Math Discovery Lab: Square Roots, Multiples of 10, Rational vs Irrational
Teaching Everything
131 Followers
Grade Levels
4th - 10th
Subjects
Resource Type
Standards
CCSS8.NS.A.1
CCSS8.EE.A.2
CCSSMP2
CCSSMP3
CCSSMP5
Formats Included
- PDF
Pages
6 pages
Teaching Everything
131 Followers
Description
This is one of a series of self-guided discovery labs for a meaningful understanding of core mathematical concepts. Students use the familiar format of the scientific method to answer a mathematical question/problem. In this lab, students investigate the relationships among square roots, perfect squares, and positive and negative powers of ten (10). This math lab also explores when the square root of numbers such as 0.016, 0.16, 1.6, 16, 160, 1600 are rational or irrational. Full answer key and suggestions are provided.
[NOTE: Although this lab includes information regarding the positive and negative powers of 10, it isn't necessary for students to have mastered this concept prior to this lab. Students should be familiar with: perfect squares, decimals are based on 10s, and numbers ending with any amount of zeros are multiples of 10. Regardless of prior knowledge, the focus for this lab is an extension of the students' understanding of perfect squares and square roots. Differentiated student answers are provided in the answer key. If necessary, see below for a small bundle of 2 Math Discovery Labs on: Powers of 10 & Multiplying/Dividing by Powers of 10.]
Students figure out independently that math is consequential, useful, and practical, and that there’s a reason for why things work as they do. Most importantly, students are significantly more likely to understand and apply concepts they have discovered on their own. Presented in the format of the well-known scientific method, the math labs ask students to independently complete an exercise with minimal teacher instruction. The teacher provides guiding questions as needed, students record their data, observations, conclusions and interpretations. The class shares observations and solidifies the meaning and their conclusions.
OTHER MATH DISCOVERY LABS OFFERED:
• 2 Math Labs Bundled ~ Powers of 10 Lab & Multiply/Divide by Powers of 10 Lab:
https://www.teacherspayteachers.com/Product/Math-Discovery-Labs-Powers-of-Ten-10-Multiplying-and-Dividing-by-Tens-10s-2039514
• Bundled 16 Math Labs: https://www.teacherspayteachers.com/Product/Math-Discovery-Labs-16-Bundled-2036782
CONCEPTS:
Adding Integers
Multiply/Divide Integers
Powers of 10
Multiply/Divide by Powers of 10
Inequalities
Integer Exponents
Square Roots
Linear Functions: Slope
Linear Functions: y=mx
Linear Functions: y=mx + b
Quadratic Functions: y=ax^2
Quadratic Functions: y=ax^2 + c
Quadratic Functions: y=ax^2 + bx
Ellipse
Golden Ratio
Template to Create Your Own Math Labs
[NOTE: Although this lab includes information regarding the positive and negative powers of 10, it isn't necessary for students to have mastered this concept prior to this lab. Students should be familiar with: perfect squares, decimals are based on 10s, and numbers ending with any amount of zeros are multiples of 10. Regardless of prior knowledge, the focus for this lab is an extension of the students' understanding of perfect squares and square roots. Differentiated student answers are provided in the answer key. If necessary, see below for a small bundle of 2 Math Discovery Labs on: Powers of 10 & Multiplying/Dividing by Powers of 10.]
Students figure out independently that math is consequential, useful, and practical, and that there’s a reason for why things work as they do. Most importantly, students are significantly more likely to understand and apply concepts they have discovered on their own. Presented in the format of the well-known scientific method, the math labs ask students to independently complete an exercise with minimal teacher instruction. The teacher provides guiding questions as needed, students record their data, observations, conclusions and interpretations. The class shares observations and solidifies the meaning and their conclusions.
OTHER MATH DISCOVERY LABS OFFERED:
• 2 Math Labs Bundled ~ Powers of 10 Lab & Multiply/Divide by Powers of 10 Lab:
https://www.teacherspayteachers.com/Product/Math-Discovery-Labs-Powers-of-Ten-10-Multiplying-and-Dividing-by-Tens-10s-2039514
• Bundled 16 Math Labs: https://www.teacherspayteachers.com/Product/Math-Discovery-Labs-16-Bundled-2036782
CONCEPTS:
Adding Integers
Multiply/Divide Integers
Powers of 10
Multiply/Divide by Powers of 10
Inequalities
Integer Exponents
Square Roots
Linear Functions: Slope
Linear Functions: y=mx
Linear Functions: y=mx + b
Quadratic Functions: y=ax^2
Quadratic Functions: y=ax^2 + c
Quadratic Functions: y=ax^2 + bx
Ellipse
Golden Ratio
Template to Create Your Own Math Labs
Total Pages
6 pages
Answer Key
Included
Teaching Duration
2 days
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Standards
to see state-specific standards (only available in the US).
CCSS8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
CCSS8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
CCSSMP2
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
CCSSMP3
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
CCSSMP5
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
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