Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.
-
Upload
simon-lamb -
Category
Documents
-
view
226 -
download
0
Transcript of Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.
![Page 1: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/1.jpg)
Content Deepening6th Grade Math
September 16, 2013Jeanne SimpsonAMSTI Math Specialist
![Page 2: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/2.jpg)
2
•Name•School•Classes you teach•Your favorite math topic to teach
Welcome
![Page 3: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/3.jpg)
3
![Page 4: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/4.jpg)
4
He who dares to teach
must never cease to
learn.John Cotton Dana
![Page 5: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/5.jpg)
acos2010.wikispaces.com•Electronic version of
handouts•Links to web resources
![Page 6: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/6.jpg)
6
Intervention
Assessment
Collaboration
Five Fundamental Areas Required for Successful Implementation of CCSS
![Page 7: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/7.jpg)
7
Instruction•Deep
conceptual understanding
•Collaborative lesson design
•Standards for Mathematical Practice
Content• Fewer standards with greater
depth• Understanding, focus, and
coherence• Common and high-demand tasks
Intervention• Common required response to
intervention framework response• Differentiated, targeted, and
intensive response to student needs
• Student equity, access, and support Assess
ment•PLC
teaching-assessing-learning cycle
•In-class formative assessment processes
•Common assessment instruments as formative learning opportunities
Collaboration
How do we teach?
![Page 8: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/8.jpg)
8
SMP1 - Make sense of problems and persevere in solving them
SMP2 - Reason abstractly and quantitativelySMP3 - Construct viable arguments and critique the
reasoning of othersSMP4 - Model with mathematicsSMP5 - Use appropriate tools strategicallySMP6 - Attend to precisionSMP7 - Look for and make use of structureSMP8 - Look for and express regularity in repeated
reasoning
Standards for Mathematical Practice
![Page 9: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/9.jpg)
9
•Capture the processes and proficiencies that we want our students to possess
•Not just the knowledge and skills but how our students use the knowledge and skills
•Describe habits of mind of the mathematically proficient student
•Carry across all grade levels, K-12
What Are The Practice Standards?
![Page 10: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/10.jpg)
10
•√ I already do this.
• ! This sounds exciting!
• ? I have questions.
Standards of Mathematical Practice
![Page 11: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/11.jpg)
11
•Problem solving•Demanding tasks•Student understanding•Discussion of alternative
strategies•Extensive mathematics
discussion•Effective questioning•Student conjectures•Multiple representations
High-Leverage Strategies
![Page 12: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/12.jpg)
12
Instruction• D
eep conceptual understanding
• Collaborative lesson design
• Standards for Mathematical Practice
Content• F
ewer standards with greater depth
• Understanding, focus, and coherence
• Common and high-demand tasks
Intervention• C
ommon required response to intervention framework response
• Differentiated, targeted, and intensive response to student needs
• Student equity, access, and support
Assessment• P
LC teaching-assessing-learning cycle
• In-class formative assessment processes
• Common assessment instruments as formative learning opportunities
Collaboration
What are we teaching?
![Page 13: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/13.jpg)
Critical Focus Areas
Ratios and Proportional Relationships
Connect to whole number multiplication and division
Applying to problems
Standards 1-3
Number Systems
Dividing fractionsNegative numbersCoordinate plane
Standards 4-11
Expressions and Equations
Variables and expressionsSolve one-step equations
Standards 12-20
Statistics
Understanding different measures of center
Standards 25-29
Geometry – Standards 21-24
![Page 14: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/14.jpg)
Recommend Emphases from PARCC Model Content Framework for Mathematics
![Page 15: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/15.jpg)
15
Ratios and Proportional Relationships
Cluster Analysis Tool
![Page 16: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/16.jpg)
Analysis Tool
Content Standard
Cluster
Which Standards
in the Cluster Are Familiar?
What’s New or
Challenging in These
Standards?
Which Standards
in the cluster Need
Unpacking or
Emphasizing?
How Is This Cluster
Connected to the Other 6-8 Domains
and Mathematical Practice?
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1 Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities.
![Page 17: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/17.jpg)
17
UNDERSTANDING
•6.RP.1 – Understand the concept of a ratio, and use ratio language to describe a relationship between two quantities.
•6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship.
