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The Algebra Clan

The Algebra Clan. Mom, Pop and all the Relatives. Border tile problem. Table. Make a table showing the numbers of blue tiles for water and white tiles for the border for the first six square pools.

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The Algebra Clan

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  1. The Algebra Clan Mom, Pop and all the Relatives

  2. Border tileproblem

  3. Table • Make a table showing the numbers of blue tiles for water and white tiles for the border for the first six square pools. • What are the variables in the problem? How are they related? How can you describe this relationship in words?

  4. Graph • Make a graph that shows the number of blue tiles in each square pool. Make a graph that shows the number of white tiles in each square pool. • As the number of the pool increases, how does the number of white tiles change? How does the number of blue tiles change? How does this relationship show up in a table and in the graph? • Use your graph to find the number of blue tiles in the seventh square.

  5. Patterns & Generalizations • Can there ever be a border for a square pool with exactly twenty-five white tiles? Explain why or why not. • Find the number of blue (white) tiles in the 10th pool. The 25th pool. The 100th pool. • If there are 144 blue squares, what is the side length of the square pool including the border? How many white tiles are needed for the border?

  6. Algebraic Reasoning • What are the variables in this situation? What quantities are changing? • How are the variable related? • As one variable increases, what happens to the other variable? • How can you represent this relationship using words, concrete objects, pictures, tables, garphs or symbols? • How can you build connections among representations? • How can you use this relationship to predict information about the variables?

  7. Draining a swimming pool • Expressions vs. Equations • How does knowledge of ratios and proportions enter into this? • Purple tiles to green tiles; other proportion problems • What’s the learning progression?

  8. Knots in a Rope • Collecting real data • What questions can be asked about this? • What expressions and equations can be written, and what questions do they answer? • What kind of graph can be drawn?

  9. The Cruise Ship In small groups, determine an approach 7.RP.2 b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

  10. Gas Mileage – just for fun • Whose car had the largest gas tank? • Whose car ran out of gas fist? • Whose car went farthest (at same speed) • Whose car got worst gas mileage?

  11. What’s the family tree? • Using the Common Core Collaborative Cards, find your group and arrange the cards to show connections.

  12. Solving equations with integers -8x + (-2) = -5x What the heck does it take? Authentic situations involving negative numbers Thermometer Problems Elevator Problems Happy and Grumpy People Hot and Cold Cubes Biking Across Town

  13. Where does this leave us? • What are the big questions you’re grappling with?

  14. Teaching Practices • Feldman observation form • IES Practice Guide • How many times in a week do you do each of these? 0-3, 4-10, more?

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