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    1. 1 Exponents
      Exponents There's one more operation besides addition, subtraction, multiplication, and division. That's exponentiation, notated by superscript (e.g. x2 or ex ), or sometimes -- ...
    2. 2 Square Roots
      Square Roots How do we do them? A square root of a number b is a solution of the equation x 2 =b . Every number except 0 has two square roots, a positive and a negative.&nbs ...
    3. 3 Writing Number Patterns in Function Notation
      Writing Number Patterns in Function Notation Given a number pattern, or a sequence of numbers a 1 , a 2 , a 3 ,…, a n ,… we some ...
    4. 4 Rational Numbers (Advanced)
      Rational Numbers (Advanced) The rational numbers are those numbers which can be expressed as a ratio between two integers. For example, the fractions 1/3 and -1111/8 are both rational numbers. Al ...
    5. 5 Number Systems: Naturals, Integers, Rationals, Irrationals, Reals, and Beyond
      Number Systems: Naturals, Integers, Rationals, Irrationals, Reals, and Beyond The Natural Numbers The natural (or counting) numbers are 1,2,3,4,5, etc. There are infinitely ...
    6. 6 Irrational Numbers
      Irrational Numbers An irrational number is a real number that cannot be expressed in the form , when a and b are integers(b ≠ 0).  In decimal form, it never terminates (ends) or repeat ...
    7. 7 Square of a Binomial
      Square of a Binomial The square of a binomial is always a trinomial.  It will be helpful to memorize these patterns for writing squares of binomials as trinomials. ( ...
    8. 8 Functions: Describing Behavior
      Functions: Describing Behavior A function table (T-table) shows you the relationship between pairs of numbers. The relationship is defined by a rule, and this rule applies to all the pairs of numb ...
    9. 9 Dividing Decimals
      Dividing Decimals Dividing with decimals is a bit more difficult. These days, most teachers don't mind much if you use a calculator. But it's good to know how to do it yourself, too, and you ...
    10. 10 Word Problems
      Word Problems A word problem requires you to find an answer from the facts of the problem. Here are some steps to follow: Understand the problem. (Read and re-read it!) Do you ...
    11. 11 Pascal's (Zhu Shijie's) Triangle
      Pascal’s (Zhu Shijie’s) Triangle Pascal’s Triangle is a special triangular arrangement of numbers used in many areas of mathematics.  It is named after the famous 17th cen ...
    12. 12 Operations with Decimals
      Operations with Decimals Adding and Subtracting Decimals Adding and subtracting decimals is easy if you're comfortable with carrying and borrowing. Just line up the decimal points, and (if necessary ...
    13. 13 Converting Decimals to Fractions: Repeating
      Converting Decimals to Fractions: Part B In Part A of this lesson, we saw how to convert a terminating decimal number to a fraction. If a decimal is repeating (in other words, after a while, some ...
    14. 14 Square Roots
      Square Roots How do we do them? test square root: 2 ( 7 5 ) 9 3 4 ...
    15. 15 Rational Numbers
      Rational Numbers Any number that can be written as a fraction with integers is called a rational number. For example, are rational numbers. (Note that there is more than one way to writ ...
    16. 16 Inductive Reasoning
      Inductive Reasoning Inductive Reasoning is a reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you can use inductive reasoning to decide the next successive t ...
    17. 17 Exponent Tables and Patterns
      Exponent Tables and Patterns There are many interesting patterns to be found in the tables of powers of whole numbers. Powers of 2 Powers of 3 Pow ...
    18. 18 Golden Rectangle
      Golden Rectangle The Golden Rectangle, also called the perfect rectangle by some, is a rectangle in which the ratio of its length to its width is the Golden Ratio.  Many believe that this is ...
    19. 19 Fibonacci Numbers (Sequence)
      Fibonacci Numbers (Sequence): 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 . . . The Fibonacci numbers (The first 14 are listed above) are a sequence of numbers defined recursively by the ...
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    1. 1
      Problem: JM-137b Page: 402 Title: Foundations for Algebra: Year 1

      Write the given numbers and continue each pattern on your paper.

      1/6,1/3, _____, _____, 5/6, _____

       
    2. 2
      Problem: JM-137a Page: 402 Title: Foundations for Algebra: Year 1

      Write the given numbers and continue each pattern on your paper.

      1/8, , 3/8, ____, _____, _____, _____, _____

       
    3. 3
      Problem: 10-126 Page: 445 Title: Algebra Connections

      Find a rule that represents the number of tiles in the tile pattern in the figure.

       
    4. 4
      Problem: 1-66a Page: 31 Title: Algebra Connections

      The pattern, shown in your textbook, is composed of nested squares.

      Draw the next figure in the pattern.

       
    5. 5
      Problem: 1-67b Page: 32 Title: Algebra Connections

      How does the pattern grow? Explain how you know.

