Let’s Get to Know Let’s Get to Know Each Other!Each Other!How many distinct handshakes are How many distinct handshakes are there in our group?there in our group?

Your TaskYour Task

Determine the number of distinct handshakes Determine the number of distinct handshakes there are in our group.there are in our group. Individually meet/greet and shake hands with as Individually meet/greet and shake hands with as

many people as you can in 2 minutes.many people as you can in 2 minutes. When you shake their hands, tell them your name When you shake their hands, tell them your name

and where you teach.and where you teach. Work with a partner to devise a plan for determining Work with a partner to devise a plan for determining

the number of distinct handshakes there are in our the number of distinct handshakes there are in our group.group.

Test your plan using chart paper.Test your plan using chart paper.

DebriefDebrief

Compare/contrast methods on chartsCompare/contrast methods on charts In your group, write on white-board as In your group, write on white-board as

many different problem solving strategies many different problem solving strategies as you can for which you see evidence.as you can for which you see evidence.

Food for thought:Food for thought: Are all problem solving strategies Are all problem solving strategies

appropriate for any problem?appropriate for any problem?

Problem SolvingProblem Solving Definitions Definitions

Problem solvingProblem solving is what you do is what you do when you don’t know what to do! when you don’t know what to do! The key word is The key word is “stuck”.“stuck”.

Problem-solvingProblem-solving is a process where is a process where an individual uses previously an individual uses previously acquired knowledge, skills, and acquired knowledge, skills, and understanding to satisfy the understanding to satisfy the demands of an unfamiliar situation.demands of an unfamiliar situation.

Problem SolvingProblem Solving Definitions Definitions

A mathematical problem may be A mathematical problem may be described as described as problem-solvingproblem-solving if its if its solution requires creativity, insight, solution requires creativity, insight, original thinking, or imagination.original thinking, or imagination.

In In problem-solvingproblem-solving the initial reaction the initial reaction is, is, “I don’t know what to do”.“I don’t know what to do”.

Make A ListMake A ListAn organized list is useful to An organized list is useful to show all possible solutions.show all possible solutions.

How many differentHow many different

outfits can you make ifoutfits can you make if

you have two shirts andyou have two shirts and

four pairs of pants?four pairs of pants?

Red shirt, blue pants Red shirt, khaki pants

Yellow shirt, blue pants Yellow shirt, khaki pants

Red shirt, green pants Red shirt, black pants

Yellow shirt, green pants Yellow shirt, black pants

Guess and CheckGuess and CheckGuess at a problem’s answer Guess at a problem’s answer and check it. Keep trying until and check it. Keep trying until you are correct.you are correct.

The sum of two numbersThe sum of two numbers

is 27, their product isis 27, their product is

180.180.What are the twoWhat are the twonumbers?numbers?

Guess: 13 + 14 = 27Guess: 13 + 14 = 27

13 * 14 = 18213 * 14 = 182

Guess: 12 + 15 = 27Guess: 12 + 15 = 27

12 * 15 = 18012 * 15 = 180

YES!YES!

Draw a Picture or Draw a Picture or DiagramDiagramUse a picture or diagram to Use a picture or diagram to solve the problemsolve the problem

What are the possibleWhat are the possible

combinations forcombinations for

families with twofamilies with two

children?children?

B G

B G B G

Find a PatternFind a PatternUse a pattern to get from one Use a pattern to get from one numeral to the nextnumeral to the next

Lisa is drawing aLisa is drawing a

pyramid. She puts onepyramid. She puts one

block in the top row, twoblock in the top row, two

in the second, four in thein the second, four in the

third, eight in the fourth. third, eight in the fourth.

If she continues thisIf she continues this

pattern, how manypattern, how many

blocks will be in the tenthblocks will be in the tenth

row?row?

Work BackwardsWork BackwardsUse inverse operations to solve Use inverse operations to solve problems.problems.

