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Understanding Key Mathematical Concepts for 6th Grade: Equations, Inequalities, and More

This resource provides a comprehensive overview of essential mathematical concepts tailored for 6th graders. It covers topics such as constants, properties of fractions, equations, equivalent equations, inequalities, integers, and the order of operations (PEMDAS). The guide includes definitions and examples to illustrate critical principles, such as the multiplication property of -1, nested parentheses, opposites, reciprocals, and more. Students will also learn about repeating and terminating decimals, solutions, solution sets, and the trial and error method.

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Understanding Key Mathematical Concepts for 6th Grade: Equations, Inequalities, and More

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  1. 6th Grade Unit 6 By Drew

  2. Constant term • Some ting that stay the same like A+0=A no mater what a is it will be a added to 0 • Examples • Bx0=0 • U-0=U

  3. Division of fractions property • When you dived fraction you flip the second fraction and multiply it • Examples • 2/4 dived by ¾ it would be 2/4 * 4/3 • 7/8 dived by 5/8 would be 7/8 * 8/5

  4. Equation • An equation is when you use a letter to replace a number • Examples • W+9=12 W=3 • S-7=20 S=27

  5. Equivalent equations • A Equivalent equations is seeing if two equations are equal • Examples • 1+3+a=a+3+1 • 2x4+b=4x2+b

  6. Inequality • Inequality – not being equal • 2+2≠5 • 90/3≠21

  7. Integers • A number that is not a decimal or a fraction such as … • 7 • 12 • 21

  8. Multiplication property of -1 • Any positive number X -1 is that number – • Any negative number X -1 is positive number • 10 X (-1)=-10 • -10 X (-1)=10

  9. Nested parentheses • Nested parentheses are parentheses are parentheses in parentheses • (2+2)X8)+4= • (3+3)X6)x3

  10. Open sentence • Open sentence is a sentence that says something about math matrices • 5+5=10 • The opposite of 3 is -3

  11. Opposite of a number • A opposite of a positive number is a negative number and other way a round • The opposite of 3 is -3 • The opposite of -17 is 17

  12. Order of operations • PEMDAS (please excuse my dear aunt sally) Order in which you solve an equation. • Parentheses • Exponents • Multiplication and Division • Addition and Subtraction

  13. Reciprocal • A reciprocal is a flipped fraction and a reciprocal times its fraction is always one • ½ 2/1 • 9/7 7/9 • ¾ X 4/3=1

  14. Relation symbol • Symbols that show how numbers compare to each other. • 3>2 • 2x10=19+1

  15. Repeating decimals • A Repeating decimals are decimals that go on for ever • 1/3=0.33333… • Pie 3.14…

  16. Solution • An answer to a problem • 4+4=8 • 9X9=21

  17. Solution set • The set containg all the solution • 2+2 the set would have 4 in it • 8X3 the set would have 24

  18. Terminating decimals • A decimal number that has digits that don’t go on forever. • 0.23 • 0.75 • Rather then .66666…

  19. Trial and error method • To find a solution, try one method. If it fails, try different methods until you find the answer. • Example: show your work.

  20. Variable • A letter that takes the place of a number. • 3+x=4 • X=1 5x=15 X=3

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