![Page 18: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/18.jpg)
18
Kim and Bob ran equally fast around a track. Kim started first. When she had run 9 laps, Bob had run 3 laps.
When Bob had run 15 laps, how many laps had Kim run?
Explain your reasoning.
![Page 19: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/19.jpg)
19
Solving ProportionsSolve Kanold, p. 94
• The traditional method of creating and solving proportions by using cross-multiplication is de-emphasized (in fact it is not mentioned in the CCSS) because it obscures the proportional relationship between quantities in a given problem situation.
• If two pounds of beans cost $5, how much will 15 pounds of beans cost?
![Page 20: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/20.jpg)
20
Ratios and Proportional Relationships Progression, pages 6-7
• Although it is traditional to move students quickly to solving proportions by setting up an equation, the Standards do not require this method in Grade 6. There are a number of strategies for solving problems that involve ratios. As students become familiar with relationships among equivalent ratios, their strategies become increasingly abbreviated and efficient.
![Page 21: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/21.jpg)
21
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.a. Make tables of equivalent ratios relating quantities with
whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed.
c. Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
![Page 22: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/22.jpg)
22
1. The ratio of free throws that Omar made to the ones he missed at practice yesterday was 7:3. If he attempted 90 free throw at practice, how many free throws did Omar make?
made 7
missed 3
Attempted 90
9 x 7 = 6390 ÷ 10 = 9
Omar made 63 free throws.
9
9 9 9
9 9 9 9 9 9
![Page 23: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/23.jpg)
23
2. At FDR High School, the ratio of seniors who attend college to those who do not is 5:2. If 98 seniors do not attend college, how many do?
![Page 24: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/24.jpg)
24
3. At Mesa Park High School, the ratio of students who have driver’s licenses to those who don’t is 8:3. If 144 students have driver’s licenses, how many students are enrolled at Mesa Park High School?
![Page 25: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/25.jpg)
25
4. Of the black and blue pens that Mrs. White has in a drawer in her desk, 18 are black. The ratio of black pens to blue pens is 2:3. When Mrs. White removes 3 blue pens, what is the new ratio of black pens to blue pens?
![Page 26: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/26.jpg)
26
Geometry
Unpacking Standards
![Page 27: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/27.jpg)
27
Unpacking the Standards
Step 1: Target a standardStep 2: Chunk the Main
CategoriesStep 3: Identify all
standard components
Step 4: Identify the Developmental Progression
Step 5: Identify Key Vocabulary
Step 6: Add Clarifying Information
“To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand, and be able to do. (Unpacking) may also be used to facilitate discussion among teachers and curriculum staff and to encourage coherence…(Unpacking), along with on-going professional development is one of many resources used to understand and teach the CCSS.”
-North Carolina Dept of Public Instruction
![Page 28: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/28.jpg)
28
Why are we Unpacking Standards?
To understand what the standards are asking students to know, understand, and be able to do
To make time for professional discussion about the standards
To build upon and use common terminology when discussing the implementation of the standards
Unpacking is standards is not a substitute document for the Common Core Standards, it is a
record of the conversation of those who are involved in the process of digging into the
standards.
![Page 29: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/29.jpg)
29
Step 1 – Target a Standard
•6.G.1 – Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles, or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
![Page 30: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/30.jpg)
302.G.3Partition circles and
rectangles into two, three, or four
equal shares
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
Partition
Builds on 1.G.3 Needed for 3.G.2
partition
Equal shares
rectangle HalvesHalf of
circle
Partition a shape into fourths in different ways
Pattern Blocks
Fraction Bars/Circles
Describe
ThirdsThird of
FourthsFourth of
whole
Identicalwhole
2/2 = one whole
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four fourths
2.G.3
Recognize that equal shares of identical
wholes need not have the same shape
2.G.3
Recognize
The final product….
![Page 31: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/31.jpg)
31
Example2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Step 2: Chunk the Main Categories
1.All Standard(s) in the cluster(s)
2.Identify Key Verbs
2.G.3Partition
circles and rectangles into two,
three, or four equal shares
Describe RecognizePartition
![Page 32: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/32.jpg)
32
Step 3: Identify all standard components
Components from CCSS:
Analyze nouns and verbsWhat do students need to do?
Include bullets, examples, footnotes, etc.
