Unit: Area and Surface Area
Lesson 14: Nets and Surface Area

Previously, students learned about polyhedra, analyzed and defined their features, and investigated their physical representations. Students also identified the polygons that compose a polyhedron; they recognized a net as an arrangement of these polygons and as a two-dimensional representation of a three-dimensional figure.

This lesson extends students' understanding of polyhedra and their nets. They practice visualizing the polyhedra that could be assembled from given nets and use nets to find the surface area of polyhedra.

This Nrich problem is an appealing way for children to recognize, interpret, describe and extend number sequences. Developing their own patterns, as in the later part of the activity, provides an opportunity for them to justify their own thinking, and evaluate others' patterns.

Students will complete the missing part of the number bond using addition or subtraction.

An interactive applet and associated web page that introduce the concept of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As it is being dragged a base and altitude are shown continuously changing. Demonstrates that the altitude may require the base to be extended. The text on the page lists the properties of a triangle and lists the various triangle types, with links to a definition of each. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

This Nrich problem is based on the story of the three bears which is a good context in which to talk about ratio and proportion. In this case, it leads on to calculating with fractions.

Isatou Ceesay observed a growing problem in her community where people increasingly disposed of unwanted plastic bags, which accumulated into ugly heaps of trash. She found a way to be the agent of change by recycling the bags and transforming her community. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Use plastic bags to develop a new product (i.e. jump rope).

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

Students will be able to determine the value of the underlined number in each number.

Math Playground provides grade-level appropriate activities for math Operations and Algebraic Thinking with a variety of activities to engage students and strengthen their skills.

This Nrich question tackles proportion in a real context. It also needs systematic thinking to sort out the information and take a step-by-step route to the solution.

Unit 7: Rational Numbers
Lesson 4: Ordering Rational Numbers

This lesson solidifies what students have learned in the past several lessons about the ordering of rational numbers on the number line. Students practice ordering rational numbers and use precise language to describe the relationships between numbers plotted on a number line (MP6). These phrases include “greater than,” “less than,” “negative,” and “opposite.”

Unit 3: Unit Rates and Percentages
Lesson 17: Painting a Room

In this culminating lesson, students make material and cost estimates for a home improvement project, applying and integrating many concepts and skills from the past three units.

Students determine the area of the walls of a bedroom, estimate the amount of paint needed to paint them, and determine the cost associated with the project (MP4). Along the way, they reason about areas of two-dimensional figures, convert units of measurements, solve ratio and rate problems, and work with percentages. Though there is a single correct measure for the total area of the walls to be painted, the amount of paint needed will depend on some assumptions and decisions students make about the work involved. The problem requires students to make some decisions about how to approach the task and which tools to use (MP5).

Depending on instructional choices made, this lesson could take one or more class meetings. The time estimates for the two main activities are intentionally left blank because the time will vary based on instructional decisions made. Variables affecting the amount of time needed include how much guidance and autonomy students are given, how elaborate the presentation of their work is expected to be, and how much time is taken for sharing solutions at the end.

With encouragement and ideas from his family, Papa, based on the real-life inventor Lodner Phillips, builds a working submarine that takes his family on a ride to the bottom of Lake Michigan. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Students will use materials on hand to design a solution to a problem they see in their school or at home. The invention should meet the needs of fellow students, teachers, bus drivers, principals, siblings, friends, or even parents.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

This Nrich activity offers free exploration that can help youngsters with their development of the concepts associated with fractions. It provides a chance for meaningful mathematical discussion and sharing of current understanding, in addition to offering opportunities for challenging misconceptions.

Unit 2: Introducing Ratios
Lesson 15: Part-Part-Whole Ratios

Up to this point, students have worked with ratios of quantities where the units are the same (e.g., cups to cups) and ratios of quantities where the units are different (e.g., miles to hours). Sometimes in the first case, the sum of the quantities makes sense in the context, and we can ask questions about the total amount as well as the component parts. For example, when mixing 3 cups of yellow paint with 2 cups of blue paint, we get a total of 5 cups of green paint. (Notice that this does not always work; 3 cups of water mixed with 2 cups of dry oatmeal will not make 5 cups of soggy oatmeal.) In the paint scenario, the ratio of yellow paint to blue paint to green paint is . Furthermore, if we double the amount of both yellow and blue paint, we will double the amount of green paint. In general, if the ratio of yellow to blue paint is equivalent, the ratio of yellow to blue to green paint will also be the equivalent. We can see this is always true because of the distributive property:

a : b : (a+b) is equivalent to 2a : 2b : (2a+2b) because 2a + 2b = 2(a+b).

These ratios are sometimes called “part-part-whole” ratios.

In this lesson, students learn about tape diagrams as a handy tool to represent ratios with the same units and as a way to reason about individual quantities (the parts) and the total quantity (the whole). Here students also see ratios expressed not in terms of specific units (milliliters, cups, square feet, etc.) but in terms of "parts" (e.g., the recipe calls for 2 parts of glue to 1 part of water).

This Nrich problem is in three parts, with each part becoming more open-ended and requiring more reasoning, giving students a chance to develop their skills at solving problems with fractions and then applying those skills in a more challenging context. By listening to others' approaches, students will be encouraged to persevere and continue to improve on their solution to the final part of the problem.

Pearl Diver is a fun, interactive web-based game and app for iPad and iPhone. Players learn the number line while diving for pearls amidst shipwrecks and sunken ruins. This learning game addresses standard mathematic concepts included in the current Common Core curriculum such as:
-understanding numbers, ways of representing numbers, and number systems
-understanding and representing commonly used fractions
-understanding fractions as part of unit wholes and as locations on number lines
-comparing and ordering fractions, and finding their approximate locations on the number line
Pearl Diver is supported by supplementary materials including teacher’s guide, learner’s guide, “Teaching With Pearl Diver” video, and printable resources. It is available in English and Spanish. This game is available free on the Apple App Store.
This project was sponsored by NSF and developed by the Learning Games Lab in collaboration with researchers and mathematicians in the College of Education and College of Arts and Sciences at New Mexico State University.

Press Release Links:
http://newscenter.nmsu.edu/Articles/view/7833

Pearl Diver ACE award
http://newscenter.nmsu.edu/Articles/view/5230

Funding for Math Snacks (includes image of Pearl Diver)
http://newscenter.nmsu.edu/Articles/view/4828

Links to scholarly publications:

Trespalacios, J., & Chamberlin, B. (2012). Pearl Diver: Identifying numbers on a number line. Teaching Children’s Mathematics, 18, 446-447.

In this Nrich problem students apply their knowledge of area and percentages to extend their understanding.

Unit 3: Unit Rates and Percentages
Lesson 11: Percentages and Double Number Lines

In the previous lesson, students learned to find percentages of 100 and percentages of 1 in the context of money (100 cents and $1). In this lesson, they explore percentages of quantities other than 100 and 1 in a variety of contexts. All of the tasks use comparison contexts—describing one quantity relative to another quantity—rather than part-whole contexts.

Students continue to have double number lines as a reasoning tool to use if they want. In several cases the double number line is provided. There are two reasons for this. First, the equal intervals on the provided double number line are useful for reasoning about percentages. Second, using the same representation that was used earlier for other ratio and rate reasoning reinforces the idea of a percentage as a rate per 100 (MP7). It is perfectly acceptable, however, for students to use strategies other than double number lines for solving percentage problems.