CCoommmmuunniiccaattiioonn PPrroommppttss

Why?

What if … ?

Give an example of …

Is there a counter-example?

Do you see a pattern?

Is this always true?

What do you think would happen if … ?

How is this the same as/different from … ?

How does this connect to … ?

Can you explain that in another way?

If this is true then what else is true?

Describe what you did …

Compare this to ….

Explain your solution to …

What evidence can you give to …

List the …

Would a picture or diagram make your explanation clearer?

Hypothesize/ Estimate

Do/

Transform/Manipulate

Infer/Conclude

Reflect

Plan/

Model/Formulate

IInnqquuiirryy MMooddeell FFllooww CChhaarrtt

Explore/Investigate

Mathematical Models and Actions

Physical

Picture/ Diagram

Model 1 Model 2 Model 3 Model 4

Numerical

Model Number Number of Blocks1 12 33 64 10

Algebraic

where N represents the number of blocks and n represents the model number

Graphical

y = .5X^2+.5X+0

Communication

2)1( +

=nnN

Predict, Represent, Explore, Interpret, Transform

, M

anipulate, Conclude, R

eflect, Make C

onnections

Act it out or make a model.

Make a picture or diagram.

Look for a pattern.

Guess and check.

Make an organized list.

Make a table or chart.

Make a simpler problem.

Work backwards.

Use logical reasoning.

Problem-Solving Strategies

DD D

24 x 6 = 26 x 6 =

1.

2.

3.

2 +3 5

Understand the Problem

11.. TThhiinnkk aabboouutt tthhee pprroobblleemm..

22.. TTaallkk tthhrroouugghh tthhee pprroobblleemm wwiitthh aa ppaarrttnneerr..

33.. SSeelleecctt aa ssttrraatteeggyy,, ttoooollss,, oorrggaanniizzeerr,, aanndd mmaatteerriiaallss..

44.. EEssttiimmaattee tthhee ssoolluuttiioonn..

55.. SSoollvvee aanndd rreepprreesseenntt tthhee pprroobblleemm..

66.. RReefflleecctt:: iiss tthhee ssoolluuttiioonn rreeaassoonnaabbllee??

77.. LLooookk ffoorr ppaatttteerrnnss aanndd rruulleess..

88.. EExxppllaaiinn aanndd jjuussttiiffyy yyoouurr tthhiinnkkiinngg iinn ddiiaaggrraammss,, wwoorrddss,, ttaabblleess,, mmooddeellss,, aanndd nnuummbbeerrss oorr ssyymmbboollss..

RReepprreesseennttaattiioonnss MMaakkee OOuurr TThhiinnkkiinngg VViissiibbllee

The more ways we represent our thinking, the deeper our

understanding becomes.

Pictures/Diagrams

Concrete Materials/ Models Visual Text

Charts/Graphs/ Tables

Written Symbols/ Equations Context

Oral and Written Language

Day 1 Day 2 Day 3

12 x 36 12n + 2 = 26

75 cents

1

2