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Problem Solving

Teacher info

Problem Solving

The Dog, the Goose and the Bag of Corn

The farmer takes the goose across and leaves the dog with the corn. The farmer then goes back across the stream and gets the corn. He takes the goose back across with him because he cannot leave it with the corn. He then gets the dog and takes it across leaving it on the other side with the corn. He then goes back across once again, gets the goose and returns to the other side of the stream with all safely across and not eaten!

Problem Solving

“Let’s Make Some CENTS of This!”

Sam has 50 cents in nickels and dimes. How many of each type of coin could he have? Organize your information and present the possible answers in your Math Journal.

After you list all the possible ways he could have 50 cents in nickels and dimes, what if I said that he has exactly 7 coins? What would the answer be now?

Problem Solving

Let’s Make Some Cents of This!

Sam could have the following coins:

1 dime & 8 nickels

2 dimes & 6 nickels

3 dimes & 4 nickels

4 dimes & 2 nickels

if he has exactly 7 coins he would have 3 dimes and 4 nickels!

Problem Solving

“Stop It!”At a stop sign, 2 cars are stopped in front of a car, and 2 cars are stopped behind a car. ‘What is the fewest number of cars that could be stopped at this stoplight?Show how you solved this problem in your Math Journal.

Problem Solving

Stop it!

The fewest number of cars The fewest number of cars that could be stopped at the that could be stopped at the stoplight is 3!stoplight is 3!

“The Pet Problem” One bright and sunny day, a truck delivered a box of new animals to the pet store. Hannah needed to count the number of animals in the box. When she peeked in, she saw many snakes and tarantulas all mixed up! She carefully counted 18 heads and 64

legs.How many snakes were in the box and how many tarantulas? Show how you solved this problem by writing down your thinking in your Math Journal.

Problem Solving

Problem Solving

THAT’S RIGHT! There would be 8 tarantulas and 10 snakes!

The pet problemCOUNT THEM AS THEY APPEAR!

CLICK HERE FOR ANSWER

Problem SolvingPYRAMID OF MYSTERYDuring an ancient exploration, these numbers were discovered written on the walls of a pyramid. They found a pattern in the numbers…can you?

1 1 1

1 2 1 1 3 3 1

1 4 6 4 1 1 5 10 10 5 1

----- ----- ----- ----- ----- ----- ----- What is the number pattern, and what numbers go into the empty spaces? Copy and complete this pattern in your Math Journal.

Problem Solving

1 1 1

1 2 1 1 3 3 1

1 4 6 4 1 1 5 10 10 5 1

1 6 15 20 15 6 1

PYRAMID OF MYSTERY

Problem Solving

Problem Solving

Sally and the Peanuts

Sally had peanuts in all!!

PROBLEM SOLVING

Place the numbers 1-9 in the nine circles below so that the sum of each side of the triangle is equal to 20.

6

PROBLEM SOLVING

Place the numbers 1-9 in the nine circles below so that the sum of each side of the triangle is equal to 20.

6

8

1

5

9

2

4 7 3

PROBLEM SOLVING

Place the numbers from 1-9 in the nine circles below making the sum of each of the two columns equal 25.

25 25

PROBLEM SOLVING

Place the numbers from 1-9 in the nine circles below making the sum of each of the two columns equal 25.

25 25

2

7

5

3 6

4 9

8

1

PROBLEM SOLVING

BOB WAS SHORTER THAN GEORGE AND JOAN WAS TALLER THAN GEORGE. WAS JOAN SHORTER THAN BOB, OR WAS SHE TALLER THAN BOB?

PROBLEM SOLVING

PROBLEM SOLVINGLYNN, MICKEY, & TRACY WERE THE BEST READER, SPELLER, AND ARTIST IN THE CLASS. LYNN WAS TALLER THAN THE BEST SPELLER. MICKEY WAS YOUNGER THAN THE BEST ARTIST. MICKEY WAS TALLER THAN LYNN. WHICH STUDENT WAS THE BEST READER? SPELLER? ARTIST?

PROBLEM SOLVING

LYNN--ARTIST

MICKEY--READER

TRACY--SPELLER

PROBLEM SOLVING

Boys and dogs

Looking out in the backyard one day, I saw an assortment of boys and dogs. Counting heads, I got 22. Counting legs, I got 68. How many boys were in the yard? How many dogs?

