Curriculum Map: Grade 4 Math 2014
Course: Math 4 Blue
Subtopic: General
Grade(s): None specified
Unit: Chapter 1: Place Value, Addition, and Subtraction to One Million
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-T.1.1.1 (Advanced) Demonstrate an understanding that in a multi-digit whole number (through 1,000,000), a
digit in one place represents ten times what it represents in the place to its right. Example:
Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens
place.
M04.A-T.1.1.2 (Advanced) Read and write whole numbers in expanded, standard, and word form through 1,000,000.
M04.A-T.1.1.3 (Advanced) Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in
each place, using >, =, and < symbols.
M04.A-T.1.1.4 (Advanced) Round multi-digit whole numbers (through 1,000,000) to any place.
M04.A-T.2.1.1 (Advanced) Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and
including 1,000,000).
Big Ideas: Students will understand that:
Essential Questions:
Place value can be used to compare, add, subtract, and estimate with How can you.......... whole numbers.
describe the value of a digit, read and write numbers through hundred thousands, compare and order numbers, round numbers, rename a whole number, add whole numbers, subtract whole numbers, and use the strategy draw a diagram to solve comparison problems
with addition and subtraction?
Concepts:Students will know...
Competencies (including Transfer goals):Students will be able
Place Value to One Million to independently use their learning to...
Addition of Whole Numbers
Model the 10-to 1 relationship among place-value positions in the
Subtraction of Whole Numbers
base-ten number system.
Read and write whole numbers in standard form, word form, and
expanded form.
Compare and order whole numbers based on the values of the digits
in each number.
Round a whole number to any place.
Rename whole numbers by regrouping.
Add whole numbers and determine whether solutions to addition
problems are reasonable.
Subtract whole numbers and determine whether solutions to
subtraction problems are reasonable.
Use the strategy draw a diagram to solve comparison problems with
addition and subtraction.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Page 1 of 28
Online Skills Practice
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Place Value Whiteboards
Rounding by thinking of a number line
Number tile activities
Read and write numbers
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Place Value Whiteboards
Number Tile Activities
Page 2 of 28
Unit: Chapter 2: Multiply by 1 - Digit Numbers
Subject: Mathematics
Timeline: 3 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-T.2.1.2 (Advanced) Multiply a whole number of up to four digits by a one-digit whole number and multiply 2
two-digit numbers.
M04.A-T.2.1.4 (Advanced) Estimate the answer to addition, subtraction, and multiplication problems using whole
numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding
powers of 10).
M04.B-O.1.1.1 (Advanced) Interpret a multiplication equation as a comparison. Represent verbal statements of
multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 * 7 as
a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know
that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 *
8 or 24 = 8 * 3.
M04.B-O.1.1.2 (Advanced) Multiply or divide to solve word problems involving multiplicative comparison,
distinguishing multiplicative comparison from additive comparison. Example: Know that 3 *
4 can be used to represent that Student A has 4 objects and Student B has 3 times as many
objects not just 3 more objects.
Big Ideas: Students will understand that:
There are many strategies to chose from to multiply by 1-digit
numbers.
Concepts:Students will know...
Strategies to multiply by 1-digit numbers.
*The Distributive Property *Expanded Form
*Place Value and Partial Products
*Mental Math and Properties
Essential Questions:
How can you.........
model multiplication comparisons,
estimate products by rounding and determine if exact answers are
reasonable,
use the Distributive Property to multiply a 2-digit number by a 1-digit
number,
use expanded form to multiply a multi-digit number by a 1 digit
number,
use place value and partial products to multiply by a 1-digit number,
use mental math and properties to help you multiply numbers,
use regrouping to multiply a 2-digit number by a 1-digit number,
use regrouping to multiply,
and represent and solve multistep problems using equations?
When can you use the draw a diagram strategy to solve a multistep
multiplication problem?
How does a model help you solve a comparison problem?
How does understanding place value help you multiply tens,
hundreds, and thousands?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
Relate multiplication equations and comparison statements.
Solve problems involving multiplicative comparison and additive
comparison.
Multiply tens, hundreds, and thousands by whole numbers through
10.
Estimate products by rounding and determine if exact answers to
multiplication problems are reasonable.
Use the Distributive Property to multiply a 2-digit number by a 1-digit
number.
Use expanded form to multiply a multi-digit number by a 1-digit
number.
Use place value and partial products to multiply a multi-digit number
by a 1-digit number.
Use mental math and properties to multiply a multi-digit number by a
1-digit number. Use the draw a diagram strategy to solve multistep problems.
Use regrouping to multiply a 2-digit number by a 1-digit number.
Use regrouping to multiply a multi-digit number by a 1-digit number.
Represent and solve multistep problems using equations.
Page 3 of 28
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 4 of 28
Unit: Chapter 3 - Multiply 2-Digit Numbers
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-T.2.1.2 (Advanced) Multiply a whole number of up to four digits by a one-digit whole number and multiply 2
two-digit numbers.
Big Ideas: Students will understand that:
There are many strategies that can be used to multiply 2-digit
numbers.
Essential Questions:
What strategies can you use to multiply by tens?
What strategies can you use to estimate products?
How can you..............
use area models and partial products to multiply 2-digit numbers,
use place value and partial products to multiply 2-digit numbers,
use regrouping to multiply 2-digit numbers,
find and record products of two 2-digit numbers,
use the strategy draw a diagram to solve multistep multiplication
problems?
Concepts:Students will know...
Competencies (including Transfer goals):Students will be able
To multiply by tens
to independently use their learning to...
Estimate products
Use place value and multiplication properties to multiply by tens.
To multiply using partial products
Estimate products by rounding or by using compatible numbers.
To multiply with regrouping
Use area models and partial products to multiply 2-digit numbers.
To chose a multiplication method
Use place value and partial products to multiply 2-digit numbers.
To use multiplication of 2-digit numbers to solve word problems
Use regrouping to multiply 2-digit numbers.
Choose a method to multiply 2-digit numbers.
Use the strategy draw a diagram to solve multistep multiplication
problems.
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use area models and partial product investigation
Page 5 of 28
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 6 of 28
Unit: Chapter 4 - Divide by 1-Digit Numbers
Subject: Mathematics
Timeline: 3 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-T.2.1.3 (Advanced) Divide up to four-digit dividends by one-digit divisors with answers written as wholenumber quotients and remainders.
Big Ideas: Students will understand that:
You will divide by 1-digit numbers.
Essential Questions:
How can you: use multiples to estimate quotients?
use models to divide whole numbers that do not divide evenly?
use remainders in division problems?
divide numbers through thousands by whole numbers through 10?
use compatible numbers to estimate quotients?
use the Distributive Property to find quotients?
use repeated subtraction and multiples to find quotients?
use partial quotients to divide by 1-digit divisors?
use base-ten blocks to model division with regrouping?
use place value to know where to place the first digit in the quotient?
divide multidigit numbers and check your answers?
use the strategy draw a diagram to solve multistep division
problems?
Concepts:Students will know...
Competencies (including Transfer goals):Students will be able
to estimate quotients using multiples
to independently use their learning to...
to investigate remainders
use multiples to estimate quotients
to interpret the remainder
use models to divide whole numbers that do not divide evenly
to divide tens hundreds, and thousands
use remainders to solve division problems
to estimate quotients using compatible numbers
dived tens, hundreds, and thousands by whole numbers through 10
to use the Distributive Property to find quotients
use compatible number to estimate quotients
to divide using repeated subtraction
use the Distributive Property to find quotients
to divide using partial quotients
use repeated subtraction and multiples to find quotients
to model division with regrouping
use partial quotients to divide
to place the first digit
use base-ten blocks to model division with regrouping
to divide by 1-digit numbers
use place value to determine where to place the first digit of a
to use the draw a diagram to solve multistep division problems
quotient
divide multidigit numbers by 1-digit divisors
solve problems by sing the strategy draw a diagram
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Page 7 of 28
Learning Activities:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use Distributive Property, Repeated Subtraction, Partial Quotients, and division models to solve division problems.
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
1.
() Page 8 of 28
Unit: Chapter 5 - Factors, Multiples, and Patterns
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.B-O.2.1.1 (Advanced) Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a
whole number is a multiple of each of its factors. Determine whether a given whole number
in the interval 1 through 100 is a multiple of a given one digit number. Determine whether
a given whole number in the interval 1 through 100 is prime or composite.
