Name: Math Unit 1, 5th grade
KUD
Unit: Number Theory – Sept 1-Sept 30, 2010
U.E.Q.
Why is it important to know the factors of numbers?
Which standards/anchors are students learning in this unit?
M5.A.3.1; M5.A.1.4; M5.D.1.1; M5.D.1.2
By the end of this unit, students will be able to…..
Know:
I Understand THAT:
*What is a rectangular array?
*Rows and columns in an array
represent a factor to a number
model What are factors?
*How to find Factors
*A prime number has only two
factors of 1 and itself
*Composite numbers have more
than two factors.
*How to find a square number
*How to find the square root
*How to make a factor tree
*Divisibility rules
*All numbers have divisibility
rules to help me decide if a
number is prime or composite.
How to use exponential notation
Key vocabulary
Rectangular array
Number model
Turn-around-rule
Factor
Product
Factor pair Remainder
Divisibility Factor rainbow
Quotient
Prime and Composite
Square number
Exponential notation
Un-squaring or Square root
* every number has a unique
prime factorization
Do:
*draw various kinds of arrays
*Write number models that
represent an array
*compare arrays to every day
pictures and items in the
classroom or building
*factors and divisibility are
related because multiplication
and division are inverse
*find fact families
operations; because of this
patterns exist between the two. *identify factor pairs through
factor rainbows, arrays, factor
captor
* check divisibility rules by
using a chart.
*List prime and composite
numbers on a table.
*use and write exponential
notation.
*find a square number and the
square root of a number.
* make a factor tree and write
the prime factorization.
Lesson 1 – Arrays and factor pairs 1.1-1.4
Unit Essential Question: Why is it important to know the factors of numbers?
Lesson Essential Question:
How do I use arrays to represent factor pairs?
Answer: The first factor in a number model represents the row and the 2nd number
represents the columns. The total number of dots equals the product.
What do students need to learn to be able to answer the Essential Question?
Assessment Prompt #1: How does a number model represent an array?
Assessment Prompt #2: What is a factor pair and show an example?
Assessment Prompt #3: How does the memorization of multiplication facts help me to
understand factor pairs?
Activating Strategy: Use Geo-boards for students to form rectangular arrays
-----------------------------------------------------------------------------------------------------------Key vocabulary to preview: Product, Rectangular array, Number model, , Turn-aroundrule, Factor, Factor pair, Divisible by, Product,
Teaching Strategies: active instruction, pair/share, journal work
Graphic Organizer: Vocabulary Chart
-----------------------------------------------------------------------------------------------------------Instruction:
Begin the class by handing out geo-boards and rubber bands and ask the students to make
rectangles. Have them write down the number of rows and columns for each array they
make.
Explain number model. AP#1 using think/pair/share.
AP #1: How does a number model represent an array?
Continue using your teacher’s guide and student journal pages 5-8. for lesson 1.2
Begin with lesson 1.3 math message and then ask AP#2.
AP #2: What is a factor pair and show an example?
Then continue with Lesson 1.3 in teacher’s guide and student journal pages 9-11.
Follow journal page12 and SRB page 306 for Lesson 1.4. When finished with lesson 1.4
ask AP#3.
AP #3: How does the memorization of multiplication facts help me to understand factor
pairs?
Summarizing Strategy:
Number 1 answers the lesson essential question and number 2 writes it down and is
prepared to share.
Lesson 2 – Prime and Composite 1.5-1.6
Unit Essential Question: Why is it important to know the factors of numbers?
Lesson Essential Question:
How do I use divisibility rules to determine prime or composite numbers?
Answer: A prime number has only 2 factors (1 and itself) –I check to see how many
factors a number has using divisibility rules.
What do students need to learn to be able to answer the Essential Question?
Assessment Prompt #1:How do I know that a number is divisible?
Assessment Prompt #2: How can I use a factor rainbow to help me find all factor pairs?
Assessment Prompt #3: How are divisibility rules helpful?
