The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and to use this understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

This task gives students word problems with a given a set of a specified size and a specified number of subsets. The questions ask the student to find out the size of each of the subsets.

In these lessons students will explore the paintings of Horace Pippin and Wayne Thiebaud and the mobiles of Alexander Calder to discover and practice math and visual art concepts. Background and biographical information about the work of art and artist, guided looking with class discussion, and activities with worksheets using mathematical formulas and studio art provide the framework for each lesson.

This brief article discusses the Count the Beat project, which incorporates music into math instruction. The instructors in this project began each lesson with a brief math exercise followed by a more in-depth music task utilizing number lines, fractions, ratios, and/or probability. While music professionals carried out this project the article does offer some suggestions for application in the math classroom without music professional.

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool.

This task requires students to think of dimes and pennies as fractions of dollars.

This problem provides students practice in fractions (tenths) and challenges students' addition and subtraction skills. Students are given a cake with the numbers zero to nine on it. They are asked to cut the cake into three pieces with three cuts so that the numbers on each piece add to the same total. The Teachers' Notes page offers rationale, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of the problem.

This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.

This three-act math task utilizes videos and questioning to help students explore multiplying a whole number by a fraction.

This problem requires students to have a good understanding of fractions and challenges children to visualize 3D shapes. Students are asked how to divide a doughnut into eight equal pieces using only three cuts. The Teachers' Notes page includes rationale, suggestions for implementation, discussion questions, and ideas for extension with a link to a worksheet and support.

This problem involves fraction multiplication that can be solved with pictures or number lines.

This three-act math task utilizes videos and questioning to help students explore multiplying a whole number by a fraction.

This article describes the progression from halves, to thirds and fourths, as well as fair sharing as a means of teaching more abstract fractions to young students. Throughout the article activities are suggested to support the learning, as well as a link to a six-minute video which shows two children working on a difficult sharing situation practically with a teacher who questions appropriately to get the thinking going. Two of the activities mentioned in the article, "Happy Halving" and "Bowl of Fruit" are cataloged separately.

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. Because the Egyptians represented fractions differently than we do, it can also help students understand that there can be many ways of representing the same number.

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.

Exploring Antarctica: Standard 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).