Integers
40 Questions
0 IXL Skills
🎨 Pedagogical Dimensions
Switch between different teaching approaches for this topic.
**Lesson Plan: Adding and Subtracting Positive and Negative Numbers** **Objective:** Students will learn how to add and subtract positive and negative integers using a number line and the concepts of "balloons" and "weights." --- ### 1. **Can You Do This? Check-In** Let’s begin with a quick check! **Question:** What is \(5 + (-3)\)? Try to solve this on your own. --- ### 2. **Introduction to Positive and Negative Numbers** - **Positive Numbers**: Represented by a "+" sign or no sign at all (e.g., \(5\) is the same as \(+5\)). - **Negative Numbers**: Represented by a "−" sign (e.g., \(-3\)). **Visual Aid:** Show a number line. Explain that on a number line, positive numbers go right and negative numbers go left. --- ### 3. **Using the Balloon and Weight Analogy** - **Balloons (Positive Numbers)**: They lift up. - **Weights (Negative Numbers)**: They pull down. --- ### 4. **Adding Positive Numbers** **I Do:** Example: \(2 + 3\) - Positive \(2\) plus Positive \(3\) equals Positive \(5\). - Written as \((+2) + (+3) = (+5)\). **We Do:** Let’s try one together: \(4 + 2\). What do we get? **You Do:** Now, try \(7 + 1\). What is your answer? --- ### 5. **Subtracting Positive Numbers** **I Do:** Example: \(6 - 3\) - Positive \(6\) minus Positive \(3\) equals Positive \(3\). - Written as \((+6) - (+3) = (+3)\). **We Do:** Let’s solve \(8 - 5\) together. What do we get? **You Do:** Now try \(10 - 6\). What is your answer? --- ### 6. **Adding a Negative Number** **I Do:** Example: \(6 + (-3)\) - Positive \(6\) plus Negative \(3\) equals Positive \(3\). - Written as \((+6) + (−3) = (+3)\). **We Do:** Let’s solve \(5 + (-2)\) together. What do we get? **You Do:** Now, try \(7 + (-4)\). What is your answer? --- ### 7. **Subtracting a Negative Number** **I Do:** Example: \(6 - (-3)\) - Positive \(6\) minus Negative \(3\) equals Positive \(9\). - Written as \((+6) - (−3) = (+9)\). **We Do:** Let’s try \(10 - (-2)\) together. **You Do:** What is \(14 - (-4)\)? --- ### 8. **Understanding the Rules** - **Like Signs**: - \((+)(+)\) or \((-)(-)\) becomes Positive. - **Unlike Signs**: - \((+)(-)\) or \((-)(+)\) becomes Negative. **We Do:** Let’s try \(3 + (-2)\) together. **You Do:** Now, what about \(25 - (-4)\)? --- ### 9. **Starting with a Negative Number** **I Do:** Example: \(-3 + (+2)\) - Start at \(-3\) on the number line and move up \(2\) to \(-1\). **We Do:** Let’s solve \(-5 + (+3)\). **You Do:** Now try \(-4 + (-2)\). --- ### 10. **Wrap-Up and Play!** You’ve done a great job learning about integers today! Remember, it’s all about practicing these concepts. **Activity Suggestion:** Try playing "Casey Runner" to practice your skills with positive and negative numbers. ### 11. **Celebrate!** No matter what answers you got, I celebrate your effort! You’ve put in great work to learn how to add and subtract integers. Keep practicing, and you'll become even better at it! --- **End of Lesson**
#1
Level 1
What is the value of 4 + 5?
Explanation: Imagine scoring runs in cricket. If you score 4 runs and then 5 more, you have a total of 9 runs.
#2
Level 1
What is the value of 10 - 3?
Explanation: If you start with 10 runs and take away 3 runs, you are left with 7 runs.
#3
Level 1
What is 5 + (-2)?
Explanation: Think of it as losing runs. Starting with 5 runs and losing 2 gives you 3 runs.
#4
Level 1
What is the value of 0 + 6?
Explanation: Adding zero to any number does not change its value. So, 0 + 6 = 6.
#5
Level 1
What is 7 - 5?
Explanation: If you have 7 runs and subtract 5 runs, you have 2 runs left.
#6
Level 1
What is the value of -3 + 4?
Explanation: Starting with a loss of 3 runs and scoring 4 runs gives you a total of 1 run.
#7
Level 1
What is the value of -2 - 5?
Explanation: If you start at -2 and lose 5 more runs, you end up at -7.