M04.B-O.3.1.1 (Advanced) Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
Big Ideas: Students will understand that:
There is a need to find factors and multiples. Number patterns can
be generated and described
Concepts:Students will know...
to model factors
to use divisibility to factor numbers
to use the Make a List strategy to solve problems with common
factors
to relate factors and multiples
to determine if a number is prime or composite
to make and describe patterns
Essential Questions:
How can you:
use models to find factors?
tell whether one number is a factor of another number?
use the make a list strategy to solve problems with common factors?
tell whether a number is prime or composite?
make and describe patterns?
How are factors and multiples related?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
find all factors of a number by using models
determine whether a number is a factor of another number
solve problems by using the strategy make a list
understand the relationship between factors and multiples, and
determine whether a number is a multiple of a given number
determine whether a number is prime or composite
make and describe patterns
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Page 9 of 28
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Factors are Few ……Multiples are Many
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Page 10 of 28
Unit: Chapter 6 - Fraction Equivalence and Comparison
Subject: Mathematics
Timeline: 3 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-F.1.1.1 (Advanced) Recognize and generate equivalent fractions.
M04.A-F.1.1.2 (Advanced) Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the
conclusions.
Big Ideas: Students will understand that:
There are strategies to be used to compare fractions and write
equivalent fractions.
Concepts:Students will know...
to use models to show equivalent fractions
to generate equivalent fractions
to write fractions in simplest form
to write a fractions with a common denominator
to find equivalent fractions with Make a Table strategy
to compare fractions using benchmarks
to compare fractions using common numerators and denominators
to order fractions
Essential Questions:
How can you:
use models to show equivalent fractions?
use multiplication to find equivalent fractions?
write a fraction as an equivalent fraction in simplest form?
write a pair of fractions as fractions with a common denominator?
use the strategy Make a Table to solve problems using equivalent
fractions?
use benchmarks to compare fractions?
compare fractions?
order fractions?
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
use models to show equivalent fractions
use multiplication to generate equivalent fractions
write and identify equivalent fractions in simplest form
use equivalent fractions to represent a pair of fractions as
fractions with a common denominator
use the strategy Make a Table to solve problems using
equivalent fractions
compare fractions using benchmarks
compare fractions by first writing them as fractions with a
common numerator or a common denominator
compare and order fractions
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Page 11 of 28
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use Fraction Bar activities
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
1.
() Page 12 of 28
Unit: Chapter 7 - Add and Subtact Fractions
Subject: Mathematics
Timeline: 3 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-F.2.1.1 (Advanced) Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4,
5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions
as the final answer).
M04.A-F.2.1.2 (Advanced) Decompose a fraction or a mixed number into a sum of fractions with the same
denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the
decomposition by an equation. Justify decompositions (e.g., by using a visual fraction
model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 +
1 + 1/12 = 12/12 + 12/12 + 1/12
M04.A-F.2.1.3 (Advanced) Add and subtract mixed numbers with a common denominator (denominators limited to 2,
3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be
simplified; and no improper fractions as the final answers).
M04.A-F.2.1.4 (Advanced) Solve word problems involving addition and subtraction of fractions referring to the same
whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10,
12, and 100).
Big Ideas: Students will understand that:
You can add and subtract fractions that have the same denominator.
Essential Questions:
When can you add or subtract parts of a whole?
How can you:
write a fraction as a sum of fractions with the same
denominators?
add fractions with like denominators using models?
subtract fractions with like denominators using models?
add and subtract fractions with like denominators?
rename mixed numbers as fractions greater than 1 and rename
fractions greater than 1 as a mixed numbers?
add and subtract mixed numbers with like denominators?
rename a mixed number to help you subtract?
add fractions with like denominators using the properties of
addition?
use the strategy Act it Out to solve multistep problems with
fractions?
Concepts:Students will know...
to add and subtract parts of a whole
to write fractions as sums
to add fractions using models
to subtract fractions using models
to solve problems by adding and subtracting fractions
to rename fractions and mixed numbers
to add and subtract mixed numbers
to subtract with renaming
to use the properties of addition to add fractions
to solve problems using mulistep fraction problems
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
understand that to add or subtract fractions they must refer to
parts of the same whole
decompose a fraction by writing it as a sum of fractions with the
same denominators
use models to represent and find sums involving fractions
use models to represent and find differences involving fractions
solve word problems involving addition and subtraction with
fractions
write fractions greater than 1 as mixed numbers and write
mixed numbers as fractions greater than 1
add and subtract mixed numbers
rename mixed numbers to subtract
use the properties of addition to add fractions
use the strategy Act it Out to solve multistep fraction problems
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Page 13 of 28
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use Fraction Bar activities
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Page 14 of 28
Unit: Chapter 8 - Multiply Fractions by Whole Numbers
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-F.2.1.5 (Advanced) Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number).
