| Code |
Description |
| MA.7.GR.1.1: | Apply formulas to find the areas of trapezoids, parallelograms and rhombi.Clarifications:
Clarification 1: Instruction focuses on the connection from the areas of trapezoids, parallelograms and rhombi to the areas of rectangles or triangles.
Clarification 2: Within this benchmark, the expectation is not to memorize area formulas for trapezoids, parallelograms and rhombi.
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| MA.7.GR.1.2: | Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.Clarifications:
Clarification 1: Within this benchmark, the expectation is not to find areas of figures on the coordinate plane or to find missing dimensions. |
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| MA.7.GR.1.3: | Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.Clarifications:
Clarification 1: Instruction includes the exploration and analysis of circular objects to examine the proportional relationship between circumference and diameter and arrive at an approximation of pi (π) as the constant of proportionality.
Clarification 2: Solutions may be represented in terms of pi (π) or approximately.
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| MA.7.GR.1.4: | Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.Clarifications:
Clarification 1: Instruction focuses on the connection between formulas for the area of a rectangle and the area of a circle.
Clarification 2: Problem types include finding areas of fractional parts of a circle.
Clarification 3: Solutions may be represented in terms of pi (π) or approximately.
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| MA.7.GR.1.5: | Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.Clarifications:
Clarification 1: Instruction focuses on seeing the scale factor as a constant of proportionality between corresponding lengths in the scale drawing and the original object.
Clarification 2: Instruction includes the understanding that if the scaling factor is k, then the constant of proportionality between corresponding areas is k² .
Clarification 3: Problem types include finding the scale factor given a set of dimensions as well as finding dimensions when given a scale factor.
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This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| The Meaning of Pi: | Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi. |
| Eye on Circumference: | Students are asked to solve a problem involving the circumference of a circle. |
| Circumference Formula: | Students are asked to write the formula for the circumference of a circle, explain what each symbol represents, and label the variables on a diagram. |
| Circle Area Formula: | Students are asked to write the formula for the area of a circle, explain what each symbol represents, and label the radius on a diagram. |
| Center Circle Area: | Students are asked to solve a problem involving the area of a circle. |
| Broken Circles: | Students are asked to complete and explain an informal derivation of the relationship between the circumference and area of a circle. |
| Space Station Scale: | Students are asked to find the ratio of the area of an object in a scale drawing to its actual area and then relate this ratio to the scale factor in the drawing. |
| Flying Scale: | Students are asked to find the length and area of an object when given a scale drawing of the object. |
| Octagon Area: | Students are asked to find the area of a composite figure. |
| Composite Polygon Area: | Students are asked to find the area of a composite figure. |
| Name |
Description |
| Clean It Up: | Students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment and the community. They will apply their knowledge of how litter can impact ecosystems along with some math skills to make recommendations for cleanup zones to prioritize. Students will explore the responsibilities of citizens to maintain a clean environment and the impact that litter can have on society in this integrated Model Eliciting Activity.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom. |
| Guiding Grids: Math inspired self-portraits: | Students will create a proportional self portrait from a photo using a gridded drawing method and learn how a grid system can help accurately enlarge an image in a work of art. Students will use the mathematical concepts of scale, proportion and ratio, to complete their artwork. |
| Breaking Up is Hard to Do: | Student will use geoboards to decompose composite figures and polygons into squares, rectangles, and triangles in order to find the total area. |
| Fish Kribs: | In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawings and proportions to design the perfect fish tank.
- First, students have to complete a ranking activity of items that will be included in their scale drawing along with three types of fish.
- Next, students will conduct a pH lab activity to gain knowledge about how pH levels will affect population and the ecosystem within the tank.
