An Overview of the Common Core State Standards for Mathematical Practice for use with the Common...

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.

8 Standards of Mathematical Practice

Standard 1: Make sense of problems and persevere in solving them

Standard 2: Reason abstractly and quantitativelyStandard 3: Construct viable arguments and

critique the reasoning of othersStandard 4: Model with mathematicsStandard 5: Use appropriate tools strategicallyStandard 6: Attend to precisionStandard 7: Look for and make use of structureStandard 8: Look for and express regularity in

repeated reasoning

Grouping the Standards of Mathematical Practice(McCallum, 2011)

Standard 1: Make sense of problems and persevere in

solving them

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

Standard 1: What might it look like for a student with significant

cognitive disabilities?

“Key Words” as an example of the

“suspension of sense making”

Key words don’t work!

We tell them—more 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?

Standard 2: Reason abstractly and quantitatively

• 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

Standard 3: Construct viable arguments and

critique the reasoning of others

• 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

Grouping the Standards of Mathematical Practice(McCallum, 2011)

Standards 2 & 3: What might they look like for a student with significant cognitive disabilities?

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.

Representational proportions

=

Concrete Proportions

=

= X

= X

= X

Standard 4: Model with mathematics

• 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

Standard 5: Use appropriate tools

strategically

• 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

Grouping the Standards of Mathematical Practice(McCallum, 2011)

Standards 4 & 5: What might they look like for a student with significant cognitive disabilities?

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?

Using Hundreds Board to Solve Relatively Difficult Problems

Using Hundreds Board to Solve Relatively Difficult Problems

Original Cost: 100%

Using Hundreds Board to Solve Relatively Difficult Problems

Using Hundreds Board to Solve Relatively Difficult Problems

Original Cost: 100%

27,000Sale Cost

Using Hundreds Board to Solve Relatively Difficult Problems

27,000

How muchis each 10th

of the whole?

Using Hundreds Board to Solve Relatively Difficult Problems

How muchis each 10th

of the whole?

3,375 3,375 3,375 3,375 3,375 3,375 3,375

3,375

Using Hundreds Board to Solve Relatively Difficult Problems

Original Cost: 100%

3,375 x 10

Standard 6: Attend to precision

• 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

Standard 6: What might they look like for a student with

significant cognitive disabilities?

We also use the word “same” when it doesn’t

really apply.

Are these the same?

4+4 = 7+1

31 1

Are these the same?

Standard 7: Look for and make use of structure

• 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

Standard 8: Look for and express regularity in repeated reasoning

• 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

Grouping the Standards of Mathematical Practice(McCallum, 2011)

Standards 7 & 8: What might they look like for a student with significant cognitive disabilities?

Multiplication

6 * 7= ?

Multiplication 6 * 7 = 6 (5) + 6 (2) = 426 * 7 = 42 or 30 + 12 = 42

----------OR-----------

6 * 7 = 6 (6) + 6 (1) = 426*7 = 42 or 36 + 6 = 42

THANK YOU!

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