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Distributive Property of Multiplication Guided Notes & Doodles | 6th Grade Math
$4.25
Overview
- Standards: CCSS 6.EE.A.3, CCSS 6.EE.A.4
- Unit: 6th Grade → Unit 5: Algebraic Expressions
- Grade: 6th Grade
Get the Lesson Materials
Distributive Property of Multiplication Guided Notes & Doodles | 6th Grade Math
$4.25
Learning Objectives
After this lesson, students will be able to:
- Define the distributive property
- Explain why the distributive property works
- Apply the distributive property and combining like terms to simplify expressions
- Understand real-life applications of the distributive property, such as to scale recipes and calculate discounts
Note: This lesson covers positive integer coefficients only. See extensions for harder practice!
Prerequisites
Before this lesson, students should be familiar with:
- Know how to combine like terms in expressions
- Basic multiplication and division skills
- Understanding of the concepts of factors and multiples
- Basic understanding of fractions and decimals (optional, but helpful)
Materials
- Pencils
- Colored pencils or markers
- Distributive Property Guided Notes (positive coefficients only!)
Key Vocabulary
- Distributive Property
- Expressions
- Factors
- Terms
Procedure
Introduction
- As a hook, ask students why understanding math concepts like the distributive property can be helpful in real-life situations, such as grocery shopping and scaling recipes. Refer to the last page of the guided notes as well as the FAQs below for ideas.
- Use the guided notes to introduce the distributive property. These guided notes contain positive integer coefficients only. Therefore, students do not need to have mastered negative integer rules to learn this lesson. Walk through the key points of the topic of the guided notes to teach. Students will need to know how to combine like terms to simplify expressions further. If they have not yet learned combining like terms, or need a review, consider using my Combining Like Terms lesson plan.
- Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.
- Check for Understanding. Have students walk through the “You Try!” section. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.
- Use the guided notes to introduce how to simplify expressions using the distributive property and combining like terms. Walk through the key points of the topic of the guided notes to teach. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.
- Check for Understanding. Have students walk through the “You Try!” section. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.
Practice
- Have students practice the distributive property and combining like terms using the worksheet activity provided. Walk around to answer student questions.
- Fast finishers can dive into the color by number activity for extra practice. You can assign it as homework for the remainder of the class.
Real-Life Application
- Bring the class back together, and introduce the concept of scaling recipes using the distributive property.
- Explain that the distributive property can be used to scale recipes up or down, depending on how many servings are needed. Give an example recipe and demonstrate how to use the distributive property to scale it up or down.
- Refer to the FAQ for more ideas on how to teach it!
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for the distributive property, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. There’s different versions depending on your students' needs:
- Positive integer only. This is ideal for students who haven’t mastered negative integer rules yet. It has a heart theme perfect for Valentine's Day.
- Positive & negative integers. This is ideal for students who have already mastered negative integer rules. It has a winter theme perfect for the holidays.
Additional Print Practice
A fun, no-prep way to practice the distributive property is Doodle & Color by Number — it's a fresh take on color by number or color by code. It includes 3 levels of practice, and there's different versions depending on your students' needs:
- Positive integers only. This is ideal for students who haven’t mastered negative integer rules yet. It has a heart theme perfect for Valentine's Day.
- Positive & negative integers. This is ideal for students who have already mastered negative integer rules, and it comes in a desert theme perfect year-round!
FAQs
The distributive property is a mathematical rule that says that you can multiply a single term by a group of terms inside a set of parentheses, and the result will be the same as if you had multiplied each term inside the parentheses separately and then added the results together. This property is often used to simplify algebraic expressions.
The distributive property works because it allows you to distribute a factor to all terms within a set of parentheses, making it easier to simplify expressions. This mathematical rule is a way to break down complex expressions into simpler ones. Applying the distributive property to an expression like 3 * (2 + 4) allows us to simplify it to 3 * 2 + 3 * 4. Distributing the 3 to both terms inside the parentheses results in the same value. We can then simplify further to get 6 + 12 = 18. Thus, 3 * (2 + 4) and 3 * 2 + 3 * 4 both equal 18, proving the distributive property.
To use the distributive property to simplify expressions, follow these steps:
- Identify the factor that needs to be distributed
- Identify the terms inside the parentheses that the factor needs to be distributed to
- Multiply the factor by each term inside the parentheses
- Write the simplified expression by combining like terms, if possible
For example, if you have the expression 3(x + 2), you would:
- Identify the factor that needs to be distributed:
3 - Identify the terms inside the parentheses that the factor needs to be distributed to:
xand2 - Multiply the factor by each term inside the parentheses:
3(x) + 3(2) - Write the simplified expression by combining like terms, if possible:
3x + 6
If you have students that need more of a visual explanation, I find this Khan Academy video helpful:
The distributive property is an important concept in math because it allows us to break down complicated problems into smaller, more manageable parts. This not only makes math easier to understand, but it also helps us solve problems more efficiently. Additionally, the distributive property is used in many real-world situations, such as scaling recipes and calculating discounts.
Here are some common mistakes to avoid when using the distributive property:
- Forgetting to distribute the factor to all terms inside the parentheses, e.g. forgetting to multiply the factor by both
xand2in the expression3(x + 2) - Distributing the factor incorrectly, e.g. distributing the factor
3to onlyxand not2in the expression3(x + 2) - Forgetting to simplify the expression after distributing the factor, e.g. leaving the expression
3(x + 2)as is after distributing the factor3
The distributive property is a fundamental concept in mathematics that has numerous real-life applications. Here are some examples:
- Scaling recipes: The distributive property can be used to scale recipes up or down, depending on the number of servings needed. By multiplying the ingredients within a recipe by a common factor, the recipe can be adjusted to fit the desired number of servings.
- Calculating discounts: The distributive property can also be used to calculate discounts. For instance, if a store is offering a 20% discount on all items, the distributive property can be used to calculate the sale price of an item by multiplying the original price by 0.8.
- Comparing prices: The distributive property can be used to compare prices at the grocery store. By breaking down the cost of an item into its unit price, consumers can easily compare the cost of similar items sold in different quantities or sizes.
- Engineering: The distributive property is used in engineering to distribute loads evenly across structures. For instance, in bridge design, it is used to distribute the weight of the bridge evenly across its supporting structure.
- Physics: The distributive property is used in physics to simplify equations and make them easier to solve. For instance, it can be used to simplify equations related to work and energy.
These are just a few examples of the real-life applications of the distributive property. The concept is widely used in many fields and can be applied to a variety of situations.
The distributive property can be used to scale recipes by multiplying the quantities of the ingredients within a recipe by a common factor. For example, suppose a recipe needs 2 cups of flour, 1 cup of sugar, and 1/2 cup of butter to make 12 cookies. If you want to make 24 cookies, you can use the distributive property to double the quantities of each ingredient: 4 cups of flour, 2 cups of sugar, and 1 cup of butter.
In general, if a recipe serves n people and you want to serve m people instead, you can scale the recipe by multiplying the quantities of each ingredient by m/n.
By using the distributive property to scale recipes, you can easily adjust the ingredients based on the number of servings you need. Here’s a step by step example:
- Multiply all of the ingredients in the original recipe by the scaling factor. For example, if the original recipe calls for 1 cup of flour and you are scaling it by a factor of 2, you would use 2 cups of flour in the scaled recipe.
- Divide the desired number of servings by the original number of servings to get the scaling factor. For example, if the original recipe serves 4 and you want it to serve 8, the scaling factor is 8/4 = 2.
- Determine how many servings you want the recipe to make.
- Find the original recipe, which serves a certain number of people.