Download 3.1 - Gr5 - Division with Fractions - Unit Presentation - 2021-2022

DIVISION WITH FRACTIONS
Grade 5
01/04/2022 - 01/20/2022
Revised: 11/22/2021
UNIT PLAN
DAY
TARGET
STANDARD
Day 1
I can interpret a fraction as division of the numerator by the
denominator.
MAFS.5.NF.2.3
Day 2
I can solve word problems involving division of whole numbers
with fractions or mixed numbers as the quotient.
MAFS.5.NF.2.3
Day 3
I can determine situations that could be represented by fractions
or whole numbers.
MAFS.5.NF.2.3
Day 4
I can interpret division of a unit fraction by a non-zero whole
number and compute such quotients.
MAFS.5.NF.2.7
MAFS.5.NF.2.7a
Day 5
I can solve real world problems involving division of unit fractions
by non-zero whole numbers.
MAFS.5.NF.2.7a
MAFS.5.NF.2.7c
UNIT PLAN
DAY
TARGET
STANDARD
Day 6
I can interpret division of a whole number by a unit fraction and
compute such quotients.
MAFS.5.NF.2.7
MAFS.5.NF.2.7b
Day 7
I can solve real world problems involving division of whole
numbers by a unit fraction.
MAFS.5.NF.2.7b
MAFS.5.NF.2.7c
Day 8
Review Day
N/A
Day 9
Assessment Day
N/A
Day 10
Re-teach/Flex Day
N/A
Day 11
Re-teach/Flex Day
N/A
Day 12
Re-Teach/Flex Day
UNIT SCALE - GOAL
LEVEL
Students will be able to:
𝑎
3
GOAL
• Interpret a fraction as division of the numerator by the denominator ( =
𝑏
a ÷ b). Solve word problems involving division of whole numbers leading
to answers in the form of fractions or mixed numbers. (5.NF.2.3)
• Interpret division of a unit fraction by a non-zero whole number and
compute such quotients (5.NF.2.7a)
• Interpret division of a whole number by a unit fraction and compute such
quotients (5.NF.2.7b)
• Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions
(5.NF.2.7c)
UNIT SCALE – ON YOUR WAY TO THE GOAL
LEVEL
Students will be able to:
𝑎
2
• Interpret a fraction as division of the numerator by the denominator ( =
𝑏
a ÷ b) (5.NF.2.3)
• Represent division problems by creating pictorial representations
(5.NF.2.7a, 5.NF.2.7b, 5.NF.2.7c)
1
• Identify the fraction bar (horizontal line or slanted line between the
numerator and denominator) as a division sign (5.NF.2.3)
• Represent division problems by creating concrete representations
(5.NF.2.7a, 5.NF.2.7b, 5.NF.2.7c)
UNIT SCALE – ABOVE THE GOAL
LEVEL
4
Students will be able to:
• Explain the pattern observed when dividing the numerator by the
denominator of a fraction greater than 1 versus a fraction less than 1
(5.NF.2.3)
• Explain the difference between dividing a unit fraction by a whole
number and dividing a whole number by a unit fraction (5.NF.2.7a,
5.NF.2.7b)
• Identify a situation in their life which involved dividing unit fractions by
non-zero whole numbers or whole numbers by unit fractions and explain
why being able to do the math is beneficial (5.NF.2.7c)
UNIT RESOURCE SLIDE
Student Slides
Student Slide Deck
*If the hyperlink on the slide
does not work, copy and
paste the link from the notes
into Google Chrome.
Student Handouts
Day 3 Determine Situations
Represented By Fractions Or
Whole Numbers
Compilation of Daily Formatives
(Handouts may also be included
in the student slide deck.)
Anchor Charts
Dividing Fractions
ADDITIONAL RESOURCES
Standards
Optional Suggestions for Additional
Practice from iReady Teacher Toolbox
Optional Suggestions for Additional
Practice from Think Central
Unit Number
Lesson Number
Student Resource
MAFS.5.NF.2.3
2
12
Standards Practice
MAFS.5.NF.2.7.a
2
17 - 18
Standards Practice
MAFS.5.NF.2.7.b
2
17 - 18
Standards Practice
MAFS.5.NF.2.7.c
2
17 - 18
Standards Practice
Think Central
Teacher Guide
How would you mentally solve this problem?
