Module 6 lays the conceptual foundation for multiplication and division in Grade 3 and for the idea that numbers other than 1, 10, and 100 can serve as units.  Topics in this module include:  Formation of Equal Groups, Arrays and Equal Groups, Rectangular Arrays as a Foundation for Multiplication and Division, and The Meaning of Even and Odd Numbers.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This 25-day module builds directly on students’ work with multiplication and division in Module 1. Module 3 extends the study of factors from 2, 3, 4, 5, and 10 to include all units from 0 to 10, as well as multiples of 10 within 100. Similar to the organization of Module 1, the introduction of new factors in Module 3 spreads across topics. This allows students to build fluency with facts involving a particular unit before moving on. The factors are sequenced to facilitate systematic instruction with increasingly sophisticated strategies and patterns.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In this 43-day module, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This short video and interactive assessment activity is designed to teach fourth graders about greatest common factor.

This short video and interactive assessment activity is designed to teach third graders about grouping with illustrations - word problems.

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

This short video and interactive assessment activity is designed to teach fourth graders about finding the total number: given remainder and number needed.

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

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

This short video and interactive assessment activity is designed to teach fourth graders about using multiplication replacement to find a new amount.

This short video and interactive assessment activity is designed to teach fourth graders about multiple rounds of multiplication - multiplying 3 digits by 1 digit.

Unit 4: Dividing Fractions
Lesson 4: How Many Groups? (Part 1)

This lesson and the next one extend the “how many groups?” interpretation of division to situations where the “group” can be fractional. This builds on the work in earlier grades on dividing whole numbers by unit fractions.

Students use pattern blocks to answer questions about how many times a fraction goes into another number (e.g., how many 2/3s are in 2?), and to represent multiplication and division equations involving fractions. In this lesson, they focus on situations where the quotient (the number of groups) is a whole number.

This lesson is the first in a group of six lessons that trace out a gradual progression of learning—from reasoning with specific quantities, to using a symbolic formula for division of fractions (MP8).

Unit 4: Dividing Fractions
Lesson 5: How Many Groups? (Part 2)

In this lesson, students continue to work with division situations involving questions like “how many groups?” or “how many of this in that?” Unlike in the previous lesson, they encounter situations where the quotient is not a whole number, and they must attend to the whole when representing the answer as a fraction (MP6). They represent the situations with multiplication equations (e.g., “? groups of 1/2 make 8” can be expressed as ? x 1/2 = 8) and division equations (8 / 1/2 = ?).

Unit 4: Dividing Fractions
Lesson 8: How Much in Each Group? (Part 1)

Previously, students looked at division situations in which the number of groups (or the fraction of a group) was unknown. They interpreted division expressions as a way to find out that number (or fraction) of groups. In this lesson, students encounter situations where the number of groups is known but the size of each group is not. They interpret division expressions as a way to answer “how much in a group?” questions.

Students use the same tools—multiplication and division equations and tape diagrams—and the same structure of equal-sized groups to reason about “how much in a group?” questions (MP7). They also continue to relate their reasoning in quantitative contexts to their reasoning on abstract representations (MP2). Students find both whole-number and non-whole-number quotients, recognizing that, like the number of groups, the amount in one group can also be a whole number or a fraction.

Unit 4: Dividing Fractions
Lesson 9: How Much in Each Group? (Part 2)

This lesson allows students to practice finding the amount in one group, and to interpret, represent, and solve different kinds of division problems with less scaffolding. In one activity, students are not explicitly told whether the division situations involve finding the number of groups or finding the amount in each group. They decide on an interpretation that would enable them to solve a division problem. Students are also required to identify relevant information (from a video, a picture, or written statements) that would help them answer questions.

Because the tasks in this lesson are not scaffolded, students will need to make sense of the problems and persevere to solve them (MP1). As students move back and forth between the contexts and the abstract equations and diagrams that represent them, they reason abstractly and quantitatively (MP2).

This short video and interactive assessment activity is designed to teach fourth graders about selecting the quotient using given statements.

This short video and interactive assessment activity is designed to teach fifth graders about selecting the quotient with the correct number of digits.