Northfield Community School
Math Curriculum
Unit Title: Number and Operations in Base Ten
Unit 1
Grade Level: 5
Summary of Unit: The focus of this unit is to develop place-value concepts for whole
numbers through billions and decimals through thousandths.
Add, subtract, multiply and divide decimals through hundredths.
Stage 1 – Desired Results
CCSS for Mathematical Practices:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
CCSS for Mathematical 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.
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.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.
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard
algorithm.
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.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.
Understandings (ENDURING)









The base ten number system
and decimals are related.
There is more than one way
to represent numerical
values.
Estimation is an important part
of our real world application of
math.
The process of estimating uses
rounding.
Rounding is necessary in real-life
applications such as monetary
calculations.
The location of a decimal
point determines the size of a
number.
The place-value structure of
decimals and use this structure
to read, write, and compare
decimals.
Decimals are rounded in a way
that is similar to the way whole
numbers are rounded.
Decimal numbers can be rounded
to an estimate when exact numbers
are not needed for the situation at
hand.
Essential Question(s):














Operation strategies with

What is the value of a place?
What is a number and how does
it act?
How do you compare numbers?
Why do we have rules in math?
How do we use basic facts in
real life?
Why does placement or position of
a number matter?
How is place value different
from number value?
How is the ordering of
decimals the same as ordering
whole numbers and how is it
different?
How do operations with decimals
compare to operations with whole
numbers?
How are the four basic
operations related to one
another?
How can estimation skills and
algorithms reinforce one
another?
How do number properties assist
in computation?
What determines a reasonable
estimation for a given situation?
What is the purpose of














decimals are similar to those used
with whole numbers.
You can add or subtract whole
numbers by breaking apart
numbers using place value.
Adding and subtracting decimals
is similar to adding and
subtracting whole numbers.
Our number system is based
on groups of ten.
Place value can help us compare
and order numbers.
Decimal place value is an extension
of whole-number place value,
which is based on groups of ten.
Place value can be used to write
numbers in different but
equivalent forms.
Multiplying whole numbers
and decimals is similar to
multiplying whole numbers.
Multiplying decimals by
decimals is similar to
multiplying whole numbers.
Multiplication and division
are inverse operations of each
other. Rules for
multiplication and division of
whole numbers also apply to
decimals.
Division facts can be
extended by using patterns
and place value.
Divisibility rules can help in
solving some problems
mentally.
To find quotients you can use a
process that involves estimation,
multiplication, and subtraction.
The steps for dividing do not
change when there are zeros in
the quotient.
Checking your answer against the
problem helps you to know if you















estimation?
What are some ways to represent
large numbers?
How can you represent
decimals?
What are equivalent decimals?
How are place values related?
How can you name the same
number in different ways?
Why add? How can you add
mentally? How can you
subtract mentally?
How can you round whole
numbers and decimals?
How can you estimate sums?
How can you estimate
differences?
How do you add and
subtract whole numbers?
How can you add and subtract
decimals?
How do symbols help us
to communicate in math?
How do I know if my
answer makes sense?
Why do we need to know how
to estimate and do math “in our
heads?”
How does the location of digit
in the number affect the size of
a number?
How do we solve real world
application problems?
answered the right question, if you
used the right information, and if
your answer is reasonable.
Students will be able to:

























Read decimal numbers through thousandths from written words or placevalue format.
Write decimal numbers through thousandths from written words or from
decimal numbers presented
Round decimal numbers to any place.
Identify the symbols for the terms greater than, less than, and equal to.
Compare the value of two decimal numbers through thousandths, using the
symbols >, <, or =.
Write the standard, word and expanded forms of whole numbers to billions
and identify the value of digits in whole numbers.
Compare and order numbers through millions.
Write decimals in standard, whole and expanded form through thousandths,
identify the value of digits in decimal numbers and name equivalent decimals.
Compare and order decimals through thousandths.
Use place-value ideas to write multiples of 100, 1000, and 10,000 in different
ways.
Compute sums and differences mentally using the commutative and
associative properties of addition, compatible numbers and compensation and
by counting up.
Round whole numbers through millions and decimals through thousandths.
Use rounding to estimate sums and differences of whole numbers and
decimals.
Compute sums and differences of two whole numbers greater than 10,000.
Compute sums of decimals involving tenths, hundredths, and thousandths.