#8
Level 1
What is 8 + 0?
Explanation: Adding zero does not change the number. So, 8 + 0 = 8.
#9
Level 1
What is the value of 12 - 8?
Explanation: If you have 12 runs and take away 8 runs, you are left with 4 runs.
#10
Level 1
What is 5 - (-3)?
Explanation: Subtracting a negative number is like adding. So, 5 - (-3) = 5 + 3 = 8.
#11
Level 2
What is the value of 3 + (-7)?
Explanation: You start with 3 runs and lose 7 runs, resulting in -4.
#12
Level 2
What is the value of -8 + 2?
Explanation: Starting at -8 and adding 2 runs gives you -6.
#13
Level 2
What is 10 + (-15)?
Explanation: If you have 10 runs and lose 15 runs, you end up with -5.
#14
Level 2
What is -4 - (-6)?
Explanation: Subtracting a negative means adding. So, -4 - (-6) = -4 + 6 = 2.
#15
Level 2
What is 9 - 12?
Explanation: You start with 9 runs and lose 12 runs, resulting in -3.
#16
Level 2
What is -3 + (-5)?
Explanation: Adding two negative numbers combines their losses, so -3 + (-5) = -8.
#17
Level 2
What is 15 - (-5)?
Explanation: Subtracting a negative is like adding runs. So, 15 - (-5) = 20.
#18
Level 2
What is the value of 6 + (-9)?
Explanation: If you score 6 runs and lose 9 runs, you end up at -3.
#19
Level 2
What is -1 - 4?
Explanation: Starting at -1 and losing 4 more runs results in -5.
#20
Level 2
What is 7 + (-3)?
Explanation: If you have 7 runs and lose 3, you are left with 4 runs.
#21
Level 3
What is -6 + 3 + (-4)?
Explanation: Combine the numbers: -6 + 3 = -3, then -3 + (-4) = -7.
#22
Level 3
What is -5 - 7?
Explanation: Losing 5 runs and then 7 more gives you -12 runs.
#23
Level 3
What is 4 + 3 - 8?
Explanation: Combine: 4 + 3 = 7, then 7 - 8 = -1.
#24
Level 3
What is -10 + 5 - 3?
Explanation: Combine: -10 + 5 = -5, then -5 - 3 = -8.
#25
Level 3
What is 6 - 4 + (-2)?
Explanation: Calculate: 6 - 4 = 2, then 2 + (-2) = 0.
#26
Level 3
What is -2 + (-3) + 5?
Explanation: Combine: -2 + (-3) = -5, then -5 + 5 = 0.
#27
Level 3
What is 1 + (-6) - 5?
Explanation: Calculate: 1 + (-6) = -5, then -5 - 5 = -10.
#28
Level 3
What is 3 - 4 + (-2)?
Explanation: First, calculate: 3 - 4 = -1, then -1 + (-2) = -3.
#29
Level 3
What is -1 - (-3)?
Explanation: Subtracting a negative is like adding: -1 - (-3) = -1 + 3 = 2.
#30
Level 3
What is 5 - 7 + 3?
Explanation: Calculate: 5 - 7 = -2, then -2 + 3 = 1.
#31
Level 4
What is 7 + (-9) + 5?
Explanation: Calculate: 7 + (-9) = -2, then -2 + 5 = 3.
#32
Level 4
What is -8 + 4 + (-6)?
Explanation: Combine: -8 + 4 = -4, then -4 + (-6) = -10.
#33
Level 4
What is 12 - 9 - 5?
Explanation: First calculate: 12 - 9 = 3, then 3 - 5 = -2.
#34
Level 4
What is -4 - 6 + 8?
Explanation: Calculate: -4 - 6 = -10, then -10 + 8 = -2.
#35
Level 4
What is 15 - 25 + 10?
Explanation: First calculate: 15 - 25 = -10, then -10 + 10 = 0.
#36
Level 4
What is -7 + (-5) + 3?
Explanation: Combine: -7 + (-5) = -12, then -12 + 3 = -9.
#37
Level 4
What is -9 + 15 - 12?
Explanation: Calculate: -9 + 15 = 6, then 6 - 12 = -6.
#38
Level 4
What is 20 - 30 + 10?
Explanation: First calculate: 20 - 30 = -10, then -10 + 10 = 0.
#39
Level 4
What is -5 - 2 + 4?
Explanation: Calculate: -5 - 2 = -7, then -7 + 4 = -3.
