UNIT 1 - Trenton Public Schools

5th Grade Math Curriculum

UNIT 1

CAR © 2009

Unit title: 5th grade math Understanding Place Value ~ Unit 1 Grade Level: 5

Timeframe: Marking Period 1

45 Days (9 weeks) ~ September through mid-November

8+ weeks MAJOR content + incorporate additional content into 3 instructional days

5.NBT.A.1, 5.NBT.A.2, 5.NBT.B.5, 5.NBT.B.6, 5.NBT.A.3, 5.NBT.A.4 + 5.OA.A.1 + 5.OA.A.2

Unit Focus and Essential Questions

Unit 1 Focus

Understand the place value system

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

Write and interpret numerical expressions

Essential Questions:

How does “place value” relate to the value of each digit?

In a number where all the digits are the same, how does each identical digit represent a different value?

How do 8 pennies compare to 8 dimes? How do 7 dimes compare to 7 one dollar bills? How do 9 ten dollar bills compare to 9 one dollar bills? How do 6 hundred dollar bills compare to 6 ten dollar bills?

When do digits represent different amounts of the same thing?

How can digits represent the same amount of different things?

What number represents five tens? 8 tens? 8 hundreds? Five hundreds?

How does one hundred differ from one thousand? How does one hundred differ from one ten? They all have 1’s & 0’s.

Which digit of a number tells us the largest amount of some-thing?

Which digit represents the smallest amount of some-thing?

When we write multiple digits beside each other, how can we know the value each digit represents?

When we add the values represented by each digit, what do we get?

What value does the first digit to the right of a decimal point represent? A digit to the immediate left of a decimal point represents what value?

CAR © 2009

How does a number’s standard form compare to its expanded form?

How does a number’s written form compare to its standard form?

What value do digits two places to the right of a decimal point represent? When adding or subtracting quantities, why does it make sense to group the same values represented by each digit? When multiplying a single digit number with a multi-digit number, why does it make sense add similar values represented

by the products of each digit? When multiplying a double digit number with another multi-digit number, how do we combine the products represented

by the values of each digit? New Jersey Student Learning Standards

Standards/Cumulative Progress Indicators (Taught and Assessed):

5.NBT.A.1 - 8 days** 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. Left # Right

x 10 x 1/10

(10)10 (1)10 (1/10)10 3,160 316 31.6 100 10 1

5.NBT.A.2* - 8 days** 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* - 5 days Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.6* - 5 days

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.

CAR © 2009

5.NBT.A.3 - 8 days** 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).

1 1/10 1/100 1/1000 or or or or

1000 100 10 1

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 - 8 days** Use place value understanding to round decimals to any place.

5.OA.A.1 - 1 day (integrate into major content,, i.e., 5.NBT.A.3)

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2 - 2 days (integrate into major content,, i.e., 5.NBT.B.5, 5.NBT.A.3)

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.

Key:

Green = Major Clusters; Blue = Supporting;

Yellow = Additional Clusters

CAR © 2009

*NJ State benchmarked standard

**OPTIONAL (not required) – entire instructional topics do NOT have to be taught consecutively: consider Spacing Learning Over Time (S.L.O.T.)

http://dwwlibrary.wested.org/media/learning-together-about-spacing-learning-over-time

21st Century Skills Standard and Progress Indicators:

Think like a mathematician & the 8 Mathematical Practices (8MPs)! The Common Core State Standards for mathematical practice (8MPs) describe habits of mind students internalize with practice:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others*

4. Model with mathematics**

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Real-world problem solving is a vital 21st century skill all students need to compete globally. MP4 (modeling/application) Sub-Claim D (18% of raw points) in PARCC math claims structure – only 3 tasks on PARCC. MP3 and MP6 (expressing mathematical reasoning) fall under Sub-Claim C (22% of raw points) in PARCC math claims structure – only 4 tasks on PARCC.

Communication and teamwork are vital 21st century skills students all students should develop. Constructivist, team-building, cooperative learning routines include:

o Think-pair-share

o Group conference o Bounce ideas off each other

o State your claim o Respectfully disagree o Each one teach one

o Group presentation o Team spokesman/spokeswoman

Metacognition and inquiry-based teamwork helps students become self-directed learners, as problem solving and communication skills develop and students take ownership of their own thinking (and hence, learning).Challenging students to “explain” their reasoning helps their metacognition – ability to pay close attention to their own thinking:

o What (exactly) am I doing now? Why am I doing it? o How do I know? Does this really make sense? Why or why not?

PARCC Released items: http://tinyurl.com/gr5PARCCreleaseditems2016

http://dwwlibrary.wested.org/media/learning-together-about-spacing-learning-over-time

http://tinyurl.com/gr5PARCCreleaseditems2016

CAR © 2009

PARCC Evidence Statements: http://parcc-assessment.org/assessments/test-design/mathematics/math-test-specifications-documents PARCC Model Content Frameworks: http://parcc-assessment.org/resources/educator-resources/model-content-frameworks

Suggested performance tasks from https://illustrativemathematics.org : 5.NBT.A.1 Which number is it?

5.NBT.A.1 Millions and Billions of People

5.NBT.2 Marta’s Multiplication Error: https://www.illustrativemathematics.org/content-standards/5/NBT/A/2/tasks/1524

5.NBT.B.5 Elmer's Multiplication Error

5.NBT.A.3 Placing Thousandths on the Number Line

5.NBT.A.4 Rounding to Tenths and Hundredths

5.OA.A.1 Using Operations and Parentheses

5.OA.A.1 Watch out for Parentheses 1

Additional performance tasks from NC Department of Public Instruction: http://3-5cctask.ncdpi.wikispaces.net/Fifth+Grade+Tasks

Reasoning task: 5.C.7-4/4.NBT (2015 PARCC PBA released item 13)

Units: tens, hundreds, thousands & millions

Part A Write this number in expanded form: 670,503

Part B Show or explain how to write 8,523 in expanded form using 15 hundreds.

Part C A student used 80 ten thousands in the expanded form of the number 6,807,590.

Show or explain how 6 hundred thousands, 80 ten thousands, 7 thousands, 5 hundreds and 9 tens can or cannot be used to represent 6,807,590.

If it cannot be used, show how you would correct it and still use 80 ten thousands.

http://parcc-assessment.org/assessments/test-design/mathematics/math-test-specifications-documents

http://parcc-assessment.org/resources/educator-resources/model-content-frameworks

https://illustrativemathematics.org/

https://www.illustrativemathematics.org/content-standards/5/NBT/A/1/tasks/1799




https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812





https://www.illustrativemathematics.org/content-standards/5/OA/A/1/tasks/1596



http://3-5cctask.ncdpi.wikispaces.net/Fifth+Grade+Tasks

CAR © 2009

Modeling task: 5.D.1/5.NBT.5, 5.NBT.6 (2014 PARCC PBA practice test item 16)

Greg’s water bottles

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Reasoning task: 5.C.4-3/5.NBT.6 (Smarter Balanced sample item 1890, claim 3)

Jasmine’s area model equation

Help Jasmine find the number which equals 363 when divided by 4.

CAR © 2009

Modeling task: 5.D.1/5.NBT, 5.OA.2 (2015 PARCC PBA released item 14)

Katie’s jewelry Katie went to a craft store to purchase supplies she needs to make two types of jewelry. This table shows the cost of the supplies Katie needed.

This table shows the supplies needed to make each piece of jewelry.

Katie purchased the exact amount of supplies to make 1 bracelet and 2 necklaces.

Part A Write an expression to determine the cost of supplies to make 1 bracelet.

Part B Write an expression to determine the cost of supplies to make 2 necklaces.

Part C Katie started with $40. How much did she have left after purchasing the supplies?

CAR © 2009

Reasoning task: 5.C.4-3/5.NBT.6 (2014 PARCC PBA practice test item 15)

A division & multiplication area model

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Reasoning & Modeling Task: 5.C.4-3, 5.D.1/5.NBT.6 (McGraw-Hill benchmark task)

Division model problem

Now write a brief story or scenario which uses the numbers you put into your division problem. Be sure your story’s conclusion relates to your solution to the division problem modeled.

Farmer Jim solves a problem (Eureka Math 5th grade, Module 1 – Topic A) Farmer Jim keeps 12 hens in every coop. If Farmer Jim has 20 coops, how many hens does he have in all? If every hen lays 9 eggs, how many eggs will Farmer Jim collect? Explain your reasoning using words, numbers, or pictures.