Take standard apart according to the verbs to separate skills within the standard
What do the students need to know?
lt blue
![Page 33: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/33.jpg)
33
Example 2.G.3
Partition circles and rectangles into two, three, or four equal
shares
Partition RecognizeDescribe
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four
fourths2.G.3
Recognize that equal shares of identical wholes need not have
the same shape2.G.3
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
![Page 34: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/34.jpg)
34
Step 4: Identify the Developmental Progression
Questions to consider when looking at the developmental progression of the standards…
•How would you utilize these chunks (blue) for scaffolding toward mastery of the entire standard?
• Where would you start when teaching this standard?
• What is the chunk that demonstrates the highest level of thinking?
![Page 35: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/35.jpg)
35
Vertical AlignmentUsing the progression document(s) from Ohio Department of Education and CCSS Writing Team:
Look to the grade level(s) below to see if the standard is introduced.
Look to the grade level(s) above to see if the standard is continued.
Code each standard on the poster with: builds on introduced needed for or mastered
and the grade level to which the standard aligns.
![Page 36: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/36.jpg)
36
Introduced?Mastered?
Needed for?Builds on?
2.G.3Partition circles and rectangles into two, three, or four equal
shares
Partition RecognizeDescribe
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four
fourths2.G.3
Recognize that equal shares of identical wholes need not have
the same shape2.G.3
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
Builds on 1.G.3
Needed for 3.G.2
![Page 37: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/37.jpg)
37
Step 5: Identify Key Vocabulary
Identify content vocabulary directly from the standard. Identify additional vocabulary students will need to know to meet the standard.
green
![Page 38: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/38.jpg)
382.G.3Partition circles and
rectangles into two, three, or four
equal shares
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
Partition
Builds on 1.G.3 Needed for 3.G.2
partition
Equal shares
rectangle HalvesHalf of
circle
Describe
ThirdsThird of
FourthsFourth of
whole
Identicalwhole
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four fourths
2.G.3
Recognize that equal shares of identical
wholes need not have the same shape
2.G.3
Recognize
Partition circles and rectangles into two equal
shares, using the word halves,
half of2.G.3
![Page 39: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/39.jpg)
39
Step 6: Add Clarifying Information
Kid-friendly language to add clarity Clarifying pictures, words, or phrasesDefinitions, examplesSymbols, formulas, pictures, etc.
CAUTION: do not replace important vocabulary that is included in the standard.
yellow
![Page 40: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/40.jpg)
402.G.3Partition circles and
rectangles into two, three, or four
equal shares
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
Partition
Builds on 1.G.3 Needed for 3.G.2
partition
Equal shares
rectangle HalvesHalf of
circle
Partition a shape into fourths in different ways
Pattern Blocks
Fraction Bars/Circles
Describe
ThirdsThird of
FourthsFourth of
whole
Identicalwhole
2/2 = one whole
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four fourths
2.G.3
Recognize that equal shares of identical
wholes need not have the same shape
2.G.3
Recognize
Partition circles and rectangles into two equal
shares, using the word halves,
half of2.G.3
![Page 41: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/41.jpg)
41
Transfer Unwrapping to Chart
![Page 42: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/42.jpg)
42
Divide and conquer…
•6.G.2 – Volume of right rectangular prism
•6.G.3 – Polygons in the coordinate plane
•6.G.4 – Nets and surface area
![Page 43: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/43.jpg)
432.G.3Partition circles and
rectangles into two, three, or four
equal shares
Partition circles and rectangles into two equal shares, using
the word halves, half of2.G.3
Partition
Builds on 1.G.3 Needed for 3.G.2
partition
Equal shares
rectangle HalvesHalf of
circle
Partition a shape into fourths in different ways
Pattern Blocks
Fraction Bars/Circles
Describe
ThirdsThird of
FourthsFourth of
whole
Identicalwhole
2/2 = one whole
Partition circles and rectangles into three equal shares, using
the word thirds, third of2.G.3
Partition circles and rectangles into four equal shares, using
the word fourths, fourth of
2.G.3
Describe the whole as two halves, three thirds, four fourths
2.G.3
Recognize that equal shares of identical
wholes need not have the same shape
2.G.3
Recognize
Partition circles and rectangles into two equal
shares, using the word halves,
half of2.G.3
Main Idea of Standard
Key Verbs
Take standard apart according to the verbs to separate skills within the standard.
