Back to Details M6B - Q4 - Unit 1 Review Open in Editor

M6B - Q4 - Unit 1 Review

Complete Study Guide for Tomorrow's Unit Test

📚 Mathematics 🎓 Grade 6 ⏱️ 50 minutes

Learning Objectives

  • Recall and correctly use vocabulary for the four operations: sum, difference, product, factor, quotient, dividend, divisor

  • Identify factors, multiples, prime and composite numbers, and compute GCF and LCM

  • Convert between fractions and decimals, simplify fractions, and work with mixed numbers and improper fractions

  • Identify variables, coefficients, constants, and terms; apply order of operations and properties to evaluate and simplify expressions

Progress 9 sections
1

Introduction

~2 minutes

Tomorrow is your Unit 1 test. This study guide covers everything from all four lessons. Read through each section carefully, then work through all 24 practice questions at the end. If you get a question wrong, go back and re-read that section before moving on.

The four topics covered: 1. The Language of Operations 2. Number Relationships and Place Value 3. Fractions and Decimals 4. Expressions, Equations, and Reasoning

💡 Test-Taking Strategy

On the test, read every question carefully before answering. Underline key vocabulary words. Show your work on computation problems. If you get stuck, skip the question and come back to it.

2

Part 1: Language of Operations Review

~5 minutes

Mathematics has its own vocabulary. Knowing these terms is essential for understanding word problems and communicating your thinking.

Addition: The result of adding is called the sum. The numbers being added are called addends.
• Example: In 7 + 5 = 12, the sum is 12.

Subtraction: The result of subtracting is called the difference.
• Example: In 15 - 8 = 7, the difference is 7.

Multiplication: The result of multiplying is called the product. The numbers being multiplied are called factors.
• Example: In 6 x 4 = 24, the product is 24, and the factors are 6 and 4.
• Multiplication is commutative: 6 x 4 = 4 x 6. The order of factors does not change the product.

Division: In 56 / 8 = 7:
• 56 is the dividend (the number being divided)
• 8 is the divisor (the number you divide by)
• 7 is the quotient (the result)

💡 Inverse Operations

Addition and subtraction are inverse operations (they undo each other). Multiplication and division are also inverse operations.

Fact Family Example: 3, 7, 21
• 3 x 7 = 21
• 7 x 3 = 21
• 21 / 7 = 3
• 21 / 3 = 7

If you know one fact, you can write the whole family.

Learn to spot these signal words that tell you which operation to use:

OperationSignal Words
Additionsum, total, combined, altogether, increased by, more than
Subtractiondifference, decreased by, fewer, less than, remaining, left
Multiplicationproduct, times, doubled, tripled, of, each, per
| Division | quotient, divided, split, shared equally, per, ratio |

3

Part 2: Number Relationships and Place Value Review

~6 minutes

Factors are numbers you multiply together to get a product. Multiples are what you get when you multiply a number by 1, 2, 3, 4, ...

- Factors of 12: 1, 2, 3, 4, 6, 12
• First five multiples of 4: 4, 8, 12, 16, 20

Prime numbers have exactly two factors: 1 and themselves. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23.
• The number 1 is neither prime nor composite.
• The number 2 is the only even prime number.

Composite numbers have more than two factors. Examples: 4, 6, 8, 9, 10, 12, 14, 15.

💡 GCF and LCM

Greatest Common Factor (GCF): The largest factor shared by two or more numbers.
• GCF of 12 and 18: Factors of 12 = {1, 2, 3, 4, 6, 12}. Factors of 18 = {1, 2, 3, 6, 9, 18}. Common = {1, 2, 3, 6}. GCF = 6.

Least Common Multiple (LCM): The smallest multiple shared by two or more numbers.
• LCM of 4 and 6: Multiples of 4 = {4, 8, 12, 16, ...}. Multiples of 6 = {6, 12, 18, ...}. LCM = 12.

When to use GCF: Splitting things into equal groups, simplifying fractions. When to use LCM: Finding common denominators, scheduling problems.

Each digit in a number has a value based on its position.

