Grade 4 Module 3 Focus PPT

Report
A Story of Units
A Story of Units
Grade 4 – Module 3 – Second Half
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A Story of Units
Session Objectives
• Examination of the development of mathematical
understanding across the second half of the module
with a focus on the Concept Development within the
lessons.
• Introduction to mathematical models and
instructional strategies to support implementation of
A Story of Units.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Agenda
Introduction to the Module
Concept Development
Module Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Curriculum Overview of A Story of Units
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Module Overview – First Half
• Scan over the Topic
Titles and lessons for
Topics A-D.
• Form a general
understanding of where
the first half of the
module begins and
where it ends.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Module Overview – Second Half
• Scan over the Topic
Titles and lessons for
Topics E-H.
• Form a general
understanding of where
the second half of the
module begins and
where it ends.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Agenda
Introduction to the Module
Concept Development
Module Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Topic E: Division of Tens and Ones with
Successive Remainders
• Read Topic Opener E.
• What types of models will
be used?
• What Standard is
addressed?
• What is the content of the
Topic?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Divide with Remainders Fluency
T: How many groups of ___ are in ___?
T: Prove it by counting by ____.
T: Show and say how many groups.
T: How many left?
Lesson 14, Fluency
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12÷3
13÷3
15÷5
17÷5
20÷4
23÷4
50÷5
55÷5
A Story of Units
Divide a 2-digit number by a 1-digit
number with a remainder using an array
and a tape diagram
13 ÷ 6
Lesson 14, Problem 3
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A Story of Units
Debrief: Solve a division problem using an
array and the area model.




