Curriculum Guide
Grade 8 – Math Standard 1.1
Math.1.1 - In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line.
Related Colorado Department of Education Sample Units:
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Power Trip (Concepts: Properties of integer exponents, equivalent expressions, comparison, scientific notation, quantities)
It’s All Greek To Me (Concepts: Pythagorean Theorem, right triangle, indirect measurement, rational numbers, irrational numbers, division,
integers, terminate, repeat, decimals, approximation, representation, number line)
Essential Questions - 21st Century Skills and Readiness Competencies (District):
1. Why are real numbers represented by a number line and why are the integers
represented by points on the number line?
2. Why is there no real number closest to zero?
3. What is the difference between rational and irrational numbers?
4. How can you demonstrate that every number has a decimal expansion?
5. How can you convert a decimal expansion that repeats into a rational number?
6. How can the use of rational approximations of irrational numbers compare the size
of irrational numbers?
7. What are square roots? Cube roots?
8. How can we apply the properties of integer exponents to generate equivalent
numerical expressions?
9. What are scientific notations and why do we use them?
Evidence Outcomes (District):
1. Define irrational numbers.
2. Demonstrate informally that every number has a decimal expansion.
3. For rational numbers, show that the decimal expansion repeats eventually.
4. Convert a decimal expansion which repeats eventually into a rational number.
5. Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram, and estimate the value
of expressions.
6. Apply the properties of integer exponents to generate equivalent numerical
expressions.
7. Use square root and cube root symbols to represent solutions to equations of the
formx2 = p and x3 = p, where p is a positive rational number.
8. Evaluate square roots of small perfect squares and cube roots of small perfect
cubes.
9. Use numbers expressed in the form of a single digit times a whole-number power of
ten to estimate very large or very small quantities, and to express how many times as
much one is than the other.
10. Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used.
11. Use scientific notation and choose units of appropriate size for measurements of
very large or very small quantities.
12. Interpret scientific notation that has been generated by technology.
Academic Vocabulary (District):
real numbers
rational numbers
irrational numbers
decimal expansion
square root
cube root
equivalent numerical expression
integer exponents
number line
estimate
Assessment (District):
All assessments are found in the suggested activities links, correlating with their
numbers, unless listed below.
1. Assessment can be found inside the lesson plan at the bottom (e.g., Have students
explain the sentence: "Squaring and finding square roots are inverse operations." They
should use models, algebra, and math vocabulary.)
2. Use the Jeopardy game as a review before the test. Observe the students as they
answer the questions.
expressions
approximations
scientific notation
integer
perfect square
power
base
exponent
perfect cube
law/properties of exponents
3. Assessment can be found in the packet.
4. Assessment can be located at the end of the lesson in Lesson Segment Three.
5. Assessment strategies can be found at the end of the lesson. Scroll down to bottom
of the lesson.
6. Observe individual students playing the game to determine that they can order five
out of six cards correctly.
7. The activity score is the assessment.
8. Assessment options: 1. Students create their own PowerPoint game (Jeopardy, 20
Questions, etc.) using links provided. 2. A link to the exponent game is located under
extension.
9. Within the lesson, there are several worksheet options for assessment.
10. Several worksheets located within the site can be used as assessment.
11. Student scores can be taken as assessment.
12. Assessments are located within the lessons. Several different lessons are located
within the site.
13. Scores from game can be used as assessment. Teacher may observe that
students are answering questions correctly as informal assessment.
14. This score can be used as an assessment with Activities 3 and 4.
15. This is an interactive lesson, so the teacher can set up students to complete the
lesson on computers or the teacher can copy problems and put them into a
PowerPoint and have students answers questions aloud. If a CPS system (clickers or
a student response system) is available, you can take questions and put them into an
activity using the clickers.
16. Assessment is found at the end of the lesson; use questions #1-6.
17. Assessment is the activity score.
Suggested Activities/Strategies (District):
For all activities listed below, the links are numbered to correlate with each activity.
1. Use the Square Roots Go Rational Lesson Plan. Students recall and model the
square root as the length of one side of a square. But what if the square is not a
perfect square? This collection of activities explores the square roots of not-so-perfect
squares and develops an algorithm to express the not-so-perfect square root as a
rational value.
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Square Roots Go Rational Lesson Plan
2. Use the Square Root Jeopardy Game for review before a quiz or test. Teacher can
divide the class into small groups and the groups can compete for the most points.
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2. Square Root Jeopardy
3. Use the Rational, Irrational Numbers Lesson Plan to classify numbers and explore
the difference between the decimal expansions of rational and irrational numbers.
