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Perfect Squares and Square Roots Guided Notes & Doodles | 8th Grade Sketch Notes
$4.25
Overview
- Standard: CCSS 8.EE.A.2
- Unit: 8th Grade → Unit 1: Real Numbers
- Grade: 8th Grade
Get the Lesson Materials
Perfect Squares and Square Roots Guided Notes & Doodles | 8th Grade Sketch Notes
$4.25
Learning Objectives
After this lesson, students will be able to:
- Define perfect squares and square roots
- Identify perfect squares and square roots of given numbers
- Apply the concept of perfect squares to solve equations in the form x² = p
- Explain a real-life math application involving perfect squares and square roots
Prerequisites
Before this lesson, students should be familiar with:
- Basic multiplication and division skills
- Understanding of the concept of square numbers
- Basic understanding of exponents and how they relate to repeated multiplication
- Understanding of the concept of radicals and square roots
- Ability to perform basic operations with rational numbers (optional, but helpful)
Materials
- Pencils
- Colored pencils or markers
- Perfect Squares and Square Roots Guided Notes
Key Vocabulary
- Perfect squares
- Square roots
- Equations
- Rational numbers
Procedure
Introduction
As a hook, ask students why designers need to understand perfect squares and square roots when designing bathroom tiles. Refer to the real-life application on the last page of the guided notes for ideas.
Use the first page of the guided notes to introduce perfect squares. Walk through the key points of identifying perfect squares and the properties of perfect squares. Refer to the FAQs for a walk-through on this, as well as ideas on how to respond to common student questions.
Continue using the guided notes to introduce square roots. Walk through the key points of square roots and how to find the square root of a perfect square. Refer to the FAQs for a walk-through on this, as well as ideas on how to respond to common student questions.
Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.
Practice
Have students work through the problems on the "You Try" page, either collaboratively or independently. Walk around and spot-check student answers on the check for understanding activity.
Fast finishers can dive into the color by code activity included in the resource 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 applying perfect squares and square roots in real-life scenarios. Explain to the students that understanding perfect squares and square roots can be useful in various situations, such as designing bathroom tiles.
To engage the students, ask them to imagine that they have been hired as interior designers to create a pattern for a set of bathroom tiles. Explain that they need to come up with a design that uses perfect squares and square roots to determine the dimensions of the tiles.
Encourage students to think about how they can use the concept of perfect squares and square roots to ensure that the tiles fit well and create an aesthetically pleasing pattern. Emphasize the importance of accurately calculating the dimensions of the tiles using square roots.
Refer to the FAQ or additional resources for more ideas on how to teach the real-life application of perfect squares and square roots.
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for perfect squares, square roots, and related concepts, try the Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.
Here is an activity to explore:
Additional Print Practice
A fun, no-prep way to practice perfect squares, square roots, and related concepts is with the Doodle Math activities. They’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.
Here is an activity to try:
FAQs
Perfect squares are numbers that can be expressed as the product of an integer multiplied by itself. For example, 4 is a perfect square because it can be written as 2 x 2.
Square roots, on the other hand, are the inverse operation of squaring a number. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 x 4 = 16.
To determine if a number is a perfect square, you can try to find its square root. If the square root is a whole number, then the original number is a perfect square. For example, the square root of 49 is 7, so 49 is a perfect square.
Determining the square root is akin to asking, "What number, when multiplied by itself, gives me the original number?" Exploring various approaches can simplify the process of finding square roots:
- Prime Factorization: For smaller numbers, prime factorization comes in handy. Break the number into its prime factors and group them in pairs. The product of the factors in each pair is the square root. For instance, the prime factors of 25 are 5 and 5, leading to a square root of 5.
- Estimation: Begin with an estimated square root and square it to gauge proximity to the original number. Refine your estimate based on the outcome and iterate until you achieve desired accuracy.
- Long Division: Deconstruct the number into pairs of digits from the right. Through successive subtractions of decreasing multiples of smaller numbers squared, you gradually deduce the digits of the square root. This systematic process enables you to approximate the square root more precisely with each step.
For students that need a more visual explanation, I find the Khan Academy video helpful:
The square root of a perfect square is always a whole number. In other words, if a number is a perfect square, its square root is an integer. Likewise, if the square root of a number is an integer, then the original number is a perfect square.
Perfect squares and square roots are not just for math class; they can be pretty handy in real-life situations that are relatable to middle schoolers. Here are some examples:
- Video Games: In games where you can build things, like Minecraft, you might want to build a perfect square building or room. Knowing how perfect squares work can help you plan the dimensions more accurately.
- Sports: In baseball, the distance from one base to another is often a perfect square. In some sports games, you might want to calculate distances quickly, and knowing your square roots can help.
- Art and Design: When you're making art or crafts that involve geometric shapes, knowing about perfect squares can help you create designs that are proportionally accurate.
- Gardening: If you're helping your family in the garden and you have a square plot, you'd use the square root to find the length of each side if you know the total area.
- Shopping: If you're buying a large square pizza and want to compare it with a round one to see which has more area for the same price, you might use square roots to help with your decision.
- Map Reading: Sometimes, maps use a grid system. Knowing how to work with square roots can help you more accurately estimate distances between places on the map.
- DIY Projects: If you're building a model or assembling a piece of furniture that's square-shaped, knowing the concept of perfect squares and square roots can help you ensure that your project has the right dimensions.
- Puzzle Games: Some puzzle games like Sudoku involve the use of perfect squares, and understanding these can give you an edge in solving them more efficiently.
So, perfect squares and square roots are not only cool math concepts but also tools you can use to solve everyday problems!
Perfect squares and square roots can be used in equations that involve variables raised to the power of 2. For example, the equation x² = 9 can be solved by finding the square root of both sides, which gives x = ±3. The square root of a perfect square can help simplify equations and find possible solutions.
To practice working with perfect squares and square roots, you can use the digital activities like Perfect Squares and Square Roots Google Sheets Pixel Art as well as print worksheets like Perfect Squares and Square Roots Doodle Math for further practice.