ALGEBRA
DO NOWS
Objective: Students
will be able to identify numerical and algebraic expressions and their
associated operations.
Number 1 Have students count off to determine how many students are in
class. Ask, "How many pairs of shoes are in this classroom?" Then ask, "How
many shoes are in this classroom?" Student ex plain how to find the answer.
Help students arrive at the __expression (number of students) multiplied by (2
shoes/student). Point out that they can rewrite this as the algebraic
__expression 2n where n = number of students.
Number 2 Draw a 2x3 array of dots of squares on index cards for each
group. Point out that the array can be described by the __expression 2x3 = 6.
Ask students to write another __expression that describes the array. (answer 2
+ 2 + 2 = 6) Next, make a 2x4 array of dots. Ask students to identify two ways
to describe the array and the total number of dots. (answer 2 + 2 + 2 + 2 = 8;
2 multiplied by 4 = 8) Continue with several other examples. Students will
name an algebraic __expression that describes an array with two rows and y
columns. (answer 2y)
Number 3 Dunn Middle School students have an annual candy sale to raise
funds for the school. The school gets 50 cents for every candy bar sold. The
candy bars come 12 to a box. The organizers of the fundraiser hope that each
student can raise $60. To meet that goal, how many boxes of candy bars must a
student sell? (answer algebraically)
Objective: Students will be able to recognize positive and negative
integers and their opposites.
Number 1 Students draw a picture of the following action: two people
walked 5 steps forward, then 3 steps backward. They then walked 2 steps forward
followed by 4 steps backward. Where were the people when they finished?
(answer where they started) Indicate to students that they can use a number
line to illustrate the path the people walked.
Number 2 Students work in groups to play a game called "General
Directions." Direct each group to use masking tape to create a -20 to +20
number line on the classroom floor. Have students take turns being "The
General" and giving directions such as "The General says stand on +3" "The
General says move to the opposite of -7." and "The General says give the
absolute value of the number you're at."
Objective: Students will be able to find the sums of positive and
negative integers.
Number 1 Show students a mathematical square puzzle. The puzzle is
sometimes called a "magic square." In the square, the numbers in each row,
column, and diagonal add up to the same sum. Have students complete the
squares. (Students fill in the numbers in parentheses. I have put the answers
in, but they are left blank for the students to do.)
5 -9 (1) 2 (7) (6)
(-5) -1 (3) 9 5 (1)
-3 (7) -7 4 (3) (8)
Objective: Students will be able to simplify expressions with one
variable by combining like terms.
Number 1 Students will answer the question: "How many toes are in this
classroom?" Try to have them recognize that number of toes = 10 times (number
of students). Ask how they can use the same information to describe the number
of toes in any classroom, home, or movie theater. {answer (10)(x) where x =
number of people}& nbsp;
Number 2 Students simplify without using pencil and paper.
problems answers
2x + 3x + 7 (5x + 7)
3y + 4y + 9 (7y + 9)
-25h + 22h + 4 (-3h + 4)
k + k + k + 7k (10k)
9 - 3r - 10r (9 - 13r)
Objective: Students will be able to find the perimeters of regular
polygons using formulas for perimeter.
Number 1 Ask students to describe ways in which they could find the
distance around-perimeter-of a classroom object such as a bulletin board,
doorway, or computer screen. Focus on responses that suggest measuring two
sides and multiplying rather than measuring all four sides.
Number 2 Draw a square. Label each side of the square as s. Ask
students to find the perimeter. Students will show that finding the perimeter of
the square involves repeated addition. Ask another student to use the addition
information to develop a formula for perimeter using multiplication.
Objective: Students will be able to indicate that the sum of opposite
numbers is zero. Students will be able to recognize that adding zero to a
number does not change the number. Students will be able to determine that zero
times any number is zero.
Number 1 Students solve two given problems: "I'm thinking of a number.
No matter what number I add to it, the sum is always the same as the number I
added. What is the number?" "I'm thinking of a number. No matter what number
I multiply it by, the product is always the number I started with. What is the
number?" (answer both questions is zero)
________________________________
Number 2 Students work in groups to play a game called "General
Directions." Direct each group to use masking tape to create a -20 to +20
number line on the classroom floor. Have students take turns being "The
General" and giving directions such as "The General says stand on +3" "The
General says move to the opposite of -7." and "The General says give the
absolute value of the number you're at."