Instructional Plan Standards Based Assessment

Cumulative Pre-Assessment Diagnostic Assessment - MI

Standard/SWBAT Student Strategies Based on Instructional Framework

Formative Assessment

Activities and Resources Standards Based Assessment

CAR © 2009

NJSLS.MATH.CONTENT.5.NBT.1

5.NBT.A.1 - 8 days**

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.

(MAJOR content)

-----------------------------------

Claim: students understand the

quantitative relationships between

digits in the place value positions of

a multi-digit number.

Evidence: students can EXPLAIN

that a digit in one place represents:

a. 1/10 of what it represents in the

place to its left.

And

b. ten times what it represents in

the place to its right.

Tasks: may compare a digit in the

tenths position to a:

Thousandths digit

Or a Tens digit

little to no “context”

Performance: students soon use

whole number exponents to denote

powers of 10 and compare them

when expressed exponentially

(i.e.10⁴ > 10² or 10³ < 10⁴).

Extend the concept to multiple

places…………………………..

Number Talk Direct Instruction

Option 1 - EngageNY

Option 2 – NJCTL presentation

Option 3 - MyMath Centers (rotating)

Teacher Center – teacher works w/ 1-4 students

Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments

Individual Center – Students focus on skills based on , EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.

Technology Center – Math

Manipulative Center – Students use tools, such as base 10 blocks.

Interdisciplinary Center – Students solve interdisciplinary math; write their own number stories; listen to music/sing songs to help learn the content.

Record metacognitive thinking in student journals

Review Classwork Exit Ticket

PARCC Released Items 2016, Item #3

http://tinyurl.com/2016PARCCr

eleaseditems

During grade level meetings, teacher PLCs agree on common classwork/question s. Selected tasks most closely match assessment questions in column 5.

Additionally, teachers encourage metacognition– students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)

How is the 2 in

542 different from

the value of the 2

in 324?

What does 2 digit

represent in

2897?

How about in

1.026?

EngageNY, 2016, Module 1, Topic A (lessons 1-2)

https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-lesson-1


https://www.engageny.org/resource/math-studio-talk-common-core-instruction-5nbt

NJCTL Decimal Concepts Presentation 2015-11-16, (slides 15-40)

https://njctl.org/courses/math/5th-grade-math/decimal-concepts/

PARCC Released Items 2016, Item #3

http://tinyurl.com/2016PARCCreleaseditems

PARCC Released Items 2015, PBA Item #1, http://tinyurl.com/gr5PARCC-

PBAreleased2015

PARCC EOY Item #28 http://tinyurl.com/gr5PARCC-

EOYreleased2015

Illustrative Mathematics 5.NBT.A.1 Which number is it?

5.NBT.A.1 Millions and Billions of People

Achieve the Core Coherence Map http://achievethecore.org/coherence-

map/#5/22

NJCTL Math Labs – RAFT resources… http://www.raftbayarea.org/readpd

f?isid=600

MyMath (Teacher login available) Ch.1 Lesson 1 Place Value Millions

www.connected.mcgraw-hill.com

(10)10 (1)10 (1/10)10

3,160 316 31.6

100 10 1 1 hundred 1 ten 1 one

The “Touchpoint” standards based assessments (quizzes) are in edConnect nj. Grade 5 Math - Touchpoint – 5.NBT.1 --------------------------------------------------

Build the concept:

The arrows indicate the value is

1/10 of the 5 to the left and 10

times the 5 to the right

--------------------------------------------------

--34.567

In the above number, compare the place which the 5 digit represents to the place represented by the:

a. 7 digit b. 3 digit

Explain the size of each place

compared to the 5’s place.

What value does each digit represent

in this number? Explain.












http://tinyurl.com/gr5PARCC-PBAreleased2015

http://tinyurl.com/gr5PARCC-PBAreleased2015

http://tinyurl.com/gr5PARCC-EOYreleased2015




http://achievethecore.org/coherence-map/#5/22


http://www.raftbayarea.org/readpdf?isid=600

http://www.raftbayarea.org/readpdf?isid=600

http://www.connected.mcgraw-hill.com/

CAR © 2009

NJSLS.MATH.CONTENT.5.NBT. 2

5.NBT.A.2* - 8 days**

Explain patterns in the

number of zeros of a

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.

(MAJOR content) --------------------------------------------------------------------

Claim: students understand

exponents & scientific notation;

students write powers of 10 using

whole number exponents.

