SUPPORTING STUDENT'S MATHEMATICAL REASONING WITH THE MATHEMATICAL PRACTICES

-----------------------Jennifer Bay-Williams, PhD

University of Louisville

@JBayWilliams

WEBINAR #2Enhance your Tasks,

Enhance Student Reasoning

Today’s Agenda■ Opening Task: Crossing the River■ Revisit Big Ideas of MPs & Math Reasoning

Reasoning.■ Look for Math Practices #2, 7, & 8 in Tasks■ Enhance Tasks with Math Practices #2, 7, & 8.■ Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

A group of 8 adults and 2 children need to cross a river. A small boat is available that can hold 1 adult, or 1 child, or 2 children. Everyone can row the boat.

How many one-way trips does it take for them all to cross the river?

What if there were different numbers of adults? How many trips would be required in the following situations? • 6 adults and 2 children?• 15 adults and 2 children? • 3 adults and 2 children?• 100 adults and 2 children?

Today’s Agenda✔Opening Task: Crossing the River■ Revisit Big Ideas of MPs & Math Reasoning

Reasoning.■ Look for Math Practices #2, 7, & 8 in Tasks■ Enhance Tasks with Math Practices #2, 7, & 8.■ Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

Crossing the River Problem

Mathematical reasoning is….[finish the sentence].

Mathematical Reasoning Process (NCTM, 2011)

Conjecturing and

Generalizing

Justifying and Refuting

Investigating Why

Which Routine or Instructional Strategy did you try – share a highlight!

1. 3-Reads (Version 1 or 2)2. Numberless problems3. PICS, GETS, SIP, etc4. Other Graphic Organizers (which one(s)

Today’s Agenda✔Opening Task: Crossing the River✔Revisit Big Ideas of MPs & Math Reasoning

Reasoning.■ Look for Math Practices #2, 7, & 8 in Tasks■ Enhance Tasks with Math Practices #2, 7, & 8.■ Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

Relationship of the Mathematical Practices (Kelemanik, Lucenta, & Creighton, 2016)

Relationship of the Mathematical Practices (Kelemanik, Lucenta, & Creighton, 2016)

Cara’s Problem

Filling the Fish Tank

How many squares?

• Draw a 4 × 4 square.

• Find all the possible squares.

• Repeat for a 5 × 5 square.

• What patterns do you notice?

10 + = 4 + (3 + )

* Find a number to replace the square and a number to replace the triangle so that the equation is true.

* Find more pairs of numbers that will make the equation true.

* What do you notice about your number pairs?

Today’s AgendaOpening Task: Crossing the RiverRevisit Big Ideas of MPs & Math Reasoning

Reasoning.Look for Math Practices #2, 7, & 8 in Tasks■ Enhance Tasks with Math Practices #2, 7, & 8.■ Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

Task: Eduardo had 19 toy cars. Erica came over to play and brought 15 toy cars. How many cars did they have altogether?

How might you enhance the task to focus on a selected Mathematical Practice?

Enhance a Task with a Math Practice

Task: Eduardo had 19 toy cars. Erica came over to play and brought 15 toy cars. How many cars did they have altogether?

How tall is a stack of 25 of the ice cream cones pictured here?

How might you enhance the task to focus on a selected Mathematical Practice?

2.25 cm

5.1 cm

Enhance a Task with a Math Practice

How tall is a stack of 25 of the ice cream cones pictured here?

2.25 cm

5.1 cm

Enhance a Task

Today’s AgendaOpening Task: Crossing the RiverRevisit Big Ideas of MPs & Math Reasoning

Reasoning.Look for Math Practices #2, 7, & 8 in TasksEnhance Tasks with Math Practices #2, 7, & 8.■ Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

ENHANCING TASKS +

QUESTIONINGIntentional Focus on ONE Math Practice

Math Practice 2 Task A

Fifty-eight students, with 6 teachers, went on a field trip. They could fit 15 people in each van. How many vans will they need in order to take everyone on the trip?

5 × 1.5 = n

Math Practice 2 Task B

Reflecting on the Tasks

MP#2

How do you see the MP?

Which Supporting

MPs 3, 4, 5, 6? What specific

questions might you

pose?

Math Practice 7 Task A

Which calculations will generate the same result as 38 × 5:

(a)19 × 10

(b)40 × 5 – 2

(c) 30 × 5 + 40

Math Practice 7 Task B

What is the perimeter when there are 50 shapes?

Reflecting on the Tasks

MP#7

How do you see the MP?

Which Supporting

MPs 3, 4, 5, 6? What specific

questions might you

pose?

Math Practice 8 Task A

What rule or equation describes the number of triangles and squares you will need for Figure 20? Figure n?

Math Practice 8 Task B

9 + 7 = 9 + 3 = 4 + 9 = 8 + 9 = 9 + 9 =

10 + 7 = 10 + 3 = 4 + 10 = 8 + 10 = 10 + 9 =

Reflecting on the Tasks

MP#8

How do you see the MP?

Which Supporting

MPs 3, 4, 5, 6? What specific

questions might you

pose?

Today’s AgendaOpening Task: Crossing the RiverRevisit Big Ideas of MPs & Math Reasoning

Reasoning.Look for Math Practices #2, 7, & 8 in TasksEnhance Tasks with Math Practices #2, 7, & 8.Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2

Shandi’s Running GoalShandi has a goal to run a total of 800 laps around her school’s track this year. Her plan is to run exactly 4 laps a day. Which of the following expressions represents the total number of laps Shandi will have left after d days?

a. 800 – 4db. 800d – 4c. 4d – 800d. 4 – 800d

Shandi’s Running GoalShandi has a goal to run a total of 800 laps around her school’s track this year. Her plan is to run exactly 4 laps a day. Which of the following expressions represents the total number of laps Shandi will have left after d days?

a. 800 – 4db. 800d – 4c. 4d – 800d. 4 – 800d

Create an illustration or explanation to support your answer.

We have been on tasks!Cross the RiverCara’s CandyFilling the TankHow Many Squares?Missing Value EquationsCounting CarsStacking Ice Cream ConesMP 2 Tasks (Van & Equation)MP 7 Tasks (Perimeter & Equivalent

Expressions)MP8 (Pattern Block Equations &

Facts Patterns)Shandi’s Running Goal

Which tasks might you try

(adapted to your grade/children)?

Challenge: Enhance 3 different

tasks, one for each of these MPs, in your teaching this

upcoming month!

Today’s AgendaOpening Task: Crossing the RiverRevisit Big Ideas of MPs & Math Reasoning

Reasoning.Look for Math Practices #2, 7, & 8 in TasksEnhance Tasks with Math Practices #2, 7, & 8.Enhance Tasks + Questioning■ Generalize & Summarize

Webinar 2