Compute differences of decimals, involving tenths, hundredths, and
thousandths.
Estimate products and quotients with numbers up to ten-thousands.
Mentally compute products of whole numbers using patterns of multiplication
properties.
Use rounding and compatible numbers to estimate products of whole numbers
and products of decimals, and identify estimates as overestimates or
underestimates.
Use the standard algorithm to multiply whole numbers with multi-digits.
Mentally multiply any decimal by a power of ten.
Use rounding to estimate products of decimal numbers.
Use standard algorithm to find whole number quotients for numbers up to a
four digit dividend and a two digit divisor.
Illustrate and explain calculations using models, arrays and equations.
Give appropriate strategies and alternate strategies for solving word




problems.
Tell in words what is known and what needs to be determined in given word
problems
Tell whether and why the work shown for given problems is correct or
not.
Checking your answer against the problem helps you to know if you answered
the right question, if you used the right information and if your answer is
reasonable.
Review and apply key concepts, skills, and strategies learned in this and
previous units.
Stage 2 – Assessment Evidence
Assessment Evidence will be comprised of, but not limited to, the following
suggested activities:
Performance Task(s):
Title:
High Roller Revisited
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial, Bodily/Kinesthetic
Students will work in groups of two to four to play the game “High Roller
Revisited.” Roll a die nine times. Use the nine numbers to make the greatest number
possible. Record your number in one of the nine boxes after each roll. Once your
number is written down you may not make changes to your number. Pass the die to
the next student and continue to play until all students in the group have had five
turns to roll the die.
Create a game board or chart with boxes in a row labeled with the place value from
millions to hundredths with 5 blank rows underneath for students to fill in their
numbers.
After all nine rolls have been completed, the students compare with their group
members to determine who came up with the greatest number. The game should be
played multiple times for students to begin to develop strategies for
number placement.
Students should discuss their strategies for playing the game. Different types of die
could be used. For example, instead of the traditional 1-6 die, students could use
0-5 or 5-9 dice. After the game is played several times, students should discuss what
they figured out about playing the game. Also, students should discuss what
problems they encountered when playing the game. Problems could include rolling
lots of small numbers and deciding where to place them, rolling a 3 and its
placement.
Questions to ask the students:
What do you do with a 1 if the ones place is already
filled? How do you decide where to place a four?
Extension: Have students write about the strategies they use to play the game.
Encourage them to write all they can about what strategies they use when they play.
Suggestions: Students could also try to make the least number by playing the game
“Low Roller.” Players could keep score of who had the greatest or least number
during the game. Students could be required to write the word name for each number
they built using both words and expanded notation.
Websites: AAA Math:
Interactive mathematical practice opportunities with place value of
decimals
http://www.aaamath.com/plc51b-placevalues.html
Title:
No Bones About It
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Jane goes to the grocery store to buy bones for her dog. The butcher tells her that
bones come in 3- pound packages for $4.50 or in 5-pound packages for $6.58.
Jane wants at least 17 pounds of bones. How many packages of each size should
she purchase to get the best buy?
Make a table to organize your work. Answer using complete sentences.
Title:
Punctuality
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Josh’s watch loses 3.75 seconds every hour. He didn’t notice this until he was 18
minutes late for an important meeting one day. How many days has Josh’s watch
been losing time?
Write a full explanation of your answer including all calculations used to solve.
Title:
The Allowance
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
After a boy complains for several days about his allowance, his father tells the boy
that he will give him a choice. If he agrees to do his chores every day, the father
will increase his allowance. However, the boy must choose between two payment
plans.
Plan A: $15.00 per month for one year
Or
Plan B: $0.01 on the first week, $0.02 on the second week, $0.04 on the third
week, $0.08 on the fourth week, $0.16 on the fifth week, and so on for one year.
The boy chase Plan A.
Explain why this was a mistake. Use a table to organize the work for Plan B.
Title:
Select A Sign
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Group the digits by adding operational signs
1
2
3
4
5
6
7
8
9
= 100
Record all of your trials and show your final answer.
Title:
Race Day
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
The winner of a 26-mile marathon averaged a speed of 1 mile every 6 minutes.
How much longer did it take the 50th finisher to complete the race if he or she ran
1
at a speed of one mile in 6 2 minutes?
Write a full explanation of your answer including all calculations used to solve.
Title:
Miniature Tree Height Project
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Karen, Lou, and Jeff each bought a miniature tree. They measured the height of
their trees once a month over the five months from December to April.
