Unit 6
Equations & Inequalities
Equations & Inequalities
Intro:
In the last lesson, we saw that an elephant weighs more than a skittle.
A mathematical sentence that declares that two things are not equal is called an inequality.
A mathematical sentence that declares that two things are not equal is called an inequality.
This elephant weighs approximately 4,586 pounds and the average skittle weighs 0.002335 pounds.
Or:
Or:
4586 > 0.002335
Notebook:
There are 5 types of inequalities.
Let's graph all the solutions to "m is less than four" on a number line.
What numbers make this inequality true? How many numbers are there?
What numbers make this inequality true? How many numbers are there?
There's not just one answer, is there? In fact, there are infinite answers. not only can we follow the numbers all the way to negative infinity, we can also count the fractions of numbers in between each integer. Halves, thirds, fourths, fifths, sixths, etc.
Let's shade in all the answers that make this inequality true. Let's make a big arrow pointing to the left, as if to say, "There are billions of answers that way. This problem has infinite answers."
Let's shade in all the answers that make this inequality true. Let's make a big arrow pointing to the left, as if to say, "There are billions of answers that way. This problem has infinite answers."
The farther to the right you go on the number line, the larger the number is.
Similarly, the farther to the left you go on the number line, the smaller the number is.
But what about 4? Is 4 an answer? Is 4 less than 4?
4 is not less than 4. 4 is equal to 4. We represent this with a hollow dot at 4, as if to say,
"Hey buddy, not four. Four IS NOT an answer to this problem."
Can you graph x < -9?
Similarly, the farther to the left you go on the number line, the smaller the number is.
But what about 4? Is 4 an answer? Is 4 less than 4?
4 is not less than 4. 4 is equal to 4. We represent this with a hollow dot at 4, as if to say,
"Hey buddy, not four. Four IS NOT an answer to this problem."
Can you graph x < -9?
What about those other two symbols?
These two symbols are "OR statements." There are two paths to make the inequality true. When we state that a number is greater than OR equal to -7...
....there are two ways to make this true. Either we can substitute a number greater than 7 into the variable, or we can substitute a number equal to 7. We represent the added answer of 7 with a solid dot on the number line.
Classwork & Homework:
-- EngageNY
State Test Practice:
California Standards:
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
CCSS.Math.Content.6.NS.C.7.a
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
CCSS.Math.Content.6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
CCSS.Math.Content.6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
CCSS.Math.Content.6.NS.C.7.a
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
CCSS.Math.Content.6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
CCSS.Math.Content.6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.