An area model is a useful tool you can use to model certain fraction concepts. Here are some math concepts you can model with fraction sticks and area models:. A prevalent theme in the Grade 4 Common Core standards is understanding equivalent fractions, or, more precisely, the notion that a fraction remains the same when you multiply the numerator and denominator by a non-zero whole number.

Understanding equivalent fractions is important when comparing and ordering fractions, adding and subtracting fractions with unlike denominators, and reducing fractions to their lowest term. This is a great time for students to experiment informally with fraction sticks. After various opportunities to experiment informally with fraction sticks and write down their observations, they will be ready to learn a more formal rule: when you multiply the numerator and denominator by the same non-zero number, you will obtain an equivalent fraction.

If your students are ready to be challenged with the symbolic form, you can explain:. Next, divide the area of the unit square into four horizontal rectangles to demonstrate that you're multiplying both the numerator and denominator by 4.

**Adding Fractions With Rectangle Models**

What is the new fraction represented by the shaded area? To demonstrate this with an area model, begin by dividing the unit square vertically into thirds. What fraction is represented by the intersection of the two shaded areas? Close brillion ss1201 manual. Blog Menu. What is an area model?

Here are some math concepts you can model with fraction sticks and area models: Equivalent Fractions A prevalent theme in the Grade 4 Common Core standards is understanding equivalent fractions, or, more precisely, the notion that a fraction remains the same when you multiply the numerator and denominator by a non-zero whole number.

Next, divide the unit square horizontally into fourths. Share below!Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages.

Additionally, there are length, area, region, and set models. Adjust numerators and denominators to see how they alter the representations and models. Use the table to keep track of interesting fractions. Modes Choose LengthAreaRegionor Set on the bottom right to show different representations of the fractions.

Set also lets you choose from four different objects. Adjust the numerator and denominator at the bottom to change the fraction. What is the result? How does the result relate to the values shown for mixed number, decimal, and percent? When the numerator is greater than the denominator, what do you notice?

What does the picture look like if the numerator is greater than the denominator? What if the numerator is less than the denominator? Add the fraction to the table. What is the decimal equivalent? Add this result to the table. What do you notice about the values in the table? Change to the length model and look at each fraction's model. What do you notice? Join Now. View Cart. NCTM Store. Toggle navigation MENU. Log In Not a member? Fraction Models Grade: 3rd to 5th, 6th to 8th Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages.

This interactive is optimized for your desktop and tablet. Instructions Modes Choose LengthAreaRegionor Set on the bottom right to show different representations of the fractions. Change the possible denominator values using the Narrow RangeLimitedand Wide Range tabs at the top. You can also change values on the model.We are being inundated with emails from districts, schools, teachers and parents who are looking for offline activities due to the fact that many families do not have the number of electronic devices needed for multiple children to do online learning while parents work from home.

Use code Learnathome at checkout. The three major categories of fraction models are the area model, linear model, and set model. Having students repeat an activity with a different model and asking them to make connections between models can also be useful. Too often, students learn rules for manipulating written fractions before they have developed an understanding of fraction concepts.

Useful manipulatives include rectangular, or circular fraction sets, pattern blocks, geoboards and tangrams. Hence, students should have opportunities to work with both rectangular and circular models. When purchasing rectangular or circular fraction sets keep in mind that those with pieces that are not labeled provide more opportunities for learning. Consisting of blocks in six geometric shapes they are referred to as green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons.

Geoboards can be used to explore a range of math concepts including properties of shapes, area, and perimeter.

### Mathematical model

Available in a variety of sizes they also provide an engaging way for students to partition wholes into equal areas and to explore equivalent fractions using an area model. Sample Activities: Partition a Square ver. Frequently used for exploring geometry, they can also be used for problem solving tasks involving fractions.

Sample Activity: The Warlord's Puzzle. Either number lines are drawn and subdivided or physical materials are compared on the basis of length. Useful manipulatives include Cuisenaire rods or fraction strips that are easily connected to ideas about fractions on a number line.

Cuisenaire Rods are rectangular rods, each of a different color and size, that can be used to help students develop understanding of a range of math concepts including addition, subtraction, multiplication, length, area, volume, and fractions.