Miniature Tree Height (m)
Karen’s Tree
Lou’s Tree
Jeff’s Tree
December
0.794
0.510
0.788
January
0.932
0.678
0.903
February
1.043
0.84
1.22
March
1.356
1.34
1.452
April
1.602
1.551
1.61
Interpret the data in the table above to answer the following questions:
1.
2.
3.
4.
5.
Title:
Who had the tallest tree at the beginning?
Whose tree was the tallest at the end of April?
Whose tree grew fastest during the first month?
Whose tree grew by the most from December to April?
Predict whose tree will reach 2 meters in height first.
How Much Flour?
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Julie has a bread recipe that calls for 1.75 pounds of flour.
She wants to make this recipe three times. How much flour does she need?
She has no flour at home. How many 5-pound bags of flour should she buy to
make the recipe three times?
A ton is 2,000 pounds. Estimate how many loaves of bread she could make a ton
of flour?
Write a full explanation of your answer including all calculations used to solve.
Title:
The Dilemma At The Deli Counter
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
In a grocery store, all of the scales measure in decimals. Explain or draw diagrams
to show your reasoning for the following situations.
1. Ricardo buys 3.2 ounces of a sliced Italian ham called prosciutto (pruh
SHOO toh) to make sandwiches. Each sandwich uses 0.4-ounce slice of
prosciutto. How many sandwiches can he make?
2. Ms. Difanis buys 11.6 pounds of hamburger for a cookout. How many
quarter-pound (0.25) burgers can she make?
3. Write a number sentence that shows the operations you would use to find
your solutions in parts 1 and 2.
4. The answer to part 2 is not a whole number. What does the answer mean?
Title:
Leah’s Lengthy Trip
Bloom’s Taxonomy: Analysis & Evaluation
Gardner’s MI: Logical/Mathematical, Visual/Spatial
Leah filled her gas tank at the start of a trip and noted that her mileage indicator
read 15,738.1 miles. When her mileage indicator read 16,167.6, she needed gas
again. It took 18.2 gallons of gas to fill the tank. About how many miles did her
car go on each gallon?
Write a full explanation of your answer including all calculations used to solve.
Performance Task Rubric
General Scoring Rubric (to be used for all applicable tasks):
Score of 3: Student shows a correct and/or appropriate answer and shows work
and/or an explanation that demonstrates full and complete understanding.
Score of 2: Student has minor flaws in the answer, but the work and/or
explanation is acceptable and the reasoning is appropriate.
Score of 1: Student does not have a reasonable explanation or show sufficient
work, resulting in a demonstration of only limited understanding.
Score of 0: Student shows no understanding of the problem or how to arrive at a
solution.
OTHER EVIDENCE:
Daily Warm-Up and Open-Ended Questions
Daily Homework
Observation of Classroom Activities
Quizzes
Tests
Diagnostic Assessments
District Assessments
State Assessments
Student Reflection and Self-Assessment
Reflection is an essential component of effective self-assessment; it occurs “when
students think about how their work meets established criteria; they analyze the
effectiveness of their efforts, and plan for improvement”
Students will revisit the essential question for each section to explain what they
have learned, enhance their level of comprehension, apply the concepts, gain
knowledge, and reflect upon what they now understand.
In an effort to self-assess, students will reflect upon some or all of the following:
 What did I learn today?
 What did I do well?
 What am I confused about?
 What do I need help with?
 What do I want to know more about?
 What am I going to work on next?
Stage 3 – Learning Plan
Select a performance task from Stage 2 based on individual progress in this unit.
Day 1- Introduction to Chapter 1
Day 2- Lesson 1.1 Place Value and Patterns
Recognize the 10 to 1 relationship among place-value positions.
Day 3- Lesson 1.2 Place Value of Whole Numbers
Read and write whole numbers through hundred millions.
Day 4- Lesson 1.3 Algebra- Properties
Use properties of operations to solve problems.
Day 5- Lesson 1.4 Algebra- Powers of 10 and Exponents
Write and evaluate repeated factors in exponent form.
.Day 6- Lesson 1.5 Algebra- Multiplication Patterns
Use a basic fact and a pattern to multiply mentally by multiples of 10, 100, and
1,000.
Day 7- Mid-Chapter Checkpoint- Quiz on Lessons 1.1 through 1.5
Day 8- Lesson 1.6 Multiply by 1-Digit Numbers
Multiply by 1-digit numbers.
Day 9- Lesson 1.7 Multiply by 2-Digit Numbers
Multiply by 2-digit numbers.