Objective: Students will be able to find the sums of positive and
negative integers.
Number 1 Show students a mathematical square puzzle. The puzzle is
sometimes called a "magic square." In the square, the numbers in each row,
column, and diagonal add up to the same sum. Have students comp lete the
squares. (Students fill in the numbers in parentheses. I have put the answers
in, but they are left blank for the students to do.)
5 -9 (1) 2 (7) (6)
(-5) -1 (3) 9 5 (1)
-3 (7) -7 4 (3) (8)
Objective: Students will be able to simplify expressions with one
variable by combining like terms.
Number 1 Students will answer the question: "How many toes are in this
classroom?" Try to have them recognize that number of toes = 10 times (number
of students). Ask how they can use the same information to describe the number
of toes in any classroom, h ome, or movie theater. {answer (10)(x) where x =
number of people}
Number 2 Students simplify without using pencil and paper.
problems answers
2x + 3x + 7 (5x + 7)
3y + 4y + 9 (7y + 9)
-25h + 22h + 4 (-3h + 4)
k + k + k + 7k (10k)
9 - 3r - 10r (9 - 13r)
Objective: Students will be able to find the perimeters of regular
polygons using formulas for perimeter.
Number 1 Ask students to describe ways in which they could find the
distance around-perimeter-of a classroom object such as a bulletin board,
doorway, or computer screen. Focus on responses that suggest measuring two
sides and multiplying rather than measuring all four sides.
Number 2 Draw a square. Label each side of the square as s. Ask
students to find the perimeter. Students will show that finding the perimeter of
the square involves repeated addition. Ask another student to use the addition
information to develop a formula for perimeter using multiplication.
Objective: Students will be able to indicate that the sum of opposite
numbers is zero. Students will be able to recognize that adding zero to a
number does not change the number. Students will be able to determine that zero
times any number is zero.
Number 1 Students solve two given problems: "I'm thinking of a number.
No matter what number I add to it, the sum is always the same as the number I
added. What is the number?" "I'm thinking of a number. No matter what number
I multiply it by, the product is always the number I started with. What is the
number?" (answer to both questions is zero)
________________________________
Number 2 Have students identify the operation or variable indicated by
the blank.
Problems Answers
3 ___ 0 = 0 (multiply)
3 ___ 0 = 3 (+)
n ___ 0 = 0 (multiply)
n ___ 0 = n (+)
a + ___ = 0 (-a)
-a + ___= 0 (a)
(a + b) ___ 0 = (a + b) (+)
(a + b) ___ 0 = 0 (multiply)
Objective: Students will be able to identify the root of a number as an
equal factor of the number.
Number 1 Give each group unit cubes from a set of base ten blocks or
sugar cubes to make a 5x5 square. Students will count the number of cubes in
the square. (answer-25) The group will build a block that is 5 cubes tall, 5
cubes wide, and 5 cubes long. Then they will count the number of smaller cubes
contained in the large block. (answer-125) They will show how to get these
answers.
Objective: Students will evaluate complex expressions following the order
of operations.
Number 1 Students will calculate the value of (3)(6) + 2. They will
write how they evaluated the __expression. Lead students to recognize the order
in which terms are added or multiplied makes a difference in the result. {(3
multiplied by 6) + 2 = 20; 3 multiplied by (6 + 2) = 24}
Number 2 Students will be planning a party for the class. They have a
budget of $200. Have small groups develop plans for the party, including
purchasing refreshments, decorations, and entertainment. Each group should
present a formal plan indicating what items they intend to purchase, how many of
each item they will buy, and how much each item will cost. Plans should allso
indicate date, time, and location of the party. Have groups present their
plans. Then have the class vote on which plan is the most complete and
reasonable.
Number 3 Students will write a verse, rhyme, rap, or anagram to help
them remember the order of operations. Two examples are EPMDAS, from the first
letters of "exponents, parentheses, multiply,divide, add, subtract," and "Every
Person Must Dance At Sunset," which uses the initial letters to make a mnemonic,
or memory device.