CHAPTER 4.4 - 4.6 Inequalities and so much more...

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CHAPTER 4.4 - 4.6 Inequalities and so much more...

More or Less  An inequality is a number sentence that contains the symbols, ≤, ≥, =, ≠  x<7 is an inequality

More or Less  A solution to an inequality with a variable is a value for the variable that makes it true.  x<7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X =6,5,4,3,2,1,0

More or Less  Which of the numbers 4, 5, and 6 are solutions of x + 3 > 7?  Replace the variable with the numeral 4 4 + 3 > 7 False  Replace the variable with the numeral 5 5 + 3 > 7 True If the expression is true for 5 and the value of 6 is greater than the value of 5, we assume that 6 + 3 > 7 is also true.

More or Less  Which of the numbers 8, 9, 10, 11, and 12 are solutions to the inequality? X ≥ 8 X + 4 ≤ 13 X – 5 ≥ 5 X ≤ 6 + 2

More or Less Sometimes numbers satisfy two inequalities at the same time. 5 ≤ c ≤ 10 What are the two inequalities that make up this sentence? c ≥ 5 c ≤ 10

More or Less  Use the number line to solve both inequalities 5 ≤ c ≤ 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time for Practice  Open your practice book to page 4.4  Complete all problems  When you are finished, let me know.  Once 4.4 is correct, you will have a problem solving sheet to complete

Time for Practice  Solve the inequality. 21 ≤ b ≤ 32 What are all the possibilities of b?

Mental Math 4.5  Use the properties and mental math to solve addition and subtraction problems.  Commutative Property a + b = b + a  Associative property (a + b) + c = a + (b + c) Do these two properties work for subtraction? Why not?

Mental Math  Compensation-change one addend to a multiple of 10 and then adjust the other addend to keep the balance.  37 + 25 = (37 + 3) + (25 – 3) (40 + 22) (62) 37 + 2540 + 22

Mental Math  Use the Commutative or Associative Properties, or use compensation to solve the following problems: N + 15 = 15 + 3 (16 + 5 ) + 4 = 16 + (n + 4) 17 + 24 17 + ( 23 + 3) N = 3 Commutative N = 5 Associative (17 + 3) + (24 – 3) 20 + 21 41 Compensation (17 + 3) + 23 20 + 23 43 Associative and Compensation

Mental Math  If a rule used for one example is true for all examples, it is CLOSED  Rule: Any number increased by one will result in the next number in the series: 6 + 1 = 7  The Closure Property states that if a rule for one example is true for all examples, it is closed.  When you add two even numbers together, the result will be an even number. (6 + 8 = 14)  Test to see if this is true for all even addends.

Mental Math  The Closure Property states that if a rule for one example is true for all examples, it is closed.  Check to see if each set of numbers and operation satisfy the Closure Property:  Odd numbers and addition  Even numbers and multiplication  Odd numbers and multiplication  Odd numbers and subtraction Not Closed Closed Not Closed

Write an Equation 4.6  When you use an equation to solve a word problem you are using an organizational structure.  Think about what the problem is asking you to find.  Look for key words to determine what operation or operations to use.  Think about what information is missing.  The information that is missing will be represented by your variable.

Write an Equation 4.6 Mary ordered 4 chicken salads to take home for dinner. Her bill came to \$24. How much was each salad? Think about what the problem is asking you to find. I need to find the price of one salad.

Write an Equation 4.6 Mary ordered 4 chicken salads to take home for dinner. Her bill came to \$24. How much was each salad?  Look for key words to determine what operation or operations to use. Each means I need to divide \$24 by 4.

Write an Equation 4.6 Mary ordered 4 chicken salads to take home for dinner. Her bill came to \$24. How much was each salad?  Think about what information is missing. N x 4 = 24 24 ÷ 4 = N

Write an Equation 4.6 Mary ordered 4 chicken salads to take home for dinner. Her bill came to \$24. How much was each salad?  Clearly state your answer with any explanation it needs. Each salad cost \$6.

Write an Equation 4.6 Steve completed some homework papers on Monday. On Tuesday, he finished 6 papers. On Wednesday, he completed 3 more. On Thursday, Steve had no homework. By Friday, Steve had completed a total of 15 papers of homework. How many did he complete on Monday? Think about what the problem is asking you to find. Look for key words to determine what operation or operations to use. Think about what information is missing. Clearly state your answer with any explanation it needs.

Write an Equation 4.6 Steve completed some homework papers on Monday. On Tuesday, he finished 6 papers. On Wednesday, he completed 3 more. On Thursday, Steve had no homework. By Friday, Steve had completed a total of 15 papers of homework. How many did he complete on Monday ?  If H = the homework Steve completed on Monday, then H + 6 + 3 = 15 H + 9 = 15 15 – 9 = H H = 6 Steve completed 6 homework papers on Monday

Homework  You will complete Challenge Sheet 4.6 for homework.  Write an equation for each side of the triangle.  The circles are the products (multiplication)  The boxes are the multiples  Find the solution for all of the variables