36 ÷ 12
Day 1 – Interpret a Fraction as Division
How would you mentally solve this problem?
48 ÷ 24
Day 1 – Interpret a Fraction as Division
DAILY LEARNING TARGET – Interpret a Fraction as Division
I can interpret a fraction as division of the numerator by
the denominator.
STANDARD/S
MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by
𝑎
the denominator ( = a ÷ b). Solve word problems involving
𝑏
division of whole numbers leading to answers in the form of
fractions or mixed numbers, e.g., by using visual fraction models or
equations to represent the problem.
Day 1 – Interpret a Fraction as Division
Three piano players share 9 hours of practice time.
How many hours will each player get to practice?
9÷3=?
Day 1 – Interpret a Fraction as Division
Molly and four friends want to share four oranges.
How much of the four oranges will each person receive?
4÷5=a
How many oranges are there to share?
How many people are sharing the four oranges?
What equation can represent the question? Use a to represent the unknown.
What are the next steps?
Day 1 – Interpret a Fraction as Division
Molly and four friends want to share four oranges.
How much of the four oranges will each person receive?
4
=
5
4÷5
Dividend – Numerator
Divisor – Denominator
Day 1 – Interpret a Fraction as Division
What is the relationship between division
and multiplication?
4
5
=4÷5
4
5x ? =4
5
Day 1 – Interpret a Fraction as Division
Additional Practice Problems
1. Draw a visual fraction model to
solve for d.
4÷7=d
2. Alberto and his five friends want to
share three apples. How much of the
three apples will each person receive?
Day 1 – Interpret a Fraction as Division
CHECK YOUR UNDERSTANDING
6÷8=𝑐
1. Draw a visual fraction model to solve for
the value of c.
2. Rewrite the division equation as a
multiplication equation.
Day 1 – Interpret a Fraction as Division
STATION NAME
DESCRIPTION
MUST DO or EXTRA TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 1 – Interpret a Fraction as Division
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 1 – Interpret a Fraction as Division
How would you mentally solve this problem?
50 ÷ 25
Day 2 – Fractions or Mixed Numbers as the Quotient
How would you mentally solve this problem?
56 ÷ 14
Day 2 – Fractions or Mixed Numbers as the Quotient
DAILY LEARNING TARGET – Fractions or Mixed Numbers as the Quotient
I can solve word problems involving division of whole
numbers with fractions or mixed numbers as the quotient.
STANDARD/S
MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by
𝑎
the denominator ( = a ÷ b). Solve word problems involving
𝑏
division of whole numbers leading to answers in the form of
fractions or mixed numbers, e.g., by using visual fraction models or
equations to represent the problem.
Day 2 – Fractions or Mixed Numbers as the Quotient
Kasandra picked 14 apples for her 4 friends. If
each friend gets the same amount, what fraction
does each friend receive? Use any strategy to
solve.
14 ÷ 4 = a
.
4 apples
14
4
=
4 apples
2
3
4
=
1
3
2
4 apples
2 apples
left over
1 1 1 1 1 1 1 1
+ + + + + + +
4 4 4 4 4 4 4 4
Day 2 – Fractions or Mixed Numbers as the Quotient
John and Sidney bought 17 candy bars. They want to
equally share the candy bars between themselves
and 4 other friends. How many candy bars does each
friend get?
• With your groups, write an equation that represents
the word problem and the unknown.
• Solve for the unknown.
• Prove your answer with a drawing or visual using
fraction models.
Day 2 – Fractions or Mixed Numbers as the Quotient
• Sidney solved the problem; Her work is below.
• John solved the problem. His work is below.
6 17
-
6 (6 x 1)
11
-
6 (6 x 1)
Is the work correct?
Explain why or why not.
5
Day 2 – Fractions or Mixed Numbers as the Quotient
Additional Practice Problems
1. Use a fraction model to solve for c.
18 ÷ 5 = c
2. Kasandra picked 16 pounds of oranges
for her 5 friends. If each friend gets the
same amount, what fraction does each
friend receive? Use any strategy to solve.
