2022 Dice Project Hub

Topics for Today:

PROJECT INFORMATION:

Hey Falcon Algebra Students -- here is the place to come for all your project needs.  

Below are all the paper documents for the project:

1. Project Information Form/Rubric
2. Data Entry Dice Project.pdf
3. Frequency Tables
4. Think Sheet

Electronic Files

• Data Spreadsheet - Student Copy
• Student Gsheet

Need Dice?  

• Use these Virtual Dice

Interested in the extra credit?

• Virginia Lottery, Pick 5

Welcome Back, Falcons!

Hey Everyone!

I'm looking forward to the start of another amazing year at Field School.

Please bookmark this site as it will be your one-stop location for anything you need for Algebra I class this year!

GO FALCONS!

Every boy known, every boy a brother 

Scatterplots - Day 2

Topics for Today:

We covered a few more examples of scatterplots and line of best fit and completed a Desmos activity to see how they are used with real data.


(Graphic Source: https://www.learnbyexample.org/r-scatter-plot-ggplot2/)

Sections Covered in Textbook:

1-9: Graphing Data on the Coordinate Plane (pages 59-64)
6-6: Scatter Plots and Equations of Lines (pages 318-323)

Resources & Tutorials:

1) Desmos activity from class code: 63WGDD

Scatterplots Day 1

Topics for Today:

A scatter plot is a graph that relates two sets of data.
To make a scatter plot, plot the two groups of data as ordered pairs.

Most scatter plots are in the first quadrant of a coordinate plane because the data are usually positive numbers.


You can use scatter plots to look for trends in the data.  Three scatter plots below show the types of relationships two sets of data may have:

Sections Covered in Textbook:

1-9: Graphing Data on the Coordinate Plane (pages 59-64)
6-6: Scatter Plots and Equations of Lines (pages 318-323)

Resources & Tutorials:

1) What is a scatter plot?
2) How do you make a scatter plot?
3) List of videos discussing scatter plots and correlation.

4) Scatter Plots Class Notes

Dividing Polynomials

Topics for Today:

It may have been some time since you had to perform long division, and long division is a multi-step process like so many we have seen in Algebra.  If you follow the procedure, you will arrive at your answer (quotient).  The process for dividing polynomials is similar to long division of constants.

You should recall from earlier mathematics courses that the process for long division is as follows:

1. Figure out how many whole times the divisor divides into the dividend and place that number on top of the divisor.
2. Multiply this number by the divisor, and subtract this number from the dividend.
3. Bring down the next number in the divisor. 
4. Repeat until you have no more numbers in the dividend to bring down. 
5. If your final subtraction problem results in "0", you have no remainder; otherwise, your remainder is a part of a whole and should be represented as a fraction with the remainder number in the numerator, and the divisor in the denominator.  

---> When dividing polynomials by a binomial, we will look to the variable part of the binomial to make our decision on what divides into the dividend.  

Image Source: https://mathbitsnotebook.com/Algebra2/Polynomials/POPolyDivide.html

Sections Covered in Textbook:

12-5: Dividing Polynomials (pages 662-666)

Resources & Tutorials:

1) Review of Long Division
2) Dividing Polynomials (long division)
3) Cool Math - Dividing Polynomials Examples (not a video)
4) Dividing Polynomials Class Notes

Multiplying and Dividing Rational Expressions

Topics for Today:

Rational expressions can be multiplied or divided just like regular fractions. Recall from yesterday's lesson that a rational expression is just a fraction with polynomials in the numerator and denominator.  As with dividing regular fractions, when we divide rational expressions, we must multiply by the opposite of the divisor (invert and multiply, or as some of you like to say, keep, change, flip!)

We should always focus on taking out common factors as soon as we can.  This process helps to ensure that our eventual answer is in simplest terms.

