(adapted from UC Berkeley ELD=AIM)
TYPE OF LESSON: / x exploratory / x developmental
□ transitional / □ review / □ enrichment/extension
STANDARD(s):
CCS 8.F
Define, evaluate, and compare functions.
1. Understand that a function is a rule that assigns to each input exactly
one output. The graph of a function is the set of ordered pairs
consisting of an input and the corresponding output.
2. Compare properties of two functions each represented in a different
way (algebraically, graphically, numerically in tables, or by verbal
descriptions). For example, given a linear function represented by a table
of values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.
3. Interpret the equation y = mx + b as defining a linear function, whose
graph is a straight line; give examples of functions that are not linear.
For example, the function A = s2 giving the area of a square as a function
of its side length is not linear because its graph contains the points (1,1),
(2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.
4. Construct a function to model a linear relationship between two
quantities. Determine the rate of change and initial value of the
function from a description of a relationship or from two (x, y) values,
including reading these from a table or from a graph. Interpret the rate
of change and initial value of a linear function in terms of the situation
it models, and in terms of its graph or a table of values.
5. Describe qualitatively the functional relationship between two
quantities by analyzing a graph (e.g., where the function is increasing
or decreasing, linear or nonlinear). Sketch a graph that exhibits the
qualitative features of a function that has been described verbally.
LESSON OBJECTIVE(s)
Students will be constructing a table and graph (both on paper and on .xl) based on properties of their rope. They will have to interpret the meaning of slope and y-intercept in the context of this problem. By analyzing slope, groups must find their “partner group” which is the group that has the same rope thickness as their rope.
MATERIALS:
General Resources
Knots on a Rope worksheet (1 per student)
(6) pieces of rope of (3) different thicknesses
- cut the 6 pieces of rope into the different lengths between 85cm-100cm.
graph paper
pencils
rulers / Technology
Computer lab with Excel
PRIOR KNOWLEDGE: Students should know how to create an X/Y table and a graph. They should have knowledge of the following terms:
- Slope (positive/negative)
- Y-intercept
- Writing an equation (slope-intercept form)
Haverhill Public Schools
Mathematics … Lesson Plan Template
Haverhill Public Schools
Mathematics … Lesson Plan Template
PROCEDURE/ITINERARYActivator
Tell the students that they will be given a rope and by the end of the lesson, they will have to find their “partner group”. The partner group has the same thickness rope as they do. They will make this discovery by analyzing tables and graphs.
Break the students up into (6) groups. Each group should have 4-5 students in each. You may assign roles to students (knot tier, measurer, etc.) but all students will complete their own worksheet. / Developer
Discuss the rope and about tying knots. Have a quick discussion on why one student from each group should be the “knot tier” and one should be the “measurer” (discuss human error).
Give each group a rope and let the students begin “Knots on a Rope” worksheet.
Students will create a table and graph on graph paper first and then move to the computer lab to put all the information into .xl. / Closer
Students will display their data/graphs on .xl. Groups will walk around the computer lab carefully studying the graphs in order to find their “partner group.”
Students will answer questions on slope and y-intercept, and relate the meanings in the context of the activity.
SUGGESTIONS FOR DIFFERENTIATION
Adaptations
Students may have difficulty relating the slope and the y-intercept in context of the activity. You may want to leave these questions for a group discussion.
- slope -> how much the rope was decreasing by tying each knot
- - y-intercept -> the length of the rope before any knot was tied / Extensions
FORMATIVE ASSESSMENT:
By analyzing the tables and graphs (slope, y-intercept) students must find their partner group that had the same thickness as their rope and support their answers in terms of slope.
Submitted: Tiffany Corcoran
Name:______
Knots on a Rope
Before we start this activity, give yourselves a group or team name.
Group Name:______
1. You will collect data showing how the length of your rope changes as you tie more knots in the rope. Before you begin, discuss in your group what you expect to find. Write your group’s prediction about what will happen:______.
2. Stretch the rope tightly and measure its length (use centimeters) before you tie any knots. Record the length in the table below. Tie one knot in the rope, stretch tightly, and measure the new length. Record it in the table. Continue tying knots, one at a time (make sure the knots do NOT overlap), stretching the rope, and measuring the length each time. Record all your measurements in the table.
Note: Try to be consistent and precise in the way you measure each time.
x=number of knots / y - length of rope (cm)0
1
2
3
4
5
6
3. Plot your data accurately on graph paper. Remember to label your axes and give your graph a title.
4. How does your data look when graphed? Why do you think that is? ______.
5. On your graph, draw a straight line that fits your data points as well as you can make it fit.
6. Using Exel or a similar graphing program, display your table and your graph on the computer. Be sure to indicate your group name. The graph should include the data points.
7. Put away your rope in a desk. It needs to be out of sight.
Now that the ropes are put away and out of sight, you should know that:
· There were three types of rope handed out.
· Each type of rope has a different thickness.
· Each type of rope was handed out to two different groups. Let’s call a pair of groups with the same type of rope “partner groups.”
8. Walk around the room with your group, carefully studying all the computer displays. Find your partner group.
Our Group Name:______
Our Partner Group Name:______
9. How did you find each other? Explain. ______.
10. Together with your partner group, choose a name for your type of rope. Write it down, as well as the names of the other types.
Name for our type of rope: ______
Names for the other types of rope: ______
______
11. Order the three types of rope from thickest to thinnest:
1. ______
2. ______
3. ______
Explain how you know this. ______.
12. Order the six pieces of rope by their original length, before you tied any knots. Order them from shortest to longest, using the six group names on the displays.
1.______
2.______
3.______
4.______
5.______
6.______
Explain how you know this. ______.
13. What is the y-intercept of your line? What is its meaning in the context of this activity? ______.
14. What is the slope of your line? What is its meaning in the context of this activity? ______.
15. Is the slope a positive or a negative number? Why? ______.
16. Can you write an equation for the line?
Congratulations! You’re done!