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GGRRAADDEE 55

This curriculum is part of the Educational Program of Studies of the Rahway Public Schools.

ACKNOWLEDGMENTS

Dr. Kevin K. Robinson, Program Supervisor of STEM

The Board acknowledges the following who contributed to the preparation of this curriculum.

Vincent Crisafi

Christine H. Salcito, Assistant Superintendent

Subject/Course Title: Date of Board Adoptions:

Mathematics October 16, 2012

Grade 5 Revised August 26, 2014

Revised August 22, 2017

RAHWAY PUBLIC SCHOOLS CURRICULUM

UNIT OVERVIEW

Content Area: Mathematics – Unit I

Unit Title: Understanding the Place Value System

Target Course/Grade Level: Grade 5

Unit Summary

During Unit 1 students write and evaluate numeric expressions with parentheses, brackets and braces. They will explain that a

digit is ten times what it would represent in the place to its right. Students will also see patterns in the number of zeros in the

product when it is multiplied by powers of ten. Lastly, they will multiply and divide whole numbers and compare two

decimals.

Approximate Length of Unit: 44 days

Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21st Century Life and Careers, Science and

Technology

LEARNING TARGETS

Language Arts Literacy Standards:

RL.5.1 Quote accurately from a text when explaining what the test says explicitly and when drawing inferences from the

text.

RL.5.2 Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or

drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.

RL.5.3 Explain the relationships or interactions between two or more individuals, events, ideas or concepts in a historical,

scientific, or technical text based on specific information in the text.

RL.5.4 Determine the meaning the words and phrases as they are used in a text, including figurative language such as

metaphors and similes.

RI.5.2 Determine two or more main ideas of a text and explain how they are supported by key details; summarize the

text.

RI.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a

historical, scientific, or technical text based on specific information in the text.

RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5

topic or subject area.

W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a

single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse

partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

SL.5.2 Summarize a written text read aloud or information presented in divers media and formats, including visually,

quantitatively, and orally.

21st Century Life and Careers:

9.1.4.A.1 Recognize and problem and brainstorm ways to solve the problem individually or collaboratively.

9.1.4.A.3 Determine when the use of technology is appropriate to solve problems.

9.1.4.A.5 Apply critical thinking and problem-solving skills in a classroom and family settings.

9.1.4.C.1 Practice collaborative skills in groups, and explain how these skills assist in completing tasks in different

settings - at home, in school, and during play.

9.1.4.F.3 Explain the importance of understanding and following rules in family, classroom and community settings.

Reading/Language Arts – Read aloud “The History of Counting” by Denise Shmandt-Besserat (Harper Collins 1999)

which traces the invention of counting in different cultures. Ask volunteers to summarize orally the method of

counting that interested them.

Reading/Language Arts – Have volunteers read “The Great Number Rumble: A story of Math in Surprising Places by

CoraLee and Gillian O'Reilly (Annick Press, 2007), which presents a myriad of ways math affects us in our everyday

lives. Have students share ways they use multiplication and division in their everyday lives.

Science – Review with students the names of the planets in order of increasing distance from the sun: Mercury,

Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. 1. Diameter of Jupiter: 142,800 2. Diameter of Saturn: 120,537

Have students write each measure in word form and expanded form. Challenge students to find the diameters of other

planets and write each measure in both forms.

Science – Share these facts about elephants with students. 1. Elephants eat about 300 pounds of food each day. 2.

Elephants spend at least 16 hours per day eating.

Have students make a table showing how much food elephants eat each day, week, month, and year. Then have them

do the same for the number of hours elephants spend eating during each time period. (Students may use a calculator)

Content Standards

5.OA.A.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without

evaluating them. e.g. 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.

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.

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.

5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm.*(benchmarked)

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.

5.NBT.A.3. Read, write, and compare decimals to thousandths.

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).

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.

5.NBT.A.4. Use place value understanding to round decimals to any place.

Unit Understandings

Students will understand that…

Write and interpret numerical expressions

Understand the place value system

Perform operations with multi-digit whole numbers and with decimals to hundredths

Unit Essential Questions:

What is the easiest way to compare and order whole numbers?

What are some methods you can use to estimate sums, differences, products and quotients?

What are the different ways to write numbers?

Why do you think the Order of Operations is the way it is?

What are compatible numbers?

How is multiplying by ½ the same as dividing by 2?

Write a real world problem for the expression 5m-20?

Why is the number you are dividing called a dividend?