Day 10- Lesson 1.8 Relate Multiplication to Division
Use multiplication to solve division problems.
Day 11- Lesson 1.9 Problem Solving- Multiplication and Division
Use the strategy solve a simpler problem to solve problems.
Day 12- Review on Lessons 1.1 through 1.9
Day 13- Chapter Test Lessons 1.1 through 1.9
Day 14- Introduction to Chapter 2
Day 15- Lesson 2.1 Place the First Digit
Place the first digit in the quotient by estimating or using place value.
Day 16- Lesson 2.2 Divide by 1-Digit Divisors
Divide 3- and 4- digit dividends by 1-digit divisors.
Day 17- Lesson 2.3 Investigate- Division with 2-Digit Divisors
Model division with 2-digit divisors using base-ten blocks.
Day 18- Lesson 2.4 Partial Quotients
Use partial quotients to divide by 2-digit divisors.
Day 19- Mid-Chapter Checkpoint- Quiz on Lessons 2.1 through 2.4
Day 20- Lesson 2.5 Estimate with 2-digit Divisors
Estimate quotients using compatible numbers.
Day 21- Lesson 2.6 Divide by 2-Digit Divisors
Divide by 2-digit divisors.
Day 22- Lesson 2.7 Interpret the Remainder
Solve division problems and decide when to write a remainder as a fraction.
Day 23- Lesson 2.8 Adjust Quotients
Adjust the quotient if the estimate is too high or too low.
Day 24- Lesson 2.9 Problem Solving- Division
Solve problems by using the strategy draw a diagram.
Day 25- Review on Lessons 2.1 through 2.9
Day 26- Chapter 2 Test
Day 27- Introduction to Chapter 3
Day 28- Lesson 3.1 Investigate- Thousandths
Model, read and write decimals to thousandths.
Day 29- Lesson 3.2 Place Value of Decimals
Read and write decimals through thousands.
Day 30- Lesson 3.3 Compare and Order Decimals
Compare and order decimals to thousandths using place value.
Day 31- Lesson 3.4 Round Decimals
Round decimals to any place.
Day 32- Lesson 3.5 Investigate- Decimal Addition
Model decimal addition using base-ten blocks.
Day 33- Lesson 3.6 Investigate- Decimal Subtraction
Model decimal subtraction using base-ten blocks.
Day 34- Mid-Chapter Checkpoint- Quiz on Lessons 3.1 through 3.6
Day 35- Lessons 3.7 Estimate Decimals Sums and Differences
Make reasonable estimates of decimal sums and differences.
Day 36- Lessons 3.8 Add Decimals
Add decimals using place value.
Day 37- Lesson 3.9 Subtract Decimals
Subtract decimals using place value.
Day 38- Lesson 3.10 Algebra- Patterns with Decimals
Identify, describe, and create numeric patterns with decimals.
Day 39- Lesson 3.11 Problem Solving- Add and Subtract Money
Solve problems using the strategy make a table.
Day 40- Lesson 3.12 Choose A Method
Choose a method to find a decimal sum or difference.
Day 41- Review on Lessons 3.1 through 3.12
Day 42- Chapter 3 Test
Day 43- Introduction to Chapter 4
Day 44- Lesson 4.1 Algebra- Multiplication Patterns with Decimals
Find patterns in products when multiplying by powers of 10.
Day 45- Lesson 4.2 Investigate-Multiply Decimals and Whole Numbers
Model multiplication of whole numbers and decimals.
Day 46- Lesson 4.3 Multiplication with Decimals and Whole Numbers
Multiply a decimal and a whole number using drawings and place value.
Day 47- Lesson 4.4 Multiply Using Expanded Form
Use expanded form and place value to multiply a decimal and a whole
number.
Day 48- Lesson 4.5 Problem Solving- Multiply Money
Solve problems using the strategy draw a diagram to multiply money.
Day 49- Mid-Chapter Checkpoint- Quiz on Lessons 4.1 through 4.5
Day 50- Lesson 4.6 Investigate- Decimal Multiplication
Model multiplication of decimals.
Day 51- Lesson 4.7 Multiply Decimals
Place the decimal point in decimal multiplication.
Day 52- Lesson 4.8 Zeros in the Product
Multiply decimals with zeros in the product.
Day 53- Review on Lessons 4.1 through 4.8
Day 54- Chapter 4 Test
Day 55- Introduction to Chapter 5
Day 56- Lesson 5.1 Algebra-Division Patterns with Decimals
Find patterns in quotients when dividing by powers of 10.
