The document discusses developing higher level mathematical thinking through reasoning and problem solving. It focuses on teaching multiplication and division concepts using arrays and grouping models. For multiplication, arrays allow students to see the relationship between factors and products. Division is taught using fair sharing and measurement models. Students are guided to break problems into smaller steps and use known facts.
MTAP Program of Excellence in Mathematics
Grade 5 Session 2
Contents:
-Multiplication and Division of Whole Numbers
-PRIME FACTORIZATION
is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition. We cover two methods of prime factorization: find primes by trial division, and use primes to create a prime factors tree.
-Greatest Common Factor
-Least Common Multiple
-Problem Solving
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
MTAP Program of Excellence in Mathematics
Grade 5 Session 2
Contents:
-Multiplication and Division of Whole Numbers
-PRIME FACTORIZATION
is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition. We cover two methods of prime factorization: find primes by trial division, and use primes to create a prime factors tree.
-Greatest Common Factor
-Least Common Multiple
-Problem Solving
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
2. Mathematical Reasoning
The process of problem solving involves
Making conjectures
Recognizing existing patterns
Searching for connections to known
mathematics
Translating the gist of a problem into
mathematical representation
3. Mathematical Reasoning
Putting together different pieces of
information
Developing a range of strategies to use
Verifying the correctness of the solution
Applying skills that require and strengthen
student’s conceptual and procedural
competencies
4. Connecting to and building on students’
prior knowledge
Multiplication
Division
10. Advantages of Arrays
as a Model
Models the language of multiplication
4 groups of 6
or
4 rows of 6
or
6 + 6 + 6 + 6
11. Advantages of Arrays
as a Model
Students can clearly see the difference
between (the sides of the array)
and the (the area of the array)
7 units
4
units
28 squares
factors
product
15. Advantages of Arrays
as a Model
They can be used to support students in
learning facts by breaking problem into
smaller, known problems
For example, 7 x 8
7
8
3
5
35 21 = 56
+
7
8
4
4
28 28 = 56
+
57. Using Groups
John has 20 candy kisses. He plans to
share the candy equally between his 5
friends for Valentine’s Day. How many
kisses will each friend get?
58. Using Groups
Jane made 24 cookies and each of her
Valentine’s Day boxes holds 6 cookies.
How many boxes can she make?
59. Difference in counting?
Measurement
4 for you, 4 for you, 4 for you
…And so on
Like measuring out an amount
Fair Share
1 for you, 1 for you, 1 for you, 1 for you
2 for you, 2 for you, 2 for you, 2 for you
…And so on
Like dealing cards
61. Division
KNOW:
Total Number of Objects
Number of Groups OR Number in Each Group
FIND:
Number in Each Group Number of Groups
Fair Share
(Partitive)
Measurement
(Quotative)
66. Division
95 4
How many tens can you place in each
group?
How many tens does that use up?
How many are left?
Trade the leftover tens for ones.
67. Division
95 4
How many ones do you have now?
How many can you place in each group?
How many ones does that use up?
How many are left?
So we were able to put 23 in each group
with 3 leftover (23 R3)
68. Division
435 3
Build the number 435 using base 10 blocks
How many hundreds can you place in each
group?
How many hundreds does that use up?
How many are left?
Trade the leftover hundreds for tens.
69. Division
435 3
How many tens can you place in each
group?
How many tens does that use up?
How many are left?
Trade the leftover tens for ones.
70. Division
435 3
How many ones can you place in each
group?
How many ones does that use up?
How many are left?
So we were able to put 145 in each group
with none leftover.
71. 47 ÷ 6
6 Groups
6 ) 47
1
2
3
6
12
18
Can I put at least 3 in each group?
72. 47 ÷ 6
6 Groups
6 ) 47
1
2
3
6
12
18
6 groups of 3 uses ___ pieces.
3
–18
29
How many pieces are left?
Can I put 3 more in each group?
18
73. 47 ÷ 6
6 Groups
6 ) 47
1
2
3
6
12
18
6 groups of 3 uses ___ pieces.
3
3
–18
29
–18
11
How many pieces are left?
Can I put 3 more in each group?
18
74. 47 ÷ 6
6 Groups
6 ) 47
1
2
3
6
12
18
How many more can I put in each group?
3
3
1
–18
29
–18
11
– 6
5
How many pieces are left?
Can I put any more in each group?
6
6 groups of 1 uses ___ pieces.
75. 47 ÷ 6
6 Groups
6 ) 47
1
2
3
6
12
18
3
3
1
–18
29
–18
11
– 6
5
7 R5
We have __ in each group with ___ left
5
7
77. 338 ÷ 7
7 Groups
7) 338
1
2
3
5
10
7
14
21
35
70
I can make 7 groups of at least 10.
70
140
210
350
Can I make 7 groups of at least 100?
7 groups of 1 ten is 7 tens or ___
7 groups of 3 tens is __ tens or ___
7 groups of 2 tens is __ tens or ___
7 groups of 5 tens is __ tens or ___
1’s 10’s
So the answer is between 10 and 100
78. 338 ÷ 7
7 Groups
7) 338
–210
128 1
2
3
5
10
7
14
21
35
70
70
140
210
350
1’s 10’s
7 groups of 30 uses ___ pieces.
How many pieces are left?
Can I put any more tens in each group?
210 30
79. 338 ÷ 7
7 Groups
7) 338
–210
128
– 70
58
1
2
3
5
10
7
14
21
35
70
70
140
210
350
1’s 10’s
7 groups of 10 uses ___ pieces.
How many pieces are left?
Can I put any more tens in each group?
70 10
30
80. 338 ÷ 7
7 Groups
7) 338
–210
128
– 70
58
– 35
23
1
2
3
5
10
7
14
21
35
70
70
140
210
350
1’s 10’s
7 groups of 5 uses ___ pieces.
How many pieces are left?
Can I put any more ones in each group?
35
10
30
5
How many ones can I put in each group?
81. 338 ÷ 7
7 Groups
7) 338
–210
128
– 70
58
– 35
23
– 21
2
1
2
3
5
10
7
14
21
35
70
70
140
210
350
1’s 10’s
7 groups of 3 uses ___ pieces.
How many pieces are left?
Can I put any more ones in each group?
21
10
30
5
3
82. 338 ÷ 7
7 Groups
7) 338
–210
128
– 70
58
– 35
23
– 21
2
1
2
3
5
10
7
14
21
35
70
70
140
210
350
1’s 10’s
10
30
5
3
We have ___ in each group with ___ left
48 2
48 R2