JUST FOR FUN. 2. How far can you walk into a forest? 5. Rearrange the letters of NEW DOOR to make one word.

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Howard Arron Hodge
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1 JUST FOR FUN Use logical reasoning to answer the questions below. 1. How man four-cent postal cards are there in a dozen?. How far can ou walk into a forest? 3. How much dirt is there in a hole that is three feet wide, four feet long, and two feet deep? 4. There was a blind beggar who had a brother, but this brother had no brothers. What was the relationship between the two? 7. Horace claimed that x 10 = x 11 is a true statement. What was his explanation? 5. Rearrange the letters of NEW DOOR to make one word. 8. What do all of the following words have in common? deft hijack calmness canop laughing first stupid crabcake 6. If six glasses are arranged in a straight line and the first three are full of water and the last three are empt, what is the fewest number of glasses that can be moved so that the glasses alternate: empt, full, empt? 9. A train that is one mile long traveling at 60 mph enters a tunnel that is one mile long. How long until the train is out of the tunnel? 10. Divide 30 b 1 and add 10. What is our answer? 11. What mathematical smbol can be placed between and 3 so that the resulting expression names a number between and 3? 1. A student correctl shows that 1 of 1 is seven. How? Exploring Linear & Non-Linear Relationships 3

2 Objectives: The learner will: analze situations and formulate sstems of equations to solve problems. investigate methods for determining the solution sets for sstems of linear equations using and translating among concrete models, graphs, algebraic representations, and verbal models. explore the parent quadratic function using tabular and graphic methods, determine the effect of parameter changes on the parent graph, and analze real-world situations modeled with quadratic functions. simplif and perform operations on powers, and identif and simplif polnomials, performing the operations of addition, subtraction, and multiplication. Activit I 4

3 Brainstorm different linear situations we can graph on the same graph. 5

4 Activit II Compare the speed ou write with our right hand to the speed ou write with our left hand b writing one letter in each box on the next page. Use the letters T and X which represent TX (capital letters). Right Hand Data Time (s) # of squares completed Left Hand Data Time (s) # of squares completed 6

5 7

6 8

7 9

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9 Activit II cont Discussion Questions: 1. What s the best wa to compare these two sets of data?. What tpe of graph should we use? 3. Should we have (0,0) on our graph? 4. Examine our data, what tpe of graph would best represent our data? 5. What are some similarities and differences with our data? 11

10 6. Is there an intersecting point for the graphs? 7. Is it possible for the graphs to have more than one intersecting point? Activit III Examine the graphs below and record our observations

11 Activit IV Create a stor problem for the graph illustrated 13

12 Activit V Place the numbers from 1 15 in the appropriate place according to the following rules: 1. All even numbers must be inside the triangle.. All odd numbers must be inside the ellipse. 3. All multiples of 5 must be inside the trapezoid. 14

13 Basket of Coconuts Work with our group to solve this problem. You ma solve it using an strateg. 1. Five baskets contain coconuts. The first and second baskets together have a total of 5 coconuts. The second and third baskets have 43 coconuts. The third and fourth baskets have 34 coconuts. The fourth and fifth baskets have 30 coconuts. And the first and fifth baskets have 47 coconuts. How man coconuts are in each basket?. Solve the problem another wa. Describe how this method is similar to or different from the method ou used in problem 1. 15

14 Examining Quadratic Functions (Graphing) Use the vertex form ax ( h) + kto examine the role of a, k, and h in quadratic functions. Graph the functions on graph paper using different colored dots to plot each function and b using the colored wire to connect the dots. Set 1 1 = x = 3 = 4 4 = 6 5 = 3 x x x x Set 1 = x = x + 3 = x 3 4 = x = x 6 Set 3 16

15 1 = x = ( x+ ) 3 = ( x 4) 4 = ( x 6) 5 = ( x+ 3) Set 4 1 = x = x 3 = 5 x 4 = 5 x Set 5 1 = x = ( x+ ) 3 = ( x 4) 4 = ( x 4) 5 = ( x 4) 3 17

16 Polgons & Diagonals Jake discovered a relationship between the number of sides in a polgon and the number of its diagonals. 1. Complete Jake s table: Number of Sides (x) Number of Diagonals (). Describe patterns ou notice in the table. 18