- Finally, students will adjust their item selection and re-engineer their tank drawing to support their findings and additional information provided by the client. Students must determine what objects would be beneficial to the living things that the students chose in relation to available space and pH balance.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom. |
| How Fast Can One Travel on a Bicycle?: | Students investigate how the pedal and rear wheel gears affect the speed of a bicycle. A GeoGebra sketch is included that allows a simulation of the turning of the pedal and the rear wheel. A key goal is to provide an experience for the students to apply and integrate the key concepts in seventh-grade mathematics in a familiar context. |
| Discovering Dilations: | This resource is designed to allow students to discover the effects of dilations on geometric objects using the free online tools in GeoGebra. |
| Circumference/Rotation Relationship in LEGO/NXT Robots or Do I Wheely need to learn this?: | 7th grade math/science lesson plan that focuses on the concept of circumference and rotation relationship. Culminates in a problem-solving exercise where students apply their knowledge to the "rotations" field in programming a LEGO/NXT robot to traverse a set distance. |
| Building Graduation Caps: | Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity. |
| My Favorite Slice: | The lesson introduces students to sectors of circles and illustrates ways to calculate their areas. The lesson uses pizzas to incorporate a real-world application for the of area of a sector. Students should already know the parts of a circle, how to find the circumference and area of a circle, how to find an arc length, and be familiar with ratios and percentages. |
| Finding Area with Hands-On Measurement: | This lesson allows students to apply the area of triangles, quadrilaterals, and trapezoids to composite figures, and gives students a chance to work with classmates to find the area by taking measurements and making the necessary calculations. Students will also see the relationship between the area formulas for rectangles, triangles, trapezoids, and polygons. |
| How Many Degrees?: | This lesson facilitates the discovery of a formula for the sum of the interior angles of a regular polygon. Students will draw all the diagonals from one vertex of various polygons to find how many triangles are formed. They will use this and their prior knowledge of triangles to figure out the sum of the interior angles. This will lead to the development of a formula for finding the sum of interior angles and the measure of one interior angle. |
| Raising Your Garden MEA: | Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. |
| How does scale factor affect the areas and perimeters of similar figures?: | In this lesson plan, students will observe and record the linear dimensions of similar figures, and then discover how the values of area and perimeter are related to the ratio of the linear dimensions of the figures. |
| Name |
Description |
| Running around a track II: | The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race. |
| Running around a track I: | In this problem, geometry is applied to a 400 meter track to find the perimeter of the track. |
| Paper Clip: | In this task, a typographic grid system serves as the background for a standard paper clip. A metric measurement scale is drawn across the bottom of the grid and the paper clip extends in both directions slightly beyond the grid. Students are given the approximate length of the paper clip and determine the number of like paper clips made from a given length of wire. |
| Eight Circles: | Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area. |
| Floor Plan: | The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given. |
| Surface Area and Volume: | In this activity, students adjust the dimensions of either a rectangular or triangular prism and the surface area and volume are calculated for those dimensions. Students can also switch into compute mode where they are given a prism with certain dimensions and they must compute the surface area and volume. The application keeps score so students can track their progress. This application allows students to explore the surface area and volume of rectangular and triangular prisms and how changing dimensions affect these measurements. This activity also includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Running around a track II: | The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race. |
| Running around a track I: | In this problem, geometry is applied to a 400 meter track to find the perimeter of the track. |
| Paper Clip: | In this task, a typographic grid system serves as the background for a standard paper clip. A metric measurement scale is drawn across the bottom of the grid and the paper clip extends in both directions slightly beyond the grid. Students are given the approximate length of the paper clip and determine the number of like paper clips made from a given length of wire. |
| Eight Circles: | Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area. |
| Floor Plan: | The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Running around a track II: | The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race. |
| Running around a track I: | In this problem, geometry is applied to a 400 meter track to find the perimeter of the track. |
| Paper Clip: | In this task, a typographic grid system serves as the background for a standard paper clip. A metric measurement scale is drawn across the bottom of the grid and the paper clip extends in both directions slightly beyond the grid. Students are given the approximate length of the paper clip and determine the number of like paper clips made from a given length of wire. |
| Eight Circles: | Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area. |
| Floor Plan: | The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given. |