PROBLEM SOLVING

Boys and dogs

PROBLEM SOLVING

I AM A THREE-DIGIT WHOLE NUMBER.I AM AN ODD NUMBER.ONE OF MY DIGITS IS 7.

I AM DIVISIBLE BY 5.I AM LESS THAN 700.

I HAVE NO EVEN DIGITS.I AM ALSO DIVISIBLE BY 3.I AM GREATER THAN 200.

EACH OF MY DIGITS IS DIFFERENT.I AM A MULTIPLE OF 25.

?GUESS MY NUMBER?

PROBLEM SOLVING

I AM:

?GUESS MY NUMBER?

SYMMETRY

AFHJMQRTWYIn your journal, copy all the letters above that have at least one line of symmetry. Make sure you print the letters as they are shown on here. Then, take a red marker, and draw at least one line of symmetry on each letter.

A H M

T W Y

SYMMETRY

AFHJMQRTWY

Mental ComputationThe answer is 36…what

is the question? Some sample questions might be…

What is 3 x 2 x 6?

How many inches are in one yard?What is a quarter, a dime, and a

penny worth?How many eggs in three dozen?

What is 12 x 3?

Mental ComputationNow YOU come up with a 4

question riddle about each of these answers!

The answer is 12.The answer is 24.The answer is 13.

The answer is 100.

Mental ComputationRiddle me this and riddle me

that

You can solve riddles…just like that!

I am less than 10.

I am an odd number.

I am more than 6.

I am a multiple of 3.

What number am I???

Mental ComputationRiddle me this and riddle me

that

You can solve riddles…just like that!What number am I???

9

Mystery Numbers RevisitedIf you count by fives, I have one left over.

I am a multiple of 7.

My tens digit is twice my ones digit.

The sum of my digits is 3.

What’s the Mystery Number??

Mystery Numbers RevisitedIf you count by fives, I have one left over.

I am a multiple of 7.

My tens digit is twice my ones digit.

The sum of my digits is 3.

What’s the Mystery Number??

21

If the day before the day before yesterday was Monday, what is the day after the day after tomorrow?

If the day before the day before yesterday was Monday, what is the day after the day after tomorrow?

Today

Tomorrow The day after tomorrow

The day after the day after tomorrow

Day before the day before yesterday

MONDAY

The day before yesterday

TUESDAY

Yesterday

WEDNESDAY THURSDAY

FRIDAY SATURDAY

1 2 3 4 5 6 7 8 9 10

1 4

Number of dots on each side

Total number of dots

1 2 3 4 5 6 7 8 9 10

1 4

Number of dots on each side

Total number of dots

After completing the table in your journal, see if you can find at least three patterns.

List them in your Math Journal.

1 2 3 4 5 6 7 8 9 10

1 4 9 16 25 36 49 64 81 100

Number of dots on each side

Total number of dots

WHY DO WE CALL THESE NUMBERS SQUARE NUMBERS?

EXPLAIN YOUR ANSWERS IN YOUR JOURNAL.

?

? ?

? ? ?

1

6 5

2 4 3

This is one solution!

4

3 2

5 1 6

Here is another...

# of triangleTotal # of dots

1 2 3 4 5 6 7 8 9 10

1 3 6

After completing the table in your journal, see if you can find at least three patterns.

List them in your Math Journal.

# of triangleTotal # of dots

1 2 3 4 5 6 7 8 9 10

1 3 6

After completing the table in your journal, see if you can find at least three patterns.

List them in your Math Journal.

10 15 21 28 36 45 55

# of triangleTotal # of dots

1 2 3 4 5 6 7 8 9 10

1 3 6

WHY DO YOU SUPPOSE THIS IS CALLED A TRIANGULAR PATTERN?

RECORD YOUR ANSWER IN YOUR JOURNAL.

PROBLEM SOLVINGTHAT’S ALL FOLKS!

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TEACHERS

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PATTERNS GRAPHING GEOMETRY FRACTIONS measurement PROBLEM DECIMALS SOLVING

Problem SolvingThe entire focus of elementary math is to encourage independent problem solving. Most of the process can be written a Math Journal. Here are some suggested questions that students could use as a format when writing in their journal.

1. Did I state the problem or question?

2. Did I write as a mathematician & use appropriate vocabulary.

3. Did I state the strategies I used?

4. Is my reasoning logical?

5. Did I show a picture, graph or table, of the problem?

6. Is my answer reasonable & is it labeled?

7. Did I summarize & justify my answer?