Day 57- Lesson 5.2 Investigate- Divide Decimals by Whole Numbers
Model division of decimals by whole numbers.
Day 58- Lesson 5.3 Estimate Quotients
Estimate decimals quotients.
Day 59- Lesson 5.4 Division of Decimals by Whole Numbers
Divide decimals by whole numbers.
Day 60- Mid-Chapter Checkpoint- Quiz on Lessons 5.1 through 5.4
Day 61- Lesson 5.5 Investigate- Decimal Division
Model Division by decimals.
Day 62- Lesson 5.6 Divide Decimals
Place the decimal point in decimal division.
Day 63- Lesson 5.7 Write Zeros in the Dividend
Write a zero in the dividend to find a quotient.
Day 64- Lesson 5.8 Problem Solving- Decimal Operations
Solve multistep decimal problems using the strategy work backward.
Day 65- Review on Lessons 5.1 through 5.8
Day 66- Chapter 5 Test
Unit Resources/References Needed:
Textbook References:
Go Math! -Grade 5 Houghton Mifflin Harcourt Publishing Company
Chapters 1 through 5
Materials Needed:
Printed Materials from Go Math! Grade 5
Connected Mathematics 2- Bits and Pieces II- Computing With Decimals and
Percents by Lappan, Fey, Fitzgerald, Friel, Phillips
Common Core State Standards
National Council for Teachers of Mathematics Standards
Various Materials for Performance Tasks and Instructional Activities
SMART Technology
Technology Integration:
Go Math! Grade 5 Online, http://www-k6.thinkcentral.com
www.hmheducation.com/gomath
www.smckids.com
Illuminations activities on for Grade 5.
http://illuminations.nctm.org/Activities.aspx?grade=2
SMART Software and Hardware Products
SMART Exchange
http://exchange.smarttech.com/#tab=0
IXL Math – Practice and Lessons
http://www.ixl.com/
Research, Development and Accountability, Mathematics Performance Task Bank
ww.rda.aps.edu/mathtaskbank/fi_html/pfactask.htm
AAA Math:
Interactive mathematical practice opportunities with place value of
decimals
http://www.aaamath.com/plc51b-placevalues.html
Illuminations activities on Number Sense and Operations
http://illuminations.nctm.org/WebResourceList.aspx?Ref=2&Std=0&Grd=0
NCTM Technology Principles and Standards for School Mathematics
http://standards.nctm.org/document/eexamples/index.htm#6-8
4. INDIVIDUAL ACCOMMODATIONS
Extra support:
Refer to Houghton Mifflin Harcourt Go Math! Grade 5 Mathematics Teacher’s Edition for
“Extra Support.” The section labeled “If students need lesson support…” provides resources
by chapter for those who need additional assistance. If time and supervision allows, break
students into small groups and re-teach the lesson. Have the students work together in pairs or
small groups to try to work through the problems. Use appropriate manipulatives to explain
the concepts in a different way.
Enrichment or early finishers:
Refer Houghton Mifflin Harcourt Go Math! Grade 5 Mathematics Teacher’s Edition for
“Enrichment Strategies.” The section labeled “If students are ready for enrichment…”
provides resources by chapter for enrichment and extension. If time and supervision allows,
give students the opportunity to peer tutor students who are struggling. This will allow
students to demonstrate what they have learned. Completion of IXL topics will reinforce and
introduce concepts.
Various Learning Styles:
Refer to Houghton Mifflin Harcourt Go Math! Grade 5 Mathematics Teacher’s Edition for
“Differentiated Instruction.” Teach each lesson with components that appeal to students
various learning styles. Focus on kinesthetic, auditory, visual, and tactile. If time and
resources allow, employ the use of manipulatives, math journals, modeling, group discussions,
and other appropriate types of alternative assessment.
Limited English proficiency:
Refer Houghton Mifflin Harcourt Go Math! Grade 5 Mathematics Teacher’s Edition for
“Language Support”. Ensure that vocabulary is previewed with the student. If possible,
provide pictures for the student to help reinforce the vocabulary.
5. TEACHER REFLECTION







Were my students talking about the subject, or was I doing all of the talking and
students were just listening to me?
Were my students engaged at the beginning of the lesson?
How much time did I spend reviewing homework, and how much time did I spend on
new material?
Did the students respond to “How” and “Why” questions?
Did my students have an opportunity to discuss and/or write about the topic?
What changes would I make next time the lesson is taught?
What steps do I need to take next in this topic?