ThousandsHundredsTensOnes.TenthsHundredthsThousandths
1,000100101.0.10.010.001
In the number 4,362.715:
• The 3 is in the hundreds place (value = 300)
• The 7 is in the tenths place (value = 0.7)
• The 1 is in the hundredths place (value = 0.01)
• The 5 is in the thousandths place (value = 0.005)

Reading decimals correctly: Say "and" for the decimal point, then read the digits and say the place value of the last digit.
• 3.45 = "three and forty-five hundredths"

4

Part 3: Fractions and Decimals Review

~7 minutes

A fraction represents division and parts of a whole.
• In 3/4: the numerator (3) tells how many parts you have. The denominator (4) tells how many equal parts make a whole.
• 3/4 also means 3 divided by 4.

Equivalent Fractions: Multiply or divide both numerator and denominator by the same number.
• 2/3 = 4/6 = 6/9 = 8/12 (multiply by 2, 3, 4)

Simplifying Fractions: Divide both numerator and denominator by their GCF.
• 8/12: GCF of 8 and 12 is 4, so 8/12 = 2/3

Improper Fractions and Mixed Numbers:
• Improper fraction: numerator >= denominator (e.g., 7/4)
• Mixed number: whole number + fraction (e.g., 1 3/4)
• To convert: 7/4 = 7 divided by 4 = 1 remainder 3 = 1 3/4
• To convert back: 1 3/4 = (1 x 4 + 3) / 4 = 7/4

💡 The Reciprocal

The reciprocal of a fraction is what you get when you flip the numerator and denominator.
• Reciprocal of 3/4 is 4/3
• Reciprocal of 5 is 1/5 (since 5 = 5/1)
• A number times its reciprocal always equals 1: 3/4 x 4/3 = 12/12 = 1

Reciprocals are essential for dividing fractions: to divide by a fraction, multiply by its reciprocal.

Fraction to Decimal: Divide the numerator by the denominator.
• 3/4 = 3 divided by 4 = 0.75
• 1/3 = 1 divided by 3 = 0.333... (repeating)

Decimal to Fraction: Read the decimal, write it as a fraction, simplify.
• 0.6 = 6/10 = 3/5
• 0.25 = 25/100 = 1/4

Common Equivalents to Memorize:

FractionDecimalFractionDecimal
1/20.51/30.333...
1/40.252/30.666...
3/40.751/50.2
1/80.1251/100.1
Adding Fractions:
• Same denominator: Add the numerators, keep the denominator. 2/7 + 3/7 = 5/7
• Different denominators: Find the LCM, create equivalent fractions, then add. - 1/3 + 1/4: LCM of 3 and 4 = 12, so 4/12 + 3/12 = 7/12

5

Part 4: Expressions, Equations, and Reasoning Review

~8 minutes

Variable: A letter or symbol that represents an unknown number (e.g., x, n, y).

Expression: A mathematical phrase with numbers, variables, and operations, but no equals sign.
• Examples: 5x + 3, 2n - 7, 4(a + b)

Equation: A mathematical sentence with an equals sign showing two expressions are equal.
• Examples: 5x + 3 = 18, 2n - 7 = 9

Think of it this way: an expression is like a phrase, and an equation is like a complete sentence.

📖 Parts of an Expression

In the expression 5x + 3y - 2:

- Terms are separated by + and - signs: 5x, 3y, and 2
• Coefficient: The number multiplied by a variable. In 5x, the coefficient is 5.
• Constant: A term with no variable. Here, the constant is 2.
• Like terms: Terms with the same variable raised to the same power. 5x and 3x are like terms. 5x and 3y are NOT like terms.

Combining like terms: 5x + 3x = 8x, but 5x + 3y cannot be simplified.

💡 Order of Operations: PEMDAS

P - Parentheses first E - Exponents next M/D - Multiplication and Division, left to right (EQUAL priority) A/S - Addition and Subtraction, left to right (EQUAL priority)

Critical rule: Multiplication does NOT always come before Division. They have the same priority and are done left to right. Same for Addition and Subtraction.