Evidence: students reason about

the place value system (itself)

and

use whole number exponents to

denote powers of ten.

Tasks: focus specifically on place

value; do not serve another goal-

multiplying multi-digit numbers.

Reasoning 5.C.3

Performance: students clearly

communicate well-organized,

complete responses; evaluate and

justify conclusions; critique other

responses; show counterexamples.

Math Practices 7, 3 & 6

Number Talk

Direct Instruction

Option 1 - EngageNY

Option 2 – NJCTL

Option 3 - MyMath Centers (rotating)

Teacher Center –Teacher works with 1-4 students.

Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).

Individual Center – Students focus on skills based on EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.

Technology Center

Manipulative Center – Students use tools, such as base 10 blocks.

Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories; they listen to music/sing songs to help learn the content.


PARCC Released Items, EOY Item #9 http://tinyurl.com/gr5PARCC

-EOYreleased2015

During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.

Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)

Record metacognitive

thinking in student journals

EngageNY 2016 Module 1, Topic A (lesson 3)


Module 2, Topic A (lesson 2) https://www.engageny.org/resource/grade-5-

mathematics-module-2-topic-lesson-2

Module 2, Topic B (lesson 24) https://www.engageny.org/resource/grade-5-

mathematics-module-2-topic-g-lesson-24

https://www.engageny.org/resource/grade-5-mathematics-module-2

NJCTL Division Presentation 2015-11-25, (Patterns in Mult. & Division: slides 26-88 ) https://njctl.org/courses/math/5th-grade-

math/division/attachments/unit-3-division/

PARCC Released Items 2016, Item #4 http://tinyurl.com/2016PARCCreleaseditems


map/#5/22

MyMath (Teacher login available) Ch.1 Lesson 5 Understanding Place Value


523 x 103 = 523,000 The place value of

523 is increased by 3 places.

5.223 x 102 = 522 The place value of

5.223 is increased by 2 places.

52.3 ÷ 101 = 5.23 The place value of

52.3 is decreased by one place.

Multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 × 10 × 10 as large (400.0). Each shift to the left increases 10 times the previous position; 1 thousand = 1,000 = 10³

The standards assessments below are in EdConnect. These are the quiz/test for that standard.

Grade 5 Math – Touchpoint – 5.NBT.2

Illustrative Mathematics: Marta’s multiplication error

https://www.illustrativemathematics. org/content-

standards/5/NBT/A/2/tasks/1524

Multiplying by 104 is multiplying

by 10 four times

102 which is 10 x 10=100

103 = 10 x 10 x 10=1,000

Connect the pattern of zeros when you multiplying by powers of 10.

Decimal moves right…

2.5 x 103 = 2.5 x (10 x 10 x 10) = 2.5 x 1,000 = 2,500.

Decimal moves left… 350. ÷ 103 =

350 ÷ 1,000 = 0.350 = 0.35

Divide by 10 = multiply by 1/10

350/10 = 35

35 /10=3.5

3.5 /10 =.0.35, or 350 x 1/10,

35 x 1/10,

350 x 1/10 =

35 x 1/10 =

3.5 x 1/10 =

36 x 10 = 36 x 101 = 360

36 x 10 x 10= 36x 102 = 3600

36 x 10 x 10 x 10 =

36 x 103 = 36,000

36 x 10 x 10 x 10 x 10 =

36 x 104 = 360,000

See patterns with zeros

http://www.corestandards.org/Math/Content/3/OA/A/2/

http://www.corestandards.org/Math/Content/3/OA/A/2/







https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-g-lesson-24

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-g-lesson-24



https://njctl.org/courses/math/5th-grade-math/division/attachments/unit-3-division/










CAR © 2009


5.NBT.B.5* - 5 days**

Fluently multiply multi-

digit whole numbers

using the standard

algorithm.

(MAJOR content) --------------------------------------

Claim: students use the standard

algorithm to fluently multiply

multi-digit whole numbers.

Evidence: students can fluently

multiply multi-digit whole numbers

using the standard algorithm;

Tasks: untimed & assess accuracy,

using up to 3 digit x 4 digit

numbers; pure mental strategy not

obvious – written work required;

little to no “context”

Performance: students (use place

value to) assess reasonableness of

products from multi-digit numbers

after using standard algorithm.

