1
(No Transcript)
2
An Overview of the Common Core State Standards
for Mathematical Practicefor use with the
Common Core Essential Elements
The present publication was developed under grant
84.373X100001 from the U.S. Department of
Education, Office of Special Education Programs.
The views expressed herein are solely those of
the author(s), and no official endorsement by
the U.S. Department should be inferred.
3
8 Standards of Mathematical Practice

• Standard 1 Make sense of problems and persevere
  in solving them
• Standard 2 Reason abstractly and quantitatively
• Standard 3 Construct viable arguments and
  critique the reasoning of others
• Standard 4 Model with mathematics
• Standard 5 Use appropriate tools strategically
• Standard 6 Attend to precision
• Standard 7 Look for and make use of structure
• Standard 8 Look for and express regularity in
  repeated reasoning

4
Grouping the Standards of Mathematical Practice

• (McCallum, 2011)

5
Standard 1 Make sense of problems and persevere
in solving them
6

• Mathematically proficient students
• explain the meaning of a problem and look for
  solutions
• analyze
• make conjectures about the form and meaning of
  the solution to plan a solution pathway
• monitor and evaluate their progress
• explain correspondences between equations, verbal
  descriptions, tables, and graphs or draw diagrams
  to show relationships or trends.
• check their answers to problems using a different
  methods

7
Standard 1 What might it look like for a student
with significant cognitive disabilities?
8
Key Words as an example of the suspension of
sense making

• Key words dont work!

9
We tell themmore means add

• Erin has 46 comic books. She has 18 more comic
  books than Jason has. How many comic books does
  Jason have.
• But is our answer really 64 which is 46 18?

10
Standard 2 Reason abstractly and quantitatively
11

• Mathematically proficient students
• make sense of quantities and their relationships
• bring two complementary abilities to bear on
  problems involving quantitative relationships
• the ability to decontextualize
• the ability to contextualize
• Quantitative reasoning entails habits of creating
  a coherent representation of the problem at hand

12
Standard 3 Construct viable arguments and
critique the reasoning of others
13

• Mathematically proficient students
• understand and use stated assumptions,
  definitions, and previously established results
• make conjectures
• analyze situations by breaking them into cases
  and, can recognize and use counterexamples.
• reason inductively about data
• compare the effectiveness of two plausible
  arguments, distinguish correct logic or reasoning
  from that which is flawed
• listen or read the arguments of others, decide
  whether they make sense

14
Grouping the Standards of Mathematical Practice

• (McCallum, 2011)

15
Standards 2 3 What might they look like for a
student with significant cognitive disabilities?
16
Why does this work?

• If Sam can mow one lawn in 2 hours, how many
  lawns can he mow in 8 hours?
• Write a proportional relationship that represents
  the situation.

17
Representational proportions

18
Concrete Proportions
X
X
X

19
Standard 4 Model with mathematics
20

• Mathematically proficient students
• apply the mathematics
• identify important quantities in a practical
  situation and map their relationships
• analyze relationships mathematically to draw
  conclusions
• Routinely interpret their mathematical results in
  the context of the situation

21
Standard 5 Use appropriate tools strategically
22

• Mathematically proficient students
• consider the available tools when solving a
  mathematical problem
• are sufficiently familiar with tools appropriate
  for their grade or course
• know that technology can enable them to visualize
  the results
• identify relevant external mathematical
  resources, and use them to pose or solve problems
• are able to use technological tools to explore
  and deepen their understanding of concepts

23
Grouping the Standards of Mathematical Practice

• (McCallum, 2011)

24
Standards 4 5 What might they look like for a
student with significant cognitive disabilities?
25
Your New Car!
You are buying a new car that is on sale for
27,000. This is 80 of the Original cost of the
car. What was the Original cost of the car?
26
Using Hundreds Board to Solve Relatively
Difficult Problems
27
Using Hundreds Board to Solve Relatively
Difficult Problems
Original Cost 100
28
Using Hundreds Board to Solve Relatively
Difficult Problems
29
Using Hundreds Board to Solve Relatively
Difficult Problems
27,000 Sale Cost
Original Cost 100
30
Using Hundreds Board to Solve Relatively
Difficult Problems
27,000
How much is each 10th of the whole?
31
Using Hundreds Board to Solve Relatively
Difficult Problems

3,375
3,375
How much is each 10th of the whole?
3,375
3,375
3,375
3,375
3,375
3,375
32
Using Hundreds Board to Solve Relatively
Difficult Problems
3,375 x 10
Original Cost 100
33
Standard 6 Attend to precision
34

• Mathematically proficient students
• try to communicate precisely to others
• use clear definitions in discussion with others
  and in their own reasoning
• state the meaning of the symbols they choose
• are careful about specifying units of measure
• calculate accurately and efficiently

35
Standard 6 What might they look like for a
student with significant cognitive disabilities?
36
We also use the word same when it doesnt
really apply.
37
Are these the same? 44 71
38
(No Transcript)
39
Are these the same?
40
Standard 7 Look for and make use of structure
41

• Mathematically proficient students
• look closely to discern a pattern or structure
• recognize the significance of an existing line in
  a geometric figure and can use the strategy of
  drawing an auxiliary line for solving problems.
• can step back for an overview and shift
  perspective
• can see complicated things as single objects or
  as being composed of several objects

42
Standard 8 Look for and express regularity in
repeated reasoning
43

• Mathematically proficient students
• notice if calculations are repeated, and look
  both for general methods and for shortcuts
• maintain oversight of the process, while
  attending to the details
• continually evaluate the reasonableness of their
  intermediate results

44
Grouping the Standards of Mathematical Practice

• (McCallum, 2011)

45
Standards 7 8 What might they look like for a
student with significant cognitive disabilities?
46
Multiplication 6 7 ?
47
Multiplication 6 7 6 (5) 6 (2)
42 6 7 42 or 30 12
42 ----------OR----------- 6 7 6
(6) 6 (1) 42 67 42 or 36 6
42
48
THANK YOU! For more information, please go to
www.dynamiclearningmaps.org