Probability and Statistics Activity: Do You Know Your s? (Part 1) TEKS: (4.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to: (A) use concrete objects or pictures to make generalizations about determining all possible combinations of a given set of data or of objects in a problem situation; and (4.1), operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. The student is expected to: (A) use place value to read, write, compare, and order whole numbers through 999,999,999; and (4.3), operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. The student is expected to: (A) use addition and subtraction to solve problems involving whole numbers; and (4.4), operation, and quantitative reasoning. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to: (C) recall and apply multiplication facts through 12 x 12; (D) use multiplication to solve problems (no more than two digits times two digits without technology); and (4.14) Underlying processes and mathematical tools. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) use tools such as real objects, manipulatives, and technology to solve problems. (4.15) Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language. Do You Know Your s? (Part 1) Page 1
The student is expected to: (A) explain and record observations using objects, words, pictures, numbers, and technology; and Note: Portions of this lesson address TEKS at other grade levels as well; however, the intent of the lesson fits most appropriately at the grade level indicated. Overview: Students will randomly choose three number tiles or cards. Then, they will find all of the possible combinations for making a two-digit number from the number tiles or cards drawn. Next, they will identify which of the following characteristics describes the two-digit number: two-digit number is even, two-digit number is odd, two-digit number has repeated digits, sum of the digits is even, sum of the digits is odd, product of the digits is even, and product of the digits is odd. They will use this information later in the lesson to score points during a game. They will then place two sets of the three number tiles or cards drawn into a container. One student will draw two number tiles (or two cards) and create a two-digit number. The student will then record and identify the characteristics that describe the two-digit number and record the points scored by the number. The first student will then place the two tiles or cards back in the container and the next player will repeat the previous steps. The winner is the first player to get at least 50 points. Materials: Two sets of 1-9 number tiles for each group (or use Cards Handout/Transparency 1) 2 containers such as a paper bag or a plastic bowl for each group Do You Know Your s? Recording Sheet Handout/Transparency 2a Do You Know Your s? Recording Sheet (Sample Data) Handouts/Transparencies 2b and 2c Do You Know Your s? Score Sheet Handout/Transparency 3a Do You Know Your s? Score Sheet (Sample Data) Handout/Transparency 3b Grouping: Time: Groups of 2 4 students 60 to 90 minutes Lesson: Procedures 1. Give each group two sets of number tiles or number cards from 1-9. Have each group place both sets of tiles or Notes If you do not have access to number tiles, you can use the number cards provided on Handout/Transparency 1. Do You Know Your s? (Part 1) Page 2
Procedures cards into a container. 2. Have the group randomly choose three number tiles or cards, one at a time, without replacement, and place them on the table. 3. Give each group a copy of Do You Know Your s? Recording Sheet (Handout/Transparency 2a). Tell the students to use the tiles or cards to find all of the possible combinations that form a 2-digit number. Have them record their data on the recording sheet. Notes Make sure that the students do not put the number tiles or cards back into the container once they ve drawn them out. For example, if the students chose 1, 2, and 5, they could make the following different two-digit numbers: 12, 21, 15, 51, 25, and 52. If the students chose 3, 4, and 4, they could make the following different two-digit numbers: 34, 43, and 44. 4. Once they have finished recording all of the possible combinations, then ask them the following questions: What is an odd number? A number is odd if it has a remainder of 1 when the number is divided by 2. numbers have 1, 3, 5, 7, or 9 in the units or ones place. What is an even number? A number is even if it has a remainder of 0 when the number is divided by 2. numbers have 0, 2, 4, 6, or 8 in the units or ones place. After they have defined what odd and even numbers are, then have them classify their own 2-digit numbers as odd or even by marking an x in the appropriate columns on the recording sheet. 5. Next, have students continue to identify characteristics of their two-digit numbers as indicated on the recording sheet. Examples of completed charts are provided on Do You Know Your s? Recording Sheet (Sample Data) Handouts/ Transparencies 2b and 2c. Do You Know Your s? (Part 1) Page 3
Procedures Have the students keep their recording sheet because they will use it for the following game and for Do You Know Your s?, Part 2. Notes 6. Students are now ready to play the game. Each student should get a scoring sheet (see Handout/Transparency 3a) so that they can keep their own score. Have students take the three number tiles or cards and place them in the second container. Then have the students place a duplicate of each tile into the second container as well. For example, if the students originally drew 1, 2, and 5 at the beginning of the lesson, they should now have 6 tiles in the second container: 1, 1, 2, 2, 5, and 5. If the students originally drew 3, 4, and 4 at the beginning of the lesson, they should still have 6 tiles in the second container: 3, 3, 4, 4, 4, and 4. Be sure to have extra number tiles or cards on hand for those groups who drew a duplicate number at the beginning. 7. If more than one player is playing the game, have each student pick a tile or card from the container, the student with the highest tile or card will go first. Then the player to the left of the player that went first goes next, etc. In case the same digits are drawn by two players, they will continue to draw until one player gets the largest digit. 8. The player will draw two tiles or cards, one at a time, without replacement, from the container with 6 tiles. The player must then decide which two-digit number he or she wishes to make using those two tiles or cards. For example, if the player draws out a 5 and a 2, he or she can either make 52 or 25. Do You Know Your s? (Part 1) Page 4
