Triangle Mystery. . .

6.EE.2    6.EE.4     6.EE.6

ACT 1:

Watch the video for Act 1.

Ask students what they noticed and what they wonder (are curious about).  Record student responses.

Have students hypothesize how the trick works.  How can the performer know the number at the top of the triangle so quickly for any number chosen?

ACT 2:

Students work on determining how the trick works based on their hypothesis.  They should be guided to show what is happening in the trick first through the use of some model that can be represented in a diagram, and then later written as an expression.  Students may ask for information such as:  “How were the other numbers generated after the start number was chosen?”  When they ask, you can tell them the bottom row are consecutive numbers after the start number.  Each number in the middle row is the sum of the 3 numbers below.  The top number is the sum of the numbers in the middle row.  OR you can give them the technology link below for further investigation.

Students may ask if they can investigate the trick using technology: http://scratch.mit.edu/projects/20831707/

Students may also ask for materials to use (they may even ask to use similar materials from the previous task) – these can also be suggested, carefully, by the teacher.

ACT 3:

Students will compare and share solution strategies.

• Share student solution paths. Start with most common strategy.
• Students should explain their thinking about the mathematics in the trick.
• Ask students to hypothesize again about whether any number would work – like fractions or decimals.  Have them work to figure it out.
• Be sure to help students make connections between equivalent expressions (i.e. the expressions 9n + 18 and 9(n + 2).
• Revisit any initial student questions that weren’t answered.