The lengths of the different colored rods increase incrementally from the smallest size 1cm long to the largest size 10 cm long. The rods are flexible because any length can be used to represent the whole. The number line is an important linear model for students to work with as it reinforces the fact that there is always one more fraction to be found between two fractions.

If purchasing commercially made strips opt for those that are unlabeled to provide more opportunities for thinking and learning. Sample Activities: Making Fraction Strips ver.A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.

## Basic Fractions Model

Mathematical models are used in the natural sciences such as physicsbiologyearth sciencechemistry and engineering disciplines such as computer scienceelectrical engineeringas well as in the social sciences such as economicspsychologysociologypolitical science. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including dynamical systemsstatistical modelsdifferential equationsor game theoretic models.

These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models.

In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments.

Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. In the physical sciencesa traditional mathematical model contains most of the following elements:. Mathematical models are usually composed of relationships and variables. Relationships can be described by operatorssuch as algebraic operators, functions, differential operators, etc.

Variables are abstractions of system parameters of interest, that can be quantified. Several classification criteria can be used for mathematical models according to their structure:.

In business and engineeringmathematical models may be used to maximize a certain output. The system under consideration will require certain inputs. The system relating inputs to outputs depends on other variables too: decision variablesstate variablesexogenous variables, and random variables. Decision variables are sometimes known as independent variables. Exogenous variables are sometimes known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random, and exogenous variables.

Furthermore, the output variables are dependent on the state of the system represented by the state variables. Objectives and constraints of the system and its users can be represented as functions of the output variables or state variables. The objective functions will depend on the perspective of the model's user. Depending on the context, an objective function is also known as an index of performanceas it is some measure of interest to the user.

Although there is no limit to the number of objective functions and constraints a model can have, using or optimizing the model becomes more involved computationally as the number increases.Jump to main content. The Fractions app lets students use a bar or circle to represent, compare, and perform operations with fractions with denominators from 1 to Choose the fraction model and number of equal parts.

Use a color to select specific parts to show a fraction of the whole. Reveal or hide numeric labels as needed. Superimpose fractions upon each other to compare fractions or see equal parts.

Fraction models are a key component of Bridges in Mathematics, second edition. Online preview available. Please note that the videos below include graphics and number overlays that are not part of the Fractions app.

### Math and Special Education Blog

Google Tag Manager. Fractions for iPad, Web, and Chrome. Prev Next. Available online or for download. Open Web App. Apple App Store. Chrome Store. App Features Use a bar or circle as the whole. Divide each whole into anywhere from 1 to equal parts. Compare fractions and represent equivalent fractions.

Add, subtract, multiply, and divide with fractions. Explore the relationship between fractions, percents, and decimals. Select the size of the whole and the number of equal parts. Hide and reveal fraction labels.

Use the drawing tools to annotate work and show understanding. Write equations and expressions with the math text tool.Create an unlimited supply of worksheets for equivalent fractions grades !

The worksheets can be made in html or PDF format — both are easy to print. You can also customize them using the generator below. Visual models are essential in helping children to grasp this idea, and the worksheets below provide just that!

Then, in 5th grade, students learn how to add unlike fractions. This procedure involves converting the fractions to equivalent fractions with a common denominator.

So, the concept of equivalent fractions is an important prerequisite to fraction addition and subtraction. Each worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file.

You can generate the worksheets either in html or PDF format — both are easy to print. To get the worksheet in html format, push the button " View in browser " or " Make html worksheet ". Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:. The following worksheets are similar to the ones above, but using larger numbers in the denominators and numerators.

With this worksheet generator, you can make worksheets for equivalent fractions. The worksheet can include problems with visual models pie images or not. There are five problem types to choose from:. You can choose to include or not include mixed numbers and improper fractions. You can control the minimum and maximum values for the numerator and the denominator. However, for the problems with visual models, the maximum denominator is limited to This workbook has been compiled and tested by a team of math experts to increase your child's confidence, enjoyment, and success at school.Join Newsletter News.

Welcome to the fractions worksheets page at Math-Drills.

This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets. This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions.

We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect.

Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack. The other fractions worksheets on this page are devoted to helping students understand the concept of fractions.

From comparing and ordering to simplifying and converting Most Popular Fractions Worksheets this Week. The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy.

Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal.

Re-use both sheets by erasing the pencil and washing off the marker. Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions.

You can also copy the fractions strips onto overhead projection slides and cut them out.