# Answers
Challenge K-3/Ages
5-8
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**
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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