Trish went to the mall and spentTrish went to the mall and spent

$23.50 on a new shirt, $6.75 on$23.50 on a new shirt, $6.75 on

lunch, and $31.25 on an new lunch, and $31.25 on an new skirt. skirt.

She had $16.50 left when she She had $16.50 left when she gotgot

home. How much money did home. How much money did sheshe

bring with her to the mall?bring with her to the mall?$23.50 + 6.75 + 31.50 + 16.50 = $77.25

$23.50 on Shirt $6.75 on Lunch $31.50 on Skirt $16.50 Left

Make a Table, Chart, or Make a Table, Chart, or GraphGraphTables, charts, and graphs help organize Tables, charts, and graphs help organize data. data.

There are 100 fifth There are 100 fifth graders in the school. graders in the school.

One fifth of them One fifth of them

like pizza, one half likelike pizza, one half like

spaghetti, one fifth likespaghetti, one fifth like

cheeseburgers, one cheeseburgers, one tenth like tacos. How tenth like tacos. How

many students like many students like each type of food?each type of food?0

5

10152025

30354045

50

P S C T

NumberofStudents

Act It OutAct It OutAct a problem out or use Act a problem out or use manipulatives.manipulatives.Four students sit at each lunch table. Sue is left-handed andFour students sit at each lunch table. Sue is left-handed and

doesn’t want to bump elbows with anyone, but she likes to sitdoesn’t want to bump elbows with anyone, but she likes to sit

next to her best friend Kate. Kate is to the left of Nancy. Allisonnext to her best friend Kate. Kate is to the left of Nancy. Allison

likes to be on the end. Where do each of the girls sit duringlikes to be on the end. Where do each of the girls sit during

lunch?lunch?

BrainstormBrainstormCreate a new way to look at a Create a new way to look at a problem.problem.

How do 6 ¼ and 9 ¾ How do 6 ¼ and 9 ¾ make 4 x 4?make 4 x 4?

$6.25 + $9.75 = $16.00$6.25 + $9.75 = $16.00

4 x 4 = 164 x 4 = 16

Use LogicUse LogicUse prior knowledge to solve problems.Use prior knowledge to solve problems.

A number is composite, and aA number is composite, and a

multiple of 6. The first digit ismultiple of 6. The first digit is

prime, but not 2. The number isprime, but not 2. The number is

less than 50 but greater than 20. less than 50 but greater than 20.

What is the number?What is the number?1.1. Composite numbers have Composite numbers have

factors other than one and factors other than one and themselves.themselves.

2.2. Prime numbers have only one Prime numbers have only one and themselves as factors.and themselves as factors.

3.3. Multiples of 6 >20, < 50: 24, 30, Multiples of 6 >20, < 50: 24, 30, 36, 42, 4836, 42, 48

SimplifySimplifyMake the numbers simpler to solve the Make the numbers simpler to solve the problem.problem.

The yard is 2,400cm long andThe yard is 2,400cm long and

1,700cm wide. How many1,700cm wide. How many

meters of fencing is needed meters of fencing is needed toto

surround the yard?surround the yard?

10cm = 1dm10cm = 1dm

10dm = 1m10dm = 1m

100cm = 1 m100cm = 1 m

P = (L x 2) + (W x 2)P = (L x 2) + (W x 2)

2,400cm = 24m1,700cm = 17mP = (24 x 2) + (17 x 2) = 82 meters of fencing

Problem-Solving StrategiesProblem-Solving StrategiesSimple ways to solve even the Simple ways to solve even the most complex problems:most complex problems:

Make a ListMake a List Guess and CheckGuess and Check Draw a Picture or Draw a Picture or

DiagramDiagram Find a PatternFind a Pattern Act It OutAct It Out

Work BackwardWork Backward Make a Table, Make a Table,

Chart, or GraphChart, or Graph SimplifySimplify Use LogicUse Logic BrainstormBrainstorm

MODEL DRAWING