Knowledge and Skills

Students will be able to…

Evaluate numerical expressions that include grouping symbols (parentheses, brackets or braces).

Evaluate numerical expressions that include nested grouping symbols (for example, 3 x [5 + (7 - 3)]).

Write a simple numerical expression when given a verbal description.

Interpret the quantitative relationships in numerical expressions without evaluating (simplifying) the expression.

Explain that a digit in one place represents 1/10 of what it would represent in the place to its left.

Explain that a digit in one place represents ten times what it would represent in the place to its right.

Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10.

Write powers of 10 using whole-number exponents.

Multiply a whole number of up to a four digits by a whole number of up two digits using the standard algorithm with

accuracy and efficiency.

Divide to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using

strategies based on place value, properties of operations, and the relationship between multiplication and division.

Represent these operations with equations, rectangular arrays, and area models.

Explain the calculation by referring to the model (equation, array, or area model).

Read and write decimals to thousandths using base-ten numerals.

Read and write decimals to thousandths using number names.

Read and write decimals to thousandths using expanded form.

Compare two decimals to thousandths using >, =, and < symbols.

Compare decimals when each is presented in a different form (base-ten numeral, number name, and expanded form).

Round decimals to any place value.

EVIDENCE OF LEARNING

Assessment

What evidence will be collected and deemed acceptable to show that students truly “understand”? :

Pre-test

Chapter Review/Test (all lessons)

Guided Practice

Let's Practice (all lessons)

Cumulative Review for Chapters

Test Prep

Teacher Made Assessment

TenMarks.com

Put on Your Thinking Cap

Learning Activities

What differentiated learning experiences and instruction will enable all students to achieve the desired results?

To differentiate, teacher may use:

Extra Practice worksheets

Re-teach Workbook

Enrichment Workbook

RESOURCES

Teacher Resources:

Math in Focus Teacher Resource Black line Masters

Math in Focus Teacher Edition

Math in Focus Big Book

Math in Focus Enrichment, re-teach, and Extra Practice worksheets

Math in Focus Student hard cover book and workbook

Teacher’s guide to transition

Everyday Counts Calendar Mathematics

Think Central MIF official website

MIF Teacher Resource CD

Equipment Needed:

Place value chips for the teachers

Place-Value Charts (TR01) for the teacher

Number Lines (TR02) for the teacher

Student Reference Book Chapter 2: Math In Focus

Calculator Keypad (TR03) for the teacher

Calculators

Table of Multiplication 1 (TR04) per student




Table of Division 1 (TR08) per student



Table of Division 4 and 5 (TR11) per student

Number/Symbol Cards (TR12) per pair

Table of Numeric Expressions (TR13) per pair

Lattice Template

Student Reference Book

Technology Resources for Students:

Game- simplify expressions using order of operations and parentheses http://www.ixl.com/math/grade-5/simplify-

expressions-using-order-of-operations-and-parentheses

Game - write variable expressions http://www.ixl.com/math/grade-5/write-variable-expressions

Game- write equations to represent word problems http://www.ixl.com/math/grade-5/write-equations-to-represent-

word-problems

Game- Multiply three-digit numbers http://www.ixl.com/math/grade-5/multiply-by-3-digit-numbers

Game - Find whole number quotients with up to 4-digit dividends and 2-digit divisors

https://learnzillion.com/lessonsets/211-find-whole-number-quotients-with-up-to-4digit-dividends-and-2digit-divisors

Game - Function tables http://www.ixl.com/math/grade-5/function-tables

Game - Graph linear functions http://www.ixl.com/math/grade-5/graph-linear-functions

Video- Generate numerical patterns using two given rules, form ordered pairs from the patterns, and graph the

ordered pairs https://learnzillion.com/lessonsets/549-generate-numerical-patterns-using-two-given-rules-form-

ordered-pairs-from-the patterns-and- graph-the-ordered-pairs

Game- Understand that place value increases ten times with each shift to the left in a multi-digit number

https://learnzillion.com/student/lessons/2389-understand-that-place-value-increases-ten-times-with-each-shift-to-the-

left-ina-multidigit-number

Game - Multiply a decimal by a power of 10 http://www.ixl.com/math/grade-5/multiply-a-decimal-by-a-power-of-ten

Game- Place value in decimal numbers http://www.ixl.com/math/grade-5/place-values-in-decimal-numbers

Game - Round decimals to any place using number lines https://learnzillion.com/lessonsets/212-round-decimals-to-

any-place-using-number-lines

MIF Virtual Manipulatives http://www-

k6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_int_9780547673844_/main.html

