High School Geometry Days 001008

8/12/2019 High School Geometry Days 001008

1/21

5

STRUCTURED CURRICULUM LESSON PLAN

Day: 001-002 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): All

TAP:

Perform arithmetic operations involving

integers, fractions, decimals, and percents

explicitly stated or within context

Choose and apply appropriate operational

procedures and problem-solving strategies to

real-world situations

Understand number systems

Understand geometric properties and

relationships; apply geometric concepts and

formulasApply a variety of estimation strategies:

standard rounding, order of magnitude, front-

ending, compatible numbers, and

compensation

Use variables, number sentences, and equations

to represent solutions and solve problems

Analyze and interpret data presented in charts,

graphs, tables, and other displays

Understand and apply principles of probability,

central tendency and variability

Demonstrate understanding of measurementconcepts and apply measurement skills

ISAT:

Solve problems requiring computations with

whole numbers, fractions, decimals, ratios,

percents, and proportions

Understand and apply geometric concepts and

relationships

Use mathematical skills to estimate,

approximate, and predict outcomes, and to

judge reasonableness of results

Identify, analyze, and solve problems using

equations, inequalities, functions, and theirgraphs

Understand and use methods of data collection

and analysis, including tables, charts, and

comparisons

Demonstrate an understanding of measurement

concepts and skills

Unit Focus/Foci

Learning the Main Functions of the Graphing Calculator

(Order of operations within expressions entered into the calculator. Finding the appropriate

dimensions for the viewing window of a graph. Exploring the functions of TRACE, TABLE,

and ZOOM.)

Instructional Focus/Foci

Learning the Operation of Important Keys on the Graphing Calculator

Materials

Classroom set of graphing calculators and users guides

Overhead graphing calculator


2/21

6

Overhead projector

Educational Strategies/Instructional Procedures

Preparation for Lesson:

Arrange desks in groups of three or four and assign a number to each group.

Opener:

(10 minutes) Allow students to have unstructured time with the calculators. Direct

them to discuss what they discover with the members of their groups.

Complete the calculator lessons.

Closer:

(Last 5 minutes) Choose one or two keys from the list and have students write a sentence

explaining when they might use that key. Students are allowed to use the calculator but not their

notes.

Integration with Core Subject(s)

LA: Understand explicit, factual information

Understand the meaning of words in context

Draw conclusions, inferring meanings from text

Apply information presented in the text

SC: Understand uses of scientific units and instruments

Understand implications of technology in our society

SS: Demonstrate an understanding of important historical events

Connection(s)

Enrichment: Have students write a paper about the impact of the microchip on society.

Fine Arts: Have students create artwork using symbols generated by the

graphing calculator.

Home: Have students find objects around their home that have electronic controls, buttons or

keys that are essential to the operation of the object. Have them write a sentence or two

about the function of the key or control.

Remediation: See Home.

Technology: See Home.


3/21

7

Assessment

Evaluate Calculator Activity 1 using the Structured Curriculum Scoring Rubric.

Homework

Have students review their notes and learn the function of each key discussed.

Teacher Notes

The first day is very important in setting the tone for the classroom. Be sure to explain school

policies regarding the appropriate use of graphing calculators (i.e., policy for checking out/in

calculators, playing games, etc.).

It is important to let the students have unstructured time with the calculators at first. Students

will be so involved with the technology that they probably will not focus on any specific task

initially.

Solutions to Calculator Activity #1:

1. 7 5. .046875

2. 387,420,489 6. 21.58

3. 59/40 7. 6.20791875

4. 1793/5000 8. .0250438775


4/21

8

TI 82/83 Calculator Lesson 1

Have the students work in pairs. Have each pair explore the graphing calculator

and make notes of their observations. (Allow 15 minutes for exploration.) Haveeach pair report their observations to the class and list their findings. The list

should include:

ON/OFF The calculator has an automatic turn-off

after approximately 6 minutes.

Press the ONkey and the same screen

will reappear.

CLEAR The clear key will give a new work

place or a clean home screen.

CONTRAST Press 2nd

and the to darken or 2nd

and

the to lighten.

The calculator displays a setting from 1-

9 in the upper right-hand corner. If the

screen is light with a contrast setting of

8 or 9, the batteries are weak. Eitherreplace or recharge the batteries.

ENTER Tells the calculator to perform the

indicated operation.

2nd Utilizes the function on the upper left

side of a key.

ALPHA Utilizes the function on the upper rightside of a key.

2nd

ALPHA Locks in the Alpha mode.


5/21

9

Have the students work along with you as you demonstrate the following:

The (-) is used for negative. The subtraction key will give an error message if

used for negative.

POWERS The x2will square the expression and

the ^ can be used for any power.

ROOTS To find a square root, use 2nd

x2. This

gives a . To find roots greater than

2, enter the index number, then MATH

5, and then the radicand.

RECIPROCAL To find the reciprocal, use x-1

.

EDITING To remove a character, place the cursor

on the character and press DEL.

To add a character, press 2nd

DEL.

DEEP RECALL To recall previous entries, press 2nd

ENTER. It can go back approximately

32 problems.