Activating Strategy: Array Graphing
-----------------------------------------------------------------------------------------------------------Key vocabulary to preview: Factor rainbow, Divisible by, Quotient, Divisibility rule,
Composite, prime
Teaching Strategies: active instruction, pair/share, journal work
Graphic Organizer: Vocabulary Chart
-----------------------------------------------------------------------------------------------------------Instruction:
Begin the class by doing math message for 1.5 and then ask . Hand out graph paper.
Group students into pairs and assign two numbers 1-20 to each pair. Have them cut out
their array and paste it next to their number on chart paper. AP#1 using think/ink/share.
AP #1: Ask pairs to write patterns they see in the arrays?
Clarify prime and composite numbers.
Continue using your teacher’s guide and student journal pages 13-15. for lesson 1.5
Begin with lesson 1.6 math message and then ask AP#2.
AP #2: How can I use a factor rainbow to help me find all factor pairs?
Then continue with Lesson 1.6 in teacher’s guide and student journal pages16-19. At the
end of the lesson ask AP#3 using think/pair/share.
AP #3: How are divisibility rules helpful?
Summarizing Strategy:
Have student 2 ink and student 1 tell the two most important things they need to
remember about prime and composites
Lesson 3 Square Numbers and Square Root -1.7-1.8
Unit Essential Question: Why is it important to know the factors of numbers?
Lesson Essential Question:
How are square numbers and square roots related?
Answer: A square number is a number times itself; a square root is a number that has 2
equal factors
What do students need to learn to be able to answer the Essential Question?
Assessment Prompt #1: What shape do all of the arrays in the math message create and
why?
Assessment Prompt #2: What does the exponent represent?
Assessment Prompt #3: How are divisibility rules helpful?
Activating Strategy: Math Message
-----------------------------------------------------------------------------------------------------------Key vocabulary to preview: Square array, Square number, Exponential notation,
Exponent, Unsquaring, Square root
Teaching Strategies: active instruction, pair/share, journal work
Graphic Organizer: Vocabulary Chart
-----------------------------------------------------------------------------------------------------------Instruction:
Begin the class by doing math message for 1.7 and then ask AP#1 using think/pair/share.
AP #1: What shape do all of the arrays in the math message create and why?
Continue using your teacher’s guide and student journal pages 20-22. for lesson 1.7
Begin with lesson 1.8 math message and then ask AP#2.
AP #2: What does the exponent represent?
Then continue with Lesson 1.8 in teacher’s guide and student journal pages 23-24. At the
end of the lesson ask AP#3 using think/pair/share.
AP #3: How do I unsquare a number?
Summarizing Strategy:
Each students writes a “Dear Mom, in Math class today I….” letter
Lesson 4 – Factor Trees 1.9
Unit Essential Question: Why is it important to know the factors of numbers?
Lesson Essential Question:
How do I find prime factorization using factor trees?
Answer: Use factor pairs to divide the product until there are only prime numbers left
What do students need to learn to be able to answer the Essential Question?
Assessment Prompt #1: Why do you think the number 1 is not used in a factor string?
Assessment Prompt #2: How do divisibility rules help me to create a factor tree?
Activating Strategy: Math Message
-----------------------------------------------------------------------------------------------------------Key vocabulary to preview: Factor string, Factor tree, Prime factorization
Teaching Strategies: active instruction, pair/share, journal work
Graphic Organizer: Vocabulary Chart
-----------------------------------------------------------------------------------------------------------Instruction:
Begin the class by doing math message for 1.9 and then discuss using think/pair/share.
Continue using your teacher’s guide and student journal pages 25-27. for lesson 1.9
AP #1 – Why do you think the number 1 is not used in a factor string?
AP #2: How do divisibility rules help me to create a factor tree?
Have the students review their graphic organizer and make sure they complete them.
Summarizing Strategy:
All students write an acrostic for the word FACTORS to summarize what they know
about them
All students answer the UEQ on the back side of their learning map.
UEQ answer: factors and divisibility are related because multiplication and division are inverse
operations; because of this, patterns exist between the two.
Word/Vocabulary
Product
Factor
Factor pair
Rectangular
Array
Number Model
Turn Around
Rule
Divisible
Example/Picture
Explain
Word/Vocabulary
Example/Picture
Explain
Product
2*2=4
The answer when
numbers are multiplied
together
Factor
2 * 2=4
The numbers that are
being multiplied
5*2=10
Two numbers (a pair)
when multiplied equal
a product.