Day 2 – Fractions or Mixed Numbers as the Quotient
Additional Practice Problems
3. Which of the following situations can be represented by
12
5
?
A. Harvey opens 5 bags of gummy bears, which she will split equally into 12
bowls for a party.
B. Juan takes 5 apples from a bag containing 12 apples.
C. Carlos has 12 packs of baseball cards with 5 cards in each pack.
D. John pours 5 equal servings of apple juice from a jug containing 12 ounces.
Day 2 – Fractions or Mixed Numbers as the Quotient
CHECK YOUR UNDERSTANDING
Mikala bought 19 subs for 9 friends. If each friend
gets the same amount, what fraction of the sub
does each friend receive? Use any strategy to solve.
Day 2 – Fractions or Mixed Numbers as the Quotient
STATION NAME
DESCRIPTION
MUST DO or EXTRA
TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 2 – Fractions or Mixed Numbers as the Quotient
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 2 – Fractions or Mixed Numbers as the Quotient
How would you mentally solve this problem?
60 ÷ 15
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
How would you mentally solve this problem?
64 ÷ 16
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
DAILY LEARNING TARGET – Determine How Situations Can Be Represented by Fractions or Whole Numbers
I can determine situations that could be represented by
fractions or whole numbers.
STANDARD/S
MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by
𝑎
the denominator ( = a ÷ b). Solve word problems involving
𝑏
division of whole numbers leading to answers in the form of
fractions or mixed numbers, e.g., by using visual fraction models or
equations to represent the problem.
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
What expression can be used for the following
situation.
Situation 1
Joy uses 24 apples to make 5 apple pies.
How many apples are in each pie?
24 ÷ 5
24
5
4
5
4
Situation 2
Twenty-four students split 5
apple pies after the bake sale.
How many apple pies does
each student get?
5 ÷ 24
5
24
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
Each expression can represent one of the follow
situations. Which ones belong to each?
Situation 1
Situation 2
Joy uses 26 bananas to make
8 loaves of banana bread.
How many bananas are in
each loaf?
Twenty-six students split 8
loaves of banana bread after
the bake sale. How many
loaves of bread does each
student get?
8 ÷ 26
26
8
2
3
8
26 ÷ 8
8
26
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
10 ÷ 3 = 𝑐
Situation 1
Situation 2
Zander and Alice are baking
and made 10 jumbo cookies.
They want to give them to 3
friends. Each friend will get the
same amount. How many
cookies will each friend get?
Zander and Alice are baking
and made 10 jumbo cookies.
They want to give enough for
themselves and 3 friends. Each
person will get the same
amount. How many cookies
will each friend get?
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
Additional Practice Problems
Each expression can represent one of the follow situations. Which ones belong to each?
Situation 1
Jose bought 22 submarine
sandwiches to share with his 7
friends. If each friends gets an
equal amount, how much of the
submarine sandwiches does each
friend get?
22 ÷ 7
7
22
Situation 2
Twenty-two students split 7
submarine sandwiches after
recess. How many sandwiches will
each student get?
1
3
7
22
7
7 ÷ 22
Day 3 – Determine Situations Represented by Fractions or Whole Numbers
CHECK YOUR UNDERSTANDING
Which of the following situations can be
16
represented by ?
6
 Hazel opens 6 bags of gummy bears, which she will split
equally into 16 bowls for a party.
 Jasper takes 6 apples from a bag containing 16 apples.
 Levi has 16 packs of baseball cards with 6 cards in each
pack.
 Harper pours 6 equal servings of apple juice from a jug
containing 16 ounces.
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
STATION NAME
DESCRIPTION
MUST DO or EXTRA
TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 3 – Determine Situations Represented by
Fractions or Whole Numbers
How would you mentally solve this problem?
72 ÷ 12
Day 4 – Division of a Unit Fraction
How would you mentally solve this problem?
84 ÷ 12
Day 4 – Division of a Unit Fraction
DAILY LEARNING TARGET – Division of a Unit Fraction
I can interpret division of a unit fraction by a non-zero
whole number and compute such quotients.
STANDARD/S
MAFS.5.NF.2.7 Apply and extend previous understandings of
division to divide unit fractions by whole numbers and whole
numbers by unit fractions.
