Homework Questions 2.5 LINEAR EXPRESSIONS AND EQUATIONS See the Student Electronic Resources for: Electronic version of this homework assignment (.doc file), including sketch pages Electronic images of all algebra pieces (Algebra Pieces.doc) Two Column Algebra Piece-Symbolic Work Paper Graph Paper 1. Model the following sequence, Black-Red Ls, L(n), with black and red tiles and: a. Step One: Loop and number each figure and Numerically determine the net value of each figure (but don t simplify). Mark your number counts on the figures. Step Two: Convert your looping ideas into Words. Step Three: Convert your looping and word ideas into Symbols Simplify your symbolic equation and check it for n = 1, 2, 3 and 4. See the provided sketch pages for figures that you can draw on to show your work BLACK RED Ls b. Describe the 100th Black-Red L. What does it look like? What is L(100)? c. Which Black-Red L will have a total of 2400 black and red tiles? Describe the figure including the number of black tiles and the number of red tiles. For this n, what is L(n)? d. What does the nth Black-Red L look like? Use your black and red n-strips and tiles, as needed, to model the figure; you do not need to show edge pieces. Sketch and describe the nth Black-Red L. Label the pieces clearly. e. If the collection of tiles in a certain Black-Red L figure is tripled and 30 black tiles are removed, the new collection of tiles will reduce to a minimal collection of 30 tiles (possibly red and possibly black). Which Black-Red L figure is it? Use algebra and/or algebra pieces to determine the solution. Clearly show your work and explain your thinking. Hint there may be more than one solution. f. For the Black-Red Ls tile sequence, the combined net value of two figures that are two figure numbers apart is 64. Which two figures are they? Use algebra and/or algebra pieces to determine the solution. Clearly show and explain your work. g. For the Black-Red Ls tile sequence, create a t-table for the net value, L(n), for figure number inputs n = 1, 2 6.
h. Plot the ordered pairs from the t-table on graph paper. Label the axes with appropriate numbers. i. Inspect the plotted ordered pairs and visually extend the pattern you see to n = 10. What do you estimate L(10) to be by just looking at the pattern of the graph? Check this value by using your previous symbolic work. 2. Model the following sequence, Black-Red Walls, W(n), with black and red tiles and: a. Step One: Loop and number each figure and Numerically determine the net value of each figure (but don t simplify). Mark your number counts on the figures. Step Two: Convert your looping ideas into Words. Step Three: Convert your looping and word ideas into Symbols Simplify your symbolic equation and check it for n = 1, 2, 3 and 4. See the provided sketch pages for figures that you can draw on to show your work BLACK RED WALLS b. Describe the 100th and the 101st Black-Red Wall figures. What do they look like? What are W(100) and W(101)? c. Which Black-Red Wall figure will have a total of 2400 black and red tiles? Describe the figure including the number of black tiles and the number of red tiles. For this n, what is W(n)? d. What does the nth Black-Red Wall figure look like for an even n and for an odd n? Use your black and red n-strips and tiles, as needed, to model the figures; you do not need to show edge pieces. Sketch and describe the even nth and the odd nth Black-Red Wall figure. Label the pieces clearly. e. If 20 black tiles are removed from four copies of the collection of tiles in a certain Black- Red Wall figure, the net value of the new collection of tiles will be 0. Which Black-Red Wall figure is it? Use algebra and/or algebra pieces to determine the solution. Clearly show your work and explain your thinking. f. For the Black-Red Walls tile sequence, the net value of the difference between two consecutive figures is -31. Which two figures are they? Use algebra and/or algebra pieces to determine the solution. Clearly show and explain your work. g. For the Black-Red Walls tile sequence, create a t-table for the net value, W(n), for figure number inputs n = 1, 2 8 h. Plot the ordered pairs from the t-table on graph paper. Label the axes with appropriate numbers.
i. Inspect the plotted ordered pairs and visually extend the pattern you see to n = 12 and n = 13. What do you estimate W(12) and W(13) to be by just looking at the pattern of the graph? Check these values by using your previous symbolic work. j. List at least three observations about the Black-Red Walls tile sequence and the graph associated with this tile sequence.
BLACK-RED Ls SKETCH PAGE Net Value L(1) = L(2) = L(3) = L(4) = Words Symbols
BLACK-RED WALLS SKETCH PAGE Net Value W(1) = W(2) = W(3) = W(4) = Words Symbols