Use all components of standard. Put in a logical sequence
Vertical alignment
Vocabulary
Clarifying information, student-friendly
![Page 44: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/44.jpg)
44
The Number System
Vertical Alignment
![Page 45: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/45.jpg)
45
Mathematics consists of pieces that make sense; they are not just independent manipulation/skills to be practiced and memorized – as perceived by many students.
These individual pieces progress through different grades (in organized structures we called “flows”) and can/should be unified together into a coherent whole.
Jason Zimba, Bill McCallum
![Page 46: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/46.jpg)
Create a chart that lists…
•What students need to know and be able to do to demonstrate mastery of these standards
•Prerequisite skills that are needed for these standards
![Page 47: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/47.jpg)
47
5th Operations and Algebraic Thinking
•Evaluate expressions with ( ), [ ], { }•Write and interpret numerical expressions•Generate numerical patterns from rules•Form ordered pairs from patterns•Graph ordered pairs on the coordinate
plane
Prerequisite Skills•Order of operations•Whole number operations
![Page 48: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/48.jpg)
48
Fluency
•The word fluent is used in the Standards to mean fast and accurate. Fluency in each grade involves a mixture of just knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies.
• Progressions for the Common Core State Standards in Mathematics
![Page 49: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/49.jpg)
49
Fluency
•Fluent in the standards means “fast and accurate.” It might also help to think of fluency as meaning more or less the same as when someone is said to be fluent in a foreign language. To be fluent is to flow; fluent isn’t halting, stumbling, or reversing oneself.
• Jason Zimba
![Page 50: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/50.jpg)
50
Fluency ExpectationsGrade Required Fluency
K Add/subtract within 5
1 Add/subtract within 10
2 Add/subtract within 20Add/subtract within 100 (pencil and paper)
3 Multiply/divide within 100Add/subtract within 1000
4 Add/subtract within 1,000,000
5 Multi-digit multiplication
6 Multi-digit division (6.NS.2)Multi-digit decimal operations (6.NS.3)
7 Solve px + q = r, p(x + q) = r
![Page 51: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/51.jpg)
51
Mathematical Fluency
![Page 52: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/52.jpg)
52
Multiplication Strategies
![Page 53: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/53.jpg)
53
Division Strategies
![Page 54: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/54.jpg)
54
Unit Fractions
![Page 55: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/55.jpg)
55
Fraction Multiplication in Grade 5
![Page 56: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/56.jpg)
56
Fraction Division in Grade 5
![Page 57: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/57.jpg)
57
Fraction Division in Grade 6•6.NS.1 – Interpret and compute quotients of
fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem.
•Examples: ▫Create a story context…▫Use a visual fraction model to show the quotient…▫Explain division using its relationship with
multiplication▫Sample problems
![Page 58: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/58.jpg)
58
6NS - Understanding•6.NS.5 – Understand that positive and
negative numbers are used together to describe quantities having opposite directions or values…
•6.NS.6 – Understand a rational number as a point on the number line…
•6.NS.6b – Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane…
•6.NS.7 – Understand ordering and absolute value of rational numbers .
![Page 59: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/59.jpg)
59
Expressions and EquationsProgression Documents
![Page 60: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/60.jpg)
• K–6 Geometry• 6-8 Statistics and Probability• 6–7 Ratios and Proportional Relationships• 6–8 Expressions and Equations• 6-8 Number Systems
• These are the documents currently available. They are working on documents for the other domains (Functions, Geometry 7-8).
Progressions Documents
http://ime.math.arizona.edu/progressions/
![Page 61: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/61.jpg)
61
Jigsaw
•Read your assigned section
•Chart paper▫Summarize what you read.▫How can this document help you in your
classroom?▫What is said about the Math Practices?
•Be prepared to share
![Page 62: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/62.jpg)
62
Understanding
•6.EE.5 – Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
![Page 63: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/63.jpg)
63
![Page 64: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/64.jpg)
64
![Page 65: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/65.jpg)
65
![Page 66: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/66.jpg)
66
Statistics and ProbabilityResources
![Page 67: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/67.jpg)
67
Illustrative Mathematics
•Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
http://www.illustrativemathematics.org/
![Page 68: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/68.jpg)
68
Buttons: Statistical Questions
•Zeke likes to collect buttons and he keeps them in a jar. Zeke can empty the buttons out of the jar, so he can see all of his buttons at once.
