Back-To-Back
Names _________________________________________________
Task 1: Arrange your seating so that you and your partner are sitting back-to-back, facing in opposite
directions. You will be attempting to explain to your partner how to draw a geometric figure you can
see, but your partner cannot.
A. With your partner, decide which of you will be the Describer and which will be the Sketcher.
The Sketcher should have a blank piece of paper in front of them.
B. The Describer describes the Task 1 diagram out loud so that the Sketcher can draw an identical
diagram on the paper.
Rules:
1. The Describer may only use words (no gestures or other visual clues) to help the
Sketcher draw the correct diagram.
2. The Describer may not look at the Sketcher’s diagram until the task is completed.
However, the Sketcher can also speak to the Describer and ask questions to help
with the drawing (but cannot use gestures or other visual clues).
C. Once time for the sketching (5 minutes) is finished, you and your partner should examine the
new diagram, compare it with the old and write down some observations about the following:
1. What words or phrases helped make the drawing more accurate?
2. What words or phrases generated confusion and made the drawing harder to draw
accurately?
3. What else helped you to communicate more accurately?
D. As the class shares results, write down a list of specific vocabulary you may want to use when
you repeat the exercise in Task 2.
Task 2: Try a new drawing. This time reverse roles—if you Described before, now you sketch. If you
Sketched before, now you describe. This second drawing will be a little bit more complex than the first
one, so you should plan to use precise mathematical vocabulary whenever possible to make the task
easier.
Task 1 Drawing:
Task 2 Drawing:
Back-to-Back Teacher Notes:
Purpose: These tasks serve to focus student attention on the usefulness of academic language and
geometric diagrams to facilitate effective communication. Raising the level of awareness about
effective mathematical communication will lead into the formal proof-making process later in the
learning cycle.
Launch: Call attention to the lesson objective: “SWBAT use academic vocabulary and geometric
diagrams to communicate mathematically more effectively.” As a starter example of such mathematical
communication, we will do Task 1. Pair up the students and give them the task sheet. Once each pair
has decided who is Describing and who is Sketching, pass out one Task 1 diagram to each Describer.
Distribute the different Task 1 diagrams so that near-neighbors are working on different diagrams. Give
5 minutes for the drawing part of the task. Circulate during the Task 1 and note examples of:
1.
2.
3.
4.
academic language being used effectively
situations where students are struggling to find a useful word
situations where ambiguous language is being used
use and/or improvement of mathematical labeling on the diagrams
Give students another 3 minutes to check the diagram for accuracy, debrief the communication
experience and to record answers to the questions for C.
Finish the launch with a full-class discussion listing observations about what made for more effective
(i.e. accurate) communication. You are listening for contributions in the same four areas as when you
were circulating. Solicit input from the pairs. As far as possible, let students raise observations as you
write them on the board. Interject your observations from circulating only if needed to stimulate more
and better student contributions. Conclude the discussion by listing important math words that would
probably be useful when working with a similar, but more complex, diagram.
Explore: This task is more complex with more potential for communication confusions. Circulate and
select and sequence 3 to 5 examples of use (or non-use) of academic language and the use of labeled
geometric diagrams (to be shared during the Discuss phase). The theme that organizes your sequencing
should be built around “techniques for avoiding ambiguous communication”—which could encompass:
1) using a more precise word or 2) referring to a common labeled diagram to be clear.
Discuss: Briefly “popcorn” a list of key vocabulary words that different pairs used that helped them
with the drawing. Then focus attention back on the objective of the lesson and use it to guide the
sequenced sharing you’ve chosen during the Explore phase. The 3 to 5 examples of student use of
academic language and/or labeled geometric diagrams should highlight the major insights generated by
the class about effective mathematical communication. Connect today’s task with the upcoming
challenge of formally proving that a conjecture is true. When you are attempting to justify a
mathematical idea, you need to use academic language carefully and have a well-labeled diagram to
prevent misunderstanding and ambiguity.
Task 1 Diagrams:
Task 2 Diagram: