2. Expressions & 3D Geometry

Lesson

Mathematics is often referred to as a language. That's why we can take practical situations and translate them into algebraic expressions or equations and vice versa.

In algebra, the variables that we write represent unknown values. It is these unknown values that we usually try to find.

Any operation can be used in algebraic expressions - in fact, any combination of operations can be used. To be able to turn written expressions into algebra, we can look for certain keywords to indicate addition, subtraction, multiplication, or division.

Addition | Subtraction | Multiplication | Division |
---|---|---|---|

plus the sum of increased by total more than added to |
minus the difference of decreased by fewer than less than subtracted from |
times the product of multiplied by of twice groups/lots of |
divided by the quotient of separated into equal parts split |

The letters $x$`x` and $n$`n` are popular choices for the unknown amount in a number sentence. However, if a letter is not specified, we can use any letter to represent the unknown number in an expression.

Careful!

We can add or multiply in any order. However, for subtraction and division, the order is important.

For example, "$5$5 less than a number" is written as $n-5$`n`−5, not $5-n$5−`n`.

Similarly, "a number divided by $8$8" is written as $n\div8$`n`÷8 or $\frac{n}{8}$`n`8 not $\frac{8}{n}$8`n`.

An equation is a type of mathematical sentence that sets two expressions equal. It means that the two expressions have the same value. As with our four operations, we can look for key phrases that indicate equality.

Equal |
---|

is/are equals amounts to |

The sum of a number and $24$24 is $35$35. Set-up an equation for this scenario.

**Think:** We have an unknown, "the number", so let's call "the number" $x$`x`. We should note some keywords which can help us after we replace "a number" with $x$`x`. An equation must have an equals sign, unlike an expression which will not.

**Do: **Using our keywords, we can translate to an equation.

$x+24=35$`x`+24=35

What does the algebraic expression $96q$96`q` represent?

96 times the number represented by q

Athe quotient of the number represented by q and 96

B96 less than the number represented by q

C96 more than the number represented by q

D

Write an equation in simplest form for:

$y$`y` is $18$18 times $k$`k`.

Roxanne has been out picking flowers, and has $40$40 in total. When she returns, she puts them in $5$5 different vases.

If she puts $p$`p` flowers in each vase, rewrite the following sentence using algebra:

"There are $5$5 groups of $p$

`p`flowers, which make $40$40 in total."

Write, read, and evaluate expressions in which letters stand for numbers.

Write expressions that record operations with numbers and with letters standing for numbers.

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.