1 Differentiation/Problem Solving & Math Grades Bob Trammel

2 Our Mission for Today Learn how to use problem solving strategies with differentiation. Select 1 or 2 problem solving item(s) from a grade level packet to use for school year Learn how ISTEP+ evaluates applied skills items for the March assessment and use this information to drive instruction.

3 Problem Solving………………… Certainly a Challenging Task for Most of Us! We are usually confronted with lots of reading that must be sorted out for understanding. The solution is not immediate……….we have to process information by using a chosen strategy.

4 In Small Groups……… Make a list of problem solving strategies.. We will share these in a couple of minutes!

5 Make a Table Problem Solving Strategies Find a Pattern Work Backwards Guess and Check Draw a Picture Make a List Symbolic Act it Out Logic

6 Using Puzzle Pieces………. Released ISTEP+ Problems at Grade Level are fantastic here. Students automatically differentiate the problem for you in most cases. Five or six puzzle piece problems take about 15 minutes to solve and debrief. I have the separate PowerPoint available for you. (Contact this service center.)

7 Ice Breaker Activity Cooperative Learning Activity Puzzle Pieces Grades Match your puzzle-piece with other similar pieces to form a problem to solve. As a learning group team, select a strategy to solve the problem. Solve the problem as a team then submit a solution to the audience. Your team must be able to justify the solution!!!

8 Problem #1 Small pieces of cheese are placed over each of the twelve numbers on the face of a circular clock. A mouse eats the cheese over the number 1 and walks clockwise around the clock, eating every third piece of cheese. If the mouse goes around the clock twice, what numbers are still covered by cheese?

9 A large square ABCD is shown. How many small squares “P” will cover the large square? Problem #2 A B C D P

10 Based on the patterns of the values in the circles, find the value of A A 3 22 Problem #3

11 Tim ate 40 cookies in 5 days. Each day he ate 3 more than the day before. How many cookies did he eat on the first day? Problem #4

12 Problem #5 Clue #1 Clue #2 = = If each is worth 20 points, how many points is each worth? Use the two clues to solve the problem. + +

13 A book was printed that uses a total of 225 digits for the page numbers (for example, page 42 uses 2 digits). If the first page is numbered 1, how many numbered pages are in the book? Problem #6

14 Problem #7 A partial 100’s board is shown Julie marks out all of odd numbers. Jerry marks out numbers that can be divided by 4. What numbers are left?

15 Problem #8 (4.5.7) Find the area of the kitchen-dining room shown in the diagram. 6 feet How many more square feet are in the dining section than the kitchen section of the room? Kitchen 24 feet 16 feet 12 feet Dining 12 feet 10 feet

16 Problem #9 (5.5.3) Find the area of the irregular shape shown in the diagram. How many square yards of carpet is needed to cover the above shape? 4 feet 24 feet 16 feet 12 feet 4 feet 7 feet

17 Problem #10 (Grade 3 Computation) Part A: Denise is buying candy for 3 of her friends. She wants to give each friend 4 pieces of candy. If each piece of candy costs 5¢, how much money will Denise spend on candy for her friends? Show All Work: Answer __________¢ Part B: How much money would she spend if one more friend showed up? Show All Work: Answer__________¢

18 A Few Problem Solving Items! Ice Cream Jamie’s Game 3 points4 points6 points Handouts

19 We have two different grade levels working at this problem.

20 The Ice Cream Problem Dairy Barn Ice Cream Flavors Vanilla Chocolate Strawberry Mint Dairy Barn Ice Cream Flavors Vanilla Chocolate Strawberry Mint Blueberry At the Dairy Barn Store, there are four different ice cream flavors on the menu. How many double-dip cones are possible if each dip is a different flavor? Below are a few blank double-dip cones for you to use to help solve the problem. You may not need to use all of the double-dip cones to solve this problem.

21 The Ice Cream Problem At the Dairy Barn Store, there are four different ice cream flavors on the menu. How many double-dip cones are possible if each dip is a different flavor? Below are a few blank double-dip cones for you to use to help solve the problem. You may not need to use all of the double-dip cones to solve this problem. Diary Barn Ice Cream Flavors Vanilla Chocolate Strawberry Mint

22 How could we differentiate this activity?

23 Jamie and Larry are playing a card game. The cards look like these. 3 points4 points6 points The deck of cards contains 25 cards. Here is how the card game is played. The deck is shuffled and placed facedown. Players take turns drawing cards. The first player who has a total of 55 points wins. Jamie won the game by scoring 55 points by using 12 cards. How many of each kind of card did Jamie have? Explain: Answer: = ______ = ________ = _______ 3 points4 points6 points3 points

24 Possible Problem Solving Strategy Make a Table + Guess and Check! 3 pt Cards 4 pt Cards 6 pt Cards Total # Cards Total Points = = 55 points = = 55 points

25 How could we differentiate this activity? 3 points4 points6 points

26 Money and Coins Beth has these coins in her pocket. How much money does she have in cents?

27 100’s Board

28 Another Strategy (Differentiation) Make a List (least to greatest?) CoinValue Penny 1¢ Nickel 5¢ Dime 10¢ Dime 10¢ Quarter 25¢ Total 51¢ 1

29 Part A. Tom is going to Cedar point this summer. Tom is 3 feet inch tall. He needs to be at least 4 feet tall in order to ride the roller coaster. How many INCHES taller must Tom be in order to ride the roller coaster? Show All Work Answer ________ inches Part B. If he grows six more inches over the year, will he be able to ride the roller coaster next year? Explain how you know if Tom is able to ride the roller coaster next summer.

30 Another Problem Solving Item Mary is 13 years old. Her brother Ray is four years old. When will Mary be twice as old as Ray?

31 Let’s Get in Grade Level Teams 3-4-5

32 Problem Solving and ISTEP+ (March Applied Skills Assessment) Applied Skills Frequency Distribution Report

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34 Problem Solving Standard for ISTEP+ See Grade Level Handouts View each of the 4 Applied Skills Items from the March 2011 ISTEP+ Assessment. Do this in grade level teams. Report out to us in about 15 minutes or so. Patterns? Do some Troubleshooting? How do I get my kids ready for this?

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50 Grade Level Problem Solving Packets As grade teams, critique the problems in each grade level packet. (3-4-5) Be prepared to identify your group’s favorite problem. These are to be used next school year in classrooms.