In this 20-day module, students build their competencies in measurement as they relate multiplication to the conversion of measurement units.  Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion.

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

In Module 1, students’ understanding of the patterns in the base ten system are extended from Grade 4’s work with place value of multi-digit whole numbers and decimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right. Toward the module’s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place.

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

In Module 2 students apply patterns of the base ten system  to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm.  Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms.  A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method.  In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses.  Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups.  An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation.

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

In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

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.

In this 25-day module, students work with two- and three-dimensional figures.  Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms.  The second half of the module turns to extending students’ understanding of two-dimensional figures.  Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths.  They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes.  This module fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volume and area.

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

In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems.  Students use the familiar number line as an introduction to the idea of a coordinate, and they construct two perpendicular number lines to create a coordinate system on the plane.  Students see that just as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates.  They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them.  This study culminates in an exploration of the coordinate plane in real world applications.

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

Module 2 explores two-dimensional and three-dimensional shapes.  Students learn about flat and solid shapes independently as well as how they are related to each other and to shapes in their environment.  Students begin to use position words when referring to and moving shapes.  Students learn to use their words to distinguish between examples and non-examples of flat and solid shapes.

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

After students observed, analyzed, and classified objects by shape into pre-determined categories in Module 2, they now compare and analyze length, weight, volume, and, finally, number in Module 3. The module supports students’ understanding of amounts and their developing number sense. The module culminates in a three-day exploration, one day devoted to each attribute: length, weight, and volume.

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

Module 4 marks the next exciting step in math for kindergartners, addition and subtraction! They begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers to reason about and solve addition and subtraction expressions and equations. In Topics A and B, decomposition and composition are taught simultaneously using the number bond model so that students begin to understand the relationship between parts and wholes before moving into formal work with addition and subtraction in the rest of the module.

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

Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.

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 greater or less than comparisons of length (english units).

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 forming largest and smallest numbers (even and odd).

This short video and interactive assessment activity is designed to teach fourth graders about forming the largest or smallest possible number.

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 second graders about understanding grouping with illustrations.

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.