MIF- Student interactivities

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?g

JumptoPage=S& g Page Id=N Technology Resources for Teachers/Parents:

MIF - Video- Whole Numbers http://www-

k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter1.html

MIF – Video – Whole Number Multiplication and Division http://www-


MIF Interactive Whiteboard http://www-

k6.thinkcentral.com/content/hsp/math/mathinfocus/common/iwb_dl_v2/contents/Main5.html

MIF Transition Resource Map

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/math_in_focus_transition_planner_9780547608563

_/launch.html

http://www.ixl.com/math/grade-5/simplify-expressions-using-order-of-operations-and-parentheses

http://www.ixl.com/math/grade-5/simplify-expressions-using-order-of-operations-and-parentheses

http://www.ixl.com/math/grade-5/write-variable-expressions

http://www.ixl.com/math/grade-5/write-equations-to-represent-word-problems

http://www.ixl.com/math/grade-5/write-equations-to-represent-word-problems

http://www.ixl.com/math/grade-5/multiply-by-3-digit-numbers

https://learnzillion.com/lessonsets/211-find-whole-number-quotients-with-up-to-4digit-dividends-and-2digit-divisors

http://www.ixl.com/math/grade-5/function-tables

http://www.ixl.com/math/grade-5/graph-linear-functions

https://learnzillion.com/student/lessons/2389-understand-that-place-value-increases-ten-times-with-each-shift-to-the-left-ina-multidigit-number


http://www.ixl.com/math/grade-5/multiply-a-decimal-by-a-power-of-ten

http://www.ixl.com/math/grade-5/place-values-in-decimal-numbers

https://learnzillion.com/lessonsets/212-round-decimals-to-any-place-using-number-lines


http://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter2.html


http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/math_in_focus_transition_planner_9780547608563_/launch.html


Useful websites for teachers to explore:

1. https://www-k6.thinkcentral.com/ePC/start.do

2. http://illuminations.nctm.org

3. http://www.ixl.com

4. http://www.k-5mathteachingresources.com

5. https://sites.google.com/site/emilou2010

6. http://www.onlinemathlearning.com

7. http://www.internet4classrooms.com

https://www-k6.thinkcentral.com/ePC/start.do

http://illuminations.nctm.org/

http://www.ixl.com/

http://www.k-5mathteachingresources.com/

https://sites.google.com/site/emilou2010

http://www.onlinemathlearning.com/

http://www.internet4classrooms.com/


UNIT OVERVIEW

Content Area: Mathematics - Unit II

Unit Title: Understanding Volume and Operations on Fractions


Unit Summary

In Unit 2 students will measure volume by counting unit cubes and by applying the formula. They will multiply multi-digit

whole numbers and add and subtract fractions with unlike denominators. They will solve word problems involving addition

and subtraction of fractions with unlike and denominators. They will interpret a fraction as a division problem. Lastly,

students will tile a rectangle with unit fraction squares to find area.



Technology

LEARNING TARGETS

Language Arts Standards:

RL.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences

from the text.

RL.5.2 Determine two or more main ideas of a text and explain how they are supported by key details; summarize the

text.

RL.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a


RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative language such as

metaphors and similes.

RL.5.5 Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution)

of events, ideas, concepts, or information in two or more text.

RI.5.2 Determine two or more main ideas of a text and explain how they are supported by key details, summarize the

text.

RI.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a


RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5

topic or subject area.

RI.5.5 Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution)

of events, ideas, concepts, or information in two or more text.

W.5.2 Write informative/explanatory text to examine a topic and convey ideas and information clearly.

W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose,

and audience. (grade-specific expectations for writing types are defined in standards 1-3 above.)

W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time

frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with

diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

21st Century Life and Career Skills:

9.1.4.A.1 Recognize a problem and brainstorm ways to solve the problem individually or collaboratively.

9.1.4.A.2 Evaluate available resources that can assist in solving problems.

9.1.4.A.3 Determine when the use of technology is appropriate to solve problems.


9.1.4.C.1 Practice collaborative skills in groups and explain how these skills assist in completing tasks in different

settings at home, in school, and during play.

9.1.4.F.3 Explain the importance of understanding and following rules in family, classroom, and community settings.

Reading/Language Arts – have students write a short story involving addition or subtraction of fractions. Students can

create their own storyline and fractions, or choose from these (½, ¼, ¾, 1/8, 7/8). Topics: School Trip, Cooking

Escapade, School Band, Planting a Garden. Invite volunteers to read their stories aloud to the class.

