Calculate the areas of scale drawings until a more efficient method emerges. Pupils find the relationship between the scale factor of a scale drawing and the scale of the areas. They determine the scale of the areas is the square of the...

The original drawing is eight units — how big is the scale drawing? Classmates determine the scale percent between a scale drawing and an object to calculate the length of a portion of the object. They use the percent equation to find...

Scale the challenge of learning about ratios and scales. Young mathematicians learn to incorporate fractional measurements when considering scales and scale factors. They use an interactive to investigate the concept and critically...

This is great go-to activity for those spring or fall days when the weather beckons your geometry class outside. Learners start with a small tree, devising strategies to accurately estimate the leaf count. They must then tackle the...

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

Review the principles of scaling areas and draws a comparison to scaling volumes with a third dimensional measurement. The exercises continue with what happens to the volume if the dimensions are not multiplied by the same...

Does it matter how many points to dilate? The resource presents problems of dilating curved figures. Class members find out that not only do they need to dilate several points but the points need to be distributed about the entire curve...

Launch a lesson that's sure to capture middle schoolers' interest! Exploration enthusiasts examine the planets of our solar system using an activity from PBS's Space series. The resource includes images and information for each planet,...

Help your class understand the magnitude of the distance between Earth and Mars with an activity that asks small groups to use balloons to create scale models of the Earth, Moon, and Mars. Class members figure out the distances...

The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure. 

How do you find the lengths of items that cannot be directly measured? The 13th installment in a series of 16 has pupils use the similarity content learned in an earlier resource to solve real-world problems. Class members determine...

Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to...

Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different...

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

The accuracy required by the design and measurement of an Olympic running track will surprise track stars and couch potatoes alike. Given a short introduction, the class then scaffolds into a detailed analysis of the exact nature of the...

Hedgerows prevent soil erosion, capture pollutants running off fields, store carbon to help combat climate change, and provide homes for predators of many pest species. The biodiversity lesson begins with an activity that...

Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...

In May of 1981, the Winter Park Sinkhole in Florida first appeared and is now referred to as Lake Rose. Scholars learn about the causes of sinkholes through an inquiry project. Then, they analyze recent data and draw conclusions to...

Many types of cancer treatments now depend on nanotechnology—a big "little" discovery. Scholars begin by removing "malignant" tissue from simulated brains, one using fluorescent markers thanks to nanotechnology and one without. This...

Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...

The coordinate plane is a popular place! Identify rotations, reflections, and dilations on the coordinate plane. Pupils work in small groups to match transformations of a figure with the description of the transformation....

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation. 

Your learners will write quadratic functions whose graphs include specific points and explore how these graphs are related to each other.