       
    6. 6
      Problem: DS-95d Page: 452 Title: Algebra 2

      Parts DS–94a and DS–94d of DS–94 represent a general pattern known as the sum and difference of cubes. Use this pattern to factor the following polynomial:

      x3 + 1

       
    7. 7
      Problem: GC-114a Page: 161 Title: Foundations for Algebra: Year 2

      The camp council is designing a patio floor for an outdoor cafeteria. They have chosen the pattern shown in figure. What is the area of the section with the pattern (a) ?

       
    8. 8
      Problem: 6-74b Page: 256 Title: Algebra Connections

      Identify the hypothesis and conclusion for the following statements. Then decide if the statement is true or false. Justify your decision. You may want to review the meanings of hypothesis and conclusion from problem 6–31.

      If Figure 2 of a tile pattern has 13 tiles and Figure 4 of the same pattern has 15 tiles, then the pattern grows by 2 tiles each figure.

       
    9. 9
      Problem: MD-35a Page: 95 Title: Foundations for Algebra: Year 2

      Marisa wanted to investigate some patterns. She wrote out some of them for you to complete.

      16, 8, 4, 2, 1, , ___, ___, ___

       
    10. 10
      Problem: 2-70b Page: 66 Title: Algebra Connections

      Examine the tile pattern. What would Figure 10 look like? How many tiles would it have? What about Figure 100?

       
    11. 11
      Problem: 3-65b Page: 117 Title: Algebra Connections

      Identify the point that does not fit the pattern.

       
    12. 12
      Problem: BP-92b Page: 325 Title: Algebra 1

      John figures he can make each pen larger if he places the squares in a square pattern instead of in a row. Is he right? Justify your answer.

       
    13. 13
      Problem: WR-26a Page: 113 Title: Algebra 1, Abridged Version

      Here is a famous number pattern called Fibonacci Numbers:

      1, 1, 2, 3, 5, 8, ...

      Copy the pattern on your paper, then list the three numbers that would appear next.

       
    14. 14
      Problem: WR-26a Page: 201 Title: Algebra 1

      Here is a famous number pattern called Fibonacci Numbers:

      1, 1, 2, 3, 5, 8, ...

      a) Copy the pattern on your paper, then list the three numbers that would appear next.

       
    15. 15
      Problem: PS-43 Page: 112 Title: Geometry

      Start with the number 6. Double it. Then double this result. Continue to double each new number until you find a pattern in the unit (one's) digits. Describe the pattern. You may want to make an organized table (list).

       
    16. 16
      Problem: MD-35b Page: 95 Title: Foundations for Algebra: Year 2

      Marisa wanted to investigate some patterns. She wrote out some of them for you to complete.

      27, 9, 3, 1, ___, ___, ___

       
    17. 17
      Problem: 1-56a Page: 29 Title: Algebra Connections

      Copy the pattern, shown in your textbook, and continue the pattern for successive powers of 3.

      In a sentence or two, describe a pattern formed by the units digits (the "ones") of the numbers in the pattern.

       
    18. 18
      Problem: DS-95a Page: 452 Title: Algebra 2

      Parts DS–94a and DS–94d of DS–94 represent a general pattern known as the sum and difference of cubes. Use this pattern to factor of the following polynomial:

      x3 + y3

       
    19. 19
      Problem: 6-85 Page: 259 Title: Algebra Connections

      Figure 2 of a tile pattern is shown. If the pattern grows linearly and if Figure 5 has 15 tiles, then find a rule for the pattern.

       
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    1. 1 Factoring Patterns - College Algebra - Math video lessons - Hotmath.com
      This page needs JavaScript, click here to fix. Sometimes Professor Burger refers to a screen off to his left, but I can't see it.Hotmath does not show that screen, ...
    2. 2 Factoring Patterns - Precalculus - Math video lessons - Hotmath.com
      This page needs JavaScript, click here to fix. Sometimes Professor Burger refers to a screen off to his left, but I can't see it.Hotmath does not show that screen, ...
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  • Hotmath-Covered Textbooks
    1. 1
      Variables and Patterns image
      Title:
      Publisher:
      Author:
      Variables and Patterns
      Prentice Hall
      Phillips, Lappan, Fey, Friel, Fitzgerald

    2. 2
      Variables and Patterns image
      Title:
      Publisher:
      Author:
      Variables and Patterns
      Prentice Hall
      Lappan, et al.

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    1. 1
      Sequences, Algebra 1
    2. 2
      Exponents and Operations with Whole Numbers, Pre-Algebra TW
    3. 3
      Multiplying Whole Numbers, Pre-Algebra TW
    4. 4
      Exponential Functions, College Algebra
    5. 5
      Manipulating Graphs: Shifts and Stretches, Precalculus
    6. 6
      Exponential Functions, Algebra 2: Intermediate Algebra
    7. 7
      Exponential Functions, Trigonometry
    8. 8
      Exponential Functions, Algebra 2: Intermediate Algebra
    9. 9
      Graphing Parabolas, Algebra 2: Intermediate Algebra
    10. 10
      Exponential Functions, Precalculus
    11. 11
      Manipulating Graphs: Shifts and Stretches, College Algebra
    12. 12
      Manipulating Graphs: Shifts and Stretches, Trigonometry
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