A B C D E

Solutions for Session 10, Grades 3-5, 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.

 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.

 Problem B3 Answers will vary. At this level, many students will see that the blue tiles are always in the shape of a square, and that there are always an even number of white tiles. Some may recognize that the number of white tiles is always a multiple of four.

 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 them to think about putting white tiles around that blue pool. How many white tiles do you need for the top? How many for the bottom? Now think about the putting tiles around the sides. How many white tiles does this require in all?

 Problem B5 Answers will vary. At this level, students should actually build the pools with two different color square tiles, then describe what they built. 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.

 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.

 Problem B7 Answers will vary. Ask students to look at two consecutive entries and think of ways to get from one to the other. Then have students continue that pattern to see if other entries are correct.

 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.

 Session 10, Grades 3-5: Index | Notes | Solutions | Video