Home School: Explain the distributive property with video links.

 Explain the distributive property

The distributive property is a fundamental concept in mathematics that states how multiplication distributes (spreads) over addition (or subtraction). Imagine you have a bunch of cookies and you want to share them equally among your friends. You could count out the cookies one by one for each friend, but there's a more efficient way!

Think of it like this:

1. You have a total number of cookies (let's say 24).
2. You have a group of friends (let's say 4).
3. You can distribute the cookies equally in two ways:

• Individually: Give each friend 24 cookies one by one (24 + 24 + 24 + 24). This is like multiplying the total number of cookies by the number of friends: 24 cookies/friend * 4 friends = 96 cookies total.
• In groups: Divide the cookies into 4 equal groups (6 cookies/group). Then, give each friend one group (6 cookies/friend * 4 groups = 24 cookies total).

Both ways lead to the same result: each friend gets 6 cookies. This is the essence of the distributive property! It tells us that multiplying a sum (or difference) by a number is the same as multiplying each term of the sum (or difference) by the number and then adding (or subtracting) the products.

Here's the mathematical formula for the distributive property:

• Multiplication over addition: A × (B + C) = (A × B) + (A × C)
• Multiplication over subtraction: A × (B - C) = (A × B) - (A × C)

Here are some real-life examples of the distributive property:

• Buying groceries: You buy 3 apples at $1 each and 2 oranges at $2 each. The total cost is (3 apples * $1/apple) + (2 oranges * $2/orange) = $3 + $4 = $7.
• Sharing pizza: You have 8 slices of pizza and 4 friends. You can give each friend 2 slices by dividing the pizza into 4 equal groups (8 slices / 4 groups = 2 slices/group) and giving each friend one group.

The distributive property is a powerful tool that can simplify calculations and make solving problems easier. It's used throughout mathematics, from basic arithmetic to calculus and beyond. So next time you see a multiplication problem with addition or subtraction, remember the distributive property and spread the math magic!

 M.O.3.1.12 model the distributive property in multiplication of 2- and 3-digit numbers by a 1-digit number.

Here's a breakdown of how to model the distributive property in multiplication of 2- and 3-digit numbers by a 1-digit number:

1. Decompose the larger number:

• Break the 2- or 3-digit number into its place value parts: hundreds, tens, and ones.

2. Apply the distributive property:

• Rewrite the multiplication as a sum of smaller products, where the 1-digit number is multiplied by each of the place value parts separately.

3. Multiply each part:

• Perform the individual multiplications between the 1-digit number and each place value part.

4. Add the partial products:

• Combine the results of the individual multiplications to find the final product.

Example with a 2-digit number:

4 x 32 = ?

Decompose 32: 30 + 2

Apply distributive property: 4 x (30 + 2)

Multiply each part: 4 x 30 = 120, 4 x 2 = 8

Add partial products: 120 + 8 = 128

Therefore, 4 x 32 = 128

Example with a 3-digit number:

6 x 459 = ?

Decompose 459: 400 + 50 + 9

Apply distributive property: 6 x (400 + 50 + 9)

Multiply each part: 6 x 400 = 2400, 6 x 50 = 300, 6 x 9 = 54

Add partial products: 2400 + 300 + 54 = 2754

Therefore, 6 x 459 = 2754

Key points:

• The distributive property allows us to break down multiplication problems into smaller, easier steps.
• It's especially helpful when multiplying larger numbers.
• It can be used with any multi-digit numbers, not just 2- and 3-digit numbers.

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Here are three video links on the distributive property of math for a 3rd grade student, each offering a different learning style and approach:

1. Fun and Engaging:

• Distributive Property Song | 3rd Grade Math | eSpark Music: This catchy song introduces the concept of the distributive property with a visual representation and a memorable tune. It's a great way to get kids hooked on the idea and encourage them to participate.

https://m.youtube.com/watch?v=kWNCnQZgsUU

2. Visual and Interactive:

• DISTRIBUTIVE PROPERTY OF MULTIPLICATION //3RD GRADE COMMON CORE MATH: This video uses clear visuals and animation to explain the steps involved in applying the distributive property. It breaks down the process into manageable chunks and encourages students to follow along with practice problems.

https://m.youtube.com/watch?v=APWCe2KtpjQ

3. Storytelling and Real-World Examples:

• Math Game - Learn the Distributive Property with the Number One: This video takes a more narrative approach, incorporating a story about pirates and treasure to introduce the distributive property. It shows real-world examples of how the concept applies in everyday life, making it relatable and engaging for young learners.

https://www.magemath.com/

Remember, the best video for your 3rd grader might depend on their individual learning style and preferences. Feel free to explore these options and see which one resonates with them the most!

I hope these links help them understand the distributive property and have fun learning about it!