Teaching students how to represent fractions on a number line can be tricky, especially when some fractions are represented on the same point.
The following scratch program helps students visualize this tricky concept – feel free to copy and modify the code if you find it useful.
We have a cupcake recipe for only 1 person, but more people are coming to a party. And…the cupcake recipe has fractions. Most people know how to add and multiply whole numbers like 3 x 3. But 1/3 + 1/3???
Your mission, if you chose to accept it: Modify the recipe below to be enough for 4 people, and show that you have the right answers using fraction strips. The party hosts need to know how much stuff to buy. And they don’t want yucky cupcakes!
This mission is important, so you need to train. I have made many cupcakes, and will be your guide. Here’s what you will do:
First, get to know your team. Ask each other about their favorite food, and if they have ever baked before. Also, ask each person what he or she knows about fractions. All this information will be useful later.
Second, learn how to use fractions strips (click the link below). These will come in handy if you have to prove that you’re right.
Third, click the button below for a handy-dandy worksheet to do a training run with your guide (that’s me). We will change the recipe to be for 2 people and use fraction strips. We will practice changing the recipe and proving we’re right.
Use the handy-dandy worksheet and the fraction strips to modify the recipe. Sometimes the number of people at the party changes. So be prepared to change the recipe amounts.
Work together in your teams. Make sure all team members agree with your answers.
Return to base when you have completed the mission for debriefing. Your guide will come along in case you have any questions.
Now for the hard part. The boss will want to make sure your recipe is correct. Use the fraction strips or any other tools you have to convince him that your cupcakes will not be yucky. Good luck!
Students who are not yet “fully operational” or able to reason using abstract concepts, can still learn form mathematical concepts with support. They typically need to develop these abstract representations of concepts in three stages, using: 1) concrete representations (like a geo-board) ; 2) semi-concrete representations (like a drawing); and 3) abstract representations (like a formula). While concrete “manipulatives,” like base-ten blocks, are widely used and effective in introducing concepts like place-value, evidence suggests that “virtual manipulatives” can be similarly effective.
Toytheater has an excellent selection of “virtual manipulatives” that students can use online, including a realistic version on fraction strips or fraction blocks. The image below will take you to their website (in a new tab) where you can explore their fraction strip app, along with other virtual manipulatives.
Comments and suggestions are always welcome. Thanks for visiting!
Fractions present students in early to middle elementary school with a big challenge. For the first time, they are faced with numbers that do not represent whole numbers, and do not follow the same operational rules as whole numbers. For that reason, in some countries – like Japan – operations with fractions are not taught until students reach fifth grade. In the U.S., the common core standards introduce fractions in third grade, but emphasize developing an understanding of fractions as numbers, and developing a strong intuitive understanding of whole number fractions before diving into addition, subtraction, multiplication, and division with mixed fractions.
The set of texts below are designed to support 2-3 lessons introducing third graders to fractions. The texts focus on connecting fractions to students’ everyday experiences, providing students with concrete experiences working with fractions, and using concrete and semi-concrete experiences to introduce the symbols used to represent fractions.
“Develop understanding of fractions as numbers for fractions with denominators 2, 3, 4, 6, and 8.” (p. 40)…“Understand a fraction 1 ∕b as the quantity formed by 1 part when a whole (a single unit) is partitioned into b equal parts; understand a fraction a ∕b as the quantity formed by a parts of size 1 ∕b”
Related MA Common Core Standards
Many states require students who are not proficient in English to learn all subjects – e.g. Math, Science, Art, and Social Studies – in English along with native speakers. For teachers, many of whom already struggle to differentiate lesson plans for students with different academic backgrounds, learning styles, and interests, the requirement to teach equivalent content to students at varying levels of English proficiency poses yet another challenge.
The texts below are designed to provide equivalent content instruction (along with content-specific academic language) to students at three levels of English proficiency – early intermediate (“WIDA 2-3”) intermediate (“WIDA 4-5”) and advanced to native speaking (“WIDA 6” and native speakers). The basic template is also designed to be further differentiated in terms of complexity – for example, by using more complex assessments or examples.
In any case, check out the texts below – hope you like them, and don’t hesitate to leave comments or suggestions! [note, links will open a new tab outside of this website]
