This short video and interactive assessment activity is designed to teach fifth graders about dividing by 9.

This short video and interactive assessment activity is designed to teach third graders about dividing by 9.

Unit 4: Dividing Fractions
Lesson 10: Dividing by Unit and Non-Unit Fractions

This is the first of two lessons in which students pull together the threads of reasoning from the previous six lessons to develop a general algorithm for dividing fractions. Students start by recalling the idea from grade 5 that dividing by a unit fraction has the same outcome as multiplying by the reciprocal of that unit fraction. They use tape diagrams to verify this.

Next, they use the same diagrams to look at the effects of dividing by non-unit fractions. Through repetition, they notice a pattern in the steps of their reasoning (MP8) and structure in the visual representation of these steps (MP7). Students see that division by a non-unit fraction can be thought of as having two steps: dividing by the unit fraction, and then dividing the result by the numerator of the fraction. In other words, to divide by 2/5 is equivalent to dividing by 1/5, and then again by 2. Because dividing by a unit fraction 1/5 is equivalent to multiplying by 5, we can evaluate division by 2/5 by multiplying by 5 and dividing by 2.

This short video and interactive assessment activity is designed to teach fourth graders about number patterns based on the multiplication table.

This short video and interactive assessment activity is designed to teach third graders about division terms.

This short video and interactive assessment activity is designed to teach third graders about dividing by 1 digit numbers to find work.

This short video and interactive assessment activity is designed to teach fourth graders about dividing to find the time.

This short video and interactive assessment activity is designed to teach third graders about relating multiplication and division with illustrations.

This short video and interactive assessment activity is designed to teach fourth graders about completing the number patterns based on the multiplication table.

This video explains how to determine a dividend given a division equation with a remainder.

This short video and interactive assessment activity is designed to teach fourth graders about finding the adjusted rate - word problems.

This short video and interactive assessment activity is designed to teach third graders about finding the expression not matching a given number.

This short video and interactive assessment activity is designed to teach fourth graders about finding the expression not matching a given number.

This short video and interactive assessment activity is designed to teach fourth graders about finding the incorrect equations.

This short video and interactive assessment activity is designed to teach fourth graders about finding the number from figure patterns.

This short video and interactive assessment activity is designed to teach fifth graders about finding the total using division - word problems.

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.

Unit 4: Dividing Fractions
Lesson 14: Fractional Lengths in Triangles and Prisms

In this transitional lesson, students conclude their work with area and begin to explore volume of rectangular prisms. First, they extend their work on area to include triangles, using division to find the length of a base or a height in a triangle when the area is known. Second, they undertake a key activity for extending their understanding of how to find the volume of a prism.

In previous grades, students learned that the volume of a prism with whole-number edge lengths is the product of the edge lengths. Now they consider the volume of a prism with dimensions 1 1/2 inch by 2 inches by 2 1/2 inches. They picture it as being packed with cubes whose edge length is 1/2 inch, making it a prism that is 3 cubes by 4 cubes by 5 cubes, for a total of 60 cubes, because 3 x 4 x 5 = 60. At the same time, they see that each of these 1/2-inch cubes has a volume of 1/8 cubic inches, because we can fit 8 of them into a unit cube. They conclude that the volume of the prism is 60 x 1/8 = 7 1/2 cubic inches.

In the next lesson, by repeating this reasoning and generalizing (MP8), students see that the volume of a rectangular prism with fractional edge lengths can also be found by multiplying its edge lengths directly (e.g., (1 1/2) x 2 x (2 1/2) = 7 1/2).

The first of these word problems is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems.