Unpacking the Standards for Mathematical Practice
Professional Development
September 16, 2013
Outcomes
Participants will:• Unpack the Standards for Mathematical
Practice
• Apply English Learner strategies to make meaning of the Standards for Mathematical practice (i.e. Think-Pair-Write-Share, Academic Vocabulary Instruction, Identifying Text Structures)
• Engage in strategies for problem solving for all students, including English Learners
COMMON CORE MATH STANDARDS
MATH PRACTICES
CONTENT STANDARDS
USE APPROPRIATE TOOLS STRATEGICALLY
MODEL WITH MATHEMATICS
CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS
REASON ABRSTRACTLY AND QUANTITATIVELY
MAKE SENSE OF PROBLEMS AND PERSEVERE IN FOLLOWING THEM
ATTEND TO PRECISION
LOOK FOR AND MAKE USE OF STRUCTURE
LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING
Common Core
While promoting literacy is explicitly specified across the curricula, the mathematical practices imply the same need for mathematics across the curricula.
Science
Language Arts
Social Studies
Thinking About Math Practices
Each group will beAssigned one informational
Text about a math Practice.
Create a tree map connectingThe math practice to all
Content areas.
Choose one Tier 2Word to define.
Read the passage the 2nd
Time and take notes based On the text structure.
Read the passage once and Identify the Tier 2 and Tier 3
Vocabulary words
Thinking About Math Practices
Each group will beAssigned one informational
Text about a math Practice.
Create a tree map connectingThe math practice to all
Content areas.
Choose one Tier 2Word to define.
Read the passage the 2nd
Time and take notes based On the text structure.
Read the passage once and Identify the Tier 2 and Tier 3
Vocabulary words
Read for VocabularyMathematical Practice#3
Construct Viable Arguments
Tier 2 Tier 3
Words that are not content specific, but necessary for understanding complex text.
Words that are content specific and are normally defined within the context of the text.
How can I make this accessible for my English Learners?
Thinking About Math Practices
Each group will beAssigned one informational
Text about a math Practice.
Create a tree map connectingThe math practice to all
Content areas.
Choose one Tier 2Word to define.
Read the passage the 2nd
Time and take notes based On the text structure.
Read the passage once and Identify the Tier 2 and Tier 3
Vocabulary words
ILLUSTRATION
EXAMPLES
CHARACTERISTICS, PROPERTIES
DEFINITION IN YOUR
OWN WORDS
Thinking About Math Practices
Each group will beAssigned one informational
Text about a math Practice.
Create a tree map connectingThe math practice to all
Content areas.
Choose one Tier 2Word to define.
Read the passage the 2nd
Time and take notes based On the text structure.
Read the passage once and Identify the Tier 2 and Tier 3
Vocabulary words
Thinking About Math Practices
Each group will beAssigned one informational
Text about a math Practice.
Create a tree map connectingThe math practice to all
Content areas.
Choose one Tier 2Word to define.
Read the passage the 2nd
Time and take notes based On the text structure.
Read the passage once and Identify the Tier 2 and Tier 3
Vocabulary words
Connecting Math Practice Standard #____ with critical thinking in all content areas
ScienceLanguage Arts Social Studies
When do you construct viable arguments in science, language arts etc.?
Let’s Share!
Each group needs to post their chart/charts in a designated area of the room.
Each group will present their standard to the rest of the group. Each member in each group, must present one piece.
Reflecting on my learning/Think-Pair-Write-Share. . .
What I now understand about the Common Core Standards for Math Practice is. . . .
This understanding is important because. . . .
Problem Solving in Mathematics
Part 2
Spend It!
You will need two handouts. Price sheet Recording sheet
The objective of the game is similar to “The Price is Right!”
I will give you an amount of money that you can spend. You will choose your items, total them and try to spend all of the money in your budget. The closer you get to spending all of the money, the closer you get to winning.
So if I give you a budget of $35.00 and you spend $34.59 you did a pretty good job. If you spend exactly $35.00, you WIN. If you spend $35.01, you LOSE.
Ready? Here are the rules.
Here are the rules of the game.1. You must choose five different items. Write these items in the first branch of your Tree Map.2. Write the price for each of those items in the second branch of your Tree Map.For Example:
Here are the rules of the game.
3.You may buy as many of each item as you want. 4.Record the number of units and calculate the total for those items. 5.Add this information to your Tree Map
You may use a calculator!For Example:
Finally total all of your costs. Feel free to continue to work toward winning the game. Give yourself no more than 6 minutes to play.
Good Luck.
So how did you do? Now that you have finished the game, I want you to think about the thinking behind your strategy. Analyzing how you approached this problem is your Frame of Reference.
So let’s add to your Frame of Reference.
When students solve a problem, they should answer these three questions.
So let’s add the answers to all 3 of these Frame Questions to your Spend It Tree Map.
First, think about the strategy you used to make your decisions about what to buy and how many of each item you chose. Think about WHY you chose the items you chose.
Did you
1. Start with prices that were large and then use the lesser priced items to get close to the total?
If so, your strategy was to think NUMERICALLY.
Did you
Combine items in order to get whole numbers?
If so, your strategy was to think NUMERICALLY using Base 10..
$3.00
$3.00
Did you
Think ALGEBRAICALLY?
I have $20.00 to spend and I have to buy 5 different items. Therefore, I should spend about $4.00 on each item.
$20.00 5 $4.00
If you used any of these strategies, you were thinking like a
Mathematician.
These strategies INFLUENCED
How you approached the problem.
If you chose your items based on any of the following:
“I picked the items I like.”“I picked items for breakfast. You can’t have
breakfast without coffee!”
While you might have gotten items for a great breakfast, you did NOT think like a
mathematician.
Add your strategy to your
Frame of Reference
I combined items to get to whole
dollar amounts. I used my
knowledge of base 10 and
number sense.
Now let’s think about the actual math skills and processes you needed to know in order to solve this problem.
Identify the math skills you used to solve
this problem and add them to the
Frame of Reference.
They might be something like…
I used adding and multiplying
as well as subtracting.
I also used “guess and chec
k” as well as estimating.
Many students struggle with math vocabulary, so identifying key terms you need to know is another important meta-
cognitive skill for problem solving.
I used adding and multiplying
as well as subtracting.
I also used “guess and chec
k” as well as estimating.
I need to know what “cost per unit” means.
Finally, students should be given time to reflect on how they solved a problem, what they learned in the process and how they might improve
their problem solving skills using their understanding.
I learned not to get distracted by irrelevant information. I didn’t need to focus on the type of item. I should have just paid attention to the
numbers.
I need to think about how to
solve the problem,
before rushing into just trying
to solve it.
You can solve a problem using a lot of different strategies.
I learned not to get distracted by irrelevant information. I didn’t need to focus on the type of item. I should have just paid attention to the
numbers.
I need to think about how to
solve the problem,
before rushing into just trying
to solve it.
You can solve a problem using a lot of different strategies.
I used adding and multiplying as
well as subtracting.
I also used “guess and check” as well
as estimating.
I need to know what “cost per unit” means.
I combined items to get to whole dollar amounts. I used my knowledge of base 10 and number
sense.
Notice that the information in the Frame of Reference is really the most important part
of this problem solving.
Students can then use the statements in their Frame of Reference as well as the
information they record in the map itself to show their understanding of math concepts
and problem solving.
I am incorporating the math standards
of practice into my daily instruction.
Reflection and Closure