17 3. Write an equation whose graph would include the points given b the data in our table. Graph our equation. 4. A polgon has 17 sides. How man diagonals will it have? Describe our reasoning? 5. A polgon has 09 diagonals. How man sides does it have? Describe our reasoning? Laws of Exponents Activit Sheet A 1. Write ab x ab without using exponents. DO NOT multipl them out. a. How man a s are being multiplied? How man b s are being multiplied? b. Rewrite our expression using exponents.. Write mn 4 3 x 3 mn without using exponents. DO NOT multipl them out. a. How man m s are being multiplied? How man n s are being multiplied? b. Rewrite our expression using exponents. Look at Questions 1 and above. What patterns do ou notice? What rule can ou generalize about multipling expressions with like bases? 19

18 Tr our new rule: ( x z)( xz ) ( rst)( rst)( rst ) Laws of Exponents Activit Sheet A Cont 5. Write ab ab without using exponents. DO NOT divide them out. a. Cancel out an common factors between the numerator and denominator. How man a s remain? How man b s remain? b. Rewrite our expression using exponents. 6. Write mn mn without using exponents. DO NOT divide them out. a. Cancel out an common factors between the numerator and denominator. How man m s remain? How man n s remain? b. Rewrite our expression using exponents. Look at Questions 5 and 6 above. What patterns do ou notice? 0

19 What rule can ou generalize about dividing expressions with like bases? Tr our new rule: 7. x z 6 7 x z rst rst Write Laws of Exponents Activit Sheet A Cont 3 5 ( ab ) without using exponents. DO NOT multipl out. a. How man a s are being multiplied? How man b s are being multiplied? b. Rewrite our expression using exponents. 10. Write 5 3 ( mn ) without using exponents. DO NOT multipl out. a. How man m s are being multiplied? How man n s are being multiplied? b. Rewrite our expression using exponents. Look at Questions 9 and 10 above. What patterns do ou notice? 1

20 What rule can ou generalize about raising expressions with like bases to a power? Tr our new rule: ( x z ) ( rst ) Laws of Exponents Activit Sheet B Use our TAKS formula chart to identif the following formulas: Area of rectangle: Area of triangle: Area of trapezoid: 1. Calculate the area of a rectangle that has a length of x z x z and a width of. Calculate the area of a trapezoid that has base lengths of 4 a height of st. 3 5 st and 3 5 3s t, and 3. Calculate the area of a triangle that has a base of 4 3m n. 7 8m n and a height of 4. If a rectangle has an area of x and a base of 4 x, what is its height?

21 5. If a triangle has an area of m n and a height of 16m n, what is its base? 6. Distance (d), rate (r), and time (t) are related b the formula d=rt. If a ball rolls p q feet for 4 p q minutes, what is the rate? Power Bingo Power Bingo uses game sheets of 16 squares containing monomials that are the products of an three of the following monomials. 3x 3x 3x 3x x x x x Three tiles are drawn from the sack, and the three monomials picked are announced to the class and displaed on the overhead. If a square on our game sheet contains the product of the three monomials announced, ou ma cover or mark that square. The first plaer to cover four squares in a row verticall, horizontall, or diagonall wins the game One possible monomial is 9x, the product of 3x, 3, and x. How man possible products do ou think there are? How did ou arrive at our answer?. Find all possible monomials that are products of an three of the 16 monomials listed above. Write our products on notebook paper. 3. How does the number of monomials in part compare with our answer in part 1? 3

22 4. You are almost read to pla Power Bingo. Before ou can pla, ou need to fill our game sheet with different possible products of three monomials that might be drawn from the sack. When ou are done, ou are read to pla. 5. Once ou have plaed Power Bingo, think about changes ou ma make in filling out our game sheet? Wh? Power Bingo Game Sheet Power Bingo Game Sheet 4

Resources Used Doughert, B., Matsumoto, A., & Zenigami, F. (003). Explorations in Algebra: Hands- On Lab Activities. Honolulu, Hawaii: Curriculum Research & Development Group.

23 Resources Used Doughert, B., Matsumoto, A., & Zenigami, F. (003). Explorations in Algebra: Hands- On Lab Activities. Honolulu, Hawaii: Curriculum Research & Development Group. Houston Independent School District. (004). CLEAR Curriculum. Houston, TX: Curriculum & Instruction Department. Region IV Education Service Center. (003). TAKS Mathematics Preparation Guide. Houston, TX: Region IV ESC. Semour, Dale & Beardslee, E. (1990). Critical Thinking Activities. Palo Alto, CA: Dale Semour Publications. 5

Investigation Free Fall

Investigation Free Fall Name Period Date You will need: a motion sensor, a small pillow or other soft object What function models the height of an object falling due to the force of gravit? Use a motion