Sections Covered in Textbook:

12-4: Multiplying and Dividing Rational Expressions (pages 657-661)

Resources & Tutorials:

1) Multiply and simplify rational expressions
2) How to divide rational expressions
3) List of More videos for multiplying and dividing rational expressions
4) Multiplying and Dividing Rational Expressions Class Notes

Simplifying Rational Expressions

Topics for Today:

We will now encounter polynomials in our fractions.  A rational expression is just a ratio (fraction) with polynomials in the numerator and denominator.  When we want to simplify these fractions, we follow the same rules as regular fractions: we need to divide common factors from the numerator and denominator.  To simplify, we need to look at the greatest common factor (GCF) as well as other factoring tools.  We will factor both the numerator and denominator, and then see if we have any common factors that simplify to 1.

Sections Covered in Textbook:

12-3: Simplifying Rational Expressions (pages 652-656)

Resources & Tutorials:

1) What is a rational expression?
2) Simplify Rational Expressions by factoring
3) Simplifying Rational Expressions by using opposite binomials
4) Simplifying Rational Expressions Class Notes

Inverse Variation

Topics for Today:

Inverse variation is another relationship between the x and y variables.  Inverse variation is defined by the relationship:

xy = k where k ≠ 0

As with direct variation, k is our constant of variation.  The shape of the inverse variation graphs are much different from what we've seen so far.  These graphs are a curved shape, and the larger the constants of variation, the further it moves from the origin.  There are boundaries with these functions that will be discussed in your Algebra II course.

Vocabulary:  constant of variation, inverse variation

Sections Covered in Textbook:

12-1: Inverse Variation (pages 636-642)

Resources & Tutorials:

1) What is inverse variation? 
2) How do you use the formula for inverse variation to write an equation?
3) Class Notes on Inverse Variation

Direct Variation

Topics for Today:

Although we discussed direct variation several months ago, as we discuss related topics, I felt it was a good idea to revisit this topic.  Direct variation refers to how two variables are related to each other.  In algebraic terms, a function in the form of y = kx, where k ≠ 0, is a direct variation.

This function is similar to our slope-intercept form of a line (y = mx +b).

For direct variations, there is no y-intercept, and all of these functions must pass through the origin (0, 0).  We are effectively dealing with part of our slope-intercept form, y = mx.

For direct variations, we use the variable "k" to represent the slope, which is also our constant of variation.

Vocabulary:  direct variation, constant of variation

Sections Covered in Textbook:

5-5: Direct Variation (pages 261-266)

Resources & Tutorials:

1) What is the formula for direct variation?
2) What is the constant of variation?
3) How do you use the formula for direct variation?
4) Direct Variation Class Notes

5) Lego Prices Desmos Activity - Class Code U5Q99S

Chapter 11 Review Day

Topics for Today:

We have finished the topics for Chapter 11.  We will not be discussing graphing square roots (Algebra II) nor Trigonometric Ratios (Geometry/Trig).   The top concepts from our chapter include:

• Simplifying Radicals (3 Conditions)
• No perfect square factors under the radical
• No fractions under the radical
• No radicals in the denominator of a fraction
• The Pythagorean Theorem
• Distance Formula
• Midpoint Formula
• Simplifying radicals by adding and subtracting
• Simplifying radicals by multiplying and dividing
• Rationalizing denominators
• Conjugates
• Solving Radical Equations
• Squaring both sides of an equation
• Looking for and excluding extraneous solutions
• Equations with no real solution

Sections Covered in Textbook:

Chapter 11 (Sections 11-1 through 11-5 - pages 578-612)

Resources & Tutorials:

1) See Blog Entries for April 20th through May 3rd

2) Chapter 11 Review Sheet
2) Chapter 11 Review - Answers

Solving Radical Equations

Topics for Today:

We added to our equation solving tools today by working with equations containing radicals.  To solve these equations, we must isolate the variable on one side of the equation.  Once we do that, we can "undo" taking a square root by squaring both sides.  We must be careful when squaring equations so that our process does not result in extraneous (extra) solutions.  It's always best to check our solutions to make sure they satisfy the original equation.  As with many other equation types, we may have a situation where our equation has no solutions.  In Algebra I, we do not work with imaginary numbers (in our class they are the square roots of negative numbers), so if we encounter any of these, our equation has no real solution.

Vocabulary: radical equation, extraneous solution

Sections Covered in Textbook:

11-5: Solving Radical Equations (pages 607-612)

Resources & Tutorials:

1) How do you solve radical equations?
2) How to solve a radical equation with a binomial radicand.