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3. Rational, Irrational Lesson Plan
Resources/Technology (District):
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There are several videos on Square Roots located at the Khan Academy
website. Click on the video for Approximating Square Roots and look to the
left to see numerous sites for what you may need. (Teacher/Student
Resource)
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Tutorial site for Rational/Irrational Numbers below explains how to teach
these numbers. (Teacher Resource)
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Homeschool site below explains what rational, irrational numbers are.
(Teacher Resource)
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Extra practice for rational and irrational numbers can be found at mtestprep.
4. Use the Representing Numbers Using Scientific Notation Lesson Plan.
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4. Scientific Notation Lesson Plan
5. Use the Rational or Irrational, That is the Question Lesson Plan. Students will
participate in an activity for discerning how numbers are related to each other. They
will determine whether a number is rational or irrational. Students will also be able to
order rational and irrational numbers on a number line.
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5. Rational, Irrational, That is the Question Lesson Plan
6. Use the Line Up Cards Activity. This is a very quick activity about how numbers are
related to one another. It includes how rational and irrational numbers compare.
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6. Line Up Cards Activity
7. Play the Rational/Irrational Number Game. This is a classification game and a quick
check for understanding.
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7. Rational/Irrational Number Game
8. Use the The Laws of Exponents Lesson Plan. During this activity, students will
review the laws of exponents. They will demonstrate their knowledge by creating an
interactive computer game or a podcast.
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8. Laws of Exponents Lesson Plan
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8. PowerPoints with Exponents
9. Use the Squares, Square Roots, and Exponential Expressions Lesson. This is a
complete lesson plan with essential questions, complete explanation, warm-ups,
worksheets, and assessment.
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9. Squares, Square Roots, and Exponential Expressions
10. Use the Perfect Cubes and Cube Root Lesson. Students will learn what perfect
cubes are and how to calculate the cube root of a perfect cube.
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10. Perfect Cubes and Cube Roots Lesson
11. Play the game for scientific notation. Quick game to check for understanding.
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11. Game for Scientific Notation
12. Use the Lesson Plan for higher level students on Scientific Notation. This unit is
designed to introduce the concept of Scientific Notation, explain how it is used for large
and small numbers, and show how to multiply and divide using Scientific Notation.
Although the activities were written for an Algebra I course, they could easily be
adapted for other courses.
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12. Higher Level Student Lesson on Scientific Notation
13. Play the Jeopardy Game for Scientific Notation as a quick check for understanding.
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13. Jeopardy Game
14. Number Types from Purple Math has true/false questions that can be used as an
opener for rational/irrational numbers.
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14. Number Types
15. Use the Scientific Notation Lesson to learn the basic principles of Scientific
Notation and how to convert standard numbers to scientific notation. It can
be interactive or the teacher can copy problems and use the PowerPoint.
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15. Scientific Notation Lesson Plan
16. Use the Math is Fun Number Line Lesson.
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16. Number Line Lesson
17. Play practice games in Math Playground (Roots, Exponents and Scientific
Notation) to review.
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17. Math Playground
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Purple Math is a resource for information on fractions to decimals, decimals to
fractions, percents, and conversions. This link includes in-depth instruction
tips and at the end of the link, there is a table of common conversions that
may be used as an assessment.
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Link to video clip for cubes and cubes roots: Perfect cubes/cube roots.
Illuminations from NCTM – Great Lessons and Units supporting all grades
levels
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Multiple Links to Games/Interactives
PARCC offers instructional and assessment support. Click on the tab "In the
Classroom" and at the model frameworks for math.
Illustrative Mathematics contains examples of tasks designed by the makers of
the CCSS-M (Common Core State Standards of Mathematics.)
Inside Mathematics has tasks, rubrics, and discussion questions that correlate
with PARCC and Smarter Balance.
Math Arizona has explanations and overviews for how the mathematics
strands progress from one year to the next.
Math Shell is Mathematics Assessment Resource Service (MARS) from the
Shell Centre in Nottingham, England and it contains a number of performance
tasks.
Achieve the Core is from Student Achievement Partners, a nonprofit
organization that assembles educators and researchers to design actions
based in evidence that will substantially improve student achievement.
Balanced Assessments is a site with free performance tasks to use in your
classroom.
Video on Approximating Square Roots
Rational Irrational Tutor
Rational Irrational Homeschool Site
Scientific Notation Activity
Resources for Games, Worksheets, etc
Math Worksheets 4 Kids
Homework Help
Converting Decimals Link Teacher Resource
Number Types
PowerPoint for Perfect Squares and Cubes
Scientific Notation Resource