This is a task from the Illustrative Mathematics website that is one …

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A penny is about $\frac{1}{16}$ of an inch thick. In 2011 there were approximately 5 billion pennies minted. If all of these pennies were placed in a s...

In this culminating lesson on multiplication, students continue to use the structure of …

In this culminating lesson on multiplication, students continue to use the structure of base-ten numbers to make sense of calculations (MP7) and consolidate their understanding of the themes from the previous lessons. They see that multiplication of decimals can be accomplished by:thinking of the decimals as products of whole numbers and fractions;writing the non-zero digits of the factors as whole numbers, multiplying them, and moving the decimal point in the product; representing the multiplication with an area diagram and finding partial products; andusing a multiplication algorithm, the steps of which can be explained with the reasonings above.

This lesson serves two purposes. The first is to show that we …

This lesson serves two purposes. The first is to show that we can divide a decimal by a whole number the same way we divide two whole numbers. Students first represent a decimal dividend with base-ten diagrams. They see that, just like the units representing powers of 10, those for powers of 0.1 can also be divided into groups. They then divide using another method—partial quotients or long division—and notice that the principle of placing base-ten units into equal-size groups is likewise applicable.The second is to uncover the idea that the value of a quotient does not change if both the divisor and dividend are multiplied by the same factor. Students begin exploring this idea in problems where the factor is a multiple of 10 (e.g. 8÷1=80÷10). This work prepares students to divide two decimals in the next lesson.

In the previous lesson, students learned how to divide a decimal by …

In the previous lesson, students learned how to divide a decimal by a whole number. They also saw that multiplying both the dividend and the divisor by the same power of 10 does not change the quotient. In this lesson, students integrate these two understandings to find the quotient of two decimals. They see that to divide a number by a decimal, they can simply multiply both the dividend and divisor by a power of 10 so that both numbers are whole numbers. Doing so makes it simpler to use long division, or another method, to find the quotient. Students then practice using this principle to divide decimals in both abstract and contextual situations.

This is a task from the Illustrative Mathematics website that is one …

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Seth wants to buy a new skateboard that costs \$167. He has \$88 in the bank. If he earns \$7.25 an hour pulling weeds, how many hours will Seth have t...

Students are introduced to the differences between acids and bases and how …

Students are introduced to the differences between acids and bases and how to use indicators, such as pH paper and red cabbage juice, to distinguish between them.

Students construct rockets from balloons propelled along a guide string. They use …

Students construct rockets from balloons propelled along a guide string. They use this model to learn about Newton's three laws of motion, examining the effect of different forces on the motion of the rocket.

Commercial fishing nets often trap "unprofitable" animals in the process of catching …

Commercial fishing nets often trap "unprofitable" animals in the process of catching target species. In this activity, students experience the difficulty that fishermen experience while trying to isolate a target species when a variety of sea animals are found in the area of interest. Then the class discusses the large magnitude of this problem. Students practice data acquisition and analysis skills by collecting data and processing it to deduce trends on target species distribution. They conclude by discussing how bycatch impacts their lives and whether or not it is an important environmental issue that needs attention. As an extension, students use their creativity and innovative skills to design nets or other methods, theoretically and/or through hands-on prototyping, that fisherman could use to help avoid bycatch.

As an introduction to bioengineering, student teams are given the engineering challenge …

As an introduction to bioengineering, student teams are given the engineering challenge to design and build prototype artificial limbs using a simple syringe system and limited resources. As part of a NASA lunar mission scenario, they determine which substance, water (liquid) or air (gas), makes the appendages more efficient.

Through this earth science curricular unit, student teams are presented with the …

Through this earth science curricular unit, student teams are presented with the scenario that an asteroid will impact the Earth. In response, their challenge is to design the location and size of underground caverns to shelter the people from an uninhabitable Earth for one year. Driven by this adventure scenario, student teams 1) explore general and geological maps of their fictional state called Alabraska, 2) determine the area of their classroom to help determine the necessary cavern size, 3) learn about map scales, 4) test rocks, 5) identify important and not-so-important rock properties for underground caverns, and 6) choose a final location and size.

Students learn about material properties, and that engineers must consider many different …

Students learn about material properties, and that engineers must consider many different materials properties when designing. This activity focuses on strength-to-weight ratios and how sometimes the strongest material is not always the best material.

Students use the scientific method to determine the effect of control surfaces …

Students use the scientific method to determine the effect of control surfaces on a paper glider. They construct paper airplanes (model gliders) and test their performance to determine the base characteristics of the planes. Then they change one of the control surfaces and compare the results to their base glider in order to determine the cause and effect relationship of the control surfaces.

Human beings are fascinating and complex living organisms a symphony of different …

Human beings are fascinating and complex living organisms a symphony of different functional systems working in concert. Through a 10-lesson series with hands-on activities students are introduced to seven systems of the human body skeletal, muscular, circulatory, respiratory, digestive, sensory, and reproductive as well as genetics. At every stage, they are also introduced to engineers' creative, real-world involvement in caring for the human body.

To display the results from the previous activity, each student designs and …

To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.

In this math activity, students conduct a strength test using modeling clay, …

In this math activity, students conduct a strength test using modeling clay, creating their own stress vs. strain graphs, which they compare to typical steel and concrete graphs. They learn the difference between brittle and ductile materials and how understanding the strength of materials, especially steel and concrete, is important for engineers who design bridges and structures.

Through a five-lesson series that includes numerous hands-on activities, students are introduced …

Through a five-lesson series that includes numerous hands-on activities, students are introduced to the importance and pervasiveness of bridges for connecting people to resources, places and other people, with references to many historical and current-day examples. In learning about bridge types arch, beam, truss and suspension students explore the effect of tensile and compressive forces. Students investigate the calculations that go into designing bridges; they learn about loads and cross-sectional areas by designing and testing the strength of model piers. Geology and soils are explored as they discover the importance of foundations, bearing pressure and settlement considerations in the creation of dependable bridges and structures. Students learn about brittle and ductile material properties. Students also learn about the many cost factors that comprise the economic considerations of bridge building. Bridges are unique challenges that take advantage of the creative nature of engineering.

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