The math learning center is an app and online platform that allows students to use manipulatives virtually. In this activity, students will show equivalent fractions using lines and shapes.

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.

This article is for elementary teachers putting together fraction units. There is a discussion of activities and misconceptions.

In this Nrich problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces.

This Nrich problem starts with a simple situation which can be analyzed quickly using mental methods, but which provides a starting point for tackling a more challenging problem. The challenge can be tackled at many different levels, using trial and improvement (perhaps using spreadsheets), looking for number patterns, or with a more formal algebraic approach.

Ordering fractions can seem like quite a mundane and routine task. This Nrich problem encourages students to take a fresh look at the process of comparing fractions, and offers lots of opportunities to practice manipulating fractions in an engaging context where students can pose questions and make conjectures.

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

This task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator.

This task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator.

This short video and interactive assessment activity is designed to teach fifth graders about finding the least common denominator.

This short video and interactive assessment activity is designed to teach fifth graders about finding the reciprocal of fractions.

Unit 4: Dividing Fractions
Lesson 17: Fitting Boxes into Boxes

In this three-part culminating activity, students use what they have learned to determine the most economical way to ship jewelry boxes using the United States Postal Service (USPS) flat-rate options.

In Part 1, students make sense of the task, outline what they will need to know and do to answer the question, and map out their plan. In Part 2, they model the problem, calculate the number of jewelry boxes that will fit into each shipping box, and determine the associated costs. Students experiment with different orientations for the jewelry boxes to optimize space and minimize cost. In Part 3, they present, reflect, and discuss. Students explain their strategies and reasoning (MP3) and evaluate the decisions about how to fit all 270 jewelry boxes so they ship at the lowest cost (MP4). As a class, students reflect on how the orientation of the jewelry boxes and the size of the shipping boxes affected the unit cost for shipping each box of jewelry.

Depending on the instructional choices made, this lesson could take one or more class meetings. The time estimates are intentionally left blank because the amount of time needed might vary depending on factors such as:

If students will research the flat-rate options themselves, or be provided with this information.
If each group will explore all size options or only one option.
How much organizational support is given to students.
How student work is ultimately shared with the class (e.g., not at all, informally, or with formal presentations).
Consider defining the scope of work further and setting a time limit for each part of the activity to focus students’ work and optimize class time.

The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. Perhaps more importantly, the task also purposefully relates length and locations of points on a number line, a common trouble spot for students. This task is meant for instruction and would be a useful as part of an introductory unit on fraction multiplication.

In this unit, students build on fraction concepts from previous grades to understand fractions as division. They also use visual models to make estimates, add and subtract fractions and mixed numbers, and check the reasonableness of their answers. Finally, students explore strategies for solving fraction-of problems.

This Roadmap uses instructional videos, games, simulations and guiding questions to teach about fraction equivalents.

This Nrich problem is useful for those pupils who are coming to terms with spatial representation of fractions where area is concerned rather than just length. Pupils' visualizations vary a great deal and this may prove very difficult for some and yet readily accessible to others.