----------------------------------------------------------

Build toward standard algorithm

a. Area model of multiplication

b. Partial products (left to right)

c. Partial products (right to left)

d. Standard w/ regrouping

http://achievethecore.org/pag e/1032/multi-digit- multiplication-using-the- standard-

algorithm-mini- assessment

2639 x 29 =? , 3051 x 882 =?

826 x 3569 =?

Number Talk

Direct Instruction

Option 1 - EngageNY

Option 2 – NJCTL

Option 3 - MyMath Centers

Teacher Center – The teacher works groups of 1-4 students.

Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.). 2639 x 29 =? 3051 x 882 =? 826 x 3569 =?

Individual Center – Students focus on skills based on EdConnect and PARCC data. Use Achieve the Core Coherence Map to guide remediation.

Technology Center

Manipulative Center – Students use tools, such as base 10 blocks

Interdisciplinary Center – Students complete math problems interconnected with another subject

Review Classwork

Exit Ticket PARCC Released Items 2016,

Item #7 http://tinyurl.com/2016PARCCr

eleaseditems

During grade level meetings, teacher PLCs agree on common classwork questions, referring to column 5.


Illustrative

Mathematics:

5.NBT.B.5 Elmer's

Multiplication Error

EngageNY Math, 2016,

Module 2, Topic B (lessons 3-8) https://www.engageny.org/resource/grade-5-

mathematics-module-2-topic-b-lesson-8

PARCC Released Items EOY #1, 3 & 17 http://tinyurl.com/gr5PARCC-

EOYreleased2015

Illustrative Mathematics:

5.NBT.B.5 Elmer's Multiplication Error


map/#5/22

MyMath (Teacher login available) Ch.2

Lessons 6-10 Use Partial Products…


The Partial Products algorithm https://www.sophia.org/search?q=Par

tial%20products%20algorithm

Why learn the partial products algorithm?

1. Students are still developing a sense of

place value, and partial products helps

students better understand place value

than the standard algorithm.

2. The partial products algorithm closely

matches ways people think about

numbers; mental computation easy.

3. The partial products algorithm is

clearly connected to the distributive

property a(b+c) = ab+ac .

4. The partial products algorithm closely

aligns with the ways people handle

algebraic expressions.

Grade 5 Math-Touchpoint- 5.NBT.5

A book company printed 452

books. Each book had 150

pages. How many pages did

the book company print?

There are 225 dozen

cookies in the bakery.

How many cookies

are there?

http://achievethecore.org/page/1032/multi-digit-multiplication-using-the-standard-algorithm-mini-assessment









https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-b-lesson-8




https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812




https://www.sophia.org/search?q=Partial%20products%20algorithm

https://www.sophia.org/search?q=Partial%20products%20algorithm

CAR © 2009


5.NBT.B.6 - 5 days

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 calculating using

equations, rectangular

arrays, and/or area models.

(MAJOR content)

Claim: Students use division

strategies based on place value,

properties of operations and the

relationship between multiplication

& division to find quotients of whole

numbers with up to 4-digit dividends

and 2-digit divisors

Evidence: Students represent and

explain calculations w/ equations,

rectangular arrays & area models.

Connect diagrams of concrete

referents to symbolic expressions.

Tasks: involve 3- or 4-digit

dividends & 1- or 2- digit divisors.

Performance: students check

reasonableness of answers using

multiplication or area models/arrays

Number Talks

Direct Instruction

Option 1 EngagneNY

Option 2 NJCTL

Option 3 MyMath Centers


Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (benchmarks, PARCC, etc)

Individual work center

Technology center

Review Classwork

Exit Ticket

PARCC Released Items 2016, Item #18b


During PLC meetings, teachers agree on common classwork questions similar to ones in column 5.

Metacognitive thinking – students self- assess during wait time. does

this answer make sense?” Personal mastery (out-do yourself)

NJCTL Division Presentation 2015-11-25, (Patterns in Mult& Division:slides 124-184)

https://njctl.org/courses/math/5th-grade-math/division/attachments/unit-3-

division/ EngageNY 2016,

Module 2, Topics E & F (lessons 17-23)

Multi-digit whole number division

Mental strategies (1-2 days) https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-e-overview

Partial quotients (3-4 days) https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-f-overview

MyMath (Teacher login available) Ch.3 Lessons 7 &8, Ch.4 Lessons 1-6

www.connected.mcgraw-hill.com Achieve the Core Coherence Map http://achievethecore.org/coherence-map/#5/22

2682 ÷ 25 =

(2000 + 600 + 80 + 2) ÷ 25 25 x n = 2682

25 x 100 = 2500

2682-2500 = 182

25 x m=182

25 x 7 = 175

182-175= 7 remainder… So 25 x 107 = 2500+175 + 7

1,716 students participate in Field Day.

