*This numberless application problem is the same application problem used the engage lesson: Grade 4, Module 3, Lesson 2
*Numberless word problems are used to support students in solving word problems. They allow students to discover for themselves the structure of the problems they're solving. In doing so, they will be able to successfully find the operation or operations they need to use to determine the solution.
*Numberless word problems help students develop number sense, make sense of word problems, and encourage precise mathematical vocabulary.
*Based on the work of Brian Bushart.
*Created using ideas from WI Math Institute training. Google Slides presentation created as an adaption of WiseLearn resource by Sarah Martinsen and Kelly Shaefer.
*These slides could be inserted into the free Engage New York lesson google slides from embarc.online.

This math meets ecology lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives learners opportunities to estimate small oil spills of their own making. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This math meets ecology lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives learners opportunities to estimate small oil spills of their own making. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Which piece of paper has a greater area? This 3 Act Task by Graham Fletcher begins with a short portion of a video. A sheet of paper is cut apart leaving the center piece and an outer border piece. First students make observations and estimates to begin determining which piece of paper has a greater area. Students can then use images of the original paper and the middle cut piece of paper along with a measuring tool with square units to determine the area of the pieces. Students are estimating, measuring, multiplying, adding, and subtracting to determine the area of each piece of paper.

Students investigate the property dependence between liquid and solid interfaces and determine observable differences in how liquids react to different solid surfaces. They compare copper pennies and plastic "coins" as the two test surfaces. Using an eye dropper to deliver various fluids onto the surfaces, students determine the volume and mass of a liquid that can sit on the surface. They use rulers, scales, equations of volume and area, and other methods of approximation and observation, to make their own graphical interpretations of trends. They apply what they learned to design two super-surfaces (from provided surface treatment materials) that arecapable of holding the most liquid by volume and by mass. Cost of materials is a parameter in their design decisions.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

"Each student creates parallelograms from square sheets of paper and connects them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square" (from NCTM's Illuminations).

Students use their knowledge of scales and areas to determine the best locations in Alabraska for the underground caverns. They cut out rectangular paper pieces to represent caverns to scale with the maps and place the cut-outs on the maps to determine feasible locations.

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

This resource allows students to build conceptual relationships between two-dimensional shapes and three-dimensional figures by means of nets. Students cut different nets and identify and describe the corresponding figures. Students realize and understand why surface areas are measured in square units, and volume is measured in cubic units.

This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.

Students explore whether rooftop gardens are a viable option for combating the urban heat island effect. Can rooftop gardens reduce the temperature inside and outside houses? Teams each design and construct two model buildings using foam core board, one with a "green roof" and the other with a black tar paper roof. They measure and graph the ambient and inside building temperatures while under heat lamps and fans. Then students analyze the data and determine whether the rooftop gardens are beneficial to the inhabitants.

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.

Students learn how to determine map distances and areas using the map scale. They get a feel for how much an area represents on the map in relation to the size they are suggesting for their underground caverns to shelter the Alabraska population.

This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help teachers identify and assist students who have difficulties in: Computing perimeters, areas, and arc lengths of sectors using formulas and finding the relationships between arc lengths, and areas of sectors after scaling.

Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.

Students learn about contact stress and its applications in engineering. They are introduced to the concept of heavy loads, such as buildings, elephants, people and traffic, and learn how those heavy loads apply contact stress. Through the analysis of their own footprints, students determine their contact stress.

Students are introduced to the concepts of stress and strain with examples that illustrate the characteristics and importance of these forces in our everyday lives. They explore the factors that affect stress, why engineers need to know about it, and the ways engineers describe the strength of materials. In an associated literacy activity, while learning about the stages of group formation, group dynamics and team member roles, students discover how collective action can alleviate personal feelings of stress and tension.

In this lesson, students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems. Students also identify and describe the properties of two-dimensional figures. Students are challenged to set a table for 22 using one unit lengths of paper (each unit length represents one student sitting at the table). They are asked to pretend that they all want to sit together for a dinner, and the table has to be rectangular. They must figure out what the table will look like if it must be rectangular and if everybody must sit at the table. They must determine what's the biggest table going to look like where everybody sits, and what's the smallest table going to look like where everybody sits. Students work to conceptually figure out relationships between perimeter and area in a creative and interactive way. They brainstorm ideas in groups, discuss as a class to determine the best options, and then physically set the two tables using strips of paper that represent "one unit" in length per person.