LESSON PLAN TOPIC: Algebra Essentials TITLE: The Language of Mathematics
AUTHOR: Cathy Brown
GRADE: 9-12 Integrated Discipline(s): Mathematics
NE STANDARDS
12.1 NUMERATION/NUMBER SENSE
12.1.2 By the end of twelfth grade, students will express the equivalent forms of numbers using exponents, radicals, scientific notation, absolute values, fractions, decimals, and percents.
12.2 COMPUTATION/ESTIMATION
12.2.1 By the end of twelfth grade, students will solve theoretical and applied problems using numbers in equivalent forms, radicals, exponents, scientific notation, absolute values, fractions, decimals, and percents, ratios and proportions, order of operations, and properties of real numbers.
12.6 ALGEBRAIC CONCEPTS
12.6.1 By the end of twelfth grade, students will graph and interpret algebraic relations and inequalities.
12.6.2 By the end of twelfth grade, students will solve problems involving equations and inequalities.
12.6.4 By the end of twelfth grade, students will solve problems using patterns and functions.
OBJECTIVES:
1. Students will be able to assign
values to a variable.
2. Students will be able to collect information about variables and be able to
use the information to solve for an unknown variable.
3. Students will be able to write
algebraic expressions from English language sentences.
ASSESSMENT (formative and summative)
-
Participation in class discussion will be part of overall class participation grade.
-
Points are given for right answers, showing work, neatness, following directions.
-
Points subtracted for teams who disrupt, constantly talk, or don't follow directions.
-
-
Students will be assessed through informal observation and formal written evaluation on a written test (at a later date).
MATERIALS:
-
For each group of 3 students: 8 small containers and 80 small countable objects code sheet prepared by teacher
-
Copies of graphic organizer and "mathematics language" translation sheet.
-
Copies of extra credit.
PROCEDURES: Pick teams (at first me, later student selected) When giving the problems to the people at the board, do not repeat the question. This makes the whole team listen and write down the problem.
Anticipatory Set
Mathematics, particularly Algebra has a language all its own. Today we’ll review that language and play a game in which students try to solve other teams’ "Secret numbers" using that language.
Vocabulary
None--
Activities
REVIEW: Go over
solving equations. Ensure everyone remembers how to solve equations. Use the
graphic organizer to review the cues for addition, multiplication, division,
subtraction. Go over the mathematical language translation—do the exercises in
class
PROCEDURE:
a. Divide the class into groups of 3 or 4. Instruct each
group to select a recorder to keep an account of the events beginning in step 6.
Distribute 8 containers and 80 counters to each group.
b. Each group is assigned a different letter of the alphabet
and each of the group’s 8 containers is labeled with the lowercase form of that
letter. If the same lesson is taught repeatedly, the same containers can be used
over and over.
c. Each group chooses a "secret number" between one and ten
and informs teacher of their choice. The teacher keeps a record of all "secret
numbers" on his code sheet.
d. Have each group place the "secret number of counters in
each of their eight containers.
e. Each group will now have 8 containers, each of which
contain the same number of counters and the same letter of the alphabet. Discuss
ways to express the total number of counters in all 8 containers. For example:
m+m+m+m+m+m+m+m or x+x+x+x+x+x+x+x. Build on that idea: 8m or 8x.
f. Have each group exchange some containers with one other
group. For example, 3 m’s are exchanged for 3 x’s. Each group records its
holdings in the following manner: m+m+m+m+m+x+x+x or 5m + 3x and x+x+x+x+x+m+m+m
or 5x +3m.
g. Each group confers with the teacher who checks the code
sheet to tell them the total number of counters their groups is holding. For
example, the first group has 5m + 3x counters. The teacher tells them they have
22 counters.
h. Discuss if necessary how to write an equation to express
the total number of counters. For example, 5m + 3x = 22.
i. Each group solves the equation they have developed to
solve for the unknown variable.
j. Students continue to trade until they have discovered each
group’s "secret number" or until time has run out.
k. Encourage students to keep solutions within their group so
each group can make their own discoveries on their own.
EXTRA CREDIT—announce extra credit is available by doing 10 Wins. Answers due next class.
Provision for special needs:
-
Clear, concise instructions
-
Use of visuals
-
Modeling of expectations
-
Repeating of instructions
-
Model a variety of problem solving strategies.
-
Assist students to develop criteria for choosing a strategy
-
Apply reading comprehension strategies to problem solving (i.e. deciding what the main idea is and what information is extraneous to the problem).
-
Use simpler problems of the same type to model methods.
-
Encourage students to represent problem in pictorial or other visual form before attempting solution.
-
Focus students' understanding of algebraic symbols as representing real numbers or operations.
-
Permit extended time for problem solving, including pre-solution stage trial and error.
-
Teach prediction and estimation skills.
-
Consider the use of pictorial flow charts to plan strategies before setting up equations.
-
Other modifications as needed by IEP in consultation with the special education teacher
CLOSURE:
Have students return to their desks. Why is this lesson important do you think? What are the key lessons you learned about translating "English" into Algebra?
References:
Title - Variables By - Andy Field at
http://www.lessonplanspage.com/MathVariablesAndSolvingForUnknownVars78.htm
Ideas for helping students with special needs in mathematics at http://www.bced.gov.bc.ca/specialed/landbdif/42.htm
________________________________________________________________________________________________________
What Words Tell Us to Add Subtract Multiply and Divide?
________________________________________________________________________________________________________
STUDENT NAME:_______________________________________________________
Directions: Translate these sentences into ML (mathematical language). Use letters as variables which are related to the words, and use a "let" statement to define your variables. (for example: let F= Fred’s salary, or let h= number of hours.) For sentences involving 2 unknown values, use 2 different variables.
1. The combined salaries of James and Scott equals $970.
2. Lisa worked 25 hours at $4 an hour, plus 10 more hours at $4.50 an hour to earn a total of $145.
3. Larry is four times as old as his son Curly.
4. Ten pounds less than sixty-seven pounds is fifty-seven pounds.
5. Four more than five times a number equals one less than six times the same number.
6. A woman worked a certain number of hours at $3 an hour and the same number of hours plus twenty more hours at $4 an hour, earning $150 all together.
7. a added to c B. q less than 7
8. 7 divided by n D. x less 2
9. twice b F. 6 times the quantity c minus t
10. 6 more than half of w H. twice the sum of 8 and y
11. the sum of m and n, divided J. the product of m and x, by negative 3 decreased by 7
________________________________________________________________________________________________________
Ten Wins (Extra Credit)
Name ____________________________ Date ________________
Fun with Numbers
You can use expressions to have fun with numbers. Here is a number game called Ten Wins.
Follow the steps and play Ten Wins.
Steps Expression Example
a. Pick any whole number. x 1
b. Double it. 2x 2
c. Add 20. 2x + 20 22
d. Divide that number by 2. x + 10 11
e. Subtract the number you
started with. The
result is always 10. 10 10
This game is called Ten Wins because no matter what number you start with, the result is always 10.
Write the expression for each step in the number game.
1. Steps Expression Your Number
a. Pick any whole number.
b. Add 12.
c. Double that number.
d. Subtract 8.
e. Divide by 2.
f. Subtract your original number.
g. The result is always _________.
2. Steps Expression Your Number
a. Pick any whole number.
b. Add 5.
c. Triple that number.
d. Subtract 6.
e. Divide by 3.
f. Subtract your original number.
g. The result is always ________.
3. On another sheet of paper, write another number game whose result is always the same number that you started with.
|
REFERENCE: (for game and worksheet) http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/algebra/tenwins.html