College & Career Ready
Common Core
Jennifer Woolever
East Elementary Principal
Key Points: Mathematics
Eight Mathematical Practices:
1.
Make sense of problems and persevere in solving them
2.
Reason abstractly and quantitatively
3.
Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure
8.
Look for and express regularity in repeated reasoning
Practice #1
Make sense of problems and persevere in solving them
• A teacher might assign students to work in pairs to evaluate
their approach to a problem. For example, having a partner
describe how they solved the problem or list what steps they
took to solve
• Set out different approaches to a solution, asking students
to identify “what this mathematician was thinking or trying
out” and evaluating the success of the strategy
Practice 2
Reason abstractly and quantitatively
• A teacher might ask the students to reflect on what
each number in a fraction represents as parts of a
whole
• A teacher might ask the students to brainstorm
what was the most efficient and accurate means to
finding the solution
Practice 3
Construct viable arguments and critique the reasoning of others
• This might involve having students explain and
discuss their thinking processes aloud, or signaling
agreement/disagreement with a hand signal
• A teacher might post multiple approaches to a
problem and ask students to identify rationales for
each approach as well as mistakes
Practice 4
Model with mathematics
• Practice real-world scenarios
• Students are able to make connections to their lives
with what they are learning in mathematics
• Is able to describe and demonstrate to other peers
their thought process
Practice 5
Use appropriate tools strategically
• Students understand the importance of using
manipulatives (i.e. rulers, compasses, protractors,
and other tools) when solving problems
• Students are able to select which tool is useful for
solving a particular problem
Practice 6
Attend to precision
• Students focus on clarity and accuracy
• Students use math vocabulary when
explaining the outcome
• Correctly labeling the answer
Practice 7
Look for and make use of structure
• Help learners identify and evaluate efficient
strategies for a solution
• Is able to identify what is relevant
• “Working backwards” This practice is not
emphasizing the answer, but rather process on how
they student got to that answer
Practice 8
Look for and express regularity in repeated reasoning
• students look for general methods and shortcuts
• It also requires teachers to attend to and listen
closely to their students’ “a-ha moments”
• Compare and contrast different strategies
Math Building Goal:
To have a robust fundamental knowledge of mathematics that
promotes problem solvers who communicate effectively, value different
approaches, and are confident in their mathematical abilities.
High Level of Summary of Major Work in Grades K-8
K-2
Addition and subtraction—
concepts, skills, problem solving and place value
3-5
6
7
8
Multiplication and division of whole numbers and fractions –
concepts, skills, and problem solving
Ratios and proportional relationships; early expressions and
equations
Ratios and proportional relationships; arithmetic of rational
numbers
Linear algebra and linear functions
Operations & Algebraic Thinking
Math Models
Area Model
X
by
6
4
4 x 6= A
Partial
Products
Place Value Row Model
36 x 2=
30
6
2
30
x 2
360
6
x 2
12
60 + 12 =72
Partial Products
Area Model
63 x 45 =
60
40
5
3
2400
120
300
15
=2835
Expanded Notation Method
32
x 51
2
30
100
1500
1632
Multiplying Double Digits
Borrowing or Regrouping Methods
Groups Above
Groups Below
24
X 32
48
720
768
24
X 32
48
620
768
Operations & Algebraic Thinking
Math Models
Area Model to Algorithm
The long division format is similar to the area model.
Draw two more sides on the division bracket to form a rectangle.
3
4
12
The area is 12 and the length of each side is 3 and 4.
Partial Quotients Method
23 r4
7 / 165
-70
95
-70
25
-21
4
10
10
3
Real World Context
1. Equal Groups
2. Finding Area
3. Comparison
4. Combinations
5. Algebraic Equations
AMC Theaters
Theater 4- Cloudy with a Chance of Meatballs 2
Theater 4 has 13 seats in each row. There are 24
equal rows. If the movie is sold out. How many people
attended the movie?
Theater 4
20
10
3
200
60
4
40
12
= 312
people
Extension
1/3
= 312
people
Written
Responses
Sample Question
Writing to Explain
3) Molly had the following work on her paper
40
2
80
6
3,200
160
240
12
What multiplication is problem is Molly trying to solve?
How do you know?
Rate the Response
4 Star ✪ 3 Star ✪ 2 Star ✪ 1 Star ✪
Molly is trying to solve the problem 86 x 42.
1 Star Response
Rate the Response
4 Star ✪ 3 Star ✪ 2 Star ✪ 1 Star ✪
Molly is trying to solve the problem 86 x 42. I
know this from looking at her work.
2 Star Response
Rate the Response
4 Star ✪ 3 Star ✪ 2 Star ✪ 1 Star ✪
Molly is trying to solve the problem 86 x 42. I
know because I can put the numbers back
together to form the numbers in the problem.
3 Star Response
Rate the Response
4 Star ✪ 3 Star ✪ 2 Star ✪ 1 Star ✪
Molly is trying to solve the problem 86 x 42. I
know because I can put the tens and ones
that were broken apart back together to form
the numbers Molly started with.
4 Star Response
Math Websites
o http://learnzillion.com/
o http://studyjams.scholastic.com/studyjams/jams/math/index.htm
o http://www.ixl.com/
o http://www.k-5mathteachingresources.com/
http://www.corestandards.org/
School Webpage
Common Core Link
Thank You!
Don’t forget about our
Upcoming Common Core Parent Meeting Nights
Thursday, January 9th: English Language Arts
CLOZE Reading
Text Dependent Questions
Thursday, February 27th: Assessment Practice
Writing to Explain
Sample Assessment Questions