Terumah- Scale Representation & Unit Conversion Acitivities

In Parshat Terumah, we are given blueprints for multiple sections of the Mishkan (the Holy Tabernacle that traveled with the Israelites in the desert). Together with Rashi and other commentaries, this parsha offers a wealth of information for understanding the specifics of how the Mishkan was put together. Below is a breakdown of the basic blueprint sections that are described in the parsha:

• blueprints for the Aron & its lid ~Shemot 25:10-22
• blueprints for the Shulchan (table) & information about the vessels that were stored in the Shulchan ~Shemot 25:23-30
• blueprints for the Menorah ~Shemot 25:31-40
• blueprints for the Tabernacle-spread ~Shemot 26:1-6
• blueprints for the Tent-spread (laid over the Tabernacle-spread) ~Shemot 26:7-13
• blueprints for the Tent-spread Cover (a roof covering) ~Shemot 26:14
• blueprints for the Beams & Bars of the Mishkan ~Shemot 26:15-30
• blueprints for the Parochet (a curtain/screen that enclosed the Aron as a separation) ~Shemot 26:31-33
• instructions regarding locations of each item in the Mishkan ~Shemot 26:34-35
• blueprints for the screen at the entrance of the Mishkan ~Shemot 26:36-37
• blueprints for the Mizbe'ach (altar) ~Shemot 27:1-8
• blueprints for the Courtyard area of the Mishkan ~Shemot 27:9-19

Each individual section listed above offers specific dimensions, information about materials that were used, and instructions about positioning of aspects or details pertaining to each section. With these basic blueprints, there is a plethora of activity options that can be developed. Below are a few suggestions specifically connected to the concepts of scale representation and unit conversion.

Activity Connections:

Activity ideas in increasing conceptual difficulty:

Activity suggestions can be used on a small scale for individual sections of the parsha or on a larger scale as a more extensive project recreating multiple or all sections of the Mishkan.

Younger students rely very heavily on visual learning. Even for older students, when learning about 3-Dimensional figures, it's always clearer for them if they can view or build a model for reference. 

Scale Representation:

• For younger students, providing them with a preset block size to represent the scale conversion will allow them to just focus on the construction aspect of the activity. For example, choosing a unifix cube or snap cube to be equivalent to 1 amah in each direction. Be careful in choosing a representative cube- students will need to measure length, width, and height. Keep in mind that in order to give a true representation the height of the cube will need to be the same measure as both the length and the width (ie, it must be a true cube in order to represent an amah in every direction). With a good number of the chosen block and the directions for the chosen Mishkan item to be built, students can work on building a scale model of the chosen section(s) of the Mishkan.
• Younger students will need a lot of guidance in this project. Some options are either working cooperatively in small groups with teacher guidance, or having a teacher run an activity station where students can each rotate in and work on a portion of the building activity. Students with more skill, can work individually or in groups with less teacher support to follow the blueprints and build the chosen model(s).
• (3-5) Elementary students who have familiarity with measuring using rulers and yardsticks can use other representative materials to build a model by setting a scale of, for example, 1 inch = 1 amah. Using this equivalency, students can measure out pieces of poster, cardboard, etc. to create pieces to fit together to build chosen items from the Mishkan. 
• (6-8+) As students develop their fine motor dexterity, they can draw scale representations of the items in the Mishkan, layout of the Mishkan, etc. 

Unit Conversions:

(See posts on Parshat Chayei Sarah and Parshat Shelach for understanding unit conversions.)

• Understanding different measurement systems within the parameters of familiar measurements gives students a better understanding and frame of reference for size of items. Older students can use the blueprints given and calculate what the measurements for different items would be if measured in US/Imperial or metric units. (for reference, 1 amah = between 18-24 inches)
• With blueprints converted into familiar measurements, students can model aspects of the items (height, length) for visual reference, or even build life-size models of sections of the Mishkan to give a full perspective of, for example, what the Shulchan looked like, or what the Aron looked like if you were standing next to it.

Chukat- Measuring Using Scale on a Map to Compare Distance

In this week's parsha, through chapters 20 and 21, the Jews are trying to make there way through the desert up to Israel. Along the way, they make requests to Edom, Amor, and Moab to be able to cut through their land, but their requests are denied. They are left with no choice but to travel around the outer perimeter of the Edomite, Amorite, and Moabite lands, where they are eventually able to overcome the Amorites and they end up settling in the land of the Amorites and the Moabites (which was overtaken by the Amorites). By looking at a map of their route, we can see that it appears as though their route took them much longer than if they had been able to travel in a straight path up from the Red Sea up to the Dead Sea. Is this accurate? How much farther did they travel due to their not being allowed to peacefully travel through these other lands?

We know that the Jews were at Mount Hor, where we learn of Aaron's death (Numbers 20;24-29). Let's use this stop at Mount Hor as a starting point for our calculations. So, to clarify exactly what we're investigating in order to answer our questions:

1) What is the distance between Mount Hor and Jericho (the city where Joshua first brought the Jews when they entered Israel)? I should note here that if the Jews took a more straightforward route, it's possible that their point of entry would not have been Jericho. For the purpose of calculation and comparison, however, it seemed the most logical point to use in order to maintain the same start point and end point.

2) What is the distance that was traveled instead, by going around these other nations? (For consistency, we will base our answer on the estimated route given on the map linked above.)

3) What is the difference between the distance of the straightforward route and the distance of the circuitous route?

The map that we're using conveniently gives us a scale to use to estimate the mileage. Using this scale, we can compare the distances.

Answer 1: If we draw a straight line between Mount Hor and Jericho and then measure this distance, we measure a distance of just less than 125 miles.

Answer 2: If we measure the combined distances along the estimated route given on the map, we measure a distance of approximately 312.5 miles. 

Answer 3: To find the difference between the two distances, we take the longer distance (#2) and subtract from it the shorter distance (#1) to find how far the extra distance traveled was. 
312.5 - 125 = 187.5
So, from our calculations, the Jews traveled an extra distance of 187.5 miles due to the circuitous route that they needed to take. Another way to look at this is that they traveled more than twice the distance that they actually needed to in order to reach their destination.

Mathematical Connection:
Using a map with scale measurements to measure distances allows students an opportunity to practice many important math skills which can be differentiated based on level:
*measuring with a ruler (either using a ruler to measure the distance and comparing it to the scale given, or using the scale measurement as a ruler replacement)
*using scale factor (a standard measure = a represented distance on the map)
*adding measured distances together- finding a successful technique for accurately measuring distances that may or may not be in a straight line (using string on the map to measure, marking locations on a marking paper to add distances, measuring with a ruler and adding measures together, etc.)

Additionally, such an activity also offers integration with and reinforcement of Geography skills.

Everyday Connection:
Have you ever needed to compare driving routes- whether just trying to get around town or when planning a road trip? Don't just rely on an app or GPS to tell you where to go. Check it out for yourself. Is your GPS really giving you the shortest route? (Of course, you'd have to take into account the speed limits on different roadways and other road restrictions that might keep you from really taking the most ideal route just based on looking at a map). How much farther do you need to travel if you choose to pass by a specific landmark or stop along the way?