MAFS.5.NF.2.7a Interpret division of a unit fraction by a non-zero
whole number and compute such quotients.
Day 4 – Division of a Unit Fraction
1
1
÷4=x
8
2
Describe what the equation is asking for.
Draw an illustration or make a
model to show how you would
try and solve.
Let’s discuss the model.
Day 4 – Division of a Unit Fraction
1
1
÷4=x
8
2
Describe what the equation is asking for.
Draw an illustration or make a
model to show how you would
try and solve.
Let’s discuss the model.
Day 4 – Division of a Unit Fraction
1
÷6=x
4
Describe what the equation is asking for.
Draw an illustration or make a model to
show how you would try and solve.
Let’s discuss your illustrations and models.
Day 4 – Division of a Unit Fraction
Jack solved by using the following visual.
Is Jack correct?
𝟏
𝟔
÷ 𝟔 = 𝒙; 𝒙 =
𝟒
𝟐𝟒
Day 4 – Division of a Unit Fraction
Additional Practice Problems
Describe what the equation is asking for. Draw an illustration or make a model to show how
you would try to solve.
1
3
÷4=x
1
2
÷8=x
Day 4 – Division of a Unit Fraction
CHECK YOUR UNDERSTANDING
1
÷5=x
6
Choose a strategy and solve for the quotient.
Day 4 – Division of a Unit Fraction
STATION NAME
DESCRIPTION
MUST DO or EXTRA TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 4 – Division of a Unit Fraction
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 4 – Division of a Unit Fraction
How would you mentally solve this problem?
84 ÷ 14
Day 5 – Word Problems and Unit Fractions
How would you mentally solve this problem?
90 ÷ 15
Day 5 – Word Problems and Unit Fractions
DAILY LEARNING TARGET – Word Problems & Unit Fractions
I can solve real world problems involving division of unit
fractions by non-zero whole numbers.
STANDARD/S
MAFS.5.NF.2.7a Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients.
MAFS.5.NF.2.7c Solve real world problems involving division of
unit fractions by non-zero whole numbers and division of whole
numbers by unit fractions, e.g., by using visual fraction models and
equations to represent the problem.
Day 5 – Word Problems and Unit Fractions
1
5
Amiyah has of her book left to read for a book report. She
has 3 days to finish the book. If she splits the reading evenly
among 3 nights, how much will Amiyah read each night?
=
3
6
9
12
𝟑
𝟏𝟓
15
Day 5 – Word Problems and Unit Fractions
1
2
Rosa has cup of chocolate chips to share equally into 4
batches of cookies.
How much chocolate chips are in each batch?
Rosa used a model to determine the amount of chocolate
chips in each batch. Do you agree with her?
Why or why not?
½ Cup
¼
1
2
÷4=
11
1
𝑐𝑢𝑝
÷
4
=
4
2
8
cup
Day 5 – Word Problems and Unit Fractions
Additional Practice Problems
1
3
1. Kiran has of his science
project left to complete. If he
wants to spread out the work
over the next three days, how
much will Kiran complete each
day?
1
4
2. Harris has bag of cat food. He wants to
feed his cat an equal amount over the next
4 days. How much cat food will Harris feed
his cat each day?
Day 5 – Word Problems and Unit Fractions
Additional Practice Problems
1
8
3. Dani is making muffins that call for 3 cups of flour. Her measuring cup only holds cup
of flour. How many times will Dani need to fill the measuring cup to get the 3 cups of
flour?
1
A. 3 times
8
3
B. times
8
C. 24 times
D. 11 times
Day 5 – Word Problems and Unit Fractions
CHECK YOUR UNDERSTANDING
1
6
Tonya has gallon of milk. She wants to drink
equal amounts of the remaining milk in 3 days.
How much milk will Tonya drink each day?
Day 5 – Word Problems and Unit Fractions
STATION NAME
DESCRIPTION
MUST DO or EXTRA
TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 5 – Word Problems and Unit Fractions
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 5 – Word Problems and Unit Fractions
How would you mentally solve this problem?
80 ÷ 16
Day 6 – Division of a Whole Number
How would you mentally solve this problem?
