Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Practice 5-Use appropriate tools strategically.
Name________________________________________________ Period____ Date________________Name________________________________________________ Period____ Date________________ The Slope of a Line Adapted from Exploring Algebra I with Geometer’s Sketchpad (to be done with Geogebra Sketchpad) The steepness of things—ski runs, wheelchair ramps, bike ramps, or lines in the x-y plane—can be described in lots of ways. For instance, skiers know that “black diamond” runs are steep and challenging, whereas “green circle” runs are less steep and easier. Mathematicians prefer to use numbers to describe steepness so that they can compare the steepness of objects and solve problems. In this activity you’ll explore slope, a number that describes a line’s steepness. You are going to be asked to explore four types of slope and make conjecture about what are the characteristics of each type of slope. In a new sketch (Click FILE/Click NEW), left click the small pull down menu on the LINE icon in the upper left hand corner of your screen. Draw a line segment slanting up toward the right by left clicking a location on the grid, letting go of the clicker, moving your cursor to a new location and left click again. Record the points that are listed on the left hand side of your screen. Point A (x,y)=________________ Point B (x,y)=________________ What is the length of your line? __________ units Then left click on the SLOPE icon and click your line. The slope should appear on the left hand side of your screen. Record it here. m=_______________ Exploring the attributes of slope.
Exploring the attributes of slope. And an activity with slope.
TI 73 Activity: Number Sense 5 6 0 8 1 - _ _ _ _ _ 3 4 7 0 9 What is the missing part in the problem above?
TI 73 Activity: Number Sense Is it possible to write numeric expressions using only four 4s that will equal values from 0 to 100. You may use any of the operations, parentheses, exponents, etc that are on your TI 73 calculator. Here is one example: (4X4) – (4X4) = 0
TI 73 Activity: Number Sense Graph the following equations. Y = 3x – 2 Y = ½ x + 2 Y = 2x Y = .7x – 1 What do you notice about the lines?
TI 73 Activity: Number Sense Exploring the Number Line on a TI 73.
TI 73 Activity: Cross Fencing Pastures • This investigation will help you find the area of shapes by splitting them into convenient parts whose areas are easy to find. • Turn your calculator on and choose the APPS key. Choose • 4: GEOBOARD • From the main Geoboard menu, select 2:6x6
2. To format the Geoboard, select FMAT and make • sure that the following settings are selected: • LblsOff (Labels are off) • AxesOff (Axes are off) • CoordOff (Coordinates are off) • Decimal (Measurement is in decimal form) • Select QUIT to exit the FORMAT menu.
3. On your Geoboard, construct the hexagon that your teacher has displayed and find its area by counting squares and half-squares. Check your answer using your TI-73. Your Geoboard should look like the screen that your teacher has displayed. Choose QUIT. Choose OPTN. Choose 4: Erase Board
4. For the next shape (a trapezoid), counting squares and half-squares does not work very well because some parts may not be squares or half-squares. Construct the shape that your teacher has on the screen. Find its area by using a surrounding rectangle (see your teachers screen). Check your answer using your TI-73.