Using Number Sense to Solve One-Step Equations

Lesson 2-5 & 2-6

CCS:

6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation true? Use substitution to determine whether a given number in a specified set makes an equation true 6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form

x

+

p

=

q

and

px

=

q

for cases in which

p

,

q

and

x

are all nonnegative rational numbers • •

OBJECTIVES: Solve equations using addition and subtraction Estimate and check solutions to equations

Vocabulary

An

equation

is a mathematical sentence that has an equal sign.

An

open sentence

is an equation with one or more variables in it.

A

solution

is a value that can be substituted for a variable to make the equation true.

Example: In the equation y + 3 = 8, the solution is 5.

Using Estimation

• Use mental math or estimating to determine the solutions to the equations.

• The same number properties apply to algebraic equations.

Identity Properties:

a + 0 = a 1a = a

Properties

Commutative Properties:

a + b = b + a ab = ba

Associative Properties:

a + (b + c) = (a + b) + c a(bc) = (ab)c

Example: 4x=32

Think: What times 4 equals 32? Solution: x = 8 Check the original equation:

4x=32 4(8)=32 32=32

Example: Estimate p ÷ 4 = 7.97

7.97 is close to 8. So think: What divided by 4 equals 8?

If we work backwards, we know that 8 x 4 = 32. Therefore, p is about equal to 32.

Is the given number a solution to the equation?

6n = 17; 3

Try the value out and see if it works.

6n = 17 6(3) = 17 18 = 17

This is not true, so 3 is not a solution.

Solving Addition and Subtraction Equations X + 6.2=24.8

Procedure

• Isolate the variable by performing the

inverse operation

on that variable.

• The inverse of subtraction is adding. The inverse of adding is subtracting.

• Perform the same operation on the side of the equal sign that does not have a variable.

An Equation is like a balance scale. Everything must be equal on both sides.

Example y + 13 = 25 - 13 - 13 y = 12 We want to get the y by itself. Perform the inverse operation. The inverse of adding is subtracting.

Do the same operation on the other side of the equal sign.

Check the answer in the original equation.

y + 13 = 25 12 + 13 = 25 25 = 25

Example 2

k – 12 = 4 + 12 + 12 k = 16 To get k by itself, we perform the inverse operation. The opposite of “minus 12” is “plus 12.”

Check

k – 12 = 4 16 – 12 = 4 4 = 4

Example 3

k – 10.2 = 5.5

+ 10.2

+ 10.2

k = 15.7

To get k by itself, we perform the inverse operation. The opposite of “minus 10.2” is “plus 10.2.” Remember, when adding decimals, you must line up the decimal before you can add.

Classwork:

You can use an equation - a statement that two different expressions are equal to each other - to find unknown values that make the equation true. This game introduces the concept of variables-- that something can be a 'container' for a number. You can learn more about equations by playing The Poodle Game . The poodles have lost the numbers that usually show up on their shirts. By placing each poodle on a scale and adding weights, the player can determine what number the poodle is. Here’s Hoop Shoot Again! Play this one step equation game alone or with another student. The equations in this first game involve addition and subtraction

Homework Time

p. 92, 2-44 Even