Upload
guang
View
23
Download
0
Embed Size (px)
DESCRIPTION
2010 Mathematics Institute Patterns, Functions, and Algebra Grades 3-5. Agenda. Introductions Big Topics Patterns Properties Lunch Equalities and Inequalities. Big Topics. Patterns Using Number Lines Properties Building Vocabulary Equations and Inequalities Keeping it Balanced. - PowerPoint PPT Presentation
Citation preview
Fall 2010
2010 Mathematics Institute2010 Mathematics InstitutePatterns, Functions, and Patterns, Functions, and
AlgebraAlgebraGrades 3-5Grades 3-5
2010 Mathematics Institute2010 Mathematics InstitutePatterns, Functions, and Patterns, Functions, and
AlgebraAlgebraGrades 3-5Grades 3-5
Fall 2010
AgendaAgendaAgendaAgenda
• IntroductionsIntroductions
• Big TopicsBig Topics
• PatternsPatterns
• PropertiesProperties
• LunchLunch
• Equalities and InequalitiesEqualities and Inequalities
• IntroductionsIntroductions
• Big TopicsBig Topics
• PatternsPatterns
• PropertiesProperties
• LunchLunch
• Equalities and InequalitiesEqualities and Inequalities
Fall 2010
Big TopicsBig TopicsBig TopicsBig Topics
I.I. PatternsPatterns• Using Number LinesUsing Number Lines
II.II. PropertiesProperties• Building VocabularyBuilding Vocabulary
III.III. Equations and InequalitiesEquations and Inequalities• Keeping it BalancedKeeping it Balanced
I.I. PatternsPatterns• Using Number LinesUsing Number Lines
II.II. PropertiesProperties• Building VocabularyBuilding Vocabulary
III.III. Equations and InequalitiesEquations and Inequalities• Keeping it BalancedKeeping it Balanced
Fall 2010
Unpacking Unpacking PatternsPatterns
Unpacking Unpacking PatternsPatterns
Fall 2010
Multiplication shown on a Number Line
2009 SOL 3.6
Multiplication shown on a Number Line
2009 SOL 3.6
1 2 4 5 7 8 10 11 1314 16 170
Write the multiplication number sentence that matches the hops “Factor Frog” made.
5
Fall 2010
6
Multiplication on a Number Line 2009 SOL 3.6
Multiplication on a Number Line 2009 SOL 3.6
http://illuminations.nctm.org/LessonDetail.aspx?ID=L316
Fall 2010
7
Least Common Multiple2009 SOL 4.5a
Least Common Multiple2009 SOL 4.5a
1 2 4 5 7 8 10 11 13 14 16 170 3 9 15
LCM
Fall 2010
8
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Welcome to the Welcome to the Bubble Gum Bubble Gum
FactoryFactory
Fall 2010
9
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Bubble Gum Factory Investigation
At the Bubble Gum Factory, lengths of gum are stretched to larger lengths by putting them through stretching
machines.
There are 99 stretching machines, numbered 2 through 100.
Fall 2010
10
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Fall 2010
11
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Machine 3 triples the length and so forth.
=
So, machine 23, for example, will stretch apiece of gum to 23 times its original length.
= Well…you get the point.
Fall 2010
12
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Now It Is Your Job!Now It Is Your Job!
An order has just come in for a piece of An order has just come in for a piece of bubble gum 24 inches in length. bubble gum 24 inches in length.
The factory has pieces of gum that are only The factory has pieces of gum that are only 1 inch in length, and machine number 24 is 1 inch in length, and machine number 24 is broken. broken.
*Is there any way to create a piece of bubble *Is there any way to create a piece of bubble gum 24 inches in length by using other gum 24 inches in length by using other machines? machines?
Fall 2010
13
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
Figure out whichmachines are
actually necessary.
Do we need all of them?
Fall 2010
14
Primes and Composites 2009 SOL 5.3
Primes and Composites 2009 SOL 5.3
We know that 2 is a necessary machine, but every even number has 2 as a factor…
Fall 2010
Primes and Composites2009 SOL 5.3
Primes and Composites2009 SOL 5.3
We also know that 3 is a necessary machine, but every third number has 3 as a factor.
15
Fall 2010
Primes and Composites2009 SOL 5.3
Primes and Composites2009 SOL 5.3
…and we also know that 5 is a necessary machine, but every fifth number has 5 as a factor.
16
Fall 2010
Primes and Composites2009 SOL 5.3
Primes and Composites2009 SOL 5.3
We know that 7 is a necessary machine and every seventh number has 7 as a factor.