3)  Solving Radical Equations Class Notes

Conjugates and Other Roots

Topics for Today:

We finished our discussion of operations with radical expressions today with a method to simplify fractions with radical operations in the denominator.  We discussed the topic of conjugates to rationalize denominators that fall into this category.

We also discussed different roots other than square roots, and how to find them.

Vocabulary:  conjugate, cube root

Sections Covered in Textbook:

11-4:  Operations with Radical Expressions (pages 600-605)
**Other Root Functions are not in our book.

Resources & Tutorials:

1) Divide by Conjugate Method
2) Math is Fun: Cubes and Cube Roots (not a video).
3) How do you find the cube root of a perfect cube? 
4) Fourth Roots

5) Conjugates and Other Roots Class Notes

Operations with Radical Expressions Part 1 (no conjugates)

Topics for Today:

Radicals have some similar properties as variables when we manage them in equations and expressions.  Just like variables, we can only combine radicals that are like each other.  When we combine or take away (add or subtract) radicals, we may only do so if our radicals are like each other.

We can only combine like radicals, and sometimes we need to simplify first, and then we may have like radicals that we can combine.  

The distributive property also works with radicals, including double distributing (otherwise known as FOIL).  

Finally, we discussed how to manage fractions that have binomials in the denominator that contain radicals.  We can multiply by the conjugate, which results in the difference of squares and the removal of the radical.   (*We did not get to this concept today - we will tackle it on Monday.)

Vocabulary: like radicals, unlike radicals

Sections Covered in Textbook:

11-4: Operations with Radical Expressions (pages 600-606)

Resources & Tutorials:

1) How to add radicals together with like radicands?
2) How do you subtract radicals with like radicands? 
3) How do you subtract radicals with different radicands? 
4) How to use the distributive property with radicals?
5) How to "FOIL" with radicals
6) Divide by Conjugate Method (will do on Monday)

7) Class Notes on Operations with Radical Expressions

The Distance and Midpoint Formulas

Topics for Today:

We continued with applications of square roots today and how it applies to geometric concepts.  The distance formula can be used to find the length of any line segment that is plotted on a coordinate plane.  The distance formula is a direct application of the Pythagorean Theorem.

The midpoint formula is another geometric concept.  The midpoint of a line segment divides that segment exactly in half.  To find the midpoint of a line segment, we are basically taking the average of the coordinates of the endpoints.  

Vocabulary:  distance formula, midpoint, midpoint formula

Sections Covered in Textbook:

11-3: The Distance and Midpoint Formulas (pages 591-597)

Resources & Tutorials:

1) What is the distance formula?
2) What is the midpoint formula? 
3) How to find the coordinate of a midpoint given endpoints.
4) Distance and Midpoint Formulas Class Notes

The Pythagorean Theorem

Topics for Today:

A special relationship exists with the lengths of the sides of a right triangle.  A famous Greek mathematician and philosopher by the name of Pythagoras proved its existence many years ago, although there is evidence that the ancient Babylonians knew of the relationship many centuries before.

The theorem states that if you have a right triangle (a triangle with one 90-degree angle), that the sum of the squares of its sides is equal to the square of the hypotenuse (the longest side).

Vocabulary: hypotenuse, leg, Pythagorean Theorem

Sections Covered in Textbook:

11-2: The Pythagorean Theorem (pages 584-590)

Resources & Tutorials:

1) What is the Pythagorean Theorem?
2) If you have the sides of a triangle, how can you tell if it's a right triangle?
3) Math is Fun - Pythagorean Triples
4) Pythagorean Theorem Class Notes

Simplifying Radicals Parts 1 and 2

Topics for Today:

We began our unit on radical expressions and equations today with an exploration of the process of simplifying radicals.  Just like other mathematical expressions, we have rules for what constitutes a radical in "simplest" form.

Like other algebraic concepts, there are properties that apply to radicals.

