Download Journal: Writing Expressions Homework: 1.2 Record and Practice

Lesson 2-2A Writing Expressions:
Journal: Writing Expressions
Translating Words into Algebra Homework:
 1.2 Record and Practice
Journal, p. 7&9
Language
 1.2 Record and Practice
Journal, p. 10
I. Standards
SPI 0606.3.5
Common Core
MCC6.EE.1 MCC6.EE.2 a, b
MCC6.EE.7
I can…
I can translate sentences to write expressions and equations.
I can translate expression and equations to write sentences.
I can write, read and evaluate expressions with variable.
I can identify parts of an expression using my vocabulary words:
sum, term, product, factor, quotient, coefficient.
I can solve real-world problems using algebraic expressions and equations.
II.
Preview/Preparation/ Pre-expose
Synonyms are words that have the same meaning. They are said to be synonymous. For
example: student and pupil, buy and purchase, sick and ill, quickly and speedily.
Make a list of homonyms (both with same spellings and different spellings). When students
are done, share each group’s list with the class.
Math has something like synonyms also. For example sum, together and + are synonyms.
Brainstorm other synonyms in math.
III. Direct Instruction with Real World Examples
Learning algebra is a little like learning another language. In fact, algebra is a simple
language, used to create mathematical models of real-world situations and to handle
problems that we can't solve using just arithmetic. Rather than using words, algebra
uses symbols to make statements about things. In algebra, we often use letters to
represent numbers.
Since algebra uses the same symbols as arithmetic for adding, subtracting,
multiplying and dividing, you're already familiar with the basic vocabulary.
In this lesson, you'll learn some important new vocabulary words, and you'll see how
to translate from plain English to the "language" of algebra.
The first step in learning to "speak algebra" is learning the definitions of the most
commonly used words.
http://www.math.com/school/subject2/lessons/S2U1L1DP.html
A. Vocabulary
1. Algebraic expression – a number sentence with one or more variables. The
sentence does not have an equal sign.
The following are examples of expressions:
a. 2
b. x
c. 3 + 7
d. 2 × y + 5
e. 2 + 6 × (4 - 2)
f. z + 3 × (8 - z)
2.
Constant – quantity that does not change. Only numbers. In the expression
7x2 + 3xy + 8 the constant terms are 7, 3, and 8.
3.
Variable – a letter that represents a quantity that can change. These letters
are actually numbers in disguise. In the expression 7x2 + 3xy + 8, the
variables are x and y. We call these letters "variables" because the numbers
they represent can vary—that is, we can substitute one or more numbers for
the letters in the expression.
4. Coefficients
Coefficients are the number part of the terms with variables. In 3x2 + 2y + 7xy
+ 5, the coefficient of the first term is 3. The coefficient of the second term is
2, and the coefficient of the third term is 7.
If a term consists of only variables, its coefficient is 1.
B. Direct Instruction
1.
Before you can learn Algebra, you have to learn how to change
words into algebra. We call this turning words into algebraic
expressions. Look at the sentence I wrote and watch how easy it is
to change it into an algebraic expression.
My Sentence:
Kirstin had $17 and then she found a bag of money.
What is the Known? What is the Unknown? Whenever you don’t
know something, you use a letter to take its place. We will be
using the same letter so it isn’t too confusing. We will use the
letter n.
Algebraic Expression:
17 + n
That’s easy! You just put in a letter for the amount of the
money in the bag because you don’t know how much
money there is. I think I’ll be able to learn the language
of algebra pretty quickly.
That was pretty easy. Remember expressions don’t
have equal signs!
Let’s try another one:
Hey! Try this problem:
Tom had found money in his pants pocket. He
already had $23 in his wallet. What is the expression
to show how much money does Tom has now.
I can do this one!
K: Tom found $ is his pocket and has
$23 in wallet
NTK: how much money does he have
now?
So… n + $23
Hey! I know this is an algebra
expression! But what is the variable
and what is the coefficient?
