Acting as civil engineers hired by the U.S. Department of Transportation to research how to best use piezoelectric materials to detect road damage, student groups are challenged to independently create their own experiment procedures, working with given materials and tools. The general approach is that they set up model roads using rubber mats to simulate asphalt and piezoelectric transducers to simulate the in-ground road sensors. They drop heavy bolts at various locations on the “road,” collecting data and then analyzing the voltage changes across the piezoelectric transducers caused by the vibrations of the bolt hitting the rubber. After making notches in the rubber “road” to simulate cracks and potholes, they collect more data to see if the piezo elements detect the damage. Students write up their research and conclusions as if presenting evidence to USDOT officials about how the voltage changes across the piezo elements can be used to indicate road damage and extrapolated to determine when roads need maintenance service.

This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

Unit 8: Data Sets and Distributions
Lesson 15: Quartiles and Interquartile Range

Previously, students learned about decomposing a data set into two halves and using the halfway point, the median, as a measure of center of the distribution. In this lesson, they learn that they could further decompose a data set—into quarters—and use the quartiles to describe a distribution. They learn that the three quartiles—marking the 25th, 50th, and 75th percentiles—plus the maximum and minimum values of the data set make up a five-number summary.

Students also explore the range and interquartile range (IQR) of a distribution as two ways to measure its spread. Students reason abstractly and quantitatively (MP2) as they find and interpret the IQR as describing the distribution of the middle half of the data. This lesson prepares students to construct box plots in a future lesson.

This reading goes over steps to calculate rate of reactions. Calculating rate of reactions can seem a little bit confusing, but hopefully going over this reading you’ll be more confident.

Unit 8: Data Sets and Distributions
Lesson 3: Representing Data Graphically

In this lesson, students represent distributions of numerical (and optionally categorical) data after organizing them into frequency tables. They construct dot plots for numerical data (and bar graphs for categorical data). Using graphical representations of distributions, they continue to develop a spatial understanding of distributions in preparation for understanding the concepts of “center” and “spread” in future lessons. Students make use of the structure of dot plots (MP7) to describe distributions and draw conclusions about the data.

* This unit is an adaptation of the Everyday Mathematics (EM) Kindergarten Curriculum, 4th Edition, published by McGraw Hill Education.  The source material is copyrighted and all rights are reserved.  With this in mind, only the adaptations will be explored in this document.  To access the Everyday Mathematics curriculum and some online components, your school or district must purchase them from McGraw Hill.

The Everyday Mathematics curriculum does not teach concepts in the historical unit-by-unit format.  Rather, key concepts are introduced and revisited in several units throughout the year.  The focus on returning to concept strands is referred to as "spiralling."  The spiral strand targeted in this unit is focussed on data collection and representation.  Students will learn how to represent data on (and read data from) charts and graphs.

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.

Student teams are challenged to evaluate the design of several liquid soaps to answer the question, “Which soap is the best?” Through two simple teacher class demonstrations and the activity investigation, students learn about surface tension and how it is measured, the properties of surfactants (soaps), and how surfactants change the surface properties of liquids. As they evaluate the engineering design of real-world products (different liquid dish washing soap brands), students see the range of design constraints such as cost, reliability, effectiveness and environmental impact. By investigating the critical micelle concentration of various soaps, students determine which requires less volume to be an effective cleaning agent, factors related to both the cost and environmental impact of the surfactant. By investigating the minimum surface tension of the soap, students determine which dissolves dirt and oil most effectively and thus cleans with the least effort. Students evaluate these competing criteria and make their own determination as to which of five liquid soaps make the “best” soap, giving their own evidence and scientific reasoning. They make the connection between gathered data and the real-world experience in using these liquid soaps.

This short video and interactive assessment activity is designed to teach third graders about selecting capacity by comparison.

This short video and interactive assessment activity is designed to teach fifth graders about converting capacities using illustrations (english units).

The purpose of this task is for students to select 2 numbers from a set that sum to 5 (or any other number).

This short video and interactive assessment activity is designed to teach fifth graders about single-unit, multi-step problems - word problems.

In this activity students become familiar with the words, Ňtaller/shorterÓ as they refer to height.

In this activity students become familiar with the math vocabulary more/less/same and most/least as they count and compare small groups.

In this activity students become familiar with the math vocabulary more/less/same and most/least as they count and compare small groups.

This activity builds on Sort and Count I. It also helps students become familiar with the math vocabulary more/less/same and most/least as they sort, count, and compare small groups of objects.

This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

This short video and interactive assessment activity is designed to teach third graders an overview of area and perimeter.

Unit: Area and Surface Area
Lesson 17: Squares and Cubes

In this lesson, students learn about perfect squares and perfect cubes. They see that these names come from the areas of squares and the volumes of cubes with whole-number side lengths. Students find unknown side lengths of a square given the area or unknown edge lengths of a cube given the volume. To do this, they make use of the structure in expressions for area and volume (MP7).

Students also use exponents of 2 and 3 and see that in this geometric context, exponents help to efficiently express multiplication of the side lengths of squares and cubes. Students learn that expressions with exponents of 2 and 3 are called squares and cubes, and see the geometric motivation for this terminology. (The term “exponent” is deliberately not defined more generally at this time. Students will work with exponents in more depth in a later unit.)

In working with length, area, and volume throughout the lesson, students must attend to units. In order to write the formula for the volume of a cube, students look for and express regularity in repeated reasoning (MP8).

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.