Translating Mathematical Phrases

Question

What does it mean to translate something? Explain in your own words on a sheet of paper. Be prepared to share your answer

Can you translate these words (or phrases)?1) 2EZ

2) L8R

3) AFK

4) BTW

5) NVM

6) ORLY

7) TMI

8) TTYL

9) ROTFL

10) <3

11) CYAL8R

12) IMO

13) NE1

14) MYOB

15) ^5

Question?

Why were you able to (or unable to) translate the SMS words and phrases on the previous slide?

Can you translate?

1. ... . . / - .... .. ... / .. ... / -. --- - / ... --- / -... .- -.. .-.-.-

2. -.-- --- ..- / .--- ..- ... - / -. . . -.. . -.. / - .... . / -.-. --- -.. . / - --- / - .-. .- -. ... .-.. .- - . .-.-.-

What if you had additional info?

Question?

Why were you unable to decode the messages on the previous slide at first?

Math

Mathematical language is no different than SMS messages or morse code.

You have to learn the alphabet, vocabulary, and structure of the language before you can be fluent.

Types of “Math Language”

There are four main types of “Math Language”: Expressions Equations Inequalities Word Problems

The Alphabet: Code Words and Operations

Operators Addition Subtraction Multiplication Division

It all starts with expressions… Expressions are open ended thoughts. Things that are blurted out without

necessarily creating a complete sentence Examples: “Hello” “Goodbye” “Watch out”

Mathematical Expressions

Mathematical expressions are also open ended thoughts

This means they lack the closure of an equal sign

Lots of numbers may satisfy some expressions, which often leads to the use of a variable

Variable Clues: “some number”, “a number”, “any number”

Try to translate the following…o Twelve more than a number….

o 5 less than a number….

o 3 times a number ….

o A number divided by 12…

Lets try some harder expressions… The square of “k” decreased by 7

Four times 2 plus 7

5 times the sum of a number and 2

A number divided into 5 equal parts

Again…

The difference of -4 and a number decreased by ten

14 more than twice a number “g”

Three-fifths of “r” cubed

Triple the sum of 19 and a number minus the product of that same number and 6.

Translating Equations

Equations Equations are the “step up” from an expression. In an equation, a complete mathematical thought

is presented that leads to just one answer. Much like a sentence, this complete thought

requires “punctuation” An equal sign is used in an equation to complete

the mathematical sentence and direct you to your answer.

What to look for?

When translating an equation… You need to be aware of an additional set of

“code words” that tell you to use the equal sign The main word to look for is the word “IS” Practice reading a simple number sentence and

you will notice the natural tendency to say the word “IS” in place of the equal sign: 4 + 3 = 7 “Four plus three IS seven”

Additional Code Words Some of the other code

words that tell you to use an equal sign include:

Are Was Were Will Be Gives Yields Sold For

And of course…

EQUALS!

Practice

Translate each of these equations into a sentence. 8 – 6 = 2

-5 + 34 = 29

45/5 = 9

-3 ∙ 4 = -12

What about this one?

Translate the sentence into an algebraic equation. “The number of girls in the class plus the number

of boys in the class equals the number of students in the class”

What makes this problem more challenging?

Now you try on your own

Translate each problem into an algebraic equation and then solve that equation.

1. Five more than a number is eight.

2. Two times a number is ten.

3. Six less than a number is twenty-four.

4. A number divided by five is ten.

5. The sum of nine and a number is fourteen.

6. Nine subtracted from the quotient of a number and three is twenty-one.

7. The difference of seven and three times a number is ten.

8. One-half of a number added to seven is eleven.

9. Two less than the quotient of a number and five is one.

10. The product of three and the sum of number and two is zero.

Christmas Carol Assignment

You are going to write your own version of the 12 days of Christmas using equations to replace the numbers in the original song.

Example: “On the first day of Christmas, my true love gave to me “x – 5 = -4” partridges in a pear tree”

X would equal 1 and the first day of Christmas has one gift in the carol.

Conditions

You must write an equation for each of the 12 days and the answer to the equation must match that “day” of Christmas

You may change the “my true love gave to me” part to anyone that you would like to receive gifts from

You may change the names of the gifts to anything school appropriate that you would like to receive

Requirements

Your equations must equal the correct number for the day.

You will present your final carol on a sheet of the large construction paper (front only). Be sure to give yourself space. You DO NOT have to repeat the previous days as you advance.

You must decorate your carol on the final copy with pictures (to represent the gifts) and colored outlining.

Equation Requirements

In your 12 days equations you must include:• An equation that uses a square root• An equation that uses squaring a number• An equation that uses parenthesis• At least 3 two step equations• A minimum of two equations for each of the

four main operations (+, -, x, ÷)• At least 3 equations that use negative

numbers