Browse new releases, best sellers or classics & Find your next favourite boo This Algebra In Mathematics Course Is Designed To Make Studying Mathematical Symbols. Alison Free Online Learning Is 14 Years Old. Let Us Help You Expand Your Horizons For example, green rectangle tiles can represent positive variables and yellow rectangle tiles can represent negative variables. To use algebra tiles, we place square and rectangle tiles on either.. This video is an introduction for using **algebra** **tiles**. We look at what each **tile** represents in an area model, by Lea Gaslowitz. Front Porch Math offers free.. Solve 2x - 3 = 7 with algebra tiles. To get negative tiles with paper, you can print on 2-sided paper, like astrobrights, or glue two pieces of paper together before cutting. Here we have 2 x tiles and 3 negative tiles on the left and 7 tiles on the right. To get rid of that -3 on the left, we +3 to make a zero pair

On this lesson, you will learn how to use algebra tiles for evaluating expressions and evaluating algebraic expressions. This is a fun and easy way to evalua.. Algebra Tiles are a new way of teaching algebra to students who are just beginning to learn the basic concepts. This instructable will show you how to use an Epilog laser cutter to make a set of the useful tiles. If you do not have a laser cutter, you can use Ponoko or similar laser cutting services to make yours Below are 4 examples of how to use algebra tiles to factor, starting with a trinomial where A=1 (and the B and C values are both positive), all the way to a trinomial with A>1 (and negative B and/or C values). Here is a look at the tiles in this post

Algebra Tiles. Go to the ? above for additional help! Backgrounds. Algebra Tiles Now use the above mentioned algebra tiles to model the equation on the mat. To model the above equation, we need to use two green tiles, two yellow tiles on the left side and six yellow tiles on the right side. Remove two yellow tiles from each side of the mat. Divide each side into 2 equal groups You would select three tiles and place them down one dimension of your multiplication table, place four tiles along the other dimension, fill in the rectangle created by the tiles and then count the result. You can use the same idea when multiplying Algebraic expressions Equation solving - I draw a line down the center of the paper and use the algebra tiles to solve equations. When kids tried to subtract 4 from 6x, I would take out 6 x-tiles and 4 constant tiles and say, Now, how can I combine these? The answer, Oh you can't, they aren't like terms..

Download our Algebra Tiles Starter Guide to see how you can use them to teach simplifying expressions, distributive property, solving linear equations, adding and subtracting polynomials, multiplying and dividing polynomials, and factoring polynomials. 3. Don't Just Use THEM for One Da Using Algebra Tiles Effectively (x + 3)(x - 2) = x2 + x - 6 When I listen, I hear. When I see, I remember. But when I do, then I understand. This workshop helps participants use algebra tiles effectively in their classrooms. Purpose Middle School and/or High School Teachers Participants Materials • Algebra tiles (1 set for every two. Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra. This interactive is optimized for your desktop and tablet

- In this task, you will learn how to multiply two binomials using Algebra tiles. 1. Find the product (x + 1)(x + 4). a. Build your model. Make a rectangle with a width of x + 1 and a length of x + 4. b. Fill in the area with algebra tiles. The area of an x by x is an x2 tile. c. Continue to fill in the area with algebra tiles, using an x tile.
- The first stage to using algebra tiles is to model different integers in the open workspace. Allow the students ample time to familiarise themselves with the tiles, the meanings of each colour and the concept of zero-sum pairs. Ask then to model numbers in multiple ways - using the zero-sum pairs
- Algebra tiles support the representation and manipulation of constant, linear and quadratic expressions. Expressions are built up from tiles corresponding to each of x 2, −x 2, x, −x, 1, and −1, where the shape and colour indicates the class of tile. The activities below help practice building up expressions using Algebra Tiles, using zero pairs — i.e. a pair of opposite tiles that.
- Begin with adding integers, modeling with tiles for each problem. Mix in subtract integers, showing how subtraction is the same as negative with modeling tiles. Students brainstorm different ways to say -6 - really focus on drawing out opposite, negative, and take away. Show subtracting a negative with tiles

** However, to get them comfortable with using algebra tiles and visualizing what expressions actually look like, it would be a good idea to introduce the algebra tiles early and often**. With algebra tiles, you can very quickly see which terms are like terms by looking at the shape and size of the tiles in each group: Simply rearranging the tiles. Interactive algebra tiles to aid the use of manipulatives in the classroom

