 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Solutions for Session 4, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6    Problem A1

 a. The problem to solve is 3 + x = 7. This is a PP problem, since we are working with parts of a whole and the unknown is one of the parts. Here, the units are cars. b. The problem to solve is 5 + 8 = x. This is a PW problem, since we are working with parts of a whole and the unknown is the sum of the parts. Here, the units are books. c. The problem to solve is 5 + 4 = x. This is an MR problem, since we are merging two things (Bret and Wendy's money) and the unknown is the result. Here, the units are dollars. d. The problem to solve is 4 + x = 7. This is an MC problem, since we are merging two things (rabbits) and the unknown is the change (the number of babies). Here, the units are rabbits. e. The problem to solve is x + 5 = 12. This is an MS problem, since we are merging two things (Reed's money with his parents') and the unknown is the starting point (the amount of money Reed had before). Here, the units are dollars.   Problem A2

 a. The problem to solve is 7 - 3 = x. This is an SR problem, since we are separating two things and the unknown is the result. Here, the units are cars. b. The problem to solve is x - 3 = 5. This is a CS problem, since we are comparing two things and the unknown is the starting point. Here, the units are books. c. The problem to solve is 5 - 2 = x. This is a CR problem, since we are comparing two things and the unknown is the result. Here, the units are dollars. d. The problem to solve is 7 - x = 3. This is an SC problem, since we are separating two things and the unknown is the change. Here, the units are rabbits. e. The problem to solve is 7 + x = 12. This is a missing addend problem (MC) since the change is unknown. Here, the units are dollars. f. The problem to solve is x - 3 = 5. This is an SS problem, since we are separating two things and the unknown is the starting point. Here, the units are candy bars.   Problem A3

 a. The problem to solve is 4 • \$10 = x. The units are dollars. This is an asymmetrical problem, demonstrating a multiplicative comparison. b. The problem to solve is 6 • 5 = x. The units are flavors, toppings, and sundaes. This is a symmetrical problem, demonstrating the use of a Cartesian product. c. The problem to solve is 6 • 3 = x. The units are minutes, gallons per minute, and gallons. This is an asymmetrical problem, demonstrating a rate. d. The problem to solve is 1/3 • 9 = x. The units are sessions. This is an asymmetrical problem, demonstrating partitioning. e. The problem to solve is 20 • 33 = x. The units are meters, and the result is in square meters. This is a symmetrical problem, demonstrating the use of a rectangular array to find the area of a rectangle.   Problem A4 c.

Answers will vary. Here are two examples:

 • For the partitive model, Graphic (a): Matt deals a total of 15 cards to 3 players (including himself). Each player gets the same number of cards. How many cards does each player get? (Here, you know the number of groups and need to find the number in each group.) • For the quotative model, Graphic (b): Nicole has 15 cans of soda. She gives 3 cans of soda to each of her friends. How many friends got the soda? (Here, you know the number in each group and need to find the number of groups.)   Problem A5

 a. The quotative problem is easier to solve. It is equivalent to "How many 50s would you need to get 100?" Meanwhile, the partitive problem is "If 100 items are separated into 50 equal groups, how many are in each group?" b. The partitive problem is easier. It is equivalent to "If 100 is separated into two equal groups, how many are in each group?" Meanwhile, the quotative problem is "How many twos would you need to get 100?"   Problem A6

Answers will vary. Here are some examples:

 a. Arvind wants to buy some ice cream for his coworkers. Each ice cream cone costs \$4, and Arvind has \$43. How many cones can Arvind buy? b. Michelle needs 43 batteries to keep her handheld organizer running during a long trip. Batteries come in packs of 4. How many packs of batteries will Michelle need to buy? c. Lilian bought 4 cakes for a Tuesday night party. She paid \$43 for the cakes. How much money did she pay for each cake?     