
graphing points on a coordinate plane.
one graphs points on the y axis first instead of the x axis.
Complete online interactive activity at
Complete online interactive activity at
http://studyjams.scholastic.com/studyjams/jams/math/algebra/ordered-
http://studyjams.scholastic.com/studyjams/jams/math/algebra/ordered-
pairs.htm
pairs.htm Also complete the “Test Yourself” section.
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Standards Covered
Core: Mathematics
CCSS.Math.Content.5.G: Geometry
CCSS.Math.Content.5.G.A: Graph points on the coordinate plane to solve real-world and mathematical problems.
CCSS.Math.Content.5.G.A.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., -axis and -coordinate, -axis and coordinate).
CCSS.Math.Content.5.G.A.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.
CCSS.Math.Content.5.G.B: Classify two-dimensional figures into categories based on their properties.
CCSS.Math.Content.5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and
squares are rectangles, so all squares have four right angles.
CCSS.Math.Content.5.MD: Measurement and Data
CCSS.Math.Content.5.MD.A: Convert like measurement units within a given measurement system.
CCSS.Math.Content.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real
world problems.
CCSS.Math.Content.5.MD.B: Represent and interpret data.
CCSS.Math.Content.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.
CCSS.Math.Content.5.MD.C: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
CCSS.Math.Content.5.MD.C.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
CCSS.Math.Content.5.MD.C.3a: A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
CCSS.Math.Content.5.MD.C.3b: A solid figure which can be packed without gaps or overlaps using unit cubes is said to have a volume of cubic units.
CCSS.Math.Content.5.MD.C.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
CCSS.Math.Content.5.MD.C.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
CCSS.Math.Content.5.MD.C.5a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by
multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of
multiplication.
CCSS.Math.Content.5.MD.C.5b: Apply the formulas = × × and = × for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving
real world and mathematical problems.
CCSS.Math.Content.5.MD.C.5c: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
CCSS.Math.Content.5.NF: Number and Operations-Fractions
CCSS.Math.Content.5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
CCSS.Math.Content.5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.Math.Content.5.NF.B.4b: 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.
CCSS.Math.Content.5.OA: Operations and Algebraic Thinking
CCSS.Math.Content.5.OA.A: Write and interpret numerical expressions.
CCSS.Math.Content.5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.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 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
CCSS.Math.Content.5.OA.B: Analyze patterns and relationships.
CCSS.Math.Content.5.OA.B.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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the
resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
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.
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