Procedures Next, the player should write down the twodigit number on the scoring sheet and then score the number. Here are the rules for scoring: Two-digit number is even 1 point Two-digit number is odd 2 points Two-digit number has repeated digits 3 points Sum of the digits is even 4 points Sum of the digits is odd 5 points Product of the digits is even 6 points Product of the digits is odd 7 points Then, the player will place the number tiles or cards back into the container and the next player will have a turn. 9. Each player takes turns drawing two digits and recording his or her own score. The winner of the game is the first player to get at least 50 points. Notes Example: If the player chose to make 52, he or she would get the following points: 1 point because 52 is even; 5 points because the sum of the digits is odd; and 6 points because the product of the digits is even. The total score for 52 would be 12 points. If the player chose to make 25, he or she would get the following points: 2 points because 52 is odd; 5 points because the sum of the digits is odd; and 6 points because the product of the digits is even. The total score for 25 would be 13 points. You can modify the criteria for winning the game, if you wish. The winner might be the first person to reach a specified number of points exactly, or the highest score after a certain number of rounds, or possibly the lowest score after a certain number of rounds. 10. After the game is done, engage the students in a discussion about the strategies they may have used to play the game. Possible questions to open up the discussion: Did you win or lose? Do You Know Your s? (Part 1) Page 5
Procedures If you won, what strategy did you use? If you lost, what would you do differently in order to win the next time you play? What patterns did you observe in the characteristics that described a number? For example, if the product of the digits was even, what can you tell me about at least one of the digits in the number? Notes After the discussion, have the students write a paragraph on what strategy they used to play the game or what patterns they observed in the characteristics that describe numbers. Homework: Assessment: Extensions: Have students take the Do You Know Your s? Recording Sheet (Handout/Transparency 2a) home and choose three digits. Two of the digits should be different than what they had in their game. Then have them record all of the different combinations on the recording sheet and mark all of the characteristics that describe the number as they complete the recording sheet. Assessment is done throughout the lesson through discussion with students. The completed recording sheets and scoring sheets also serve as an assessment. Have students select four number tiles or cards and create all of the possible different two-digit numbers using those four tiles or cards. Resources: North Carolina Department of Public Instruction, I. (2006, August 1). Mathematics: Instructional Resources. Retrieved December 9, 2006, from http://community.learnnc.org/dpi/math/archives/instructional_resources Do You Know Your s? (Part 1) Page 6
Cards 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 Handout/Transparency 1 Do You Know Your s? (Part 1) Page 7
Do You Know Your s? Recording Sheet The bag at your table contains two sets of number tiles or number cards from 1-9. Draw three number tiles or number cards at one time from the bag. List the three numerals that you drew below: Next, list all of the different two-digit numbers that you could form using these three number tiles or cards. Write each combination in the 1 st column in the table below. You will need to have a strategy so that you can be sure that you have found all of the possible combinations. If you have extra rows in the table, just leave them blank. If you need additional rows, add them in. Then, place an X in each column that describes a characteristic of the two-digit number. is is has Repeated Digits Sum of the Sum of the Product of the Product of the How many different two-digit numbers did you form with your three number tiles/cards? Handout/Transparency 2a Do You Know Your s? (Part 1) Page 8
Do You Know Your s? Recording Sheet (Sample Data) The bag at your table contains two sets of number tiles or number cards from 1-9. Draw three number tiles or number cards at one time from the bag. List the three numerals that you drew below: 7 2 9 Next, list all of the different two-digit numbers that you could form using these three number tiles or cards. Write each combination in the 1 st column in the table below. You will need to have a strategy so that you can be sure that you have found all of the possible combinations. If you have extra rows in the table, just leave them blank. If you need additional rows, add them in. Then, place an X in each column that describes a characteristic of the two-digit number. is is has Repeated Digits Sum of the Sum of the Product of the Product of the 72 X X X 27 X X X 79 X X X 97 X X X 29 X X X 92 X X X How many different two-digit numbers did you form with your three number tiles/cards? 6 Handout/Transparency 2b Do You Know Your s? (Part 1) Page 9
Do You Know Your s? Recording Sheet (Sample Data) The bag at your table contains two sets of number tiles or number cards from 1-9. Draw three number tiles or number cards at one time from the bag. List the three numerals that you drew below: 6 6 3 Next, list all of the different two-digit numbers that you could form using these three number tiles or cards. Write each combination in the 1 st column in the table below. You will need to have a strategy so that you can be sure that you have found all of the possible combinations. If you have extra rows in the table, just leave them blank. If you need additional rows, add them in. Then, place an X in each column that describes a characteristic of the two-digit number. is is has Repeated Digits Sum of the Sum of the Product of the 66 X X X X 63 X X X 36 X X X Product of the How many different two-digit numbers did you form with your three number tiles/cards? 3 Handout/Transparency 2c Do You Know Your s? (Part 1) Page 10
Do You Know Your s? Score Sheet Draw two number tiles or cards from the container, one at a time, without replacement. Decide what two-digit number you wish to make, record it in the chart below, and then score your number. Turn # is is has Repeated Digits Sum of the Digits is Sum of the Digits is Product of the Product of the Total Score for this Turn 1 2 3 4 5 6 7 (1 point) (2 points) (3 points) (4 points) (5 points) (6 points) (7 points) Handout/Transparency 3a Do You Know Your s? (Part 1) Page 11
Do You Know Your s? Score Sheet (Sample Data) Draw two number tiles or cards from the container, one at a time, without replacement. Decide what two-digit number you wish to make, record it in the chart below, and then score your number. Turn # is is has Repeated Digits Sum of the Digits is Sum of the Digits is Product of the Product of the Total Score for this Turn (1 point) (2 points) (3 points) (4 points) (5 points) (6 points) (7 points) 1 52 1 -- -- -- 5 6 -- 12 2 3 4 5 6 7 Handout/Transparency 3b Do You Know Your s? (Part 1) Page 12