17
Fall 2010
18
Primes and Composites2009 SOL 5.3
Primes and Composites2009 SOL 5.3
After exploring divisibility rules for 2, 3, 5, 7, 11, and 17, the prime numbers under 100 are revealed.
Fall 2010
Think/Pair/ShareThink/Pair/Share
19
Fall 2010
Properties VocabularyProperties VocabularyProperties VocabularyProperties Vocabulary
Fall 2010
Properties VocabularyProperties VocabularyProperties VocabularyProperties Vocabulary
Fall 2010
Now, they also have to name it
-Students have always had to understand the property
Addition to the Standard:
Commutative Property2009 SOL 3.20
22
Fall 2010
Commutative Property2009 SOL 3.20
Commutative Property2009 SOL 3.20
If students know:
4 + 5
Then they know :5 + 4
23
Fall 2010
Commutative Property2009 SOL 3.20
Commutative Property2009 SOL 3.20
“It is not intuitively obvious that 3 x 8 is the same as 8 x 3 or that, in general, the order of the numbers makes no difference (the commutative or order property). A picture of 3 sets of 8 objects cannot immediately be seen as 8 piles of 3 objects. Eight hops of 3 land at 24, but it is not clear that 3 hops of 8 will land at the same point.
The array, by contrast, is quite powerful in illustratingthe order property. Students should draw or build arraysand use them to demonstrate why each array represents two different multiplications with the same product.”
Van de Walle (2001)
24
Fall 2010
Commutative Property2009 SOL 3.20
Commutative Property2009 SOL 3.20
- Given experiences with arrays, If students know
3 x 7
Then they can see that it is equal to -
7 x 3
25
Fall 2010
Commutative Property2009 SOL 3.20
Commutative Property2009 SOL 3.20
6 x 2 = 2 x 6
26
Fall 2010
AutomaticityAutomaticity
If I asked you to multiply 56 x 36 using mental math, would you be able to do that with automaticity?
27
Fall 2010
Associative Property2009 SOL 4.16b
Associative Property2009 SOL 4.16b
Given a problem -
(41 + 25) + 75
How can you make it an easier problem?
41 + (25 + 75)
- Looking for friendly numbers
28
Fall 2010
Associative Property2009 SOL 4.16b
Associative Property2009 SOL 4.16b
Solving a volume problem -
5
227
(27 x 5) x 2
Becomes - 27 x (5 x 2)
29
Fall 2010
Distributive Property2009 SOL 5.19
Distributive Property2009 SOL 5.19
Partial Products
3 x 24 = 3 x 20 + 3 x 4
30
http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html
Fall 2010
Distributive Property2009 SOL 5.19
Distributive Property2009 SOL 5.19
Slice It
31
Fall 2010
Think/Pair/ShareThink/Pair/ShareThink/Pair/ShareThink/Pair/Share
Fall 2010
Equations and InequalitiesEquations and InequalitiesEquations and InequalitiesEquations and Inequalities
Fall 2010
What does the equal sign mean?
What does the equal sign mean?
34
Fall 2010
Equalities2009 SOL 4.16a Equalities
2009 SOL 4.16a
http://illuminations.nctm.org/LessonDetail.aspx?ID=L18335
Fall 2010
36
Equalities2009 SOL 3.20 Equalities2009 SOL 3.20
Fall 2010
37
Inequalities2009 SOL 3.20 Inequalities2009 SOL 3.20
Fall 2010
38
Equalities2009 SOL 3.20 Equalities2009 SOL 3.20
http://illuminations.nctm.org/ActivityDetail.aspx?id=26
Fall 2010
Equalities2009 SOL 4.16aEqualities
2009 SOL 4.16a
8 = 1 + 7
3 + 5 = 5 + 3
9 = 9
2 + 3 = 2 x 3True or False?
7 x 4 = 4 + 4 + 4 + 4
What will the students say?
39
Fall 2010
Equalities2009 SOL 4.16a
Equalities2009 SOL 4.16a
True or False?
40
Examples/Non-Examples
Fall 2010
41
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Using your cups and candy corn, construct a
model for
J = 6
Fall 2010
42
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Fall 2010
43
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Using your cups and candy corn, construct a
model for
J + 4 = 7
Fall 2010
44
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Fall 2010
45
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Fall 2010
46
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
B + 2 = 9
Fall 2010
47
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Fall 2010
48
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
B + 4 = 11
Fall 2010
49
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
http://illuminations.nctm.org/ActivityDetail.aspx?id=33
Fall 2010
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
50
http://illuminations.nctm.org/ActivityDetail.aspx?id=10
Fall 2010
Think/Pair/ShareThink/Pair/ShareThink/Pair/ShareThink/Pair/Share
Fall 2010
52
Questions?
Visit Parking
Lot