Unit 6
Equations & Inequalities
Equations & Inequalities
Intro:
Let's start with a box of oranges:
I'm not going to tell you how many oranges are in the box (yet).
On this box of oranges, there is a note:
On this box of oranges, there is a note:
Someone took 5 oranges out of the box and promised to repay the oranges later.
We can consider these negative oranges. Debt oranges, if you will. Like Mr. Barnes borrowing oranges from his cat.
We can consider these negative oranges. Debt oranges, if you will. Like Mr. Barnes borrowing oranges from his cat.
Let x = the original number of oranges in this orange box.
I weighed this box of oranges with the five oranges taken out on my scale and I found that it balanced out with 42 oranges:
In order to find x,
the original amount of oranges,
I can add five oranges to each side of the equation.
the original amount of oranges,
I can add five oranges to each side of the equation.
Notebook:
Subtraction is the inverse operation of addition.
Subtraction means adding the opposite.
Subtraction means adding the opposite.
Classwork & Homework:
-- EngageNY
State Test Practice:
California Standards:
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Content.6.EE.B.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 or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
CCSS.Math.Content.6.EE.B.6
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.
CCSS.Math.Content.6.EE.B.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.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Content.6.EE.B.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 or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
CCSS.Math.Content.6.EE.B.6
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.
CCSS.Math.Content.6.EE.B.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.