98 ÷ 14
Day 6 – Division of a Whole Number
DAILY LEARNING TARGET – Division of a Whole Number
I can interpret division of a whole number by a unit
fraction and compute such quotients.
STANDARD/S
MAFS.5.NF.2.7 Apply and extend previous understandings of
division to divide unit fractions by whole numbers and whole
numbers by unit fractions.
MAFS.5.NF.2.7b Interpret division of a whole number by a unit
fraction and compute such quotients.
Day 6 – Division of a Whole Number
1
7 ÷ because
=x
21
3
1
3
21 x = 7
X = 21
Day 6 – Division of a Whole Number
1
1
6x =
36
÷ because
=x
2
2
1+ 1+1 + 1+ 1 + 1 = 6
X=6
0 𝟏 1 𝟏𝟏 2 𝟐𝟏 3
𝟐
𝟐
3
𝟐
Day 6 – Division of a Whole Number
Additional Practice Problems
1
4
12 ÷ = x
Use a model to solve the equation
above.
9÷
1
3
=x
Use a number line to solve the equation
above.
Day 6 – Division of a Whole Number
Day 6 – Formative
CHECK YOUR UNDERSTANDING
Lena was asked to solve the following equation:
1
5 ÷ = x. She solved using the strategy below. Is
4
her solution correct? Why or why not?
0
4
1
4
2
𝟏
𝟒
4
3
4
5 ÷ = x and x =
4
4
5
𝟐𝟎
𝟒
Day 6 – Division of a Whole Number
STATION NAME
DESCRIPTION
MUST DO or EXTRA TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 6 – Division of a Whole Number
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 6 – Division of a Whole Number
How would you mentally solve this problem?
96 ÷ 16
Day 7 – Real World Problems & Whole Numbers
How would you mentally solve this problem?
24 ÷ 12
Day 7 – Real World Problems & Whole Numbers
DAILY LEARNING TARGET – Real World Problems
I can solve real world problems involving division of whole
numbers by a unit fraction.
STANDARD/S
MAFS.5.NF.2.7b Interpret division of a whole number by a unit
fraction and compute such quotients.
MAFS.5.NF.2.7c Solve real world problems involving division of
unit fraction by non-zero whole numbers and division of whole
numbers by unit fractions, e.g., by using visual fraction models and
equations to represent the problem.
Day 7 – Real World Problems & Whole Numbers
Clint asked his teacher how many thirds would
be in 8 macaroons. Clint’s teacher helped him
1
write the equation 8 ÷ = x, but Clint is still stuck.
3
How do you think he should finish solving?
Day 7 – Real World Problems & Whole Numbers
1
2
Gina has 6 cupcakes. She wants to share
them equally. If she divides each cupcake
how many people can Gina share with?
1
by ,
4
Day 7 – Real World Problems & Whole Numbers
Additional Practice Problems
1. Hope has 6 donuts from
Dunkin Donuts. If she
1
divides the donuts by , how
2
many people can Hope
share with? Draw a model to
represent your thinking.
2. David has 4 pizzas. If he divides the
1
pizza by , how many friends can David
2
share with? Draw a model to represent
your thinking.
Day 7 – Real World Problems & Whole Numbers
Additional Practice Problems
3. Mariah has 9 pounds of cookie dough. She wants to put the dough into containers so
1
that each container has .
4
Part A
Complete the following statement.
Part B
How many containers did Maria fill?
Day 7 – Real World Problems & Whole Numbers
CHECK YOUR UNDERSTANDING
1
2
Use the equation 9 ÷ = x to write a story problem,
draw a visual representation, and solve.
1. Write a story problem.
2. Draw a visual representation of the problem.
3. Solve for the value of x.
Day 7 – Real World Problems & Whole Numbers
STATION NAME
DESCRIPTION
MUST DO or EXTRA
TIME
TIME
i-Ready (Computer)
Complete online lessons
3x per week
15 each time, 45
min/week
Teacher Station
Small group time with
the teacher
Must Do, Teacher will let Teacher will decide
you know how often
Day 7 – Real World Problems & Whole Numbers
GROUP/Student
Names
Stations to Complete
TODAY
Optional Stations
Day 7 – Real World Problems & Whole Numbers