Example: 5 × (1/4) = 5/4
M04.A-F.2.1.6 (Advanced) Multiply a whole number by a non-unit fraction (denominators limited to 2, 3, 4, 5, 6, 8,
10, 12, and 100 and final answers do not need to be simplified or written as a mixed
number). Example: 3 × (5/6) = 15/6
M04.A-F.2.1.7 (Advanced) Solve word problems involving multiplication of a whole number by a fraction
(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).
Big Ideas: Students will understand that:
Multiplying fractions by whole numbers.
Essential Questions:
How can you:
write a fraction as a product of a whole number and a unit
fraction?
write a product of a whole number and a fraction as a product
of a whole number and a unit faction?
use a model to multiply a fraction by a whole number?
multiply a fraction by a whole number to solve a problem?
use the strategy Draw a Diagram to solve comparison problems
with fractions?
Concepts:Students will know...
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
multiples of unit fractions
multiples of fractions
to multiply a fraction by a whole number using models
to multiply a fraction or mixed number by a whole number
to solve comparison problems with fractions
write a fraction as a product of a whole number and a unit
fraction
write a product of a whole number and a fraction as a product
of a whole number and a unit fraction
use a model to multiply a fraction by a whole number
multiply a fraction by a whole number to solve a problem
use the strategy Draw a Diagram to solve comparison problems
with fractions
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Page 15 of 28
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use Fraction Bar activities
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Page 16 of 28
Unit: Chapter 9 - Relate Fractions and Decimals
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.A-F.3.1.1 (Advanced) Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as
30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.
M04.A-F.3.1.2 (Advanced) Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.
M04.A-F.3.1.3 (Advanced) Compare two decimals to hundredths using the symbols >, =, or <, and justify the
conclusions.
Big Ideas: Students will understand that:
Essential Questions:
Tenths and Hundredths can be recorded as fractions and decimals and How can you......
then be compared.
record tenths as fractions and decimals?
record hundredths as fractions and decimals?
record tenths and hundredths as fractions and decimals?
relate fractions, decimals, and money?
use the strategy act it out to solve problems that use money?
add fractions when the denominators are 10 or 100?
compare decimals?
Concepts:Students will know...
how to.......
relate tenths and decimals
relate hundredths and decimals
find equivalent fractions and decimals
relate fractions, decimals, and money
solve problems using money
addfractional parts of 10 and 100
compare decimals
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
record tenths as frations and as decimals
record hundredths as fractions and as decimals
record tenths and hundredths as fractions and decimals
translate among representations of fractions, decimals, and
money
solve problems by using the strategy act it out
add fractions when the denominators are 10 or 100
compare decimals to hundredths by reasoning about their size
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Page 17 of 28
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use number lines, decimal squares, and money to show the relationship between fractions and decimals.
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Page 18 of 28
Unit: Chapter 10 - Two-Dimensional Fiqures
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.C-G.1.1.1 (Advanced) Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
M04.C-G.1.1.2 (Advanced) Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines or the presence or absence of angles of a specified size. Recognize right
triangles as a category, and identify right triangles.
M04.C-G.1.1.3 (Advanced) Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric
figures and draw lines of symmetry (up to two lines of symmetry).
Big Ideas: Students will understand that:
Lines and angles can be drawn, identified , and used to name and
classify shapes.
Essential Questions:
How can you:
identify and draw points, lines, line segmetns, rays, and angles?
classify triangles by the size of their angles?
identify and draw parallel lines and perpendicular lines?
sort and classify quadrilaterals?
check if a shape has line symmetry?
find lines of symmetry?
use the strategy act it out to solve pagttern problems?
Concepts:Students will know...
How to:
identify lines, rays, and angles
classify triangles
identify parallel and perpendicular lines
classify quadrilaterals
determine line symmetry
find and draw lines of symmetry
solve pattern problems
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
identify and draw points, lines, line segments, rays, and angles
classify triangles by ths size of their angles
identify and draw parallel lines and perpendicular lines
sort and classify quadrilaterals
determine whether a figure has a line of symmetry
identify and draw lines of symmetry in two-dimensional figures
use the strategy act it out to solve pattern problems
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Page 19 of 28
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 20 of 28
Unit: Chapter 11 - Angles
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.D-M.3.1.1 (Advanced) Measure angles in whole-number degrees using a protractor. With the aid of a protractor,
sketch angles of specified measure.
