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.

This 20-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them.

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

In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers.  This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models.  Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes.  Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.

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

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 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.

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.

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.

In this lesson designed to enhance literacy skills, students learn how to read and interpret a distance–time graph.

Students are introduced to graphing on the coordinate plane, in the first quadrant, using (x, y) coordinates.

Introducing engineering concepts with Hour of Engineering website is an engaging way to get students thinking about a STEM future. Hour of Engineering is designed to inform and inspire students in upper elementary through high school about engineering. Helping your students build an innovation mindset with the adaptive tools to solve problems starts here!

By participating in the Hour of Engineering students will: Define STEM vocabulary; Display engineering literacy; Explore the engineering design process; Experiment with practical engineering skills; Solve real-world engineering challenges; Link concepts between science, technology, engineering, and math; Build engineering habits of mind like creativity, systems thinking, and collaboration.

There are three parts to the Hour of Engineering website: landing page with inspirational content, learning modules, and engineering design challenges. (1) The landing page features clickable items to inspire students about the connection between engineering, art, science, math and even music! Students can freely explore the videos and models to learn about each object before moving on to deeper learning. (2) Learning modules allow students to explore a specific engineering topic. Students can explore learning modules on their own or you can pair them with connected engineering challenges to guide a sequence of learning on a topic. (3) Engineering challenges are a gamified way for students to explore various topics, activities and objects within fields of engineering. Students participating in engineering challenges earn stars based on their interaction with learning elements. There are knowledge checks and interactive models for students to explore during a challenge.

Kindergarteners are introduced to comparing objects by their attributes. In this lesson, the kids compare objects by using the three attributes they have learned about.

Before entering first grade, young children need to have a basic understanding of measurement. They do not need to be able to use standard units of measurement, but they must be able to use the basic attributes of length.

This task gives children an opportunity to subtract a three-digit number including a zero that requires regrouping. The solutions show how students can solve this problem before they have learned the traditional algorithm.

Kindergartners measure each other's height using large building blocks, then visit a 2nd and a 4th grade class to measure those students. They can also measure adults in the school community. Results are displayed in age-appropriate bar graphs (paper cut-outs of miniature building blocks glued on paper to form a bar graph) comparing the different age groups. The activities that comprise this lesson help students develop the concepts and vocabulary to describe, in a non-ambiguous way, how height changes as children get older. The introduction to graphing provides an important foundation for both creating and interpreting graphs in future years.

Students play a game in pairs to read and recognize numbers using a 100 chart.

This short video and interactive assessment activity is designed to teach fourth graders about comparing bills with pictures.

In this lesson, students will investigate and discuss the familiarity with factors and multiples to gain a deeper understanding. Downloadable printables are included.