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Math Example--Combinatorics--Factorial Expressions: Example 7
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Algebra >> Probability and Data Analysis >> Combinatorics
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Math Example--Combinatorics--Factorial Expressions: Example 7

Math Example--Combinatorics--Factorial Expressions: Example 7

This is part of a collection of math examples that focus on combinatorics and factorial expressions.

To see the complete math example collection on this topic, click on this link

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    Common Core Standards CCSS.MATH.CONTENT.HSS.CP.B.9
    Grade Range 9 - 11
    Curriculum Nodes Algebra
        • Probability and Data Analysis
            • Combinatorics
    Copyright Year 2021
    Keywords Factorial
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    Princeton Review


    Math Examples

     

    The Math Examples Library

    Media4Math has a huge collection of instructional math examples covering a wide range of math topics. This collection of resources is made up images that you can easily incorporate into your lesson plans. 

    To see the complete collection of Math Examples, click on this link.

    In answer to the question, "Why so many examples?": Math concepts are best learned through multiple examples of increasing complexity. For example, in learning about the slope formula, students need to see examples covering these scenarios:

    • Two points in the first quadrant, positive slope
    • Two points in the first quadrant, negative slope
    • Two points in the first quadrant, zero slope
    • Two points in the first quadrant, no slope

    But this only covers points in the first quadrant. Students also need to see examples in the other quadrants, to see the impact of negative coordinates on the formula. Plus, students need to see points on two separate coordinates.

    As you can see, just with this one topic, there are dozens of possible examples to cover in order for students to get a better understanding of the nuances of working with the slope formula. Textbooks and other curriculum solutions provide a handful of examples, but hardly a comprehensive. This is where Media4Math comes in. We provide significantly more examples, each providing a detailed solution. In the case of the slope formula, click on this link to see the full set of math examples on the slope formula. 

    Below is a listing of the categories of math examples covered. To see the complete library of Math Examples, click on this link.

    • Absolute Value
    • Algebra Tiles
    • Angle Measures
    • Area and Perimeter
    • Arithmetic--Adding, Subtracting, Multiplication, and Division
    • Charts, Graphs, Plots
    • Combinatorics
    • Comparing and Ordering Numbers
    • Complex Numbers
    • Coordinate Geometry
    • Decimal Concepts
    • Equations
    • Exponential Concepts
    • Fraction Operations
    • Fraction Properties
    • Function Concepts
    • Geometric 
    • Geometric Proofs
    • Geometric Transformation
    • Inequalities
    • Language of Math
    • Linear Function Concepts
    • Logarithms
    • Math of Money
    • Measurement
    • Measures of Central Tendency
    • Number Line Math
    • Number Patterns
    • Numbers
    • Numerical Expressions
    • Percents
    • Place Value
    • Polygons
    • Polynomial Concepts
    • Probability
    • Proportions
    • Quadratics
    • Rational Concepts
    • Ratios and Rates
    • Right Triangles
    • Sequences and Series
    • Shapes
    • Solving One-Step Equations
    • Solving Other Types of Equations
    • Solving Two-Step 
    • Special Functions
    • Systems of Equations
    • Ten Frames
    • Trig Concepts
    • Vectors
    • Volume Concepts

    The Evidence Basis for Multiple Examples

    The What Works Clearinghouse has a number of evidence-based Practice Guides that focus on math practices that are associated with effective teaching. For example the Practice Guide entitled Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students has one recommendation involving showing students solved problems in order for them to better understand abstract algebraic concepts. Watch the video below to learn more about this approach.

    Having students study solved problems allows them to analyze and internalize the mathematical reasoning involved. This is what the Math Examples Library attempts to do: Solve enough problems for students to gain a firm understanding of the underlying concepts.

    The other two recommendations in the practice guide involve having students look at the mathematical structure from the standpoint of multiple representations of mathematical quantities, as well as choosing from different strategies for solving problems. The Math Examples Library also has a wealth of examples that show multiple representations and different approaches to solving math problems.

     

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