M04.D-M.3.1.2 (Advanced) Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.)
Big Ideas: Students will understand that:
Angles can be measured and used to solve problems.
Essential Questions:
How can you:
relate angles and fractional parts of a circle
relate degrees to fractional parts of a circle
use a protractor to measure and draw angles
determine the measure of an angle separated into parts
use the strategy draw a diagram to solve angle measurement
problems
Concepts:Students will know...
how to:
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
relate angles and fractional parts of a circle
relate degrees to fractional parts of a circle
use a protractor to measure and draw angles
determine the measure of an angle separated into parts
use the strategy draw a diagram to solve angle measurement
problems
relate angles and fractional parts of a circle
relate degrees to fractional parts of a circle
use a protractor to measure and draw angles
determine the measure of an angle separated into parts
use the strategy draw a diagram to solve angle measurement
problems
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Page 21 of 28
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Use protractors to measure and draw angles
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 22 of 28
Unit: Chapter 12 - Relative Sizes of Measurement Units
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.D-M.1.1.1 (Advanced) Know relative sizes of measurement units within one system of units including standard
units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and mL, L),
and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement,
express measurements in a larger unit in terms of a smaller unit. A table of equivalencies
will be provided.
M04.D-M.1.1.2 (Advanced) Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving
simple fractions or decimals; and problems that require expressing measurements given in
a larger unit in terms of a smaller unit.
M04.D-M.1.1.4 (Advanced) Identify time (analog or digital) as the amount of minutes before or after the hour. Example 1: 2:50 is the same as 10 minutes before 3:00. Example 2: Quarter past six is the same as
6:15.
Big Ideas: Students will understand that:
Essential Questions:
Relative sizes of measurements can be used How can you.....
to solve problems and to generate
use benchmarks to understand the relative sizes of measurement units
measurement tables that show a relationship.
use models to compare customary units of length
use models to compare customary units of weight
use models to compare customary units of liquid volume
make and interpret line plots with fractional data
use models to compare metric units of length
use models to compare metric units of mass and liquid volume
use models to compare units of time
use the strategy draw a diagram to solve elapsed time problems
solve problems involving mixed measures
use patterns to write number pairs for measurement units
Concepts:Students will know...
use benchmarks to understand the
relative sizes of measurement units
use models to compare customary units
of length
use models to compare customary units
of weight
use models to compare customary units
of liquid volume
make and interpret line plots with
fractional data
use models to compare metric units of
length
use models to compare metric units of
mass and liquid volume
use models to compare units of time
use the strategy draw a diagram to
solve elapsed time problems
solve problems involving mixed
measures
use patterns to write number pairs for
measurement units
Competencies (including Transfer goals):Students will be able to independently use their
learning to...
use benchmarks to understand the relative sizes of measurement units
use models to compare customary units of length
use models to compare customary units of weight
use models to compare customary units of liquid volume
make and interpret line plots with fractional data
use models to compare metric units of length
use models to compare metric units of mass and liquid volume
use models to compare units of time
use the strategy draw a diagram to solve elapsed time problems
solve problems involving mixed measures
use patterns to write number pairs for measurement units
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Page 23 of 28
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 24 of 28
Unit: Chapter 13 - Algebra: Perimeter and Area
Subject: Mathematics
Timeline: 2 Weeks
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M04.D-M.1.1.3 (Advanced) Apply the area and perimeter formulas for rectangles in real-world and mathematical
problems (may include finding a missing side length). Whole numbers only. The formulas
will be provided.
Big Ideas: Students will understand that:
Formulas can be used to find perimeter and area of rectangles.
Essential Questions:
How can you......
use a formula to find the perimeter of a rectangle
use a formula to find the area of a rectangle
find the area of combined rectangles
find an unknown measure of a rectangle given its area or
perimeter
use the strategy solve a simpler problem to sole area problems
Concepts:Students will know...
how to.....
