Introduction to EnvisionsIntroduction to EnvisionsIntroduction to EnvisionsIntroduction to EnvisionsFacilitator: Kristie MartinezFacilitator: Kristie Martinez

Reflect on your own mathematical learning. Which sentence(s) best describes the message you

received during your years as a mathematical learner?

1. Arriving at the correct answer to a problem is the most important thing.

2. The methods used to solve a problem are just as important as arriving at the correct solution.

3. There is only one way to solve a problem and it is the teacher’s way. The teacher is responsible for telling students that one way.

4. There are many ways a problem can be solved that will ultimately lead to the correct solution. It is the responsibility of students to pursue a variety of ways and justify their reasoning.

Pose the Problem

If you add 7 to itself you get 14. If you make the first number one more and the second number one less you

get the same sum.

Is this true for all counting numbers?

A Three-Part Format for Problem-Based

Instruction Getting Ready

Activate prior knowledge Be sure the problem is understood

Establish clear expectations BEFORE

Students Work Let go!

Listen activelyProvide appropriate hints

Provide worthwhile extensions

DURING

Class DiscussionPromote a mathematical community of learners

Listen actively without evaluationSummarize main ideas and identify future problems A

FTER

Benefits

• evaluate math knowledge• students begin to critique each other’s work• make connections before moving on• make math explicit• the person who talks the most, learns the

most• students prove answers• push for understanding

A problem can be defined as an activity or task that encourages

mathematics by…

• beginning where the students are

• highlighting the math that students are to learn in a problematic or engaging way

• requiring justifications and explanations for answers and methods

Mathematical Practices1. 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.

• How did you solve?• Did anyone solve it another way?

PBIL- Problem Based Interactive Learning

• This is where the math practices live

• Part 2 of the daily lesson• Focus/Engage/Pose the Problem

Four Part Daily Lesson

Core vs. More

• 1- Daily Common Core Review- (More)• 2- Problem-Based Interactive Learning

(Core)• 3- Develop the Concept: Visual (Core)• 4- Close/Assess and Differentiate (Core-

some)Part 2, Part 3 and some of Part 4- Core

Program suggests 60 mins for Part 2 and Part 3

1. Daily Common Core Review

This helps you reinforce the Common Core Standards.

2- Problem Based Interactive Learning

This part allows teaching and learning of the Mathematical Practices

•Engages students

•Students solve and discuss a problem

•Makes the important math explicit

•Deepens understanding

2- Problem Based Interactive Learning

3- Develop the Concept: Visual

Step by step visual instruction that makes the math explicit

• Visual concept development- students are able to see ideas developed in visual displays

• Visual Learning Bridge- pictorial, step-by-step bridge between the PBIL activity and the lesson. This helps students focus on one idea at a time as well as see connections within a sequence of ideas.

• Guiding questions are provided in blue print• Pictures with a purpose- representations of math

concepts

Visual Learning Animations can be used to present the Visual Learning Bridge digitally with animation.

4- Close/ Assess and Differentiate

• Close the lesson- Essential Understanding

• Daily Quick Check assesses student understanding and allows for differentiation

• Differentiated Instruction- Center activities that provide appropriate level of Intervention, Practice or Enrichment

Lesson Format• Set the Purpose• Connect• Go over vocabulary• Pose the problem- seats• Share solutions-carpet• Model/Demonstrate• Video• Guided Practice• Independent Practice- seats• Share- carpet