Social Studies – Have partners use a map of the United States and ask them to list 10 states they would like to visit.

Have them label the location of each state as north, east, south, or west in the country. Have groups share the fraction

of their states that are in each region.

Reading/Language Arts – Have students use a 15 x 15 grid to create word find puzzles for the decimal terms in this

chapter. To make their puzzles, students write one letter in each square, crossing words that share common letters.

After all the terms are filled in, students fill in the empty squares with other RANDOM letters. Have students

exchange and solve one another's puzzles.

Science – The speed of sound is 767.58 miles per hour. Have students’ research vehicles that have traveled faster that

the speed of sound, such as airplanes, rockets, and even cars. Have students present their reports to the class.

Encourage them to include visuals with their reports.

Reading/Language Arts – Have partners work together to write a hands-on activity, using activity on Page 49 of the

Student Book as a model. Encourage students to change the items being measured, the unit of measure, and the

number of decimal places to measure to in their new hands-on activity. Have pairs exchange and complete each

other's activity.

Science – Display the chart on page 30A, showing how far each animal could travel in 3 hours if it traveled at its

fastest speed.

Reading/Language Arts – Have students choose a book to read over five school days. Have them write the part of the

book they have read by the end of each day in fraction form and then in percent form. Students can record their

percents in a table. By the end of day 5, they should have read 100% of the book.

Social Studies – Brainstorm a list of students' five favorite presidents. Have students pretend the five presidents are

running for the office of class president. Then have a class election. Calculate the percent of votes each president

received.

Content Standards:

5.MD.C.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.MD.C.5a.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.

5.MD.C.5b.A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of

in cubic units.

5.MD.C.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard units.

5.MD.C.5. Relate volume to the operations of multiplication and addition and solve real world and mathematical

problems involving volume.

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.

5.MD.C.5b. Apply the formulas V = l × w × h and V = B × h 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.

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.

5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm. *(benchmarked)

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. e.g. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/1 (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. e.g. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

5.NF.B.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). 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. e.g. 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?

5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a

fraction.

5.NF.B.4a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a

sequence of operations a × q ÷ b. 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, (a/b) × (c/d) = ac/bd.]

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.

Unit Understandings:

Students will…

Understand concepts of volume


Use equivalent fractions as a strategy to add and subtract fractions

Apply and extend previous understandings of multiplication and division

Unit Essential Questions

When adding or subtracting unlike fractions what must you do first?

If you are changing a fraction to decimal, what number must your denominator be changed to?

How many wholes are needed when drawing an Improper Fraction Area Model?

How is a mixed number like a division problem containing a quotient, divisor and remainder?

How is estimation helpful when multiplying?

What are compatible numbers?



count unit cubes in order to measure the volume of a solid.

pack right rectangular prisms with cubes to find volume and multiply side lengths of the right rectangular prism to

find volume, showing that they are the same.

pack right rectangular prisms with cubes to find volume and multiply height by the area of the base, showing that

they are the same.

explain how both volume formulas relate to counting the cubes in one layer and multiplying that value by the

number of layers (height).

write the volume of an object as the product of three whole numbers.

solve real-world and mathematical problems using the formulas V = l × w × h and V = B × h.

find the volume of a composite solid composed of two right rectangular prism

multiply multi-digit whole numbers with accuracy and efficiency

produce an equivalent sum (or difference) of fractions with like denominators from the original sum (or

difference) of fractions that has unlike denominators.

add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.

add and subtract fractions, including mixed numbers, with unlike denominators to solve word problems.

represent calculations and solutions with visual fraction models and equations

estimate answers using benchmark fractions and explain whether the answer is reasonable.

estimate answers by reasoning about the size of the fractions and explain whether the answer is reasonable.

produce an equivalent sum (or difference) of fractions with like denominators from the original sum (or

difference) of fractions that has unlike denominators.

add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.

for whole number or fraction q, represent (a/b) × q as a parts of a partition of q into b equal parts [e.g. using a

visual fraction model, (3/4) x 5 can be represented by 3 parts, after partitioning 5 objects into 4 equal parts].

for whole number or fraction q, represent (a/b) × q as a × q ÷ b [e.g. showing that (2/5) x 3 is equivalent to (2 x 3)

÷ 5].

from a story context, interpret (a/b) × q as a parts of a partition of q into b equal parts.

tile a rectangle having fractional side lengths using unit squares of the appropriate unit fraction [e.g. given a 3 ¼

inch x 7 ¾ inch rectangle, tile the rectangle using ¼ inch tiles].

show that the area found by tiling with unit fraction tiles is the same as would be found by multiplying the side

lengths.