•What statistical questions could we ask about these buttons?
![Page 69: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/69.jpg)
69
North Carolina’s Lessons for LearningBake Sale Brownies (p. 3) - 6.RP.3, 6.EE.9• I can use knowledge of multiplication and division to scale recipes to make different
numbers of servings.• I can identify quantitative relationships between scaled recipes.• I can represent relationships between quantities by plotting points on the coordinate grid.
Paper Clip Comparisons (p. 13) - 6.RP.1, 6.RP.2, 6.EE.6, 6.EE.9• I can represent equivalent ratios as a ratio table, as a graph, and on a double number line.• I can analyze ratio tables to identify qualitative patterns.• I can calculate unit rates by analyzing patterns in data.
I'll Race You? (p. 19) - 6.EE.1, 6.NS.3• I can write an exponential expression as repeated multiplication.• I can evaluate an exponential expression with whole number exponents.
Block Part-y (p. 22) - 6.G.2• I can find the volume of a right rectangular prism with fractional edge lengths.• I can apply my knowledge of the formula V = lwh to determine possible fractional
dimensions of right rectangular prisms when given the volume.
How MAD Are You? A Deeper Look at Mean Absolute Deviation (p. 28) - 6.SP.5, 6.SP.2, 6.SP.3, 6..SP.4
• I can use measures of center and measures of variability to summarize data sets in context.
• I can determine measures of center and variability of a data set and use the measures to draw conclusions.
• I can connect the measures of center and variability to the shape of the data distribution within the given context.
Shakespeare vs. Rowling (p. 34) - 6.SP.5, 6.SP.2, 6.SP.3, 6.SP.4)• I can collect data and display that data on tally charts, histograms, and box plots.• I can quantitatively analyze data to determine measures of center and variability.• I can use measures of center and variability of data sets to compare data sets.
![Page 70: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/70.jpg)
70
Mathematics Assessment Project• Tools for formative and summative assessment that make
knowledge and reasoning visible, and help teachers to guide students in how to improve, and monitor their progress. These tools comprise:
• Classroom Challenges: lessons for formative assessment, some focused on developing math concepts, others on non-routine problem solving.
• Professional Development Modules: to help teachers with the new pedagogical challenges that formative assessment presents.
• Summative Assessment Task Collection: to illustrate the range of performance goals required by CCSSM.
• Prototype Summative Tests: designed to help teachers and students monitor their progress, these tests provide a model for examinations that may replace or complement current US tests.http://map.mathshell.org/
![Page 71: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/71.jpg)
Mean, Median, Mode, and RangeProjector Resources:
Computer Games: Ratings
P-71
Imagine rating a popular computer game.
You can give the game a score of between 1 and 6.
![Page 72: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/72.jpg)
Mean, Median, Mode, and RangeProjector Resources:
Bar Chart from a Frequency Table
P-72
Mean score
Median score
Mode score
Range of scores
![Page 73: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/73.jpg)
Mean, Median, Mode, and RangeProjector Resources:
Matching Cards
1. Each time you match a pair of cards, explain your thinking clearly and carefully.
2. Partners should either agree with the explanation or challenge it if it is unclear or incomplete.
3. Once agreed stick the cards onto the poster and write a justification next to the cards.
4. Some of the statistics tables have gaps in them and one of the bar charts is blank. You will need to complete these cards.
P-73
![Page 74: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/74.jpg)
Mean, Median, Mode, and RangeProjector Resources:
Sharing Posters
1.One person from each group visit a different group and look carefully at their matched cards.
2.Check the cards and point out any cards you think are incorrect. You must give a reason why you think the card is incorrectly matched or completed, but do not make changes to the card.
3.Return to your original group, review your own matches and make any necessary changes using arrows to show if card needs to move.
P-74
![Page 75: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/75.jpg)
75
Understanding
•6.SP.2 – Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
![Page 77: Content Deepening 6 th Grade Math September 16, 2013 Jeanne Simpson AMSTI Math Specialist.](https://reader035.fdocuments.net/reader035/viewer/2022081506/56649ea35503460f94ba768e/html5/thumbnails/77.jpg)
77
Feedback
3 things I learned
2 things I liked
1 thing I want to know more about