Factor pair
Rectangular Array
Number Model
::::::
2 * 6 = 12
Turn Around Rule
1*3=3
3*1=3
Divisible
8 / 2= 4
- An arrangement
of objects in rows
and columns in a
rectangle.
- A number
sentence that
models an array
or number story.
A rule for solving
mult. Or addition
problems when the
factors or addends
can be turned
around and still get
the same product or
sum.
When a larger number
can be divided by a
smaller number and
there is no remainder
Topic:
Answer
LEQ
Concept #1
Vocabulary
Answer
LEQ
Concept #2
Vocabulary
Answer
LEQ
Concept #3
Unit Essential Question:
Vocabulary
Answer
LEQ
Concept #4
Vocabulary
Answer
LEQ
Concept #5
Vocabulary
Answer
LEQ
Concept #6
UEQ Answer:
Vocabulary
Topic: all numbers are related
Concept #2: Prime and Composite
Unit Essential Question: Why is it important to know the factors of numbers?
Concept #1: Arrays and Factor Pairs
LEQ: How do I use divisibility rules to LEQ: What is the difference between square
determine prime or composite numbers? numbers and square roots?
Concept #3: Square Numbers and Square Root
LEQ: How do I use arrays to represent
factors pairs?
Vocabulary:
Square array
Square number
Exponential notation
Exponent
Unsquaring
Square root
Answer: A square number is a number that has
two factors that are exactly the same; a square root
is a number one of the 2 equal factors of a square
number.
Answer: A prime number has only 2
factors (1 and itself) I check to see how
many factors a number has using
divisibility rules.
Vocabulary:
Factor rainbow
Divisible by
Quotient
Divisibility rule
Composite
prime
1 is neither prime or composite
Answer: The first factor in a number
model represents the row and the 2nd
number of dots represents the columns
and the total number of dots equals the
product.
Vocabulary:
Product
Rectangular array
Number model
Turn-around-rule
Factor
Factor pair
Divisible
Product
Answer: Use factor pairs to divide the
product until there are only prime
numbers left
LEQ: How do I find prime
factorization using factor trees?
Concept #4: Factor String
Vocabulary
Answer
LEQ
Concept #5
Vocabulary
Answer
LEQ
Concept #6
UEQ Answer: multiplication and division are inverse operations; because of this patterns exist between the two, therefore numbers are
related
Vocabulary:
Factor string
Factor tree
Prime factorization
Topic: all numbers are related
LEQ: How do I use arrays to represent
factors pairs?
Concept #1: Arrays and Factor Pairs
Answer:
Answer:
LEQ: How do I use divisibility rules to LEQ: What is the difference between square
determine prime or composite numbers? numbers and square roots?
Concept #2: Prime and Composite
Vocabulary:
Square array
Square number
Exponential notation
Exponent
Unsquaring
Square root
Unit Essential Question: Why is it important to know the factors of numbers?
Answer:
Vocabulary:
Factor rainbow
Divisible by
Quotient
Divisibility rule
Composite
prime
Concept #3: Square Numbers and Square Root
Vocabulary:
Product
Rectangular array
Number model
Turn-around-rule
Factor
Factor pair
Divisible
Product
UEQ Answer:
Concept #4: Factor String
LEQ: How do I find prime
factorization using factor trees?
Answer:
Vocabulary:
Factor string
Factor tree
Prime factorization
Extra Notes
Word/Vocabulary
Product
Example/Picture
Explain
The answer when
numbers are multiplied
together
Factor
The numbers that are
being multiplied
Factor pair
Two numbers (a pair)
when multiplied equal
a product.
Rectangular Array
Number Model
Turn Around Rule
Divisible
- An arrangement
of objects in rows
and columns in a
rectangle.
- A number
sentence that
models an array
or number story.
A rule for solving
mult. Or addition
problems when the
factors or addends
can be turned
around and still get
the same product or
sum.
When a larger number
can be divided by a
smaller number and
there is no remainder