Assessment

What evidence will be collected and deemed acceptable to show that students truly “understand”?

Pre-test


Guided Practice



Test Prep


TenMarks.com


Learning Activities




Re-teach Workbook

Enrichment Workbook

RESOURCES

Teacher Resources:










Equipment Needed:

Solid shapes for the teacher

Number cube per pair

Nets of Cubes (TR64) per student

Net of Cube 1 (TR65) for the teacher

Net of Cube 2 and Cube 3 (TR66, 67) per student

Net 1 and Net 2 (TR68, 69) per pair

Table of prisms and pyramids (TR70) per student

Sticky notes, tracing paper, and scissors per student

Toothpicks per group (optional)

Net of a cylinder (TR71) for the teacher

35 connecting cubes per student Model of a cube for the teacher

20 connecting cubes per student and for the teacher

10 connecting cubes per student

3 pieces of Isometric Dot Paper (TR72) for the teacher and students

Drawings of rectangular prisms worksheet 1 (TR73) per student

Drawings of rectangular prisms worksheet 2 (TR74) per student

Solid shapes for the teacher

Net of Cube 1 (TR65) per student

Net of Cube 2 (TR66) per student

Table of surface area of cubes (TR75) per student

25 connecting cubes per pair

Table of Volumes of Rectangular Prisms (TR76) per student

40 connecting cubes for the teacher

Cubic liter container for the teacher

Table of Measures (TR44) per student

5 or 6 containers of various sizes and shapes for the teacher

Measuring cylinder or pitcher for the teacher

Objects in the shape of rectangular prisms for the teacher

15 connecting cubes per pair

Fraction Circles (TR14) for the teacher

Fraction Circles (TR14) for the students

Fraction Circles (TR14) per group and for the teacher

Strips of Paper (TR15) per group

Decimal Models (TR16) for the teacher


Teachers Resource Book


Game- Understand that place value increases ten times with each shift to the left in a multi-digit number

https://learnzillion.com/student/lessons/2389-understand-that-place-value-increases-ten-times-with-each-shift-to-the-left-

ina-multidigit-number

Game - Multiply a decimal by a power of 10 http://www.ixl.com/math/grade-5/multiply-a-decimal-by-a-power-of-ten

Game- Place value in decimal numbers http://www.ixl.com/math/grade-5/place-values-in-decimal-numbers

Game - Round decimals to any place using number lines https://learnzillion.com/lessonsets/212-round-decimals-to-any-

place-using-number-lines

Game- Add fractions with unlike denominators http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators

Video- Add and subtract fractions with unlike denominators https://learnzillion.com/lessonsets/216-add-and-subtract-

fractions-with-unlike-denominators

Practice: Divide fractions http://www.themathpage.com/Arith/Ar_Pr/mulf1_2.htm

Multiply fractions with models http://www.ixl.com/math/grade-5/multiply-fractions-with-models

Game - Multiply fractions http://www.funbrain.com/cgi-bin/fract.cgi

http://www.mathplayground.com/fractions_mult.html

Game- Division of fractions http://www.ixl.com/math/grade-5/divide-fractions-by-whole-numbers-word-problems

MIF Virtual Manipulativeshttp://www-



http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?gJum

ptoPage=S& g Page Id=N Technology Resources for Teachers/Parents:

MIF - Video- Fractions and Mixed Numbers http://www-


MIF - Video- Decimals

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter8.htm

ll

MIF – Video – Multiplying and Dividing Decimals http://www-


MIF - Video- Percent

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter10.ht

ml



http://www.ixl.com/math/grade-5/place-values-in-decimal-numbers



http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators

https://learnzillion.com/lessonsets/216-add-and-subtract-fractions-with-unlike-denominators


http://www.themathpage.com/Arith/Ar_Pr/mulf1_2.htm

http://www.ixl.com/math/grade-5/multiply-fractions-with-models


http://www.ixl.com/math/grade-5/divide-fractions-by-whole-numbers-word-problems

http://www-k6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_int_9780547673844_/main.html




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter8.htmll




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter10.html

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter10.html




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/math_in_focus_transition_planner_9780547608563_/la

unch.html









http://www-k6.thinkcentral.com/content/hsp/math/mathinfocus/common/iwb_dl_v2/contents/Main5.html






http://www.ixl.com/






UNIT OVERVIEW

Content Area: Mathematics - Unit III

Unit Title: More Operations on Fractions


Unit Summary

In Unit 3 students add, subtract, multiply and divide decimals to hundredths place. Students will multiply fractions by a

whole number. They will also multiply fractions by fractions. Students will explain how a product is related to the magnitude

of its factors. They will divide a whole number by a fraction and fraction by a whole number. Students will explain patterns

in the placement of the decimal when multiplying by a multiple of 10, 100, or 1000. Lastly, students will convert standard

measurement units.



