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Session 10 Session 10 Grades K-2 Part A Part B Part C Part D Part E Homework
 
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A B C D E

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Solutions for Session 10, Grades 6-8, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6| B7 | B8


Problem B1

Answers will vary. One question might ask how to use the pictures to help find the relationship between the pool number and the numbers of white and blue tiles.

<< back to Problem B1


 

Problem B2

Answers will vary. For the question above, you might discuss building each pool. For example, the blue part of Pool 1 is a 1-by-1 square and takes one blue tile, the blue part of Pool 2 is a 2-by-2 square and takes four blue tiles, etc.

<< back to Problem B2


 

Problem B3

Answers will vary. At this level, students should be able to write rules for the number of tiles of each color for each pool. The blue tiles are always in the shape of a square, with n2 blue tiles needed for Pool n. The number of white tiles is always a multiple of four, with 4(n + 1) white tiles needed for Pool n.

<< back to Problem B3


 

Problem B4

Answers will vary. At this level, teachers should encourage students to describe the shape of the blue tiles and write a rule to represent the relationship between the pool number and the number of blue tiles. Then ask the students to think about putting white tiles around that blue pool. How many white tiles do you need for the corners? How many more for the bottom and top? Now think about the putting tiles around the sides. How many white tiles does this require in all?

<< back to Problem B4


 

Problem B5

Answers will vary. At this level, students should actually build the pools with two different color square tiles and then describe what they built, thinking of the relationship between the pool number and the number of each color tile needed to build it. The process of building will help students put the patterns into words and symbols. Many students will use all these skills when solving this problem.

<< back to Problem B5


 

Problem B6

Answers will vary. All of the ideas described in the grades 3-4 section are appropriate for this level student. Many students at this level will be able to answer questions posed in the grades 5-6 section.

<< back to Problem B6


 

Problem B7

Answers will vary. Ask students to tell you how to build the 1st term. How many toothpicks will you need? Now describe how to build the 2nd term from the 1st. How many more toothpicks are needed? How many more toothpicks are needed to get from the 10th to the 11th term? Does this same rule work for getting from the 1st to the 2nd term?

<< back to Problem B7


 

Problem B8

Answers will vary. Often students see a rule to get from one entry to the next. Teachers should help students think of ways to connect each entry to its place in the list. Questions like those shown above will help get the rule N = 3n + 1, where N is the number of toothpicks needed to build term n.

<< back to Problem B8

 

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