Use tape diagrams to visually solve these problems.

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1 Use tape diagrams to visually solve these problems. 1) Jay and Nick have 2000 stickers altogether. If Jay has 600 more stickers than Nick, how many stickers does Jay have? 2) Gus s and Ike s combined running distance this week was 48 miles. If Gus ran three times as far as Ike, how many miles did Ike run? 3) Gus and Ike are playing with toy cars. The ratio of Gus s cars to Ike s cars is 7 to 3. Gus gives Ike 14 cars, so now they each have the same number of cars. How many cars do they each have now? 4) Eileen paid $8.25 for a book and a comic. The book cost twice as much as the comic. Find the cost of the book. 5) Mr. Jones gave ¼ of a sum of money to his wife. Then he divided the remainder equally among his 4 children. If each child received $600, find the sum of money. 6) John bought a bag of marbles. ¼ of the marbles were blue, 1/8 were green and 1/5 of the remainder were yellow. If there were 24 yellow marbles, how many marbles did he buy? 7) Dunkin Donuts sold 2/3 of their donuts in the morning and 1/6 in the afternoon. They sold 200 donuts altogether. How many donuts did they have left? 8) If 2/3 of a number is 12, what is the value of ½ of the number? 9) At a sale, Mrs. Brown bought a fan for $140. This was 70% of its usual price. What was the usual price of the fan? 10) 10 glasses of water can fill 5/8 of a bottle. How many more glasses of water are needed to fill up the bottle?

2 Marriage Fable It is customary in some people groups that if a young couple wants to get married they go before the leaders to get a blessing. The leaders take 6 strings and cluster them together. One end of each string is given to the young man, and the other end of string is given to the young woman. First, two of the ends of string at the young man s end are tied together. Then the two more are tied together, and then the last two. Next, two ends of the string at the young woman s end are tied together. Then the two more are tied together, and then the last two. If the strings are all tied together to form one large loop the young couple is given a marriage blessing. W hat is the possibility that all the strings w ill be tied together in one large loop?

5 Roller Derby

6 The Hare and the Tortoise Game Materials Game Board, a marker (chip), and a die Game Rules 1. The tortoise and the hare start each turn at S. 2. Each turn consists of three moves. Roll a die a total of three times per turn. After each roll, the marker is moved one place to the left if the number on the die is odd and one place to the right if the number on the die is even. 3. Scoring: The tortoise gets a point if at the end of the three moves the marker is on position P or X. The hare gets a point if the marker ends at position M, N, S, Y, or Z. Game Board M N P S X Y Z Odd Start Even

7 Record Sheet As you play the game, record where you land and the end of each turn by putting a tally mark in the appropriate space. Position Play Ends P X M N S Y Z Frequency Hare scored points. Tortoise scored points. What was the experimental probability that a player ended at each position? P(P) = P(X) = P(M) = P(N) = P(S) = P(Y) = P(Z) =

8 Solving Equations Using Strip Diagrams Solve the following problems using the Strip Diagram Method. Consider a variety of ways to set-up the algebraic equation to satisfy the solving of the problem. 1. There are 50 children in a dance group. If there are 10 more boys than girls, how many girls are there? 2. Ann has three times as much money as Brenda. Brenda has $200 less than Carol. Carol has $50 more than Ann. Find the total amount of money that Ann, Brenda, and Carol have.

9 Solving Equations Using Strip Diagrams 3. The ratio of Sam s money to Mel s money was 4:1. After Sam spent $26, Sam had $2 less than Mel. How much money did Sam have at first? 4. John is four times as old as his son. If their total age 10 years ago was 60, find their present ages. 5. A box contains a total of 200 blue, yellow, and orange beads. Twice the number of blue beads is 10 more than the number of yellow beads. There are 50 more yellow beads than orange beads. How many blue beads are there in the box?

10 Solving Equations Using the Cover up Method 1. 5(x 10) = (x + 10) = x 10 = x + 12 = x+6 2 = x+6 2 = = x = x 8 Solving Equations Using the Cover up Method

9. 5 + x 6 = 17 10. 5 + 6 x = 17 11. 5 x 6 = 17 12.