Technology

LEARNING TARGETS


RL.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences

from the text.

RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative language

such as metaphors and similes.

RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to

grade 5 topic or subject area.


W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task,

purpose, and audience.

W.5.7 Conduct short research projects that use several sources to build knowledge through investigation of

different aspects of a topic.

W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time

frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.




9.1.4.C.1 Practice collaboration skills in groups, and explain how these skills assist in completing tasks in

different settings at home, in school, and during play. 9.1.4.F.3 Explain the importance of understanding and following rules in family, classroom, and community settings.

SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse

partners on grade 5 topics and texts, building on others ideas and expressing their own clearly.

SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and

relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

SL.5.5 Include multimedia components (e.g. graphics, sound) and visual displays in presentations when appropriate to

enhance the development of main ideas or themes.

Reading/Language Arts – Have students work in groups to complete this activity.

- Create a survey or questionnaire.

- Survey 10 students – 5 girls and 5 boys.

- Choose one question from the survey and record the results on a double bar graph.

- Present findings, along with visuals to the class.

Social Studies – Relate the coordinates in a coordinate plane to latitude and longitude Using a world globe, briefly

explain latitude as the position of a point the earth's surface between the equator and poles. Explain longitude as a

position east or west from the prime meridian. Have students research online and identify the latitude and

longitude of

your city or town. Suggest that interested students research how a global positioning system uses coordinates to

show

location and report their findings to the class.

Content Standards

5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole

number by a fraction.

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.

5.NF.B.5. Interpret multiplication as scaling (resizing), by:

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.

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 a/b =

(n×a)/(n×b) to the effect of multiplying a/b by 1.

5.NF.B.6. Solve real world problems involving mixed 5.NF.B.6. Solve real world problems involving

numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.B.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers

and whole numbers by unit fractions. *(benchmarked)

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.

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.

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?

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.

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.

*(benchmarked)

5.MD.A.1. Convert a real world problems 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.

Unit Understandings

Students will…

Apply and extend previous understandings of multiplication and division

Understand the place value system


Convert like measurement units within a given measurement system

Unit Essential Questions

How do geometric relationships help in solving problems and/or make sense of phenomena?

How can measurements be used to solve problems?

How are physical models used to describe mathematical relationships?

When adding or subtracting unlike fractions what must you do first?

If you are changing a fraction to decimal, what number must your denominator be changed to?

How many wholes are needed when drawing an Improper Fraction Area Model?

How can looking for patterns be helpful when multiplying and dividing by multiples of 10, 100, and 1000?

Does the decimal point really move when you multiply by 10, 100 or 1000? Explain.



multiply fractional side lengths to find areas of rectangles.

represent fraction products as rectangular areas.

multiply a fraction by a whole number.

multiply a fraction by a fraction, in general, if q is a fraction c/d, then (a/b) x (c/d) = a(1/b) × c(1/d) = ac × (1/b)(1/d)

= ac(1/bd) = ac/bd.

compare the size of a product to the size of one of its factors, considering the size of the other factor (at least one

factor is a fraction).

explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given

number.

explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given

number.

explain that multiplying a given number by a fraction equivalent to 1 does not change the product.

multiply fractions and mixed numbers in order to solve real world problems.

represent the solution to these real world problems with visual fraction models and equations.

use a story context to interpret division of a unit fraction by a whole number.

divide of a unit fraction by a whole number and represent with visual fraction models.

use a story context to interpret division of a whole number by a unit fraction.

divide of a whole number by a unit fraction and represent with visual fraction models.

divide unit fractions by whole numbers to solve real-world problems, using visual fraction models and equations to

represent the problem.

divide whole numbers by unit fractions to solve real-world problems, using visual fraction models and equations to


explain patterns in the placement of the decimal point when multiplying or dividing a decimal by powers of 10.

write powers of 10 using whole-number exponents.

add and subtract decimals to hundredths using concrete models and drawings.

multiply and divide decimals to hundredths using concrete models and drawings.

add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of

operations, and/or the relationship between addition and subtraction.

relate the strategy to the written method and explain the reasoning used.







