Grade 6 Math: Algebra and Problem Solving

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What is a variable in algebra?
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A variable is a symbol, often a letter, that represents an unknown value.
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What is a constant in algebra?
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A constant is a fixed value that does not change.
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How can you identify a word problem that requires a variable?
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Look for phrases that indicate an unknown quantity, like 'how many,' 'how much,' or 'the number of.' These suggest the need for a variable.
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Translate the word problem into an equation: "Three more than a number is eight."
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x + 3 = 8
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How do you solve the equation x + 3 = 8?
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Subtract 3 from both sides: x = 8 - 3, so x = 5.
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If you have the equation 2x = 10, what is x?
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Divide both sides by 2: x = 10 / 2, so x = 5.
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What is transposition in algebra?
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Transposition is the process of moving terms from one side of an equation to the other to solve for a variable.
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How do you transpose x - 7 = 12 to solve for x?
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Add 7 to both sides: x = 12 + 7, so x = 19.
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Solve for y: 5y = 20.
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Divide both sides by 5: y = 20 / 5, so y = 4.
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What does it mean to solve a word problem using algebra?
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It means translating the problem into an equation with variables, then solving the equation to find the value of the unknowns.
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Solve: If a number divided by 4 is 3, what is the number?
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Let the number be x. x/4 = 3, so x = 3 * 4, thus x = 12.
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Translate the equation: Half of a number is 6.
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(1/2)x = 6
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How do you solve (1/2)x = 6 for x?
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Multiply both sides by 2: x = 6 * 2, so x = 12.
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Solve for z: z + 5 = 9.
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Subtract 5 from both sides: z = 9 - 5, so z = 4.
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How do you handle word problems with multiple operations, such as "Seven more than twice a number is 15"?
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Translate to an equation: 2x + 7 = 15, and then solve for x.
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If 3 times a number equals 18, what is the number?
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Let the number be x. 3x = 18, so x = 18 / 3, thus x = 6.
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What is the first step in solving transposed equations?
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Identify the terms to be transposed to one side to isolate the variable.
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How do you solve x/2 = 7 for x?
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Multiply both sides by 2: x = 7 * 2, so x = 14.
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Translate to an equation: "The sum of a number and its double is 21."
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x + 2x = 21
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How do you solve 3x = 21 for x?
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Divide both sides by 3: x = 21 / 3, so x = 7.
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