Download Alg 1 std 1[1].1 lesson plan

Lesson Design
Subject Area: Algebra 1
Grade Level: 8th and 9th.
Benchmark Period: I
Duration of Lesson: 2 to 3 days
Standard(s): 1.1 Use properties of numbers to demonstrate whether assertions are true or false.
Learning Objective: Whether assertions are true or false pertaining to various number systems.
Big Ideas involved in the lesson: Number sets, properties of operations (distributive, commutative,
associative), properties of equality, identity, closure.
As a result of this lesson students will:
Know: vocabulary: Rational, irrational, integers, whole, natural, real.
Properties: Commutative, associative, distributive, closure and identity.
Reciprocal, additive inverse, multiplicative inverse, opposite, counterexample, addition property of equality,
multiplication property of equality, subtraction property of equality, division property of equality, rational and
irrational numbers, natural and whole numbers, integers.
Symbols: N for natural or counting numbers.
W for whole numbers are the Natural numbers including zero
I, Z, or J for Integers. Natural numbers and their opposites including zero.
Q for rational numbers are numbers that can be written as the quotient of 2 integers, and numbers that can be
written as terminating or repeating decimals.
R for real numbers.
N, W, I, Q, and irrational numbers are all subsets of R.
Properties: Commutative, Associative, Distributive, Identity
Additive inverse is the opposite.
Multiplicative inverse is the reciprocal
Understand: Commutative Property: the order in which two numbers are added or multiplied does not change
the sum or product
Associative Property: the way you group when adding or multiplying does not change the sum or product
Distributive Property:
The product of a and (b+c)= ab+ac etc. textbook pg. 94
Identity property for addition: the sum of number and 0 is the number
Identity property for multiplication: the product of a number and 1 is the number
Be Able To Do:
 Solve problems using the relationships among operations and knowledge about the base-ten system.
 Interpret numbers, problems, and results.
 Apply the distributive property using manipulatives
 Distinguish between the commutative and associative properties
 Relate a property with an equation.
Assessments:
Formative: ABWA, Equity
What will be evidence of student
cards
CFU Questions: Embedded in lesson
knowledge, understanding &
ability?
Summative: Quiz and
Game:
Independent Practice
“Find Your Match”
assignment.
Lesson Plan
Anticipatory Set:
Go over Number powerpoint slides 1 -10
a. T. focuses students
a. KLW chart small groups and share out as whole class
1
Lesson Design
b. T. states objectives
c. T. establishes
purpose of the lesson
d. T. activates prior
knowledge
record class results on chart paper to post in classroom
b. Use properties of numbers to demonstrate whether assertions are true or false.
c. This lesson will assist you to determine if assertions are true or false pertaining to
various number systems.
d. Students will create posters illustrating the number sets using different colors.
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for
Understanding
 Pose key
questions
 Ask students to
explain concepts,
definitions, attributes
in their own words
 Have students
discriminate between
examples and nonexamples
 Encourage
students generate
their own examples
 Use participation
Continue with powerpoint to introduce all of the sets of numbers.
a. Display the property chart (see instruction file) on a transparency or project for all
students to see.
Let a, b, and c be real numbers, variables, or algebraic expressions.
b. Teacher explains concepts presented on chart while students take notes using the
Cornell format. Use term and definition with examples.
c. Each student will complete the following examples on their individual white boards.
CFU: Name the property shown.
3 x (8x4) = (3x8)x4
4+7=7+4
3 x 8 = 8x 3
4 + (9+7) = (8+9) +7
CFU: Give a counterexample to show that subtraction is not associative.
Divide class into 4 different groups. Students generate their own examples of
properties and counterexamples.
Day 2
On the board, write the expression 1/x. Ask students to give values of 1/x when x>0, starting at 1
and going up.
CFU:
 What happens to the fraction as the denominator increases?
 Can you locate it on a number line or on your ruler?
 Compare 1/6 with 1/5. Use area model if necessary.
 Are these natural numbers? Why not?
For the expression 1/x. ask students to give values of 1/x when x>0, starting at 1 and going
towards zero.
CFU:
 What happens to the fraction as the denominator decreases?
 Can you locate it on a number line or on your ruler?
 Compare 1/1/6 with 1/1/5. Use area model if necessary.
 Are these natural numbers? Why?
Give values of x<0.
CFU
 What happens to the fraction as the denominator decreases?
 Can you locate it on a number line or on your ruler?
 On your number line show 1/8, 1/5, -1/8, and –1/5. Compare their placements.
Group or pair activity:
On graph paper, graph the function y = 1/x. Make an input/output table with the following x-
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Lesson Design
values {-4, -3, -2, -1, -1/2, -1/4, ¼, ½, 1, 2, 3, 4}. There is an empty zone between the hyperbolas
and the origin. Explain the relationship between the values of x and y, and show that the graphs
never touch the axes (we could introduce the concept of asymptote), and that we cannot divide
by 0. We can also introduce the concept of “the limit of 1/0 is infinity”.
Write the following questions on the board or project the file that contains them:
1- Which of the following is true for all rational numbers?
a. x  1x
b. x  0
cx y x
d. x3  x
Instruct students to think about a rational number exclusively (not a rational that could also be an
integer, a whole or a natural).
Examples are: 1/3, -1/7… Then proceed by substituting the fraction in each of the expressions
given:
1
1
1
a. 
yields  3 which is false.
3 1/ 3
3
1
 0 is true. (absolute value is always positive).
b.
3
c.
1 1 1