What does the quotient represent in the area model?
When does the area model present a challenge in
representing division problems?
How is the whole represented in the area model?
The quotient represents a side length. The remainder
consists of square units. Why?
Lesson 15, Application Problem, Problem 2 and Debrief
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A Story of Units
Division of tens and ones
6÷3
Lesson 16, Problems 1 and 2
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36 ÷ 3
A Story of Units
Divide 2-digit numbers by 1-digit numbers,
regrouping in the tens
3 ones ÷ 2
Lesson 17, Problem 1
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3 tens ÷ 2
A Story of Units
Find whole number quotients and
remainders
86 ÷ 5
Lesson 18, Problem 2
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A Story of Units
Solve division problems using area models
48 ÷ 4
Decompose whole to part.
Lesson 20
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A Story of Units
Solve division problems using area models
96÷ 4
Compose part to whole.
Lesson 20
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A Story of Units
Division area models with remainders
Solve for 37÷2
Lesson 21, Problem 1
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A Story of Units
Topic F: Reasoning with Divisibility
• Read Topic Opener F.
• Why is this Topic placed
between multiplication and
division in the module?
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A Story of Units
Use division and the associative property
to test for factors
• Can 54 be divided evenly by 3? 2?
• Do we need to divide to determine if 5 is a factor of
54?
• Is 6 a factor of 54?
• If 54 = 6×9, then is 54 = (2×3)×9 true?
• Use the associative property to show both 2 and 3
are factors of 42.
Lesson 23
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A Story of Units
Multiples
•
•
Use division and the associative property to determine whether a whole
number is a multiple of another number (Lesson 24).
Explore properties of prime and composite numbers to 100 by using
multiples (Lesson 25).
Lesson 24 & 25
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A Story of Units
Topic G: Division of Thousands, Hundreds,
Tens and Ones
• Read Topic Opener G.
• Why is division of larger
dividends separated in this
module?
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A Story of Units
Lesson 26: Divide multiples of 10, 100 and
1,000 by single-digit numbers.
•
•
•
•
•
Take 5 minutes to read through the entire lesson.
Highlight 2 “ah-has” to share at your table.
Complete the Problem Set.
Consider today’s lesson only has a 45
minute period. What will you do to keep
the balance of rigor and honor the objective?
Share solutions and strategies.
Lesson 26
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A Story of Units
Decompose a remainder in the hundreds
place to solve a division problem.
783 ÷ 3
Lesson 27, Problem 2
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A Story of Units
Represent numerically four-digit dividend
division with divisors of 2, 3, 4, and 5,
decomposing a remainder up to three times.
4,325 ÷ 3
Lesson 29, Problem 2
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A Story of Units
Solve division problems with a zero in the
dividend or quotient.
804 ÷ 4
Lesson 30, Problem 1 and 2
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4,218 ÷ 3
A Story of Units
Interpret division word problems as either
number of groups unknown or group size
unknown.
Two hundred thirty-two people are driving to a
conference. If each car holds 4 people, including the
driver, how many cars will be needed?
Lesson 31, Problem 3
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A Story of Units
Division word problems with larger divisors
of 6, 7, 8, and 9.
Mr. Hughes has 155 meters of volleyball netting. How
many nets can he make if each court requires 9
meters of netting?
Lesson 32, Problem 3
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A Story of Units
Connect the area model to division.
Use decomposition for 1,344 ÷ 4
Lesson 33, Problem 1
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A Story of Units
Topic H: Multiplication of Two-Digit by
Two-Digit Numbers
• Read Topic Opener H.
• How have the students
prepared for this type of
multiplication?
• How are the students
prepared to use the area
model?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Fluency: Draw a Unit Fraction
T: Draw a quadrilateral with 4 equal
sides and 4 right angles.
T: Name it.
S: Square.
T: Partition it into 3 equal parts. Shade
in 1 part.
T: Write the name of the shaded
portion of the square.
Students write ⅓.
Lesson 34, Fluency
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Repeat with:
• Rhombus into fourths
• Rectangle into fifths
• Rectangle into eighths
A Story of Units
Application Problem
Mr. Goggins planted 10 rows of
beans, 10 rows of squash, 10
rows of tomatoes, and 10 rows of
cucumbers in his garden. He put
22 plants in each row. Draw an
area model, label each part and
then write an expression that
represents the total number of
plants in his garden.
Lesson 34, Application Problem
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A Story of Units
Find the product of 60 and 34 using an area model.
30
60
60×30
6 tens×3 tens
18 hundreds
1,800
Lesson 35, Problem 2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
4
60×4
6 tens×4
24 tens
240
34
x 60
240
+1, 8 0 0
2, 0 4 0
A Story of Units
Find the product of 23 and 31 using an area model.
3
20
30
1
3×30
9 tens
3×1
3 ones
20×30
6 hundreds
20×1
2 tens
31
x 23
3
90
20
+ 600
713
23×31=(3×1) + (3×30) + (20×1) + (20×30)
Lesson 36, Problem 2
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A Story of Units
4 partial product  2 partial products
Draw an area model and solve for 26×35.
Lesson 37 Problem 1
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A Story of Units
Solve 2-digit by 2-digit multiplication using
the algorithm.
Lesson 38, Problem 1
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A Story of Units
Regrouping.
Work with a partner to solve:
• 29×62
• 46×63
Lesson 32, Problems 2 and 3
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A Story of Units
Agenda
Introduction to the Module
Concept Development
Module Review
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A Story of Units
Complete the End-of-Module Assessment.
• Now with all of the mathematical knowledge and
understanding of the models, complete the
assessment.
• You may work alone or with your table to discuss
challenges or successes.
• How did Module 1 and 2 prepare you for Module 3?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Biggest Takeaway
Turn and Talk:
•
•
•
•
I am ready to…
I still want to know more about…
I am better prepared to…
My students will…
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Points
• Number disks and area models are used heavily
throughout the module to support the algorithms.
• The multiplication and division algorithms are not
expected fluencies in Grade 4.
• Unit language and place value understanding drives
the experience of the algorithms.
• Keep a balance of rigor by addressing each
component of a lesson.
• Honor and respect the objectives.
• Find a balance between success and mastery.
© 2012 Common Core, Inc. All rights reserved. commoncore.org

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