This series of problems requires students to apply their knowledge of area and perimeter to find the optimal area given a specified amount of fencing. The problems progress in difficulty as new elements are added to the situation, therefore changing the outcome. This page includes tips for getting started, solution, teachers resource page, and a printable problem page.

This activity gives students the chance to explore area and perimeter in a problem solving setting. Nine differently-sized squares need to be tiled into a rectangular frame of unknown proportions. Three prompts of solving strategies are provided. Ideas for implementation, extension and support are included along with a printable sheet of the problem.

In this problem students study motion along a path and the properties of a parallelogram. Students must navigate back to a starting point after traveling three legs in cardinal directions on a compass. Ideas for implementation, extension and support are included.

The problem requires students to not only convert miles to kilometers and gallons to liters but they also have to deal with the added complication of finding the reciprocal at some point. In the USA we use distance per unit volume to measure fuel efficiency but in Europe we use volume per unit distance. Furthermore, the unit of distance is not simply 1 km but rather 100 km.

This site teaches High Schoolers Geometric Measurement and Dimension through a series of 82 questions and interactive activities aligned to 4 Common Core mathematics skills.

This three-act math task utilizes videos and questioning to help students explore estimating and computing decimals (measurement).

An article based on data and evidence that includes charts and information that can be analyzed statistically by students.

Hiking Utah: Standard Standard 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, estimating the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, approximately twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

This brief article describes some methods of indirect measurement that have been applied throughout history to the problem of estimating the height of tall trees. Several methods involving scaling, angles, ratios, and tools are discussed.

This brief article describes the development of money used for commerce from the ancient practice of bartering and commodity trading to the present day's use of coinage and bank notes. The origins of minting coins and the functions of banks are also discussed. Links to other sources on money history are included.

This brief article describes Samuel Morse and the code first used by telegraph operators in the 19th century. The time intervals used in transmissions are detailed, and there is a connection between the code and letter frequencies in the English alphabet. Included is a link to a printable page and a Morse Code font for Windows.

In this investigation, students visualize and compare volumes in solids composed of unit cubes and look for patterns in the measurements. They work systematically to organize and analyze the results. Ideas for implementation, extension and support are included.

The sizes and distances of things in space are awe-inspiring, but hard to fathom. Things that are unimaginably massive can look tiny to us from Earth, and things that appear very large to us may be among the smallest in the sky. Although students can learn names and features of objects in the night sky, scale is one of the biggest stumbling blocks they need to overcome to actually understand what they’re looking at and to understand astronomy in general. But students have lots of daily life experience with bigger things looking smaller because of relative distance (and visa versa). How Big & How Far takes this experience of observing relative sizes and distances here on Earth and challenges students to apply it to night sky objects.

In this Night Sky Activity, the group measures how many fists tall a volunteer is. Then, students scatter and measure again, this time with outstretched fists and with much smaller and varied measurements. Students discuss how the distance you are from an object can make it appear larger or smaller. This activity sets them up to apply this idea afterwards as they observe night sky objects and attempt to better understand the actual sizes of the objects they see.

This video lesson is part of a two-part series and introduces the concept of temperature. Temperature can be a challenging concept to convey since our perception is tied to words that are relative to our own experience, which varies quite a lot. A short activity to be performed in the classroom shows the need for a temperature scale since qualitative descriptions are not adequate. Temperatures that vary from the hottest to coldest recorded temperatures on earth are shown in advance of introducing the boiling temperatures of a number of cryogenic liquids.

An article based on data and evidence that includes charts and information that can be analyzed statistically by students.

This activity is used to help students become more aware of the size of common units of measurement in the metric system. Students first make predictions of what the metric measurement will be and compare that with the actual measurement.

This activity helps students develop a sense of the relative size of quantities in the categories of temperature, speed, time duration and loudness. Learners rank their estimates of given measures in order from least to greatest and justify their decisions. Students are encouraged to do research and carry out experiments when possible. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and links to related activities.

This problem provides students the opportunity to explore fractions in a practical context as well as identify and explain patterns and justify their ideas. Solvers are shown a sequence of five squares shaded light blue and dark blue and are asked to find what fraction of the total area of each square is covered by light blue. They are also asked to work out what the next two squares would look like if they followed the pattern. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

This activity gives students a chance to make estimates and comparisons of the measures of length (height) and capacity. It presents an image of a tiny elf next to a normal size mug. Students are asked to estimate the Little Man's height and compare it with that of other objects. Next, they are asked to estimate the height and volume of the Little Man's mug. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension and support.

This problem uses the context of a growing plant in which to practice doubling and also to develop representation and recording strategies. The Teachers' Notes page offers suggestions for implementation and discussion as well as ideas for extension and support.