#40
Level 4
What is -1 - (-1) + (-3)?
Explanation: First, -1 - (-1) = 0, then 0 + (-3) = -3.
{
"antigravity_content": "# Let\u0027s Dive into Integers: The Ups and Downs of Numbers!\n\nIntegers are like the players in a cricket match \u2014 some are on the positive team (the good guys) and some are on the negative team (the tricky ones). Let\u2019s learn how to add and subtract these numbers using fun examples and simple rules!\n\n---\n\n## What are Integers?\n\n- Integers are whole numbers that can be positive, negative, or zero.\n- Positive integers are like winning runs in gully cricket.\n- Negative integers are like losing runs \u2014 no one likes those!\n\n### Visual Suggestion:\n- **Number Line Illustration:** Show a horizontal line with zero in the middle, positive numbers to the right, and negative numbers to the left.\n\n---\n\n## Adding Positive and Negative Numbers\n\n### Adding Positive Numbers\n- When you add positive numbers, it\u0027s like scoring runs in cricket.\n- **Example:** 2 + 3 = 5 (You scored 5 runs!)\n\n### Adding Negative Numbers\n- Adding a negative number is like losing runs.\n- **Example:** If you have 6 runs and you lose 3 runs, it\u2019s 6 + (-3) = 3.\n\n### Visual Suggestion:\n- **Basket Illustration:** Show a basket with balloons (positive) pulling up and weights (negative) pulling down.\n\n---\n\n## Subtracting Positive and Negative Numbers\n\n### Subtracting Positive Numbers\n- Subtracting means taking away. If you take away 3 from 6, you have 3 left.\n- **Example:** 6 - 3 = 3.\n\n### Subtracting Negative Numbers\n- Subtracting a negative number is like getting extra runs!\n- **Example:** 6 - (-3) means you add 3 instead, so it becomes 6 + 3 = 9.\n\n### Visual Suggestion:\n- **Chai Stall Illustration:** Show a chai stall where you start with 6 cups (positive) and take away 3 cups (subtracting positive) vs. adding 3 cups (subtracting negative).\n\n---\n\n## The Rules of Adding and Subtracting Integers\n\n### Like Signs Become Positive\n- If both numbers are positive or both are negative, they combine to be positive.\n- **Examples:**\n - (+2) + (+3) = +5\n - (-2) + (-3) = -5\n \n### Unlike Signs Become Negative\n- If one number is positive and the other is negative, you subtract and take the sign of the larger number.\n- **Examples:**\n - (+7) + (-2) = 5\n - (+5) + (-7) = -2\n\n### Visual Suggestion:\n- **Flowchart:** Create a flowchart showing what happens with like signs vs. unlike signs.\n\n---\n\n## Quick Recap of Integer Operations\n\n- **Adding Positive Numbers**: Just add them up! (e.g. 4 + 5 = 9)\n- **Subtracting Positive Numbers**: Take away as usual! (e.g. 10 - 3 = 7)\n- **Adding Negative Numbers**: Think of it as losing! (e.g. 3 + (-2) = 1)\n- **Subtracting Negative Numbers**: It\u2019s like scoring extra runs! (e.g. 5 - (-4) = 9)\n\n### Visual Suggestion:\n- **Cheat Sheet:** Create a cheat sheet summarizing the rules with examples from gully cricket!\n\n---\n\n## Quick Recap Box\n\n| Operation | Example | Result |\n|------------------------------|-------------------|----------|\n| Adding Positive Numbers | 4 + 5 | 9 |\n| Subtracting Positive Numbers | 10 - 3 | 7 |\n| Adding Negative Numbers | 3 + (-2) | 1 |\n| Subtracting Negative Numbers | 5 - (-4) | 9 |\n\nNow that you know the basics of integers, you can tackle any math problem with confidence \u2014 just like hitting a six in cricket! \ud83c\udfcf",
"meta": {
"difficulty_distribution": {
"1": 10,
"2": 10,
"3": 10,
"4": 10
},
"total_questions": 40
},
"questions": [
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "Imagine scoring runs in cricket. If you score 4 runs and then 5 more, you have a total of 9 runs.",
"id": 1,
"options": [
"A) 7",
"B) 9",
"C) 8",
"D) 10"
],
"question": "What is the value of 4 + 5?"
