➕ 8th Grade Math · Unit 1
Real Numbers and Exponents
22 short narrated lessons in 4 chapters, each with pictures, a quiz with a hint and a second try, and an explanation for every answer.
Standards: 8.NS.A.1 8.EE.A.2 8.NS.A.2 8.EE.A.1 8.EE.A.3 8.EE.A.4
What your child will learn
Rational and irrational numbers
- Rational Numbers as DecimalsShow that every rational number has a decimal that ends or repeats.
- Repeating Decimals to FractionsChange a repeating decimal like zero point three repeating into a fraction.
- Irrational NumbersIdentify irrational numbers like the square root of two and pi whose decimals never end or repeat.
- The Real Number SystemSort numbers into natural numbers, whole numbers, integers, rational numbers and irrational numbers.
- Rational and Irrational Numbers Review ReviewReview rational and irrational numbers, repeating decimals and the real number system.
Roots and approximations
- Square rootsFind square roots of perfect squares and solve equations like x squared equals forty-nine.
- Cube rootsFind cube roots of perfect cubes and solve equations like x cubed equals sixty-four.
- Estimating square rootsEstimate a square root like the square root of twenty between two whole numbers and to the nearest tenth.
- Comparing and ordering real numbersPlace rational and irrational numbers on a number line and put them in order.
- Roots and approximations review ReviewReview square roots, cube roots and estimating and ordering irrational numbers.
Properties of exponents
- Multiplying powers with the same baseMultiply powers with the same base by adding the exponents.
- Dividing powers with the same baseDivide powers with the same base by subtracting the exponents.
- Powers of powers and productsSimplify a power raised to a power, like two squared all cubed, by multiplying exponents.
- Zero and negative exponentsExplain why any nonzero number to the zero power is one and what a negative exponent like three to the negative two means.
- Properties of exponents review ReviewReview the rules for multiplying, dividing and raising powers, including zero and negative exponents.
Scientific notation
- Estimating with Powers of TenEstimate very large or very small quantities as a single digit times a power of ten.
- Writing Numbers in Scientific NotationWrite numbers like three million or four thousandths in scientific notation and back in standard form.
- Comparing Numbers in Scientific NotationCompare quantities in scientific notation and tell how many times bigger one is than another.
- Operations with Scientific NotationMultiply, divide, add and subtract numbers written in scientific notation.
- Scientific Notation with TechnologyRead scientific notation shown on calculators and choose sensible units for very large or small measurements.
- Scientific Notation Review ReviewReview writing, comparing and computing with numbers in scientific notation.
- Unit 1 Test: Real Numbers and ExponentsShow what you learned in the whole unit (Rational and irrational numbers, Roots and approximations, Properties of exponents, Scientific notation) by answering mixed questions.
Try a question from this unit
From the lesson “Rational Numbers as Decimals”
Which fraction has a decimal that terminates?
Show the answer
3/8. 3/8 = 0.375, which ends, because 8 = 2 × 2 × 2 has only the prime 2. The fraction 5/6 is tempting since 6 contains a 2, but its factor 3 makes it repeat: 0.8333....
Hint kids see after a wrong try: “Break each bottom number into prime factors. Which one uses only 2s and 5s?”
Key words
- rational number
- repeating decimal
- irrational number
- real number
- integer
- square root
- perfect square
- cube root
- perfect cube
- estimate
- approximation
- exponent
- base
- power
- quotient
- power of a power
- zero exponent
- negative exponent
- power of ten
- scientific notation
- standard form
- magnitude
- operations
- calculator notation
Try these lessons in Kids Shelf
Narrated lessons, pictures and quizzes for every grade from K to 8. Works offline.