Perimeter with algebra tiles you ixl multiply two polynomials using algebra tiles 1 ixl multiply two polynomials using algebra tiles 1 completing the square using algebra tiles perimeter with algebra tiles you ac 2 1 2b area and perimeter of algebra tiles mp4 you Using Algebra Tiles the students can physically exchange the variable tiles for the unit tiles. The x 2-tile is replaced by a square with side length of the given value. This allows the students to build a clear visual representation of what they are doing when they substitute the variable with a given value Algebra tiles are known as mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra.These tiles have proven to provide concrete models for elementary school, middle school, and high school students

- Algebra tiles are manipulatives that we can use to solve equations. Each shape and colour mean something, but don't worry, it's not hard to remember: To help us solve equations, we need to understand the concept of a ZERO PAIR
- Algebra tile class sets can be very expensive, so I have included a master copy of tiles that can be copied on card stock and colored by students and cut out. If you punch a hole in a Ziploc bag, students can have a set in their binders to use at home as well as at school
- manipulatives, consider using card stock. To make algebra tiles similar to those shown in the Student Edition, have students use markers to color the tiles appropriately or use colored card stock. You can also make transparencies of frequently used items such as grid paper and number lines
- Use purchased algebra tiles or provide students with the materials to create their own set of tiles. Using the small . coloured squares from the sets of algebra tiles to teach integers provides a foundation for algera concepts. Algebra tiles for the overhead projector or IWB are also useful. Note: Tiles come in various colours
- Use algebra tiles to model 2x - 3 = 5. Solution : Step 1 : How can we model the left side of the equation ? We find 2x - 3 on the left side of the equation. So we can use two positive variable tiles and three -1-tiles to model the left side of the equation. Step 2 : How can we model the right side of the equation
- Students will be combining like terms using digital Algebra Tile manipulatives. Students will drag and drop the Algebra Tiles onto the mat to model the problem and then simplify. All expressions are in terms of one variable and include x and x squ

We're here to support your family! IXL is easy online learning designed for busy parents. Master algebraand 3000+ other basic maths skills. Win fun awards In Algebra Tiles, square and rectangle shaped colored tiles are used to represent numbers and variables. As per general rule, Each small square tile, the unit tile, represents number one. If we have two tiles, then we have the number two. Red colored square tiles are used for negative numbers, while any other color could be used for positive ones Drag tiles from the tray at the left to the display area at the right. 1. Select one of the tiles and drag it to the tile area. 2 using algebra tiles. D a y 3 • Review to the students what a variable x looks like with algebra tiles. • Review the Previous Lesson • The students will be able to begin solving 2-step equations using algebra tiles using. They will refer to the concept of opposite and balance D a y 4 • The students will be able to check their solution fo 3.4A: Factoring Using Algebra Tiles Trinomials of the form ax2 + bx + c can be factored using algebra tiles (alge tiles). To do this, the tiles modeling the trinomial are laid out. Next, with the x2 tile in the upper left position the remaining tiles are arranged around it to form a rectangle

Using the algebra-tiles and the multiplication array together to illustrate the distributive property and algebraic multiplication with an Area Model. mathcast 002pt3 - Using Alge-Tiles and Multiplication Array together = Area Model for Algebra 1. Demonstrate dividing polynomials using algebra tiles and the attached Teacher Resource for Dividing Polynomials. 2. Distribute algebra tiles and copies of the Dividing Polynomials Using Algebra Tiles activity sheet. Instruct students to model each expression with the tiles, draw the model, simplify the expression, and write the simplified. ** The algebra tiles are made up of small squares, large squares, and rectangles**. The number one is represented by the small square, which is also known as the unit tile. The rectangle represents the variable x and the large square represents x2 Equations and Algebra Tiles Objective: To understand the different parts of an equation, and use algebra tiles to help us solve problems. Using Algebra Tiles to Solve Equations, Combine Like Terms, and use the Distributive Propert

a. This trinomial is made up of one x2 tile, eight x tiles, and fifteen unit tiles. b. Arrange these tiles to form a rectangle. The key is to correctly arrange the unit tiles to match the number of x tiles. c. Use algebra tiles to identify the width and length of the rectangle. d. Write an equation to show the meaning of the model for this problem I show how using Algebra Tiles can make this process easier to see in the two videos below. Factorising a quadratic expression where the coefficient of x is not 1 Factorising a quadratic expression where the coefficient of x is not 1, another example. In Part 5,. When multiplying and dividing with algebra tiles, use the terms 'times' and 'divide' as hints. If you want to find the answer to (2 * 3), you would create three rows of two (a row of two, three. Tactile Algebra Tiles can help! It provides students with concrete models for approaching abstract math concepts and procedures. Wondering how? Grab your Tactile Algebra Tiles and we'll show you how! Let's get started. Open the box of a Tactile Algebra Tiles kit and take out one steel board. We are going to use the tiles listed below

Interactive Algebra Tiles - use this to model an equation or to solve an equation Virtual Algebra Tiles - In this activity you will learn how to use Algebra Tiles to model and explore a variety of problems. Working with Algebra Tiles - Math Bits provides instructions and a template Working with Algebra Tiles PowerPoint show - 54 slides in an. When students first use algebra tiles, allow for exploration time. Sample Activities 1. Determine the number of different ways that zero (0) can be represented using tiles from a set of 3 blue one-tiles and 2 red one-tiles. 2. Use the one-tiles to model different integer values, e.g., a loss of $4; 2 metres above sea level Algebra tiles can also be used to complete the square as we did easily in class. Deriving this way can lead to a better understanding of the rules of completing the square and eventually lead to deriving the quadratic formula. Teaching math this way helps students remember and add value to formulas

- When using an area model, this involves arranging the tiles representing the polynomial into a single rectangle. To do this with the Algebra Tiles tool, represent the polynomial then drag the tiles to form a single rectangle. Identify the dimensions of that rectangle as the factors of the polynomial
- Using algebra tiles is like building a puzzle. You put some of the pieces across the top, some along the left side, and then you match them up to complete the rectangle. Here is what the board looks like: Students get an opportunity to make the mathematics much more tangible - algebra can be a very abstract concept when students are first.
- To use algebra tiles to model an equation, we place the relevant number of variable rectangle tiles and number square tiles for the left side of the equation and for the right side of the equation. Then we play around with our tiles so that we end up with the rectangle tiles by themselves on one side. We do this by moving the square tiles
- (Heddens & Speer, 2001). Algebra tiles are manipulatives that support students to visualize polynomial operations and solve equations. A set of algebra tiles consists of at least three different shapes as the following dimensions and values. In this study, we merely use the rectangle and the small square of algebra tiles in learning linea
- Algebra tiles are a brilliant tool to support students uncover algebraic structures. This webinar provides a brilliant guide for those new to using algebra tiles in the classroom The session focuses on how to use algebra tiles to uncover mathematical structures thus deepening understanding

Pairs use algebra tiles to concretely solve, and explain each step in solving, multi-step, linear, algebra equations. They then explain each step in their solving strategy to the class as the teacher connects the algebraic process in... An app to simulate algebra tiles This app is in a VERY early stage of development ----- Reminder: I am not a professional app developer. I have almost no experience in coding. I am a maths teacher doing this in his spare time. I have used the website THUNKABLE.com to create my apps I first used Algebra Tiles, back in the 90's, when I was teaching 8th grade and then continued to use them when I switched to 7th grade. Now that I'm a math coach, I've been helping teachers learn how to integrate Algebra Tiles into their lessons. This post and accompanying Desmos Activity Builder is a result of Improve your math knowledge with free questions in Model and solve equations using algebra tiles and thousands of other math skills

** Most began by using the actual algebra tiles to play around with building different images**. Then, they sketched their designs on the paper and recorded the number of tiles they would need. After writing and simplifying their expression, they cut out the necessary amount of algebra tiles from color copies of these printouts that I made ALGEBRA TILES The University of Texas at Dallas INTRODUCTION Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions. - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 4333d8-MzE4 Algebra Tiles Algebra tiles are used to model integers and variables to aid in learning addition, subtraction, multiplication, and division of positive and negative values. Algebra tiles are especially useful in modeling multiplication and division because their dimensions are based on the concept of area. They can be bought or made, and they usually consist of three shapes: small squares for.

- Get a free
**algebra****tile**template below. Or find a small set here or a large set here. You can read about**how**we**use****algebra****tiles****to**teach solving equations here. 1.**ALGEBRA****TILES**Make Abstract Concepts Concrete In researching why**algebra****tiles**are so vital for students, I came across this article. The author states, If children are. - d: x You may only use one x2-tile in each square. x You must use all the x2 and x.
- Algebra tiles can be used to represent polynomials. We can also use those tiles to solve polynomials. In this lesson, we will try to solve some polynomials using algebra tiles
- of algebra tiles (rectangles and squares) and combinations of algebra tiles. The dimensions of each tile are shown along its sides and the tile is named by its area as shown on the tile itself in the figures at right. When using the tiles, perimeter is the distance around the exterior of a figure. For additional information, see the Math Notes.

5. Combine the remaining tiles in the 3 rd box to show the sum. 6. Have students complete the You Try, drawing the tiles for each polynomial and each step; 7. Go over the you try Example 2: Use Algebra Tiles to Find the Difference. 1. Have them draw the first polynomial in the first box; 2 Algebra Tiles: Fraction Bar Grouping Symbols Example 1: 7x−1=2x+4!! Rewrite the equation as addition. 7 (1) 2 4 7 1 2 4 + − = + − = + x x x x 'Build' the equation using algebra tiles. No like terms in this equation. Goal is to find the value of one x Algebra Balance Equations Instructions Replicate the given equation by moving the blocks of X and 1 to the sides of the balance scale. Then use addition, subtraction, multiplication, and division to each side to solve for x I set a pretty average goal for myself a couple months ago to blog about all the ways to use algebra tiles. But then of course life got in the way and here I am only on post #3-- how to use algebra tiles to multiply polynomials Discover how algebra tiles help evaluate expressions. Scholars learn to use algebra tiles to substitute values in for variables and evaluate expressions. The included worksheet contains a set of evaluation problems to assess individuals'..

* PERIMETER AND AREA OF ALGEBRA TILES Using variables allows you to work with lengths that you do not know exactly*. Today you will work with your team to write expressions to represent the perimeters of different shapes using variables. 5. ALGEBRA TILES Work with your team to calculate the area and the perimeter for the following figures. a 4 of 4 Activity and Closure Questions Discuss these questions as a class. Describe how you would use algebra tiles to factor x2 + 8x + 15. Answer: Select one x2-tile, eight x-tiles, and fifteen 1-tiles.Start with the x2-tile and place three x-tiles below it and place five x-tiles to its right.Then complete the rectangular array by placing th Use algebra tiles to build an array to find each of the following quotients. Sketch each array. Write each answer as a polynomial and express remainders as fractions. 1. x2 + 5x + 4 2. 3x2 + 8x + 4 x + 2 x + 2 . 3. x2 - 2x - 8 4. x2 + 7x + 5 x + 2 x + 2 . 5. x2 + 7x + 5 6. x2 - 4x + 3. hand2mind Algebra Tiles for Kids Ages 10-17, Demonstration Algebra Tile Clings, Math Tiles for Algebra, Variables, and Integers, Homeschool Supplies (72 Pieces) 4.7 out of 5 stars 8 $19.48 $ 19 . 48 ($0.27/Item) $20.99 $20.9 Algebra Tiles. Activity 1 (20 minutes): Using the overhead, the teacher will display one of each tile to represents the size, color, and value. Students can also refer to the poster hanging in front of the class throughout the lesson for the value of each algebra tile. At this point, the teacher will pass out student sets of algebra tiles

* The Algebra Tiles do not provide a corner piece*. Since the corner piece is a very important support for beginners, I recommend you add corner pieces to your algebra tiles, either by purchasing them separately, or by just drawing them on paper. The absence of 3-D blocks is a limitation, but much can be done in two dimensions Using just the small, square tile, we introduce pupils to using Algebra Tiles at a very young age by using them as simple counters. We can ask pupils to represent a given number, say, or to use the tiles as a representation of counting up or down from a starting number Algebra Tiles. To represent zero pairs using Algebra Tiles. To model integers using zero pairs. Prerequisites: A. Students need to know that the area of a square is given by A = s2, where s is the length of a side. B. Students need to be able to represent positive and negative integers using Algebra Tiles. Getting Started: A. Introduce the unit. Page 3 of 14 MCC@WCCUSD (M3) 10/03/12! 2)!!Have!students!findthesolutionto!(43)(3)xx x2 ++÷+using!algebra!tiles!and!have!them! checkwith!their!partners.!!Have!a. Using Algebra Tiles, help the foreman design the porch and step layout by factoring the trinomial. Assessment Plan. The assessment for this particular portion of the factoring unit will be accomplished through completion of the worksheet. Bibliography. Obtained from an extended substitute assignment at Midvale Middle School..

Students will watch a tutorial about adding integers using algebra tiles as a model. Students will watch a demonstration of how to model and solve addition problems using Chip Addition in NVLM manipulatives and then follow the link to practice problems on their own. Students will study the 2 simple rules for adding integers and apply that rule with Quizlet flashcards * Today I am going to share with you how to use Algebra tiles to teach multiplying binomials*. Start by reminding your students how to find the area of a rectangle. Connect the fact that when you multiply two factors together you also are calculating the area of a rectangle with the factors as the side lengths. Polynomials work the same way • Use the tiles and your Equation Mat to solve the equation 2 2 4.x −= • The verbal description and algebraic representation for each step are provided in the table below. • As you work through the steps using the tiles and your Equation Mat, record pictures of your tiles to correspond with each step in the table. Factoring with Algebra Tiles Summary Students will be able to gain a visual understanding of factoring through the use of Algebra Tiles. This will be a hands-on cooperative group activity. Time Frame 1 class periods of 45 minutes each Group Size Pairs Life Skills Thinking & Reasoning Materials A set of Algebra Tiles for each group. An Algebra.

Distributive Property with Algebra Tiles KEY: = x = 1 = -1 Write the expression represented by each group of tiles. 1. 2. 3. Represent each expression using tiles. Draw your tiles below each expression. 4. 5. 6. The expression indicates two groups of tiles as shown below on the left. You ca Algebra Tiles are a must when starting to explore the basic concepts of algebra and pre-algebra. It is always a good idea to write the algebraic statement while 'creating' the statement with tiles. This will help your student make the connections between algebra in picture form and algebra in a text format

The intermediate grades can use Color Tiles to explore factors and multiples from a geometric perspective. Students can also use the tiles to apply fraction concepts to a problem-solving situation. Rather than relying solely on the mathematical symbols, students can use Color Tiles to test their thinking Basic rules of algebra tiles. It is anticipated that you will make these tiles as physical resources for students to use. Four operations using algebra tiles including with negative numbers. Types of number. All of the above concepts are relatively trivial and you may have used variations on the algebra tile model when teaching them

A great example of this happened in November and December, when we were using algebra tiles to represent and simplify polynomials. I modified and refined the same lesson three times, in two weeks, resulting in this lesson the third time around. It was fun, engaging, and students all seemed to understand each step of the learning.. Representing polynomials with algebra tiles. Algebra tiles are tiles of different colors and sizes. Each size corresponds to a degree of the different monomials of the polynomial. An example will make it easier to understand: This tile represents a unit. It corresponds to monomials with a degree of 0. This represents 'x' In this article, Ysbrand de Bruyn and Gila Hanna explain how to use algebra tiles to model completing the square for students. The article provides examples on how to use algebra tiles to change the equation of a parabola from standard form to vertex form Students will get a better understanding of factoring polynomials using special products using a visual model Participants will learn how to use algebra tiles to model concepts such as integer operations, arithmetic on polynomials, factoring of polynomials, completing the square, and solving equations, with connections to other topics. We will discuss reasons for using manipulatives or other concrete materials to teach fundamental algebraic concepts

** Algebra Tiles Instructions Classic algebra tiles can be used in a lot of ways to work with algebra learning**. You can adjust the length of x and y by moving the sliders. Click on the buttons to make algebra tiles appear. Click and drag on the upper left of any tile to rotate the tile by 90 degrees The use of mathematical manipulatives increases students' learning gains. Algebra tiles are an educational resource that helps students understand algebra concepts by using geometric figures. What this paper adds: Virtual Algebra Tiles is a multimedia version of the educational resource algebra tiles | Algebra tiles can be used to factor polynomials. Use tiles and the frame to represent the problem. | Use the tiles to fill in the array so as to form a rectangle inside the frame. | Be prepared to use zero pairs to fill in the array. | Draw a picture Integer tiles are used to model integers. They combine to form a Zero Pair. + Positive Integer Tile models +1 Negative Integer Tile models 1 + 8.1, 8.3 Multiplying and Dividing Integers Using Models. When the FIRST Number is.

Given a quadratic equation, the student will use tiles to factor and solve the equation Next, we use a chart to connect the algebra tiles to the algebra. The cool thing is that they actually understand why we are dividing 'b' by 2 and squaring it because they have done it with the tiles. The next day we extend to quadratics where 'a' is not equal to 1. Again we start with tiles and connect to algebra The session focuses on how to use algebra tiles to uncover mathematical structures thus deepening understanding. It will explore the use of algebra tiles when simplifying expressions and when expanding and factorising. Finally, the use of algebra tiles to support proof will be considered The NCTM Standard of representation is also being addressed. Students are using algebra squares to represent the equations and their solutions to solve the system of linear equations. Materials: Elmo Paper 14 bags of Algebra Tiles 1 Bag of Algebra Tiles with the symbol that the tile represents written on the tile 25 Algebra Tile Activity worksheet This is a good book if all you want to do is work with one variable at a time, using the very simple (and limiting) sets of blue-green-yellow-red algebra tiles. However, I recommend the Algebraic Bosse Tiles -- particularly the X, Y, Z set (340 pieces) and the accompanying Bosse Activity Books I and II from Nasco

In order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. An example would be where one is given one positive x 2 tile, three positive x tiles, and two positive unit tiles Using algebra tiles, factor 2x2 + 5x+ 3 ; that is, use the tiles to build a rectangle, and then write its area as a product. I +1) ] To factor with tiles (like you did in pan (a)), you need to determine how the tiles need to be awanged to form a rectangle. Using a generic rectangle to factor requires a different process It will explore the use of algebra tiles when simplifying expressions and when expanding and factorising. Finally, the use of algebra tiles to support proof will be considered. This session is ideal for all secondary maths teachers, non-specialist teachers or NQTs who are less experienced in the use of algebra tiles

Algebra does not even leave behind sports to make use of it. If you look closely, the players of almost all the sports, unintentionally, apply algebra. The cricketers are able to hit sixes only because they are able to calculate the force required to hit the ball and basketball players calculate the trajectory to score a point Use the algebra tiles interactive to collect like terms. How many x tiles represent the simplified expression? 1 See answer sofiagiulianam is waiting for your help. Add your answer and earn points. Taeanj Taeanj Answer: 4. Step-by-step explanation: Mark me as brainlist To conclude, the main reason I looked to use algebra tiles more was due to my worry that students struggled with the underlying structure behind algebraic problems. If we want our students to go on to excel in this subject, it is crucial they build their understanding of basic algebra on solid foundations. If you feel a similar way, I encourage. Multiplying Polynomials Using Algebra Tiles - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are A concrete introduction.

Correct answers: 2 question: Complete the description of how to solve the inequality 3x +6 < 15 using algebra tiles. +1-tiles from both sides, then divide each side into equal groups. The Remove solution is x < An equation is modeled below using algebra tiles. Which value of x makes the equation true? A. x = 7 C. x = 13 B. x = -7 D. x = -13 The algebra tiles: There is a large block with an x. Next to it are 3 small blocks with 1 math. Determine if each pair of expressions is equivalent This free tile calculator estimates the total number of tiles needed to cover an area such as a floor, wall, or roof. It can also account for the gap or overlap between tiles. In addition, explore hundreds of other calculators addressing math, finance, fitness, health, and more using_algebra_tiles_to_solve_equations 3/6 Using Algebra Tiles To Solve Equations Opt Art-Robert Bosch 2019-11-12 A fun and stunningly illustrated introduction to the art of linear optimization Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives a. b. (2x + 5)(x + 3) c. the two methods are similar because both using **algebra** **tiles** and factoring symbolically needs to think to factor of the last term which is 15. so it is either 15 x 1 or 3 x 5 same goes with using **algebra** **tiles** you have to lay 15 pieces of 1 **tiles** and come up with **how** **to** form a rectangle 5 x 3 in this case