This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to a situation requiring decomposition of the volume into two pieces, to one where a height must be calculated using the Pythagorean theorem.

This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter.  The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations.  Next students explore geometry.  Students tessellate to bridge geometry experience with the study of perimeter.  Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements.  Students solve word problems involving area and perimeter using all four operations.  The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division.

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

This google slide show is to be used as a routine in grade 4 during the third quarter. Students will be given time to notice and wonder about each slide, with their thinking guided toward geometry. Discussions will promote precise geometry vocabulary and connections between images.

This google slide show is to be used as a routine in grade 4 during the third quarter. Students will be given time to notice and wonder about each slide, with their thinking guided toward geometry and fractional reasoning. Students will then be asked to find the value of pieces, given the value of one specific piece in the image.

Explore the world of lines. Investigate the relationships between linear equations, slope, and graphs of lines. Challenge yourself in the line game!

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

In this activity, learners use their hands as tools for indirect measurement. Learners explore how to use ratios to calculate the approximate height of something that can't be measured directly by first measuring something that can be directly measured. This activity can also be used to explain how scientists use indirect measurement to determine distances between things in the universe that are too far away, too large or too small to measure directly (i.e. diameter of the moon or number of bacteria in a volume of liquid).

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

After playing a video clip of the Scarecrow from the Wizard of Oz, just after he was 'given brains' and he mentions how the Pythagorean Theorem works have students look for precision in his statement.  This site helps you challenge students to be critical mathematicians and make the Scarecrow's statement more precise.  A link to the video clip is embedded on the page.

The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.

This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.

As written, this problem gives students all of the information they need to estimate the thickness of a soda can.

his is a version of ''How thick is a soda can I'' which allows students to work independently and think about how they can determine how thick a soda can is. The teacher should explain clearly that the goal of this task is to come up with an ''indirect'' means of assessing how thick the can is, that is directly measuring its thickness is not allowed.

This rich task is an excellent example of geometric concepts in a modeling situation and is accessible to all students. In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.

This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to: use facts about the angle sum and exterior angles of triangles to calculate missing angles; apply angle theorems to parallel lines cut by a transversal; interpret geometrical diagrams using mathematical properties to identify similarity of triangles.

This Cumulative Assessment is used in conjunction with the Illustrative Mathematics Curriculum and the Unit 1-3 Cumulative Assessment Rubric. It is broken down identifying the Essential Standard associated. This assessment should be utilized with the uploaded rubric to track progress towards proficiency on each of the grade level standards.

This Check Your Readiness Assessment is used in conjunction with the Illustrative Mathematics Curriculum. It breaks down identifying the Essential Standard associated. This assessment should be utilized with the uploaded rubric to determine levels of prerequisite skills when beginning a new unit and allow for placement of interventions.

This Check Your Readiness Rubric is used in conjunction with the Illustrative Mathematics Curriculum. It breaks down each question by identifying the Essential Standard associated and then defining what an Advanced, Proficient, Basic or Below Basic student response would entail. This rubric can then be utilized to determine levels of prerequisite skills when beginning a new unit and allow for placement of interventions.