Assessment


Pre-test


Guided Practice



Test Prep


TenMarks.com


Learning Activities




Re-teach Workbook

Enrichment Workbook

RESOURCES

Teacher Resources:










Equipment Needed:

Fraction Circles (TR14) for the teacher

Fraction Circles (TR14) for the students

Fraction Circles (TR14) per group and for the teacher

Strips of Paper (TR15) per group

Decimal Models (TR16) for the teacher


Teachers Resource Book

Base 10 Blocks for the teacher

Place-Value Chips for the teacher

Number Lines 1 (TR29) for the teacher and 2 copies per student

Thousandths Models (TR30) per student

Number Lines 2 (TR31) per student

8 note cards per pair

Connecting cubes for the teacher

7 Place-Value Chart 2 (TR32) per student

Number Lines (TR02) per student

Student Resource Book


Game- Add fractions with unlike denominators http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators

Video- Add and subtract fractions with unlike denominators https://learnzillion.com/lessonsets/216-add-and-subtract-

fractions-with-unlike-denominators

Practice: Divide fractions http://www.themathpage.com/Arith/Ar_Pr/mulf1_2.htm

Multiply fractions with models http://www.ixl.com/math/grade-5/multiply-fractions-with-models

Game - Multiply fractions http://www.funbrain.com/cgi-bin/fract.cgi http://www.mathplayground.com/fractions_mult.html

Game- Division of fractions http://www.ixl.com/math/grade-5/divide-fractions-by-whole-numbers-word-problems




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?gJumpto

Page=S& gPageId=N

Technology Resources for Teachers/Parents:

MIF - Video- Fractions and Mixed Numbers http://www-


MIF - Video- Algebra http://www-

k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter5.htm




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/math_in_focus_transition_planner_9780547608563_/launch

.html

http://www.ixl.com/math/grade-5/add-fractions-with-unlike-denominators



http://www.themathpage.com/Arith/Ar_Pr/mulf1_2.htm

http://www.ixl.com/math/grade-5/multiply-fractions-with-models


http://www.ixl.com/math/grade-5/divide-fractions-by-whole-numbers-word-problems





http://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter5.htm

http://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760308_te/chapter/chapter5.htm















http://www.ixl.com/






UNIT OVERVIEW

Content Area: Mathematics, Unit IV

Unit Title: Coordinate Geometry and Classifying Figures


Unit Summary

In Unit 4 students will graph points defined by whole number coordinates in the first quadrant. They will create and graph

ordered pairs. Students will classify two dimensional shapes based on properties. They will make a line plot to display data

and use it to solve problems. They will continue to fluently multiply multi-digit whole numbers and add, subtract, multiply

and divide decimals to the hundredths place. Lastly, they will solve real world problems involving division of unit fractions.


Primary interdisciplinary connections: Language Arts Literacy, Social Studies, 21st Century Life and Career Skills, Science

and Technology

LEARNING TARGETS


RL.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing

inferences from the text.

RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative

language such as metaphors and similes.

RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text

relevant to grade 5 topic or subject area.


W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to

task, purpose, and audience.

W.5.7 Conduct short research projects that use several sources to build knowledge through investigation

of different aspects of a topic.

W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter

time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and

audiences.




9.1.4.C.1 Practice collaboration skills in groups, and explain how these skills assist in completing tasks in

different settings at home, in school, and during play.

9.1.4.F.3 Explain the importance of understanding and following rules in family, classroom, and community

settings.

SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with

diverse partners on grade 5 topics and texts, building on others ideas and expressing their own clearly.

SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts

and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable

pace.

SL.5.5 Include multimedia components (e.g. graphics, sound) and visual displays in presentations when

appropriate to enhance the development of main ideas or themes.

Reading/Language Arts

– Have students work in groups to complete this activity.

- Create a survey or questionnaire.

- Survey 10 students – 5 girls and 5 boys.

- Choose one question from the survey and record the results on a double bar graph.

- Present findings, along with visuals to the class.

Social Studies – Relate the coordinates in a coordinate plane to latitude and longitude. Using a world globe,

briefly explain latitude as the position of a point the earth's surface between the equator and

poles. Explain longitude as a position east or west from the prime meridian. Have students

research online and identify the latitude and longitude of your city or town. Suggest that

interested students research how a global positioning system uses coordinates to show location

and report their findings to the class.

