Answers

Challenge K-3/Ages 5-8

Award

Presented to MathWorld Interactive by K & H Extreme from  Upper Darby, Pennsylvania

FUN THAT NEVER ENDS

1. We started with the facts

                              4 children

                              31 pieces of candy

                         2. We are looking for ways to divide the candy

                         3. We used twizzlers, since they are long and can be divided into smaller                                 pieces

                         4. To divide the candy evenly:

                             All children would get:

                                   7 whole pieces

                                   1 half piece

                                   1 quarter piece

                         or:

                                  All children would get:

                                  15 half pieces

                                  1 quarter piece

                           or:

                                  If you divide each piece into quarters, all children would get 31                                             quarter pieces. Then we tried this:

          All children would get 7 whole pieces.

           Then draw straws. The person who pulls the smallest straw doesn't get an eighth  piece.

            3 children would get an eigth piece

Our last solution:

All four friends each get 7 pieces. Then draw straws for the last piece. The one who picks the smallest straw doesn't get an eighth piece, but the other 3 children do.

5. We checked our work by actually dividing the candy in the ways we listed.

6. Extend:

You are making Banana Splits for you and 3 friends. You have 7 bananas. How many ways can you divide the bananas so that everyone gets the same amount of  bananas?

THE NUMBER 2 is TOO Cool!

1.  the facts:  the are many ways to show the number 2

2.  What we are looking for:  How many ways can we show the number 2?

3.   Strategies:  We tried all four math facts:  addition/subtraction/multiplication/division

4.  Solutions:  addition:  1+1, 0+2, 2+0

subtraction:  we started with easy numbers:  3-2, 4-2, 5-3, 6-4, 7-5, 8-6, 9-7, 10-8 and so on.

Multiplication:  anything divided by half of itself is 2:  examples:  14 divided by 7 (half) is 2

100 divided by 50 is 2

1,000,000 divided by 500,000 is 2

5.  We checked our work by doing the above math problems for each math fact until there were no more solutions.  Note that for subtraction, we gave just a few examples, and for division a brief explanation of how many numbers can be used to show the number 2.

6.  Extend:  How many ways can you show the number 3?

  AWARD:  OUTSTANDING STRATEGIES

 pencil

Presented to MathWorld Interactive by Brain Blasters from Danville, California, USA

1. Facts: There are 4 people. Jose + 3= 4, There are 31 pieces of candy.

2. Problem: How many ways can you divide the candy?

3. Strategies:

You can use multiplication and solve this 4 X ? =31

You can use division : 31 divided by 4 =

You can use addition, adding 4’s until you get to 31:

4+4=8, 8+4=12,12+4=16,16+4=20,20+4=24,24+4=28

Then you take 31-28=3. Tells you how many pieces remain

With the remaining 3 pieces you can (a)give them away (b) eat them

(c ) keep them and divide them the following way:

Draw three squares representing the 3 extra pieces of candy.

Cut the 3 squares into fourths. Label all the parts ¼ . Each of the 4 people get ¼ of each piece. Color in ¼ on the square. Do this for all 3 pieces. Add together the pieces that you colored in. You have added ¼ + ¼ + ¼ . That is equal to ¾. Now each of the 4 people get 7 ¾ pieces.

Genna had the idea that there might be another ways to divide the candy. Her idea was that you could have 16 pieces and add 15 pieces adding up to 31.

Andrew had the idea from that there are MANY ways to divide the candy. After his idea, they have come to the conclusion that the problem never said to divide the candy equally. We checked back and reread the problem. The team agreed that there are now other ways to divide the candy. Andrew even suggested that the candy could be divided into fractional parts, and then divided.

4. Solution: 31÷ 4 = 7 ¾ if you divide them equally, many other ways of using division, multiplication, addition, and fractions if they are not divided equally.

5. Checking: We used teacher assistance, and checked each other’s work.<

Take number from a. (6) and subtract number from b. (4) example:

6-4 = 2

a. The answer will be 2 .This works for any number that you choose.

Another way to show 2 is multiplying or adding fractions:

4 x ½ = 2 because ½ of 4 =2

you can add ¼ + ¼+ ¼ + ¼ = 2

4. Solution: You can show 2 by using addition, multiplication, fractions, division

5. They checked each other’s calculations and statements

6. Challenge problem: How many ways can you show 355?

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