Problems (10 points) 1. Create 3 new addition problem that will require a 10-for-1 trade. Find the sums as demonstrated above and include diagrams of your process. For each step of the process, write down how many tens and ones you have. 2. You may be familiar with the use of the term carry to describe part of the addition algorithm. Explain how regrouping or renaming more accurately describes this process than the word carry. Extension to subtraction (5 points) 1. Represent the number 43 with base-ten blocks. For the take-away model of subtraction, what challenge do we face if we want subtract 28 from 43? 2. What can we do with the blocks so that we are able to take-away the necessary amount of blocks? Complete the subtraction problem 43-28 with base-10 blocks and show all steps with the virtual manipulatives, take screen shots and place in a document, or take pictures of your work with the printed base-ten blocks and include with your explanation. 3. You may be familiar with the use of the term borrow to describe part of the subtraction algorithm. Explain how regrouping more accurately describes this process than the word borrow. Extension to Division (5 points) 1. Let's consider the division problem 264 divided by 2. Represent the number 264 in base ten blocks and show what the operation 264 divided by 2 looks like with blocks. Include all diagrams that you created (with paper or virtual manipulatives) 2. What challenge do we face if we want to use base-10 blocks to demonstrate the division problem of 167 divided by 5? How is this problem initially different from 264 divided by 2? 3. With the base ten blocks, show how 167 can be divided into 5 equal groups. Place an equal number of the highest value blocks in each group. If this is not possible record a 0 in the hundreds place above the division frame. Make a 1-for-10 trade with the next lower value block. In some cases, it may be necessary to make more than one trade. In addition to showing how base 10 blocks can be used for division, show the division algorithm along-side your work. Question 5 (Binomial Option Pricing) A stock price model with the following parameters is given: So=100 u=1.1 d = 0.95 The riskless interest is r = 2% per period. Finally, there is a European call option with a strike price of B = 105 that matures at time t = 2. a) Fill in the stock prices in the binomial model. Find the payoffs of the put option at time t = 2. b) Find the price of the European call option at time t = 0. Explain your reasoning! Hint: The one-period state prices are given by 1+r-d (1+r) (u-d) ('up')= ('down')= = u-(1+r) (1+r) (u-d)