},
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "If you start with 10 runs and take away 3 runs, you are left with 7 runs.",
"id": 2,
"options": [
"A) 6",
"B) 7",
"C) 8",
"D) 5"
],
"question": "What is the value of 10 - 3?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "Think of it as losing runs. Starting with 5 runs and losing 2 gives you 3 runs.",
"id": 3,
"options": [
"A) 3",
"B) 7",
"C) -3",
"D) 2"
],
"question": "What is 5 + (-2)?"
},
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "Adding zero to any number does not change its value. So, 0 + 6 = 6.",
"id": 4,
"options": [
"A) 0",
"B) 6",
"C) -6",
"D) 3"
],
"question": "What is the value of 0 + 6?"
},
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "If you have 7 runs and subtract 5 runs, you have 2 runs left.",
"id": 5,
"options": [
"A) 11",
"B) 2",
"C) 1",
"D) 0"
],
"question": "What is 7 - 5?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "Starting with a loss of 3 runs and scoring 4 runs gives you a total of 1 run.",
"id": 6,
"options": [
"A) 1",
"B) 7",
"C) -1",
"D) 0"
],
"question": "What is the value of -3 + 4?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "If you start at -2 and lose 5 more runs, you end up at -7.",
"id": 7,
"options": [
"A) -7",
"B) 3",
"C) -3",
"D) -5"
],
"question": "What is the value of -2 - 5?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "Adding zero does not change the number. So, 8 + 0 = 8.",
"id": 8,
"options": [
"A) 8",
"B) 0",
"C) 1",
"D) 8.5"
],
"question": "What is 8 + 0?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "If you have 12 runs and take away 8 runs, you are left with 4 runs.",
"id": 9,
"options": [
"A) 4",
"B) 5",
"C) 3",
"D) 6"
],
"question": "What is the value of 12 - 8?"
},
{
"correct_answer": "A",
"difficulty": 1,
"explanation": "Subtracting a negative number is like adding. So, 5 - (-3) = 5 + 3 = 8.",
"id": 10,
"options": [
"A) 8",
"B) 2",
"C) 3",
"D) 5"
],
"question": "What is 5 - (-3)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "You start with 3 runs and lose 7 runs, resulting in -4.",
"id": 11,
"options": [
"A) -4",
"B) 4",
"C) -10",
"D) 10"
],
"question": "What is the value of 3 + (-7)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "Starting at -8 and adding 2 runs gives you -6.",
"id": 12,
"options": [
"A) -6",
"B) 6",
"C) -10",
"D) 10"
],
"question": "What is the value of -8 + 2?"
},
{
"correct_answer": "B",
"difficulty": 2,
"explanation": "If you have 10 runs and lose 15 runs, you end up with -5.",
"id": 13,
"options": [
"A) 5",
"B) -5",
"C) 15",
"D) -10"
],
"question": "What is 10 + (-15)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "Subtracting a negative means adding. So, -4 - (-6) = -4 + 6 = 2.",
"id": 14,
"options": [
"A) 2",
"B) -2",
"C) 10",
"D) -10"
],
"question": "What is -4 - (-6)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "You start with 9 runs and lose 12 runs, resulting in -3.",
"id": 15,
"options": [
"A) -3",
"B) 3",
"C) 21",
"D) -21"
],
"question": "What is 9 - 12?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "Adding two negative numbers combines their losses, so -3 + (-5) = -8.",
"id": 16,
"options": [
"A) -8",
"B) 8",
"C) 2",
"D) -2"
],
"question": "What is -3 + (-5)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "Subtracting a negative is like adding runs. So, 15 - (-5) = 20.",
"id": 17,
"options": [
"A) 20",
"B) 10",
"C) 5",
"D) -5"
],
"question": "What is 15 - (-5)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "If you score 6 runs and lose 9 runs, you end up at -3.",
"id": 18,
"options": [
"A) -3",
"B) 15",
"C) 3",
"D) -15"
],
"question": "What is the value of 6 + (-9)?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "Starting at -1 and losing 4 more runs results in -5.",
"id": 19,
"options": [
"A) -5",
"B) 5",
"C) 3",
"D) -3"
],
"question": "What is -1 - 4?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "If you have 7 runs and lose 3, you are left with 4 runs.",
"id": 20,
"options": [
"A) 4",
"B) -4",
"C) 10",
"D) 0"
],
"question": "What is 7 + (-3)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Combine the numbers: -6 + 3 = -3, then -3 + (-4) = -7.",
"id": 21,
"options": [
"A) -7",
"B) 7",
"C) -1",
"D) 1"
],
"question": "What is -6 + 3 + (-4)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Losing 5 runs and then 7 more gives you -12 runs.",
"id": 22,
"options": [
"A) -12",
"B) 12",
"C) -2",
"D) 2"
],
"question": "What is -5 - 7?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Combine: 4 + 3 = 7, then 7 - 8 = -1.",
"id": 23,
"options": [
"A) -1",
"B) 1",
"C) 0",
"D) 2"
],
"question": "What is 4 + 3 - 8?"
