Mathematically proficient students consider the available tools when
solving a mathematical problem.
Practice 5-Use appropriate
tools strategically.
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.
Exploring the attributes
of slope.
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.
And an activity with slope.
TI 73 Activity:
Number Sense
56081
-_____
34709
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=½x+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.
1. 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 halfsquares 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.