Montessori Math

Class Recap:

Friday, December 12. Topics Covered:
Review of Last Week's Topics

  • Today we reviewed the topics covered last week and the week before. The worksheet contains problems that we did not do last week, so we are just getting more practice on the same topcs as last week. Below is a link to the worksheet we reviewed:
  • NOTE: This is NOT Homework
  • Worksheet for December 12
    • Friday, December 5. Topics Covered:
    Chuquet Chart

    0 1 2 3 4 5 6 7 8 9 10 11 12
    1 2 4 8 16 32 64 128 256 512 1024 2048 4096

  • The Chuquet Chart is a tool used to help students learn to multiply and divide by powers of 2.
  • For example, to multiply 16 by 8, find 4 and 3 in the top row (above 16 and 8, respectively) and add them together to get 7. Then find 7 in the top row. In the cell below 7 you see 128, which is the product of 16 and 8.
  • \(16 \times 32 = 2^4 \times 2^5 = 2^9 = 512\)
  • \(1024 \div 64 = 2^{10} \div 2^6 = \frac{2^{10}}{2^6} = 2^{10-6} = 2^4 = 16\)
  • \(\sqrt[3]{512} = \sqrt[3]{2^9} = (2^9)^{1/3} = 2^{9/3} = 2^3 = 8\)
  • Other examples covered in class
    • Simplifying Radicals

  • To simplify a radical, we need to find the largest perfect square that divides into the number under the radical.
  • For example, to simplify \(\sqrt{12}\), we need to find the largest perfect square that divides into 12. The largest perfect square that divides into 12 is 4, so we can rewrite \(\sqrt{12}\) as \(\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \times \sqrt{3}\).
  • \(\sqrt{12} = 2 \sqrt{3}\)
  • Other examples covered in class
    • Rationalizing the Denominator

  • To rationalize the denominator of a radical expression, we need to multiply the numerator and denominator by the conjugate of the denominator.
  • For example, to rationalize the denominator of \(\frac{1}{\sqrt{3}}\), we need to multiply the numerator and denominator by \(\sqrt{3}\). We get \(\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}\).
  • Other examples covered in class
    • Factoring Trinomials

  • To factor a trinomial, we need to find two numbers that multiply to the constant term and add to the coefficient of the middle term.
  • For example, to factor \(x^2 + 5x + 6\), we need to find two numbers that multiply to 6 and add to 5. The numbers are 2 and 3.
  • \(x^2 + 5x + 6 = (x + 2)(x + 3)\)
    • Factoring Trinomials
  • Other examples covered in class
    • Friday, November 14. Topics Covered:
    Multiplication Property of Exponents
  • \(a^m \cdot a^n = a^{m+n}\)
  • \((a^m)^n = a^{m \cdot n}\)
  • \((a \cdot b)^m = a^m \cdot b^m\)
    • Division Property of Exponents
  • \(\frac{a^m}{a^n} = a^{m-n}\)
  • \((\frac{a}{b})^m = \frac{a^m}{b^m}\)
    • Zero and Negative Exponents
  • Let \(a\) be a nonzero number and let \(n\) be a poitive integer.
  • \(a^0 = 1\)
  • \(a^{-n}\) is the reciprocal of \(a^n: a^{-n} = \frac{1}{a^n}\)
    • Scientific Notation
  • A number in scientific notation is written as \(c \times 10^n\), where \(1 \leq c \leq 10\) and \(n\) is an integer
    • Why are we learning this?
  • Understanding exponent rules has direct application to computing numbers in scientific notation, adding or multiplying volumes of liquids, adding or multiplying areas in a room, determining volume of mulch or soil needed to cover a section of a garden or farm, cost calculation for the mulch or soil, many applications in chemistry and physics which are fundamental to any career in health, medicine, nutrition, and chemistry.
    • Homework 3, due 11/21
  • Homework 3, finish what was not completed in class.

    • Below are links to the previously given homework:

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