},
{
"correct_answer": "B",
"difficulty": 3,
"explanation": "Combine: -10 + 5 = -5, then -5 - 3 = -8.",
"id": 24,
"options": [
"A) -8",
"B) -6",
"C) -4",
"D) -12"
],
"question": "What is -10 + 5 - 3?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Calculate: 6 - 4 = 2, then 2 + (-2) = 0.",
"id": 25,
"options": [
"A) 0",
"B) 2",
"C) -2",
"D) -4"
],
"question": "What is 6 - 4 + (-2)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Combine: -2 + (-3) = -5, then -5 + 5 = 0.",
"id": 26,
"options": [
"A) 0",
"B) -6",
"C) 6",
"D) -4"
],
"question": "What is -2 + (-3) + 5?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Calculate: 1 + (-6) = -5, then -5 - 5 = -10.",
"id": 27,
"options": [
"A) -10",
"B) -5",
"C) 0",
"D) 5"
],
"question": "What is 1 + (-6) - 5?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "First, calculate: 3 - 4 = -1, then -1 + (-2) = -3.",
"id": 28,
"options": [
"A) -3",
"B) 3",
"C) -1",
"D) 1"
],
"question": "What is 3 - 4 + (-2)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Subtracting a negative is like adding: -1 - (-3) = -1 + 3 = 2.",
"id": 29,
"options": [
"A) 2",
"B) -2",
"C) 0",
"D) 3"
],
"question": "What is -1 - (-3)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "Calculate: 5 - 7 = -2, then -2 + 3 = 1.",
"id": 30,
"options": [
"A) 1",
"B) -1",
"C) 3",
"D) -3"
],
"question": "What is 5 - 7 + 3?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Calculate: 7 + (-9) = -2, then -2 + 5 = 3.",
"id": 31,
"options": [
"A) 3",
"B) 1",
"C) -1",
"D) 0"
],
"question": "What is 7 + (-9) + 5?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Combine: -8 + 4 = -4, then -4 + (-6) = -10.",
"id": 32,
"options": [
"A) -10",
"B) -6",
"C) -2",
"D) 2"
],
"question": "What is -8 + 4 + (-6)?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "First calculate: 12 - 9 = 3, then 3 - 5 = -2.",
"id": 33,
"options": [
"A) -2",
"B) 0",
"C) 3",
"D) 2"
],
"question": "What is 12 - 9 - 5?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Calculate: -4 - 6 = -10, then -10 + 8 = -2.",
"id": 34,
"options": [
"A) -2",
"B) 2",
"C) 0",
"D) -4"
],
"question": "What is -4 - 6 + 8?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "First calculate: 15 - 25 = -10, then -10 + 10 = 0.",
"id": 35,
"options": [
"A) 0",
"B) 10",
"C) -10",
"D) 5"
],
"question": "What is 15 - 25 + 10?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Combine: -7 + (-5) = -12, then -12 + 3 = -9.",
"id": 36,
"options": [
"A) -9",
"B) -11",
"C) -5",
"D) 5"
],
"question": "What is -7 + (-5) + 3?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Calculate: -9 + 15 = 6, then 6 - 12 = -6.",
"id": 37,
"options": [
"A) -6",
"B) 6",
"C) 0",
"D) 3"
],
"question": "What is -9 + 15 - 12?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "First calculate: 20 - 30 = -10, then -10 + 10 = 0.",
"id": 38,
"options": [
"A) 0",
"B) 10",
"C) -10",
"D) 5"
],
"question": "What is 20 - 30 + 10?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "Calculate: -5 - 2 = -7, then -7 + 4 = -3.",
"id": 39,
"options": [
"A) -3",
"B) -1",
"C) 1",
"D) 2"
],
"question": "What is -5 - 2 + 4?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "First, -1 - (-1) = 0, then 0 + (-3) = -3.",
"id": 40,
"options": [
"A) -5",
"B) -3",
"C) 0",
"D) 2"
],
"question": "What is -1 - (-1) + (-3)?"
}
],
"source_ixl_skills": [],
"topic": "Integers"
}