Vocabulary:  radical expression, rationalize

Sections Covered in Textbook:

11-1:  Simplifying Radicals (pages 578-583)

Resources & Tutorials:

1) What is the product property of square roots?
2) How do you use the product property of radicals to simplify a radical?
3) How do you multiply radicals?
4) Simplifying Radicals Multiplication Properties - Class Notes

5) Simplifying Radicals Division Properties - Class Notes

Chapter 10 Review

Topics for Today:

Today we reviewed Chapter 10.  This chapter was all about quadratic equations and their graphs.  When we "solve" quadratic equations, we are looking for the points where our graph either crosses or touches the x-axis.  If our graph does not touch the x-axis, we still have solutions, but they are imaginary (we'll save that topic for Algebra II, but students should know they exist!).

We used 5 methods to solve quadratic equations:

1. Graphing (using axis of symmetry, vertex, and y-intercept)
2. Algebra (good when you have no "b" value)
3. Factoring (not always possible)
4. Quadratic Formula (works for every equation)
5. Completing the square

We also worked with square roots (do you know your perfect squares???), as well as the discriminant of the quadratic formula to determine the types of solutions we have.  

We also approximated the square root values of irrational numbers based upon which perfect squares the irrational number fell between.   

Finally, we investigated the vertex form of a quadratic equation.  

 

Sections Covered in Textbook:

Chapter 10 All but 10-9:  (Pages 510-558) + Vertex Form

Resources & Tutorials:

1) See blog entries for Chapter 10 

2) Chapter 10 Review Sheet

2) Answers to Chapter 10 Review Sheet

Using the Vertex Form of a Quadratic Equation

Topics for Today:

Today we explored the vertex form of a quadratic function.  Just like linear functions that have multiple forms that are each useful for certain things (slope-intercept, standard, point-slope), quadratic functions also have multiple forms (standard and vertex) that are used for different purposes.  Up to this point we have only used standard form.  

The vertex form of a parabola is very useful because it is very easy to locate the parabola's vertex, and when exploring families of graphs it is easy to see how translations (vertical and horizontal shift as well as vertical shrink or stretch) change the size and location of the graph.  

Sections Covered in Textbook:

Concepts pulled from outside materials

Resources & Tutorials:

1) How do you convert a quadratic equation from vertex form to standard form?

2) Finding the vertex of a parabola in standard form

3) Vertex Form of Quadratic Equations Class Notes

Completing the Square

Topics for Today:

Today we explored the final way to solve quadratic equations: completing the square.  We can apply our knowledge of perfect square trinomials to set our equations up so that When we take an equation of x^2+bx+c=0  and apply algebraic properties including our perfect square trinomial pattern to solve it, we call this process “completing the square”.

We complete the square to solve so that we are able to take the square root of each side of the equation to produce our solutions.  (So far we have used factoring and the quadratic formula to solve these equations).

Here is an example of completing the square:

Sections Covered in Textbook:

10-6: Completing the Square (pages 541-546)

Resources & Tutorials:

1) Solve by completing the square
2) How to use a shortcut to factor a perfect square trinomial
3) Completing the Square Class Notes

Using the Discriminant

Topics for Today:

The quadratic formula can be used to find the solutions of any quadratic equation that is in standard form.  There is a piece of the formula called the discriminant that is very useful to determine the types of solutions that our equation will have.   Additionally, we can tell if our equation is easily factorable by looking at the discriminant.  If the discriminant is a perfect square, we have an easily factorable equation.

Sections Covered in Textbook:

10-8: Using the Discriminant (pages 554-558)

Resources & Tutorials:

1) What is the discriminant?
2) How do you use the discriminant to find out the number of solutions?
3) Using the Discriminant Class Notes

Using the Quadratic Formula

Topics for Today:

One method that can be used to solve any quadratic equation is the quadratic formula.  The quadratic formula uses the coefficients from the equation to find the values for x when y is zero.  It is highly recommended that students MEMORIZE the quadratic formula.  The quadratic formula works even when we don't have real solutions (yes, there is such a thing as an imaginary number - stay tuned - you'll become very familiar with imaginary numbers in Algebra II). 

