How to apply the associative property of multiplication in 3rd grade

📚 What is the Associative Property of Multiplication?

The associative property of multiplication states that you can change the grouping of factors in a multiplication problem without changing the product. In simpler terms, it doesn't matter which numbers you multiply first; the answer will always be the same. This is super helpful for making mental math easier!

📜 A Little History

The associative property, along with other properties like the commutative and distributive properties, wasn't formally defined until the 19th century. However, mathematicians have been using these concepts implicitly for centuries. It's a fundamental idea that helps simplify complex calculations.

🔑 The Key Principle

The associative property can be represented like this:

$(a \times b) \times c = a \times (b \times c)$

Where 'a', 'b', and 'c' are any numbers.

• 🧮 Grouping Doesn't Matter: No matter how you group the numbers with parentheses, the final answer will be the same.
• ✍️ Only Multiplication: This property only works with multiplication (and addition!). It doesn't work with subtraction or division.
• ➕ Three or More Numbers: You need at least three numbers to apply the associative property.

🌍 Real-World Examples

Let's look at some examples to see how the associative property works in action:

• 📦 Example 1: Suppose you have 2 boxes, and each box contains 3 sets of crayons, with each set having 4 crayons. You can find the total number of crayons in two ways:
  • 🔢 First way: $(2 \times 3) \times 4 = 6 \times 4 = 24$ crayons.
  • 🎨 Second way: $2 \times (3 \times 4) = 2 \times 12 = 24$ crayons.
• 🧺 Example 2: Imagine you're helping pack snacks for a field trip. You have 4 bags, each with 2 packs of crackers, and each pack has 5 crackers. You can calculate the total crackers as follows:
  • 🍪 First way: $(4 \times 2) \times 5 = 8 \times 5 = 40$ crackers.
  • 🎒 Second way: $4 \times (2 \times 5) = 4 \times 10 = 40$ crackers.

💡 Tips for Applying the Associative Property

• 🧠 Look for Easy Groupings: Try to group numbers that are easy to multiply together, like 2 and 5, or 10 and any other number.
• 📝 Rewrite the Problem: Sometimes rewriting the problem with different parentheses can make it easier to solve.
• ✅ Check Your Work: After you solve the problem, double-check your answer to make sure you didn't make any mistakes.

✍️ Practice Quiz

Use the associative property to solve these problems:

1. $(5 \times 2) \times 3 = $ ?
2. $4 \times (2 \times 5) = $ ?
3. $(3 \times 3) \times 4 = $ ?

Answers:

1. 30
2. 40
3. 36

⭐ Conclusion

The associative property of multiplication is a useful tool for simplifying multiplication problems. By grouping numbers differently, you can often make mental math easier and solve problems more efficiently. Keep practicing, and you'll master it in no time!