Introduction
Integer Multiplication and Division is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with integer multiplication and division.
What Is Integer Multiplication and Division?
Integer Multiplication and Division means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Integer Multiplication and Division
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: The number line shows three equal jumps from \(0\) that land on \(12\). Which multiplication does this represent?
- A. \(3 \times 4\)
- B. \(4 \times 4\)
- C. \(3 \times 3\)
- D. \(4 + 3\)
Why it works: The diagram shows \(3\) groups (jumps) of size \(4\) added together: \(4+4+4=12\), which is the same as \(3\times 4=12\).
Answer: \(3 \times 4 = 12\)
Visual Model 2
Question: What signs complete the table correctly?
| Problem | Sign | Result |
|---|---|---|
| \(6 \times (-9)\) | ? | \(-54\) |
| \((-8) \times (-8)\) | ? | \(64\) |
- A. Negative; Positive
- B. Positive; Negative
- C. Negative; Negative
- D. Positive; Positive
Why it works: Positive times negative gives negative (\(-54\)); negative times negative gives positive (\(64\)).
Answer: Negative; Positive
Worked Examples
Example 1
Question: The number line shows three identical jumps to the left. Which multiplication does this model?
- A. \((-1) \times (-3)\)
- B. \(3 \times (-1)\)
- C. \(3 \times 1\)
- D. \((-3) \times (-1)\)
- Three identical jumps of \(-1\) can be represented as \(3 \times (-1)=-3\).
Answer: \(3 \times (-1)\)
Example 2
Question: Which row correctly matches the expressions to their results?
| Expression | Result |
|---|---|
| \((-3) \times 5\) | ? |
| \((-3) \times (-5)\) | ? |
- A. \(-15\) and \(-15\)
- B. \(15\) and \(15\)
- C. \(15\) and \(-15\)
- D. \(-15\) and \(15\)
- Negative times positive is negative: \((-3) \times 5 = -15\).
- Negative times negative is positive: \((-3) \times (-5) = 15\).
Answer: \(-15\) and \(15\)
Example 3
Question: The number line shows 3 jumps of 2 units each to the right. Which multiplication represents this?
- A. \(3 \times 2 = 6\)
- B. \(2 + 2 + 2 = 6\)
- C. \((-2) \times (-3)\)
- D. \((-2) \times 3\)
- Three jumps of 2 units to the right starting from 0 reach 6.
- This represents \(3 \times 2 = 6\) (three groups of 2).
Answer: \(3 \times 2 = 6\)
Real-World Word Problems
Problem 1
Question: The temperature drops by 4° each hour for \(3\) hours. What is the total change in temperature?
- A. 12°
- B. -12°
- C. 7°
- D. -7°
Why it works: A drop of 4° repeated 3 times: \((-4) \times 3 = -12°\).
Answer: -12°
Problem 2
Question: A submarine descends \(2\) meters every minute for \(6\) minutes. How far below the starting point is it?
- A. \(8\) meters below
- B. \(12\) meters below
- C. \(4\) meters below
- D. \(-4\) meters below
Why it works: Descending \(2\) meters per minute for \(6\) minutes: \((-2) \times 6 = -12\) means 12 meters below.
Answer: \(12\) meters below
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
What is \(-6\times(-4)\)?
- A. \(-24\)
- B. \(-10\)
- C. \(10\)
- D. \(24\)
Question 2
Compute: \(7 \times (-5)\)
- A. \(-35\)
- B. \(35\)
- C. \(-2\)
- D. \(2\)
Question 3
What is \((-8) \times (-3)\)?
- A. \(-24\)
- B. \(11\)
- C. \(24\)
- D. \(-11\)
Question 4
Evaluate: \(-4 \times 6\)
- A. \(24\)
- B. \(-24\)
- C. \(2\)
- D. \(-2\)
Question 5
What is \(\frac{-20}{4}\)?
- A. \(5\)
- B. \(4\)
- C. \(-4\)
- D. \(-5\)
Question 6
Compute: \(\frac{-36}{-6}\)
- A. \(6\)
- B. \(-6\)
- C. \(-30\)
- D. \(30\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(24\)
The product of two negatives is positive: \((-6)\times(-4)=24\).
Question 2
Answer: \(-35\)
A positive times a negative is negative: \(7 \times (-5) = -35\).
Question 3
Answer: \(24\)
Negative times negative equals positive: \((-8) \times (-3) = 24\).
Question 4
Answer: \(-24\)
Negative times positive is negative: \((-4) \times 6 = -24\).
Question 5
Answer: \(-5\)
A negative divided by a positive is negative: \(\frac{-20}{4} = -5\).
Question 6
Answer: \(6\)
Negative divided by negative is positive: \(\frac{-36}{-6} = 6\).
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Integer Multiplication and Division becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