Vocabulary: quadratic formula

Sections Covered in Textbook:

10-2: Using the Quadratic Formula (pages 547-553)

Resources & Tutorials:

1) What is the quadratic formula?
2) How do you solve a quadratic equation using the quadratic formula?
3)  Using the Quadratic Formula class notes

Factoring to Solve Quadratic Equations

Topics for Today:

All of the work we have done on factoring has led to today's topic of solving quadratic equations by factoring.  We talked about the zero-product property (when multiplying, if one factor is zero, then the equation equals zero), and how we use it to find our solutions (also called roots or zeroes). 

An example of an equation that requires several steps to solve is included here:

Vocabulary:  zero-product property

Sections Covered in Textbook:

10-5: Factoring to Solve Quadratic Equations (pages 536-540)

Resources & Tutorials:

1) What is the zero-product property?

2) How do you use the zero product property to find solutions to an equation?

3) How do you solve a quadratic equation by factoring?

4) Factoring to Solve Quadratic Equations class notes

Solving Quadratic Equations

Topics for Today:

Solving quadratic equations was the topic of the day.  We solved these equations by graphing and by using algebra.  For quadratic equations, we have three possibilities for our solutions:  we may have two solutions, one solution, or no REAL solutions.  The rules of algebra still apply when solving numerically - whatever we do to one side of the equation, must also be done to the other side to keep the truth of the equals sign.  Students were also reminded that squaring and taking the square root are inverse operations. 

Sections Covered in Textbook:

10-4: Solving Quadratic Equations (pages 529-534)

Resources & Tutorials:

1)  How do you solve a quadratic equation with two solutions by graphing?

2)  How do you use the square root method to solve a quadratic equation with two solutions?

3)  Solving Quadratic Equations class notes

Finding and Estimating Square Roots

Topics for Today:

Today we discussed perfect squares and square roots.  Squaring and taking the square root are inverse operations.  Students will be asked to memorize the common perfect squares, and there is a Quizlet set that should hopefully make learning them fun.

Vocabulary: square root, principal square root, negative square root, radical, radicand, perfect squares

Sections Covered in Textbook:

10-3: Finding and Estimating Square (pages 524-528)

Resources & Tutorials:

1) What is a perfect square?
2) How do you find the square root of a perfect square?
3) How do you find the square root of a fraction?
4) How do you estimate a square root of a non-perfect square?

5) Finding and Estimating Square Roots class notes

Quadratic Functions

Topics for Today:

Quadratic functions are still the topic of the day.  Today we worked with the axis of symmetry and used it to find our vertex.  Because parabolas are symmetric, we are able to find points on one side of the axis of symmetry and reflect them to the other side of the axis of symmetry.  Once we have the vertex, and a few points on either side of the axis of symmetry, we can easily draw our parabola.

Sections Covered in Textbook:

10-2: Quadratic Functions (pages 517-523)

Resources & Tutorials:

1) How do you find the axis of symmetry?
2) Find the axis of symmetry and your vertex
3) Quadratic Functions Class notes

Exploring Quadratic Graphs

Topics for Today:

Today we began our work on quadratic functions.  Quadratic functions, simply stated, are functions that have a variable with the highest degree exactly equal to two.  We looked at the standard form of a quadratic function and looked at graphs of different parabolas.

Vocabulary: quadratic function, standard form of a quadratic function, parabola, axis of symmetry, vertex, minimum, maximum

Sections Covered in Textbook:

10-1: Exploring Quadratic Graphs (pages 510-516)

Resources & Tutorials:

1) What is a quadratic function?
2) What is a parabola?
3) Class Notes - Exploring Quadratic Graphs

Chapter 9 Review

Topics for Today:

Today we wrapped up our discussion of polynomials and factoring, and we discussed degrees of polynomials, names for them based upon the number of terms.  We also covered multiplying binomials and polynomials as well as factoring.  We did a class Kahoot to review for the test.  

Sections Covered in Textbook:

Chapter 9:  Polynomials and Factoring (pages 455-506)

Resources & Tutorials:

1) Chapter 9 Review Sheet

2) Chapter 9 Review Sheet Answers

Factoring Trinomials Part 2 - Split the Middle

Topics for Today:

We expanded our discussion today to include factoring polynomials where the leading coefficient is not 1.  We used the product-sum game to work with factors so we could "split the middle" of the equation, and then factor by grouping.

Sections Covered in Textbook:

9-6: Factoring Trinomials of the type ax² + bx + c (where a ≠ 1)

       (pages 486-489)

Resources & Tutorials:

1) Factor a trinomial using A-C method
    (This is a different method from what was introduced in class.)
2) Factor a trinomial with a > 1
    (This method is more like what was introduced in class.)

3) Factoring Trinomials Part 2 Class notes

Factoring by Grouping

Topics for Today:

We continued our discussion of factoring polynomials today with a brief review of the Greatest Common Factor (GCF) and how we can divide the GCF out of a polynomial by using the distributive property in reverse.

Over the next several days we will tackle factoring of many different scenarios.  Factoring by grouping is a method that is used to deal with polynomials that have more than three terms.  Most people are familiar with factoring trinomials (3-terms), so when we are faced with more factors, our options are limited for how we can proceed.

In factoring by grouping, we will take two sets of two terms and pull out/factor out a GCF.  The goal is to have a leftover quantity for both groups that match one another.  If we do get our desired outcome, then we can further factor out the quantity, leaving us with a product of two binomials.

Sections Covered in Textbook:

9-8:  Factoring by Grouping (pages 496-501)

Resources & Tutorials:

1) How do you factor a 4-term polynomial by grouping?
2) The easiest way to factor a polynomial with four terms by grouping.

3) Factoring by Grouping Notes

Factoring Trinomials Part 1

Topics for Today:

Our discussion about factoring moved to factoring trinomials today.  We played a game called the "Product-Sum" game where we analyzed a set of two numbers to see what factors create both a product and a sum.  We then related this game to how we factor trinomials.  We will always be looking to create a product (answer to a multiplication problem) and a sum (answer to an addition problem) at the same time.  Notice the coefficient that precedes the first term is one.  We'll address scenarios where the leading coefficient is NOT one in a future lesson.

Sections Covered in Textbook:

9-5: Factoring Trinomials of the type ax² + bx + c (where a=1)
       (pages 481-485)

Resources & Tutorials:

1) How do you factor a trinomial?
2) How to factor quadratic equations.

3) Factoring Trinomials Part 1 Class Notes

Multiplying Binomial Special Cases

Topics for Today:

We expanded our discussion on multiplying binomials today to include some common patterns:  squaring sums, squaring differences, and the product of a sum and a difference.  For each of these cases, we can always use the distributive property or FOIL methods to expand the product; however, as with many aspects in mathematics, recognizing patterns can save a lot of time.

Sections Covered in Textbook:

9-4: Multiplying Special Cases (pages 474-479)

Resources & Tutorials:

1) What is the formula for the square of a sum?
2) What is the formula for the square of a difference?
3) What's formula for the product of a sum and a difference?

4) Multiplying Binomial Special Cases Class Notes

Multiplying Binomials

Topics for Today:

Our topic for today was multiplying polynomials.  We focused our time mostly on multiplying two binomials together (recall that a binomial is the sum or difference of two monomials).  We focused on the number of individual products to ensure we did not leave any steps out.  Most people are familiar with the FOIL method for multiplying two binomials:

Sections Covered in Textbook:

9-3: Multiplying Binomials (pages 467-472)

Resources & Tutorials:

1) Multiply Binomials using the Distributive Property
2) Multiply Binomials using the FOIL method
3) How to Multiply Trinomials 

4) Multiplying Binomials Class Notes

Multiplying and Factoring Polynomials

Topics for Today:

We explored multiplying a monomial by a polynomial today and doing the reverse by factoring out the greatest common factor.  Multiplying and factoring are inverse (opposite) operations of each other.

