# Interdisciplinary Connections Mathematics

How The Extraordinaires^{®} Aligns with Common Core Standards for Mathematics

Design thinking and mathematics go especially well together when a lesson takes full advantage of the power of play-based learning

Many of the Design Projects that come with The Extraordinaires^{®} Design Studio inherently encourage mathematical applications and thoughtful measurement considerations when solving a Design Challenge. Add to that some of the remarkable environments in which The Extraordinaires^{®} live, and strategically devising spatial solutions becomes very important. Consider some of these Design Projects:

- Somewhere to sit – How big or small is the client? Where must the seat be placed? How will it fit with other furnishings? Should it be mobile and streamlined?
- A remote control – Hand-sized, but for whose hand? What does it control? Should it be undetectable? Ergonomic?
- A place to learn – How will the learning content make demands on the structure? Should comfort be a factor? How many students should it be built for?
- Headwear – How big is the wearer’s head? Does the wearer a smooth head or are there protrusions? How will the purpose of the headwear affect its size or weight?
- A cargo vehicle – What is the size and weight of what the client wants to transport? How will the mode of transportation affect its design? Does that vehicle need a crew?

Using the Idea Pad with its special isometric design can make planning and drawing a student’s project not just easier, but, by following the 60° and 120° angles and unit cubes, students will be able to draw three-dimensionally with no prior experience. Their work will have an illusion of depth that will make them feel like accomplished designers!

These challenges along with the Idea Pad invite students to use multiple mathematics skills, particularly those learned and practiced from the fifth grade to seventh grade by drawing on the isometric Idea Pad, estimating scale, using proportions, and converting to real-world size. Activities with The Extraordinaires^{®} can meet the following Common Core Learning Standards for Mathematics:

### Fifth Grade

**5.MD.C.3.**Recognize volume as an attribute of solid figures and understand concepts of volume measurement.**5.MD.C.3.A.**A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.**5.MD.C.3.B.**A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.**5.MD.C.4.**Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

### Sixth Grade

**6.RP.A.1.**Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.**6.RP.A.2.**Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.**6.RP.A.3.**Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.**6.RP.A.3.D.**Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.**6.G.A.4.**Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

### Seventh Grade

**7.RP.A.1.**Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.**7.RP.A.2.**Recognize and represent proportional relationships between quantities.**7.RP.A.2.C.**Represent proportional relationships by equations.**7.RP.A.3.**Use proportional relationships to solve multistep ratio and percent problems.**7.G.A.1.**Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.**7.G.A.2.**Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.**7.G.A.3.**Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Design thinking and mathematics go especially well together when a lesson takes full advantage of the power of play-based learning. All of the above standards become natural lines of inquiry for students who will be eager to use math to support their ideas and justify their designs – all while having fun!