Great! Let’s try another one!
My sentence:
Kasey found money in a box. What is the expression
for this money?
Algebraic Expression:
n
What is this called?
That’s easy! You just put in a letter for
the amount of the money in the box
because you don’t know how much
money there is. I think I’ll be able to
learn the language of algebra pretty
quickly.
IV.
Pattern Making
Look at the sentences below and the translations into
the language of algebra. Find the pattern to describe
why they are written the way they are. Work in your
groups to discuss the possibilities.
Sentences
Algebraic Expressions
Jill is three years older than Nancy
Expression for Nancy: n
Expression for Jill: n + 3
Rick weighs 56 pounds more than Ed
Expression for Ed: n
Expression for Rick: n + 56
Now try these!
Sentences
Three consecutive numbers
Three consecutive even numbers
Algebraic Expressions
Expression for the smallest: n
Expression for the next larger
number: n + 1
Expression for the largest: n + 2
Expression for the smallest: n
Expression for the next larger
number: n + 2
Expression for the largest: n + 4
V.
Pattern Making
Can you do this one?
Sentence: The difference of a number and 3
Expression: 3 - n
Help me!
Answer:
Answer
Subtraction and division are not commutative
Help! How do I know when to
add, subtract, multiply or
divide?
Write your thinking. Use complete
sentences and explain if you were
writing a textbook for fifth graders.
Explore Metacognitive Reflection
Plan, Explore, Evaluate
Why is it important to know these
phrases? Give an example of
correct use and incorrect use of
the phrase.
VI. Practice
A. Work with a partner. Match each phrase with an expression.
The product of a number and three
n÷3
The quotient of 3 and a number
4p
4 times a number
n·3
A number divided by 3
2m
Twice a number
3÷n
B. Complete the following table
Variable Expression
x+4
y - 75
3 ÷ z or
Meaning with Words
x plus 4
Operation
Addition
Meaning with Words
x plus 4
y minus 75
Operation
Addition
Subtraction
3 divided by z
Division
6 times n
Multiplication
3
𝑧
6n, 6 · n, (6)(n)
Answers
Variable Expression
Answers
x+4
y - 75
3 ÷ z or
3
𝑧
6n, 6 · n, (6)(n)
C. Write the phrase as an expression.
VI.
1.
8 fewer than 21
2.
The product of 30 and 9
Finding Patterns with Metacognition
Find my error and write an explanation of why this is an error
The quotient of a number x and 2
2 ÷x
Explore Metacognitive Reflection
Plan, Explore, Evaluate
How can we organize the clue words to help our brain remember
when to add, subtract, multiply, or divide?
Journal entry: Writing Expressions
Note page 54 and 55
VII.
Practice
A. Write the phrase as an expression
1.
14 more than a number x
2.
A number y minus 75
3. The quotient of 3 and a number z
B. Write the phrase as an expression
1.
the sum of 18 and 35
2. 6 times 50
3. 25 less than a number b
4. a number x divided by 4
5. 100 decreased by a number k
VIII.
Close
A. Translating between words and math
The distances from Charlotte, NC, to Charlotte, TN, is 470 miles. Beth already
drove part of the way before she stopped for lunch. How many miles more must
she drive to reach Charlotte, TN?
Answer
To
solve this problem, you need to find how many more miles Beth must drive.
To find how much more, subtract.
470 - m
B. Standards
SPI 0606.3.5
Common Core
MCC6.EE.1
MCC6.EE.2 a, b
MCC6.EE.7
I can translate sentences to write expressions and equations.
I can translate expression and equations to write sentences.
I can write, read and evaluate expressions with variable.
I can identify parts of an expression using my vocabulary words: sum, term,
product, factor, quotient, coefficient.
I can solve real-world problems using algebraic expressions and equations.
IX.
Secondary Rehearsal
1.2 Record and Practice Journal (BIM) p. 7&9, grade in class.
1.2 Record Practice Journal (BIM) p. 10, homework
Text p. 56 & 57