December 11, 2013Algebra and 8th GradeKimberly Tarnowieckyi

Problem Solving revisited(Worthwhile Mathematical Tasks)

Last time together October 23.

Think back over your lessons form October 24 to December 10and pick a lesson or part of a lesson that went really well.

*Learning Targets

We should be able to…1. Use “regular” math problems to promote a

deeper understanding of the process involved in solving problem.

2. Be explicit about the thought process that happens prior to solving complex problems.

3. Select Activities/Performance Tasks that allow students to process and question.

4. Allow students to ask questions, discuss their thoughts, and share their ideas.

Last time together October 23.

Think back over your lessons form October 24 to December 10and pick a lesson or part of a lesson that went really well.

Problem Solving Lesson Planning

Careful Selection of problemsWork through problems before giving to studentsThink about where students may get stuck and be

prepared to guide and probePre-Teaching prior to giving the problemBe willing to show our thinking to studentsSequencing of activities (Problem Strings)Creating Time for student workCollaborative Work (give students something to talk

about)Showing student work and multiple strategiesTime for students reflect on their process

U • Understand the Problem

P• Plan for solving the problem

S • Solve the problem

• Check the Problem

Understanding the Problem: Key Questions

What kind of

problem is it?

What is the

question asking

for?

What informatio

n am I given to solve the problem?

Planning for

Solving

Draw a picture

or graph Gues

s and Chec

kLook for a

pattern

Work Backwar

ds

Simplify the Proble

m

Use Manipulati

ve

Break into

Smaller Pieces

Check

Reasonableness

Write a solutio

n senten

ce

Substitute back in to see

if true

*Math Time

*Which candles?

*CCSSM connections*CCSS.Math.Content.8.F.B.4 Construct a function to model a

linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

*CCSS.Math.Content.HSA-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*CCSS.Math.Content.HSF-LE.B.5 Interpret the parameters in a

linear or exponential function in terms of a context.

Problems for Problem Solving need to

*Focused on important mathematics; mathematical goal aligned with the standards*Provide opportunities for discussion*Provokes thinking and reasoning about the mathematics; high level of cognitive demand*Engage students in the mathematical practices

U • Understand the Problem

P• Plan for solving the problem

S • Solve the problem

• Check the Problemhttps://www.teachingchannel.org/videos/ups-problem-solving-strategy

How students should do math: Mathematical

Practices

Make sense of problems & persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the

reasoning of others Model with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated

reasoning

* What mathematical practices do you see in the video?

*Collaborative Time

oWork in common groupsoUse the time as you see appropriate to help you

prepare for future lessons and/or assessments.oLook for opportunities to teach problem solving.oAt 2pm we will come back together and share out.