Example: 18 / 3 x 2 = 6 x 2 = 12 (left to right, NOT 18 / 6) Example: 2 + 3 x 4 = 2 + 12 = 14 (multiply first, then add) Example: (8 - 3) x 2 + 1 = 5 x 2 + 1 = 10 + 1 = 11 (parentheses first)

Commutative Property: Order does not matter.
• Addition: a + b = b + a (3 + 7 = 7 + 3)
• Multiplication: a x b = b x a (4 x 5 = 5 x 4)
• Does NOT work for subtraction or division.

Associative Property: Grouping does not matter.
• Addition: (a + b) + c = a + (b + c)
• Multiplication: (a x b) x c = a x (b x c)
• Does NOT work for subtraction or division.

Distributive Property: Multiply across addition or subtraction.
• a(b + c) = ab + ac
• Example: 3(x + 4) = 3x + 12

Identity Property: Adding 0 or multiplying by 1 leaves a number unchanged.
• a + 0 = a
• a x 1 = a

Practice converting English into math expressions:

English PhraseMath Expression
Five more than a numbern + 5
A number decreased by 8n - 8
Three times a number3n
A number divided by 4n / 4
Twice a number plus 72n + 7
Three less than a numbern - 3
Common Mistake: "Three less than a number" means n - 3, NOT 3 - n. The "less than" tells you to subtract FROM the number.

Evaluating Expressions: Substitute the given value and follow order of operations.
• Evaluate 3x + 5 when x = 4: 3(4) + 5 = 12 + 5 = 17
• Evaluate 2n^2 - 1 when n = 3: 2(9) - 1 = 18 - 1 = 17

💡 Final Reminder

You have practiced all of these concepts before. Tomorrow's test is your chance to show what you know. Work through every practice question below. If you can answer these confidently, you are ready for the test.

6

Practice: Operations Vocabulary

~4 minutes
Question 1

Match each vocabulary term to its correct definition.

Question 2

In the equation 42 / 6 = 7, what is the divisor?

Question 3

Addition and subtraction are _____ operations because they undo each other.

Question 4

A store sells 8 packs of markers with 12 markers in each pack. Which word describes the 96 markers total?

7

Practice: Number Relationships and Place Value

~5 minutes
Question 5

Select ALL the prime numbers from the list below.

Select all that apply.

Question 6

What is the Greatest Common Factor (GCF) of 24 and 36?

Question 7

What is the Least Common Multiple (LCM) of 6 and 8?

Question 8

In the number 5,280.49, what is the value of the digit 8?

Question 9

The number 1 is a prime number.

8

Practice: Fractions and Decimals

~6 minutes
Question 10

Which fraction is equivalent to 6/15?

Question 11

Convert the mixed number 2 3/8 to an improper fraction: _____

Question 12

What is the reciprocal of 2/7?

Question 13

Match each fraction to its decimal equivalent.

Question 14

Arrange these values from LEAST to GREATEST.

⋮⋮ 0.85
⋮⋮ 0.2
⋮⋮ 3/5
⋮⋮ 1/3
Drag items to reorder, then confirm
Question 15

What is 1/3 + 1/4?

9

Practice: Expressions, Equations, and Reasoning

~7 minutes
Question 16

Which of the following is an EXPRESSION (not an equation)?

Question 17

In the expression 7x + 4y - 9, match each part to its correct term.

Question 18

Evaluate: 2 + 3 x 4

Question 19

Evaluate: (8 - 3) x 2 + 4^2

Question 20

Apply the distributive property: 5(x + 3) = _____ + _____

Question 21

The commutative property works for subtraction: a - b = b - a.

Question 22

Which expression represents "three less than twice a number"?

Question 23

Evaluate 4x - 2y when x = 5 and y = 3.

Question 24

A teacher has 48 pencils and 36 erasers to divide equally into bags for students. Each bag must have the same number of pencils and the same number of erasers, with nothing left over.

(a) What is the greatest number of bags the teacher can make? (b) How many pencils will be in each bag? (c) How many erasers will be in each bag?