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
use a formula to find the perimeter of a rectangle
use a formula to find the area of a rectangle
find the area of combined rectangles
find an unknown measure of a rectangle given its area or
perimeter
use the strategy solve a simpler problem to sole area problems
use a formula to find the perimeter of a rectangle
use a formula to find the area of a rectangle
find the area of combined rectangles
find an unknown measure of a rectangle given its area or
perimeter
use the strategy solve a simpler problem to sole area problems
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Page 25 of 28
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
1.
() Page 26 of 28
Unit: Chapter 14 - Fifth Grade
Subject: Mathematics
Stage One - Desired Results
Established Goals (State and Common Core Standards, Assessment Anchors, and Eligible Content):
STATE: PA Core Anchors and Eligible Content (2014)
M05.A-T.1.1.3 (Advanced) Read and write decimals to thousandths using base-ten numerals, word form, and
expanded form. Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4
× 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)
M05.A-T.2.1.2 (Advanced) Find whole-number quotients of whole numbers with up to four-digit dividends and twodigit divisors.
M05.A-F.1.1.1 (Advanced) Add and subtract fractions (including mixed numbers) with unlike denominators. (May
include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 =
23/12
M05.A-F.2.1.4 (Advanced) Divide unit fractions by whole numbers and whole numbers by unit fractions.
M05.C-G.1.1.1 (Advanced) Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair
(x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.
Big Ideas: Students will understand that:
Essential Questions:
You can build on fourth grade content and begin to prepare for grade How do you:
5 content.
add and subtract dollars and cents
use the order of operations
divide by multiples of ten
divide with 2 - digit divisors
read and write numbers through milions
use place value to read, write, and represent decimals
round decimal amounts
use place value to compare decimals
find factore of 10, 100, and 1,000
use multiplication to describe a pattern
add fractions when one denominator is a multiple of the other
subtract fractions when one denominator is a multiple of the
other
use repeated subtraction to solve problems involving division
with fractions
write division problems as fractions
use ordered pairs to locate points on a grid
use tiing to find the area of a rectangle
find the product of 3 factors
find the area of the base of a rectangular prism
Concepts:Students will know...
how to:
add and subtract dollars and cents
use the order of operations
divide by multiples of ten
divide with 2 - digit divisors
read and write numbers through milions
use place value to read, write, and represent decimals
round decimal amounts
use place value to compare decimals
find factore of 10, 100, and 1,000
use multiplication to describe a pattern
add fractions when one denominator is a multiple of the other
subtract fractions when one denominator is a multiple of the
other
use repeated subtraction to solve problems involving division
with fractions
Competencies (including Transfer goals):Students will be able
to independently use their learning to...
add and subtract dollars and cents
use the order of operations
divide by multiples of ten
divide with 2 - digit divisors
read and write numbers through milions
use place value to read, write, and represent decimals
round decimal amounts
use place value to compare decimals
find factore of 10, 100, and 1,000
use multiplication to describe a pattern
add fractions when one denominator is a multiple of the other
subtract fractions when one denominator is a multiple of the
other
use repeated subtraction to solve problems involving division
with fractions
write division problems as fractions
Page 27 of 28
write division problems as fractions
use ordered pairs to locate points on a grid
use tiing to find the area of a rectangle
find the product of 3 factors
find the area of the base of a rectangular prism
use ordered pairs to locate points on a grid
use tiing to find the area of a rectangle
find the product of 3 factors
find the area of the base of a rectangular prism
Stage Two - Assessment Evidence
Performance Tasks/Products/Projects
Students will be assessed through:
Teacher Observation
Show What You Know
Lesson Quick Check
Mid-Chapter Checkpoint
Homework
Calendar Math
Compass
Chapter Review/Chapter Test
Quizzes
Class Participation
Grab & Go Centers
Projects
Online Skills Practice
Open Ended Questions
Other Evidence (Tests, quizzes, etc)
None
Stage Three - Learning Plan
Learning Activities:
Major learning activities include:
Vocabulary Review Activities
Related math literature books
Calendar Math
Problem of the Day
Grab and Go Centers
Online Skills Practice
Problem Solving Activities (Math Olympics)
Open Ended Questions
Materials and Resources:
Teacher Edition - Houghton Mifflin Harcourt Go Math
Student Edition and Practice Book
Math Literature Books
Calendar Math
Whiteboard
Grab and Go Differentiated Activities
Grab and Go Manipulatives
Vocabulary Notebooks
Online Teacher/Student Resources
Math Boards
Math Minutes
Problem Solving Activities (Math Olympics)
Open Ended Questions
Page 28 of 28