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.
Properties
Identity Properties:
a+0=a
1a = a
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 onestep equation game alone or with another student. The equations in
this first game involve addition and subtraction
Homework Time
p. 92, 2-44 Even