unpacking the standards for mathematical practice professional development september 16, 2013

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

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?





Content areas.





Vocabulary words

ILLUSTRATION

EXAMPLES

CHARACTERISTICS, PROPERTIES

DEFINITION IN YOUR

OWN WORDS





Content areas.





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

unpacking the standards for mathematical practice professional development september 16, 2013

Documents

informational text

vocabulary words

text structures

content areas

complex text

mathematical practices

content specific

nd time