ANSWER To display the answer in fraction form,

press MATH1 ENTER.

42

16

!!!!

3 4

81

!!!!

64

8

4 625x

5


6/21

10

To display the answer in decimal form,

press MATH2 ENTER .

STORE

To get

To assign a value to a variable, use

STO

Type 5 STO ALPHAA.

To multiply 6 times the contents of A,

type 6 ALPHAA.

5A

5

6A

30


7/21

11

Calculator Activity # 1

Use your graphing calculator to complete the following:

1. 24014

2. 99

3.3

5

7

8++++ Write the answer as a fraction.

4. . .7896 4531 Write the answer as a fraction.

Let a = .125 and b = 7.11

5. 3 2a

6. 2 3a b++++

7. ab a b2 2

8. 12 4

a b

or Find the reciprocal of a b2 4


8/21

12


Day: 003 007 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 6B2; 7A6; 8C2,4; 10A1-4

TAP:



Demonstrate understanding of measurement

concepts and apply measurement skills

ISAT:


and analysis, including tables, charts and

comparisons


concepts and skills

Unit Focus/Foci

Analyzing Data


Identifying and Determining Scatter Plots, Lines of Best-Fit, and Linear Correlations

Materials

Meter sticks

Yard sticks

Graph paper

Chart paper

RulersCopies of Analyzing Data Activities #1-5

Copies of Analyzing Data Homework 1-3


Distribute copies of Analyzing Data Activities #1-5. Read the guidelines aloud as the students

follow along silently. Answer any questions the students may have. Assign students to groups

using a method from Appendix B and monitor activities.

Have the students note the following:

Scatter plot: a graph that shows the relationship between two sets of data plotted as ordered

pairs.

Line of best-fit: A line on a scatter plot that comes as close as possible to the data points.

Correlation: The relationship between two sets of data.


9/21


10/21

14

Teacher Notes

1. Check that the students are in groups of at least five.2. Tape two or more yard sticks to an object in the room. Place the yard sticks 20 cm above the

floor. This will make measuring height easier for the students.

3. Encourage all of the students to participate.4. Remind students that line of best-fit should:a) show the direction of best-fitb) divide the points equallyc) have as many points as possible on the line


11/21

15

Guidelines for Activity 1

1. The groups should be composed of at least five people.

2. One person from each group will secure and return all materials.3. Take turns measuring and recording the information.

4. Double-check and verify all measurements before recording the information.

5. Prepare a report on group Activity 1.

6. One person from each group will present his/her groups report to the class.

ACTIVITY 1

1. Measure and record the wingspan in centimeters of each person in your group. (wingspan -

from tip of middle finger of left hand to tip of middle finger of right hand)2. Measure and record the height in centimeters of each person in your group.

3. Using graph paper, plot your data.

4. On the horizontal line, indicate the height. On the vertical line, indicate the wingspan.

Note: Although we can put the height on the vertical line, we wish to predict your wingspan.

wingspan

height

5. Place your data (ordered pairs) on the group chart paper in the front (or back) of the room.

6. Plot on one graph the data from all the groups. (This graph is called a scatter plot.)

7. Suppose a student is 175 cm tall. Use your graph to predict the students wingspan. Use the

graph of the groups to predict the students wingspan.

8. Continue with Activity 2.


12/21

16

Guidelines for Activities 2 & 3


2. One person from each group will secure and return all materials.3. Take turns measuring and recording the information.


5. Prepare a report on Activities 2 and 3.

6. One person from each group will present his/her report to the class.

ACTIVITY 2

1. Repeat steps 1-6 from Activity 1, using your foot size and forearm measurements incentimeters.

2. On the horizontal line, indicate the foot size. On the vertical line, indicate the forearm length.Note: This graph is also a scatterplot.

3. Suppose a student has a foot size of 30 cm. Use your graph to predict the students forearm

length.

Use the graph of all the groups to predict the students forearm length.

ACTIVITY 3

1. Using your graph from height vs. wingspan, use a ruler to sketch the line that you think best

approximates the data points.

2. Locate two points on the line (one near the top of the line and one near the lower end of the

line) and approximate thexandyvalues of each point. (The points do not have to be two of

the original points.)3. Use the slope-intercept form of an equation to find the equation of the line that passes

through the two points you just found.

Note: The line you are approximating is called theline of best-fit.


13/21

17

Guidelines for Activities 4-5


2. One person from each group will secure and return all materials.

3. Take turns measuring and recording the information.


5. Prepare a report on the Activities 4 and 5.

6. One person from each group will present his/her groups report to the class.

ACTIVITY 4

1. Carefully plot the following points on graph paper:

(52, 22) (49, 23) (26, 57) (28, 54) (63, 13)

(44, 20) (70, 9) (32, 50) (49, 17) (51, 24)

2. Use a ruler to sketch the line that you think best approximates the data.

3. Can you find an equation for theline of best-fit?

ACTIVITY 5

1. Measure and record the wrist size, in inches, of each member of your group.

2. Measure and record the height, in inches, of each member of your group.

3. Using graph paper, plot your data.

4. Using a ruler or a straightedge, sketch the line of best-fit.


14/21

18

Analyzing Data Homework #1

Create a scatter plot and find the line of best-fit for fast foods and desserts using the tables below:

1.