 yields a negative number greater than a positive number which is false.
3 7 3
3
 1
1
1 1
d.    which yields
 which is false.
3
27 3
 3
Teach students about counterexamples. Use Frayer Model in file. Definition: To prove that a
statement is true, you need to show that it is true for all examples. To prove that a statement is
false, it is enough to show that it is not true for all examples. For instance: “The opposite of a
number is always negative”. This is a false statement because, as a counterexample, the
opposite of -5 is 5.
2- Which of the following are false for the set of integers:
I- x 4  x 2
1
 0, x  0
IIx
III- x3  x 2
Instruct the students to think only of an integer exclusively (that is not also a whole or natural
number). Then substitute in the expressions.
Examples are: -1, -2..or any other negative integer.
   
4
2
I- 1  1 is true.
II-
1
 0 is not true
1
   
3
2
III- 1  1 is not true.
So II and III are false for the set of integers.
Guided Practice:
a. Initiate practice
3
Lesson Design
b.
c.
d.
e.
f.
activities under direct
teacher supervision –
T. works problem
step-by-step along
w/students at the
same time
Elicit overt responses
from students that
demonstrate behavior
in objectives
T. slowly releases
student to do more
work on their own
(semi-independent)
Check for
understanding that
students were correct
at each step
Provide specific
knowledge of results
Provide close
monitoring
a. Write a couple of similar problems on the board and guide the students to solve them
step by step.
1- Which of the following is true for the set of natural numbers?
a. x 4  x  0


x5 x
 1
c. x     x
 x
d. x.y  x
b.
Ask students if natural numbers can be categorized as any other type of number? (Are
they necessarily integers? Rational? Can they be negative?). Ask them to give two
examples. Have them substitute in every inequality. When correcting, take the wrong
answers and discuss with students why they don’t work.
Examples of natural numbers are:1, 2, 3, 4….
Let’s substitute and think of counterexamples at the same time:
a. 3(4-3)>0 yields 3>0 which is true. A counterexample would be any number greater
than 4 because it will yield that a negative number is greater than 0.
b. 3+5>3 is true. If we substitute with any other positive number, the equation will
always be true. There are no counterexamples.
c. 1/x is a rational number and does not belong to the set of natural numbers.
d. 3.2<3 is not true.
2- Which of the following is true for the set of whole numbers:
1
a. x 
x
4
b. x  x 2
c. x 2  x3
d. x  5  x
Whole numbers are natural numbers plus 0: 0,1, 2, 3….
Let’s substitute and think of counterexamples at the same time (give 0 and another
number as examples):
a. Doesn’t work since we cannot divide by 0.
b. Works for 0 and all other whole numbers (which are only positive). There are no
counterexamples.
c. Doesn’t work for positive numbers since the square of a number cannot be smaller
than the cube of that number.
d. 3 – 5 < 3 is a true statement but doesn’t work for the whole numbers since they are
not negative.
What opportunities will
students have to read,
write, listen & speak
about mathematics?
Closure:
a. Students prove that
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Pair Share, Group discussions, visuals in powerpoint
Choose a natural number that produces a non-natural number when you do the
Lesson Design
they know how to do
the work
b. T. verifies that
students can describe
the what and why of
the work
c. Have each student
perform behavior
calculations.
1) 5  x (Answer: x  5 )
2) 3  x (Answer: 2 and any number greater than 3)
Choose a whole number that produces a non-whole number when you do the
calculations:
1) 5x  5 (Answer: 0)
2) 2(x  1) (Answer: 0)
Choose a integer that produces a non-integer when you do the calculations:
1) 5  x (Possible answer: 6)
1
2) .x (Possible answer: 3)
2
Choose a rational number that produces a non-rational (or irrational) number when
you do the calculations:
1)
Independent Practice:
a. Have students
continue to practice
on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective,
timely feedback
Resources: materials
needed to complete the
lesson
5
x (Answer: all non-perfect squares: 2, 3, 5, 6, 7, 8,…)
See attachments for powerpoint, instruction, guided practice, closure and independent
practice.