Vocabulary: Greatest Common Factor, GCF

Sections Covered in Textbook:

9-2: Multiplying and Factoring (pages 462-465)

Resources & Tutorials:

1) How do you multiply a monomial by a polynomial?
2) How do you find the Greatest Common Factor (GCF) of monomials?
3) Factoring Monomials from Polynomials

4) Multiplying and Factoring Polynomials Notes

Adding and Subtracting Polynomials

Topics for Today:

Today we began our unit on polynomials with some definitions.  We also worked on adding and subtracting polynomials.  Like working with any variable expressions, we must always look for like terms when combining their components.  Variables raised to different powers cannot be combined by adding and subtracting.  One last concept to keep in mind is that when subtracting polynomials, you must subtract each piece of the polynomial; that is, the subtraction must be distributed to each piece of the polynomial and not just its first term.

Vocabulary:  monomial, degree of a monomial, polynomial, standard form of a polynomial, degree of a polynomial, binomial, trinomial

Sections Covered in Textbook:

9-1: Adding and Subtracting Polynomials (pages 456-461)

Resources & Tutorials:

1)  What is a monomial? 
2)  What is a polynomial? 
3)  How do you find the degree of a polynomial?
4)  How do you add polynomials? 
5)  How do you subtract polynomials? 

6) Adding and Subtracting Polynomials Class Notes

Chapter 8 Review

Topics for Today:

Today we reviewed concepts in Chapter 8 (Sections 8-1 through 8-5) in preparation for our test tomorrow.  We played a game of Jeopardy as teams using review questions from our book.

Sections Covered in Textbook:

The test will cover Sections 8-1 through 8-5 (pages 394-423)

Resources & Tutorials:

** See blog entries from February 21st through February 28th **

1) Review Jeopardy Questions
2)  Review Jeopardy Answers

Division Properties of Exponents

Topics for Today:

Today we tackled the last property of exponents that deals with division.

When dividing powers with the same base, we can simply subtract the exponents.  When dividing monomials, we must match up like bases with each other, and deal with them separately.

Sections Covered in Textbook:

8-5: Division Property of Exponents (pages 417-423)

Resources & Tutorials:

1) What's the quotients of powers rule?
2) How do you divide monomials using the quotients of powers rule?
     (*This video leaves a negative exponent - that is NOT simplest form!*)

3) Division Properties of Exponents Class Notes

More Multiplication Properties of Exponents

Topics for Today:

Today we reviewed the topics relating to exponents and exponent rules, including scientific notation.  We expanded our topic of multiplication of powers to include raising a power to a power, as well as taking a monomial to a power.  When a monomial (a number, a variable, or a product of a number and variable - this also includes whole number exponents) is raised to a power, each element of that product must be raised to that power.

Sections Covered in Textbook:

8-4: More Multiplication Properties of Exponents (pages 411 - 415)

Resources & Tutorials:

1) What the power of a power rule?
2) How do you take a monomial to a power?
3) More on the power of a product rule.

4) More on Multiplication Properties of Exponents Class Notes

Multiplication Properties of Exponents

Topics for Today:

Today we discussed how to manage multiplying powers with the same base.  We looked at several examples as well as explored how to multiply numbers together that are in scientific notation.  In summary, when multiplying powers with the same base, just keep the base and add the exponents together.  This process works for both positive and negative exponents.

Graphic Credit: https://www.onlinemath4all.com/multiply-powers.html

Sections Covered in Textbook:

8-3: Multiplication Properties of Exponents (pages 405-410)

Resources & Tutorials:

1) What is the product of powers rule? 
2) How do you find the product of powers? 
3) How do you multiply numbers using scientific notation? 

4) Multiplication Properties of Exponents Class Notes

Scientific Notation

Topics for Today:

Today we used exponents in a practical way when we learned about scientific notation.  Scientific notation is simply a way to write very large and very small numbers that follow a few rules.

Simply stated, scientific notation is the product of a number and a power of 10 that follows the format: 

a x 10ⁿ  where n is an integer and 1 ≤ a < 10

Image credit: https://pt.slideshare.net/jessicagarcia62/compute-with-scientific-notation/6?smtNoRedir=1

Vocabulary:  scientific notation

Sections Covered in Textbook:

8-2: Scientific Notation (pages 400-404)

Resources & Tutorials:

1) What's scientific notation? 
2)  How do you convert decimal notation to scientific notation? 
3) How do you convert from scientific notation to decimal notation? 
4) How do you order numbers in scientific notation? 

5) Scientific Notation Class Notes