Each team has 16 students.How many

teams get created? What to do with any

left over students?

There are 100 16’s in 1,716

Grade 5 Math- Touchpoint-5.NBT.6

PARCC Released Items EOY #12 http://tinyurl.com/gr5PARCC-

EOYreleased2015

Each ticket for a concert cost $14. The amount of ticket sales for the concert was $8,792. How many tickets were sold?

Common Core Sheets http://www.commoncoresheets.com /SortedByGrade.php?Sorted=5nbt6

9984 ÷ 6

1716 -1600

100

116 80

5

36 -32

2

4






https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-e-overview

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-e-overview

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-f-overview

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-f-overview





http://www.commoncoresheets.com/SortedByGrade.php?Sorted=5nbt6


CAR © 2009



Read, write, and compare

decimals to thousandths.

(MAJOR 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).

5.NBT.A.3b. Compare

two decimals to thousandths based on

meanings of the digits in

each place, using >, =, &

< symbols to record the

results of comparisons. -------------------------------------------------------------------------------------

Claim: students compare two

decimals to thousandths using >, =,

and < in expanded form, number

names and/or base 10 numerals.

Evidence: students use >, =, and <

symbols to represent numbers to the

thousandths in multiple (different)

forms, including base 10 numerals,

expanded form & number names.

Tasks: mixture of #representations

reflects conceptual understanding.

Performance: students read, write

& compare decimals to any place

using >, =, <, expanded form,

number names and numerals.

Number Talk

Direct Instruction

Option 1 - EngageNY

Option 2 – NJCTL




Individual Center – Students focus on skills based on EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.

Technology Center –

Manipulative Center – Students use tools, such as base 10 blocks & etc., to solve problems.


Review Classwork Exit Ticket PARCC Released Items 2016,

Items #5 & 6 http://tinyurl.com/2016PARCCr

eleaseditems



Illustrative

Mathematics:

5.NBT.A.3 Placing

Thousandths on the

Number Line

EngageNY 2016 Module 1, Topic B (lessons 5-6)

https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-b-overview

NJCTL Decimal Concepts Presentation 2015-11-16, (slides 56-93 & 94-126)


MyMath (Teacher login available) Ch.1 Lesson 6 Place Value through the

Thousandths



5.NBT.A.3 Placing Thousandths on the

Number Line

Achieve the Core Coherence Map


Use the same blocks 2 different ways:

Thousands Hundreds Tens

1000 100 10 (100)10 (10)10 (1)10

1000(1/1000) 10(1/100) 100(1/10) 1 1/10 1/100

1.0 0.1 0.01 One One-tenth One-

hundredth

Grade 5 Math- Touchpoint-5.NBT.3














CAR © 2009



Use place value

understanding to round

decimals to any place.

(MAJOR content) ------------------------------------------ Claim: students round decimals to

any place value.

Evidence: students use

understanding of place value to

round decimals to any place.

Tasks: have thin or no context.

Performance: students round

decimals to any place and choose

appropriate context given a rounded

number.

Number Talk

Direct Instruction

Option 1 - Eureka Math modules

Option 2 – SMART Presentation NJCTL











Illustrative

Mathematics:

5.NBT.A.4

Rounding to Tenths

and Hundredths

EngageNY, 2016 Module 1, Topic C (lessons 7- 8)

https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-c-overview

NJCTL Decimal Concepts Presentation 2015-11-16, (slides 127-178)


PARCC Released Items, EOY Item #28


MyMath (Teacher login available) Ch.5 Lesson 1 Rounding Decimals


Illustrative Mathematics 5.NBT.A.4 Rounding to Tenths and

Hundredths


map/#5/22

Common Core Sheets

http://www.commoncoresheets.com/Sorte

dByGrade.php?Sorted=5nbt4

MyMath (Teacher login available) Ch. Lesson Pl


NJCTL Math Labs


Gr 5 Math- Touchpoint-5.NBT.4


















CAR © 2009

NJSLS.MATH.CONTENT.5.OA.1

5.OA.A.1 - 1 day (integrate into major content,

i.e., 5.NBT.A.3, 5.NBT.B.5)

Use parentheses, brackets,

or braces in numerical

expressions, and evaluate

expressions with these

symbols.

