(10/01/96) ************************************* MathMagic Cycle 22: Level K-3 Regular ************************************* LET ME COUNT THE WAYS- 1) Tina has 3 shirts-red, blue, and yellow. She also has 2 skirts- black and white. Each day, she wears a different shirt with a different skirt. A) For how many days can she do this before she must repeat and Draw pictures of Tina and color if you wish. There is also a chart called a TREE that can help Tina to know which outfit is next to wear. It looks like this: |-----Black |---Red-------| | |-----White | | | |-----Black |--Blue-------| | |-----White | | | |-----Black |--Yellow-----| |-----White So, you can see all the possibilities and even count them. C) Uh oh, Tina accidentally ripped her yellow shirt and cannot wear it anymore. How many outfits does she have now? Draw a tree. 2) When Billy comes home from school each day, he gets a snack and a drink. His Mom lets him choose either a piece of fruit, a cookie, or a peanut butter sandwich. He can drink juice, milk, or a soda. A) Can you make a TREE that explains all the possibilities of snacks and sodas? How many snack and drink combinations are there? B) How many combinations are there if the drink is MILK? ************************************** MathMagic Cycle 22: Level K-3 Advanced ************************************** BALANCING ACT A scale can be used to measure the weight of various items, by comparing the item to a known weight. This cycle's problem will require you to do some empirical work (empirical is a scienttific term that means you will experiment and observe and then report what you see). First you will need to make a scale using a ruler (the kind with 3 holes), 3 pieces of string (all the same length) and 2 baskets (like for strawberries, milk , etc that are the same size). Tie the 3 pieces of string to the ruler through the 3 holes. Attach the two end pieces to the baskets and tie the middle string to a support. Hopefully, the scale will be balanced--if not, attach weights (paper clips, clay) to one side or the other until the scale is balanced. Before you begin, explain the differences (if any) between weight and mass. Experiment 1) Place 4 or 5 common items that are identical (pencils, erasers, etc) in basket #1. Decide on another, different item (marbles are good or paper clips) that can be used to balance them in basket #2. Then try to balance basket #1 with basket #2. Did it work right off--If not, add more to basket #1. Explain your results. Use your results to estimate the weight of 1 basket #1 item in terms of the basket #2 item. Check your results. Experiment 2) How much does one piece of paper weigh, compared to a paper clip or a pencil? Explain how you did this experiment? Which weighs more--500 sheets of paper or 500 paper clips? Experiment 3) You don't necesarilly need your scale for this. Suppose 6 oranges balance with 4 apples. And suppose 4 apples balance with 8 bananas. How many bananas will be needed to balance 9 oranges? Experiment 4) Suppose now that 12 pencils balance with 4 erasers, and that 6 erasers balance with 12 sharpeners. How many pencils would be needed to balance 6 sharpeners? ============================= Good luck MrH