In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
Know that there are numbers that are not rational, and approximate them by rational numbers.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Numbers
Decimals
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1 - Know (Irrational numbers are the numbers that aren’t rational)
2 - Understand (Numbers have a decimal expansion)
3 - Show (Rational numbers have repeating decimals)
2 - Convert (Repeating decimals into a rational number)
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1 - I know that numbers that are not rational are called irrational.
2 - I understand that all numbers have a decimal expansion.
3 - I can show that the decimal expansion for all rational numbers is a repeating decimal.
2 - I can convert a repeating decimal into a rational number.
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A. Decimal expansions can be observed and classified as either irrational or rational numbers.
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A.1 What is the term used for a number that isn’t rational?
A.2 What is meant by the tern decimal expansion?
A.3 How can one show that all rational numbers have decimal expansions that eventually repeat?
A.4 How can one convert a repeating decimal into a rational number?
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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 (e.g., ∏2).
For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Approximations
Irrational number
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3 - Use (Rational approximations or irrational numbers.)
2 - Compare (Irrational numbers)
2 - Locate (Irrational numbers on a number line)
3 - Estimate (Value of irrational numbers)
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3 - I can use rational approximations of irrational numbers.
2 - I can compare the size of irrational numbers by using rational approximations.
2 - I can locate an irrational number on a number line.
3 - I can estimate the value of an irrational number.
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A. Rational approximations can be used to compare irrational numbers, locate irrational numbers on a number line and estimate the value of the irrational numbers.
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A.1 What does the tern rational approximation mean?
A.2 How does one use rational approximations of irrational numbers?
A.3 How can one compare irrational numbers by using their rational approximations?
A.4 How can one approximately locate irrational numbers on the number line?
A.5 How can one find the estimated value for irrational expressions?
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