introduction to the standards for mathematical practice

Common Core State Standards

Standards for Mathematical Practice

Agenda

• Common Core State Standards – Introduction– 21st Century Learning Skills: 4Cs

• Mathematics– Major shifts– Standards for Mathematical Practice– Mini-lesson Activity– Discuss Coaching Strategies

Objectives

• To develop a basic understanding of the Common Core State Standards for Mathematics.

• To familiarize ourselves with the language used in the Standards.

• To discuss strategies for coaching our staff on the Standards.

Automatic recall of basic

number facts

Students were expected to

memorize, repeat, perform as

practices, plug in, recognize,

identify what they learned.

Observing and questioningExploring relationsInvestigating patternsCrafting proofsJustifying claimsConnecting discrete factsApplying learning to new contextsCriticizing arguments made by others

Thinking Mathematically

Doing Mathematics

Building a House

What do we need to build a house?

Building a House

We need to know how to build a house.

Building a House

We need to know how to design the

house.

Building a House

We need to be able to communicate

with others about our ideas.

Building a House

We need to be able to represent the cost of building a

new house.

Building a House

We need to know how and when to

use the right tools.

Building a House

We need to work with precision.

Building a House

We need to have an organized plan for building a house.

Building a House

We can use what we know to add on to

the house.

Comparison

• What does building a house have to do with mathematics?

What’s the Difference?

What’s New?

Standards for Mathematical PracticeOverarching Habits of Mind

Modeling and Using Tools

Seeing Structure and Generalizing

1. Make sense of problems and persevere in solving them.6. Attend to precision.

4. Model with mathematics.5. Use appropriate tools strategically.

7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others.

Reasoning and Explaining

Mathematical Practice #1

Make sense of problems and persevere in solving them.

“I can…” StatementsI can solve problems without giving up.

I can explain the problem to another student.

What exactly

is this

problem

asking me to

do?

Mathematical Practice #2

Reason abstractly and quantitatively.

“I can…” StatementsI can think about numbers in different ways.I can use symbols to represent a problem.

I know I need

to multiply,

but what do

these

numbers

represent?

Mathematical Practice #3

Construct viable arguments and critique the reasoning of others.

“I can…” StatementsI can explain my thinking using math vocabulary.I can explain other student’s solutions.

I can compare various solutions.

I think that

step is wrong

because…

Mathematical Practice #4

Model with mathematics.

“I can…” StatementsI can show my works in many ways.

I can use math to understand real-world problems.

Can I use

math to

represent this

situation?

Mathematical Practice #5

Use appropriate tools strategically.

“I can…” StatementsI can use math tools and explain why I chose them.I can identify the most helpful tool to use.

Do I need my

calculator for

this?

Mathematical Practice #6

Attend to precision.

“I can…” StatementsI can work carefully and check my work.

Do I need to

round my

answer? Did I

remember to

label my

answer?

Mathematical Practice #7

Look for and make use of structure.

“I can…” StatementsI can use what I know to solve new problems.

Can I break

this problem

down into

something

simpler?

Mathematical Practice #8

Look for and express regularity in repeated reasoning.

“I can…” StatementsI can discover and use shortcuts.

I can tell if I am on the right track.

Is there a

matter in this

problem that I

can use?

Mini-Lesson

In the barnyard, there is an assortment of pigs and chickens. Counting heads I get 13; counting legs I get 46.

How many pigs and

chickens are there?

Mini-LessonCats can’t add,

but they do multiply!

In just 18 months, this female cat can have 2000 descendants.

Average number of litters a female cat can have in

one year

3

Age at which a female cat can

first get pregnant

4 months

Number of kittens in a litter

Usually 4 to 6

Paradigm Shift

“How can I explain clearly so they can

understand?”

“What task can I give to build understanding?”