11 x 6 = x = x 6 = x = = 12 x = x = 12 x = x+7 12

12 Algebra Magic Instructions Pictures Alice Ben Carla Think of a number. 8 3 Add Multiply by Subtract Divide by Subtract your original number. 5 If = 33, what is? If = 30, what is? If = 15, what is? If = 34, what is?

13 Algebra Magic Instructions Pictures Dej Eli Fran Think of a number. 7 Multiply by Add Divide by Match each picture of a trick on the left with a set of instructions on the right. 1. a. Think of a number. Multiply by 3. Add b. Think of a number. Multiply by 4. Add c. Think of a number. Add 3. Multiply by d. Think of a number. Add 4. Multiply by 3.

14 Algebra Magic Make a separate algebra magic trick with at least five steps that will meet one of the bullets listed below: Final result is one more than the original number. Final result is 0. Uses all four operations. Result is same, whether steps are done backwards or forward. Instructions Pictures Giam Hiroshi Ian Think

15 Algebra Magic Instructions Pictures Description of Pictures Abbreviation Think of a number. a bucket Add 6. a bucket and 6 b + 6 Multiply by 2. 2b + 12 Subtract 2. Divide by 2. Subtract your original number. Match each abbreviation on the left with a set of instructions on the right. 1. 2b + 10 a. Think of a number. Multiply by 2. Add b + 2 b. Think of a number. Multiply by 5. Add b + 10 c. Think of a number. Add 2. Multiply by b + 5 d. Think of a number. Add 5. Multiply by 2.

16 Algebra Magic Instructions Pictures Description of Pictures Abbreviation Think of a number. a bucket b + 2 Multiply by 3. 2b + 6 Divide by 2. 3 If = + 10, then =. If 2b + 7 = b + 10, then b =. If = 11, then =. If = + 11, then =. If 4b + 5 = 3b + 7, then b =.

17 Systems: Two Versions of the Same Task Version I Draw a line through the two points (-4, 3) and (2, 6). Write the equation of the line. Draw a line through the points (-3, -6) and (2, 4). Write the equation of the line. Using the equations you found above, solve for the point of intersection of the two lines.

18 Version II. Find the intersection of the two lines, if it exists. Try to think of more than one way to solve the problem. (Problem adapted from Association of Mathematics Teacher Educators presentation by Herbel-Eisenmann & Cirillo, 2013)

19 Decide which expression equals. Do not use a calculator. Explain each result

21 Ivan s Furnace Ivan s furnace has quit working during the coldest part of the year, and he is eager to get it fixed. He decides to call some mechanics and furnace specialists to see what it might cost him to have the furnace fixed. Since he is unsure of the parts he needs, he decides to compare the costs based only on service fees and labor costs. Shown below are the price estimates for labor that were given to him by three different companies. Each company has given the same time estimate for fixing the furnace. Company A charges $35 per hour to its customers. Company B charges a $25 service fee for coming out to the house and then $25 per hour for each additional hour. Company C charges a $45 service fee for coming out to the house and then $20 per hour for each additional hour. For which time intervals should Ivan choose Company A, Company B, Company C? Support your decision with sound reasoning and representations. Consider using equations, tables, and graphs. Illustrative Mathematics Task

Fish Problem How much does a fish weigh if its tail weights 4 kilograms, its head weighs as much as its tail and half its body, and its body weighs as much as its head

22 Fish Problem How much does a fish weigh if its tail weights 4 kilograms, its head weighs as much as its tail and half its body, and its body weighs as much as its head and tail together? Dougherty, B. (2006). The Write Way Mathematics Journal Prompts and More for Algebra I. Curriculum, Research, and Development Group: Honolulu, Hawaii.

23 Warm-Up

Mathematics Workshop. For Parents of 3 & 4

Mathematics Workshop. For Parents of 3 & 4 Mathematics Workshop For Parents of 3 & 4 Objectives Participants will be able to: Learn how to help your child solve P3 & P4 Math problem sums using the Polya s problem solving approach. Learn how to