(Additional content)

Claim: students evaluate numerical

expressions containing parentheses,

brackets and braces.

Evidence: students can use nested

grouping symbols (parentheses,

brackets or braces) to evaluate

numerical expressions: for example

3 x [5 + (7 - 3)].

Tasks: Depth of nested grouping

symbols no greater than two; e.g.

3 x [6-(2+4)] ok because it has only

two sets of parenthesis or brackets.

However, 3 x [6-(2+{5-1})] has

three sets of grouping symbols, so it

is not ok.

Performance: students write and

evaluate numerical expressions w/

parentheses, brackets or braces of no

greater depth than two.

Number Talk

Direct Instruction

Option 1 - EngageNY

Option 2 – SMART Presentation NJCTL











Are we working from the inside-out?

Illustrative

Mathematics

5.OA.A.1 Using

Operations and

Parentheses

5.OA.A.1 Watch out

for Parentheses 1

Incorporate this standard into major content during one

instructional session. EngageNY, 2016 Module 4, Topic D

(lesson 10) https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-d-lesson-10

NJCTL Algebraic Concepts Presentation 2015-11-16, (slides 24-57)

https://njctl.org/courses/math/5th-grade-math/algebraic-concepts/

2 x (8 + 7) means:

“add 8 and 7, then multiply by 2” or

“2 times the quantity of 8 & 7.”

3 x (18932 + 921) means:

“three times as large as 18932 + 921”

MyMath (Teacher login available) Ch.7 Lesson 2 Order of Operations



5.OA.A.1 Using Operations and

ParenthesesD

5.OA.A.1 Watch out for Parentheses 1


http://achievethecore.org/coherence-

map/#5/24

Gr 5 Math- Touchpoint-5.OA.1

Hint: pinch your fingers together, then slowly open them apart. This is how we work from the “inside” of an expression “out.”









https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-d-lesson-10

https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-d-lesson-10








CAR © 2009

NJSLS.MATH.CONTENT.5.OA.2

5.OA.A.2 - 2 days (incorporate into major content,

i.e., 5.NBT.B.5, 5.NBT.6)

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.

(Additional content) ------------------------------------------ Claim: students write simple

numerical expressions when given

verbal descriptions or word

problems, without evaluating

(simplifying) them.

Evidence: students can write simple

expressions which record

calculations with numbers.

Tasks: to express the calculation,

“add 5 and 6, then multiply by 3,”

students write 3x(5+6). integrated

into major content, where possible.

Performance: Students interpret

numerical expressions without

evaluating them.

Number Talk

Direct Instruction

Option 1 – EngageNY

Option 2 – NJCTL




Individual Center – Students focus on skills. Use Achieve the Core Coherence Map to guide remediation.


Manipulative Center – Students use tools, such as base 10 blocks etc., to solve problems.

Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories.

Review Classwork Exit Ticket PARCC Released Items 2016,

Item #14 http://tinyurl.com/2016PARCCr

eleaseditems



Incorporate this standard into major content instruction over the course of 2 days.

EngageNY, 2016 Module 2, Topic B (lesson 6)

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-

b-lesson-6

NJCTL Algebraic Concepts Presentation 2015-11-16, (slides 58-92)


MyMath (Teacher login available) Ch.7

Lessons 3 & 4 Numerical Expressions



http://achievethecore.org/coherence-

map/#5/24

“double five and then add 26”

(2x5) +26 = 2x5 + 26

5(10 x 10)

“5 groups of (10 x 10)”

3(100) + 3(10) + 3(1)

3(100 + 10 + 1)

2(5+13)

Gr 5 Math- Touchpoint-5.OA.1 Grade 5 Math – – 5.OA.1











CAR © 2009

Summative Written Assessments

Quarterly Assessment in EdConnect

Summative Performance Assessment

Quarterly Constructed Response in EdConnect

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UNIT 1 - Trenton Public Schools

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