6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Welcome

You are helping to plan a big reception for your sister’s wedding. The reception hall has banquet tables shaped as hexagons. Six people can sit around a table. Banquet Tables

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Banquet Tables You have just found out the hall where you are holding the reception is long and narrow. There is not enough room to spread the tables out. Your brother has an idea, what if we push two tables together so that one of the sides from the first table is touching a side from the second table. What happens to the number of seats when you push two tables together?

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Banquet Tables Guiding Question: How would you find how many people can sit around any number of tables?

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Square Tables Banquet Tables Individual Investigation –Show GEOMETRICALLY: draw a minimum of 4 tables and color code how you determine the number of seats –Show NUMERICALLY: set up an arithmetic t-table, include arithmetic number sentences for 10, 5, 13, and 100 tables –Show VERBALLY: describe your visualization for the number of seats in words. –Show ALGEBRAICALLY: determine an algebraic expression that matches your visualization –Show GRAPHICALLY: create an appropriate graph

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Share your representations with a partner –Are they alike? –If they are alike, can you think of OTHER strategies to determine the number of seats? –Are they different? –If they are different, do you understand your partner’s representations? Banquet Tables

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Second Stage of the Investigation (Groups) Use: –triangles –trapezoids –hexagons as banquet table shapes Key Question: How many people can sit around one table for each of the different shapes? Banquet Tables

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Second Stage of the Investigation –Combine your results for all four shapes onto the group graph. Banquet Tables

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 Look at the graph: What are the similarities between the graphs for the different shaped tables? What are the differences? Can you see these similarities and differences in your other representations? Can you determine the number of people seated at 25 tables/35 tables from your graph? How? Group Discussion Questions

6 th G R A D E © Prepared by the LAUSD Secondary Math Unit, 2008 In your groups, develop an algebraic expression to give the total number of seats depending on the number of tables placed end to end and the number of people able to sit around a table of given size. Extension Question