Fast Foods

2.

Desserts


15/21

19

Fast Foods

Food Item Weight

(grams)

Sodium

(milligrams)Cheeseburger 111 709

Chicken Dinner 410 2,243

Fish Sandwich 164 882

French Fries 69 146

Hamburger 92 461

Frankfurter 93 728

Pizza (cheese) 110 599

Taco 75 401

Desserts

Dessert Item Carbohydrates per

serving

(grams)

Protein per serving

(grams)

Brownie 26.0 2.0

Cheesecake 27.0 5.1

Chocolate Cake 24.4 1.9

Strawberry Shortcake 61.2 4.9

White Cake 45.8 3.3

Apple Pie 43.0 2.4

Banana Custard 49.2 7.2

Cherry Pie 61.5 4.2

Lemon Meringue 55.1 4.5

Sweet Potato 37.8 7.2


16/21

20

Analyzing Data Homework 2

1. Life ExpectancyYear Age

1900 47.3

1910 50.0

1920 54.1

1930 59.7

1940 62.9

1950 68.2

1960 69.7

1970 70.8

1980 75.2

1990 77.3

2. Make a scatter plot of life expectancy.

3. Draw the line of best-fit.

4. Determine whether the graph shows a positive correlation, negative correlation,

or no correlation.

5. Write the equation of the line of best-fit.

6. Using your graph, predict life expectancy in the year 2000.


17/21

21

Analyzing Data Homework 3

We the People of the United States, in order to form a more perfect Union,establish Justice, insure domestic Tranquility, provide for the common defense,

promote the general welfare, and secure the blessings of Liberty to ourselves and

our Posterity, do ordain and establish this Constitution for the United States of

America.

1. Time 20 people of all ages take to recite the preamble of the United StatesConstitution.

2. Make a scatter plot of the data.3. Draw a line of best-fit.4. Determine whether the graph shows a positive correlation, negative correlation,

or no correlation.

5. Write an essay discussing your findings using the vocabulary from the unit.


18/21

22


Day: 008 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 6B2; 7A6; 8C2,4; 10A1-4

TAP:



Demonstrate understanding of measurement

concepts and apply measurement skills

ISAT:


and analysis, including tables, charts and

comparisons


concepts and skills

Unit Focus/Foci

Analyzing Data


Identifying and Determining Scatter Plots, Lines of Best-Fit, and Linear Correlations

Materials

Copies of Graphing Scatter Plots and Lines of Best-Fit Activity

Classroom set of graphing calculators

Graphing calculator for the overhead

Overhead projector


Distribute copies of the Graphing Scatter Plots and Lines of Best-Fit Activity. Work through

scatter plots and lines of best-fit with the students using the following data: placing gas used in

L1and miles driven in L2.

Gallons of

gas used

Miles

driven

20 330

15 24010 180

20 300

15 200

10 150


19/21

23

Answer any questions the students may have. Have the students complete the activity and

monitor their progress. Have each group give a brief description of their results.

Integration with Core Subject(s)

LA: Understand explicit, factual informationUnderstand the meaning of words in context

SC: Understand uses of scientific units and instruments

Analyze and interpret data

Apply scientific method to solve problems

SS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: Have students use statistics on their favorite sports team and show a positive

correlation, negative correlation, and no correlation.

Fine Arts: Have students create a poster using their scatter plots and articles from newspapers

and magazines that agree or disagree with their findings.

Home: See Enrichment and Fine Arts.

Remediation: Teachers Half Dozen

Technology: Have students find on the Internet the statistics on their favorite sports team.

Assessment

Teacher observation and group reports evaluated using the Structured Curriculum Project

Scoring Rubric.

Homework

Review class notes.

Teacher Notes

Prepare copies of the Graphing Scatter Plots and Lines of Best-fit Activity.


20/21

24

GRAPHING SCATTER PLOTS AND LINES OF

BEST-FIT ACTIVITY

Using your data from activity #1, Height vs. Wingspan, draw a scatter plot on your

calculator.

Scatter Plot

STAT1, enter thex-values into L1-(List one) Arrow right to L2-(List two),

enter they-values into L2. 2nd

MODEto quit. Push 2nd

Y= to get the stat plot

menu ENTER. 4 enter to turn off all the plots. 2nd

Y= ENTER.

Press ENTERto turn plot on arrow down ENTER~ for Scatter Plot to L1

ENTERto L2ENTERto mark: GRAPH. You may need to adjust

your range WINDOWto set your range.

1.

Is the graph similar to yours?

2. Does the graph show positive correlation, negative correlation, or nocorrelation?


21/21

Draw a line of best-fit on your calculator.

Line of Best-Fit

Push STATto calc push 5 ENTER Y= VARS5 to EQ 7. This plugs the

equation for the line of best-fit intoy. Push GRAPH.

1. Is the line of best-fit similar to yours?2. Approximate, using the line of best-fit, the wingspan of a person with a height

of 175 cm.

Documents

High School Geometry Days 001008