ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] (6) 3 :

3. Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

[MA2019] REG-7 (7) 2 :

2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate.

[MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 2 :

2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate. [Grade 7, 2]

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

In this video, students visit a small-town festival that features the world’s largest stainless steel skillet. In addition to a question about scaling recipes, they also are asked how increasing or decreasing the radius of a circle affects its area. The accompanying classroom activity requires students to compare the areas of the world’s largest skillet and a standard 12-inch skillet through reasoning and computation and to explore the meaning of pi through a hands-on activity. This resource is part of the Math at the Core: Middle School Collection.

Although the Scaling Up Recipes and Circles in Practice video ("Greetings from the World’s Chicken Festival") and the Scaling Up Recipes and Circles in the Real World interactive ("Sunnyside Up") can be used independently, they are deliberately designed to complement each other.

The video takes students to a small-town fall festival that features the world’s largest stainless steel skillet as well as food preparations for a crowd of 8,000 people. They are asked how they can use proportional reasoning to scale recipes and how increasing or decreasing the radius of a circle affects its area.

The interactive explores the questions asked in the video as students scale up recipes and food portions to feed a family reunion of 108 people and as they discover the mathematical relationship between the length of a circle’s radius and its area. To enhance classroom use, refer to the Interactive Guide handout and Questions worksheet that students can reference and complete as they work through the interactive.

Be sure to use the Scaling Up Recipes and Circles in the Real World Activity that can be found in the Support Materials for Teachers section for a great activity that teaches the standard(s).

   View Standards     Standard(s): [MA2015] (7) 14 :

14 ) Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7-G4]

[MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

Using circumference, this video measures the total distance traveled by two carousel riders after the carousel has rotated 10 times. Regents Review materials are designed to help high school students prepare for New York State's Regents exams.

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

The distance around a circle is called the circumference. You can find the circumference of any circle by using the formula C = 2πr. Watch the video to learn about the formula for circumference.

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

Help students learn how to determine the diameter and circumference of a circle using the media resources and bubble activity.

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

In this video you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel. Regents Review materials are designed to help high school students prepare for New York State's Regents exams.

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] REG-7 (7) 22 :

22. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

[MA2019] ACC-7 (7) 39 :

39. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. [Grade 7, 22]

[MA2019] ACC-7 (7) 41 :

41. Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems. [Grade 8, 30]

[MA2019] REG-8 (8) 30 :

30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

Uncover the secret behind how a square-wheeled tricycle can work at the National Museum of Mathematics. This interactive exercise focuses on working with the radius of various circles to find the circumference and area as well as challenging you to find the distance a square wheel travels around the track.

This resource is part of the Math at the Core: Middle School collection.

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

20. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.

[MA2019] ACC-7 (7) 36 :

36. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

In this interactive activity, students will be led through steps to calculate the circumference of a circle. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.