Content Standards:

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. e.g. 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.

5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm. *(benchmarked)

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.

*(benchmarked)

5.NF.B.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and

whole numbers by unit fractions.*(benchmarked)

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?

Unit Understandings:

Students will…

Graph points on the coordinate plane to solve real-world and mathematical problems

Analyze patterns and relationships

Classify two dimensional figures into categories based on their properties

Represent and interpret data


Apply and extend previous understanding of multiplication and division

Unit Essential Questions:

How do geometric relationships help in solving problems and/or make sense of phenomena?

How can measurements be used to solve problems?

When plotting an ordered pair, do you move on the vertical axis or horizontal axis first?

What is the difference between theoretical and experimental probability?

Knowledge and Skills:


graph points defined by whole number coordinates in the first quadrant of the coordinate plane in order to represent

real world and mathematical problems.

identify the relationship between corresponding terms and write ordered pairs.

graph the ordered pairs.

classify two-dimensional figures (triangles, quadrilaterals) based on shared attributes (e.g. parallel sides, number of

sides, angle size, side length, etc.).

arrange the categories/subcategories of figures (e.g. squares, rectangles, trapezoids, etc) in a hierarchy based on

attributes.

identify attributes of a two-dimensional shape based on attributes of the categories to which it belongs.

use measurement information to create a line plot.

using measurement information presented in line plots, add, subtract, multiply and divide fractions in order to solve

problems.

multiply multi-digit whole numbers with accuracy and efficiency.






use a story context to interpret division of a unit fraction by a whole number.

use a story context to interpret division of a whole number by a unit fraction.

divide unit fractions by whole numbers to solve real world problems, using visual fraction models and equations to


divide whole numbers by unit fractions to solve real world problems, using visual fraction models and equations to



Assessment:


Pre-test


Guided Practice



Test Prep


TenMarks.com


Learning Activities:




Re-teach Workbook

Enrichment Workbook

RESOURCES

Teacher Resources:










Equipment Needed:

Tangram Cut-Outs (TR55) per student

Centimeter rule per student

Table for Classifying Triangles (TR56) per student

Angles of a Triangle Cut-Outs (TR57) per student

Isosceles Triangle ABC Cut-Outs (TR58) per student

Grid Paper (TR18) per student

Centimeter ruler per pair

Inch ruler per pair Number Cube for the teacher

Graph of Money Collected (TR50) per student

Table of Colors (TR51) per pair

Paper Bag per pair

Paper Slip (red, blue, green, and yellow) per pair

3 pink paper slips per pair

Ruler for the teacher

Measuring Tape per pair

Coordinate Grid (TR52) for the teacher and 3 per student

Grid paper (TR18) per pair

Table of Measures (TR44) for the teacher

Masking Tape for the teacher

Sticky Labels for the teacher

Straightedge per pair

Red and Blue colored pencils

Pair of scissors per student

Colored Markers per pair

1 Blue and 4 Red connecting cubes in a paper bag for the teacher

2 Red, 3 Green, and 5 Blue connecting cubes per pair

Table of Connecting Cubes (TR53) per pair

Penny per student

Probability Meter


Game- Graph linear functions http://www.ixl.com/math/grade-5/graph-linear-functions

Game- Function tables http://www.ixl.com/math/grade-5/function-tables

Game - http://www.ixl.com/math/grade-4/choose-the-multiples-of-a-given-number-up-to-12

Game - http://www.studyzone.org/testprep/math4/e/multcommutative3p.cfm

Game- http://www.ixl.com/math/grade-4/numeric-patterns-word-problems




http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?gJumpto

Page=S&gPageId=N

Technology Resources for Teachers/Parents:

MIF - Video- Graphs and Probability





http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/math_in_focus_transition_planner_9780547608563_/launch

.html









http://www.ixl.com/math/grade-5/graph-linear-functions

http://www.ixl.com/math/grade-5/function-tables

http://www.ixl.com/math/grade-4/choose-the-multiples-of-a-given-number-up-to-12

http://www.studyzone.org/testprep/math4/e/multcommutative3p.cfm

http://www.ixl.com/math/grade-4/numeric-patterns-word-problems



http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?gJumptoPage=S&gPageId=N

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr5/reteach_and_enrich_9780547671826_/index.html?gJumptoPage=S&gPageId=N








http://www.ixl.com/





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