Hi All,
We had some fun with dice earlier this week as we learned an easy magic trick based on 7. Now let's go a bit deeper.
Ask students if they were to roll two dice, what sum they think would probably come up the most and why? After a discussion give them the opportunity to explore. Many students will not realize which sums are possible until they play around with the dice again. Then many will guess that the higher numbers like 12 or 11 will come up the most. When these numbers don't come up as often as others, it's a great discussion as to why.
This is an excellent partner problem and a dive into probability. Give each partnership the attached record sheet and have them roll and record the sums of the two dice rolled. Partners can take turns rolling and recording.
The easiest way to record is with tally marks. Point out how the more they roll, the more reliable their data will become. For example if we only roll twice and 4 comes up both times, does that mean that 4 is always going to be the most likely sum?
After students gather enough data, they will find that 7 tends to come up the most because there are more combinations with dice that yield 7 than any other sum, with 6 and 8 close behind.
To make sure this is true, have students write out all of the possible combinations. It makes for an interesting pattern, and kids love patterns.
2 (1+1)
3 (2+1) (1+2)
4 (2+2) (1+3) (3+1)
5 (3+2) (2+3) (4+1) (1+4)
6 (3+3) (4+2) (2+4) (5+1) (1+5)
7 (4+3) (3+4) (6+1) (1+6) (5+2) (2+5)
8 (4+4) (6+2) (2+6) (3+5) (5+3)
9 (4+5) (5+4) (6+3) (3+6)
10 (5+5) (6+4) (4+6)
11 (5+6) (6+5)
12 (6+6)
The tally marks students record on their charts will tend to look a lot like this pattern, given enough rolls. Is it a sure thing 7 will come up when you roll dice? No, but it has a better probability than all the other options. No betting please! This is strictly mathematical. ;)
Here's the link to the record sheet. https://drive.google.com/file/d/1r81N879HrLiXMmLyjres3js-urqLylW7/view?usp=sharing
Have fun with this!
Best,
Bob
From Reteaching Math: Data Analysis and Probability Grades 2-4 by Maryann McMahon-Nester and Bob Krech (Scholastic, 2008)
Ask students if they were to roll two dice, what sum they think would probably come up the most and why? After a discussion give them the opportunity to explore. Many students will not realize which sums are possible until they play around with the dice again. Then many will guess that the higher numbers like 12 or 11 will come up the most. When these numbers don't come up as often as others, it's a great discussion as to why.
This is an excellent partner problem and a dive into probability. Give each partnership the attached record sheet and have them roll and record the sums of the two dice rolled. Partners can take turns rolling and recording.
The easiest way to record is with tally marks. Point out how the more they roll, the more reliable their data will become. For example if we only roll twice and 4 comes up both times, does that mean that 4 is always going to be the most likely sum?
After students gather enough data, they will find that 7 tends to come up the most because there are more combinations with dice that yield 7 than any other sum, with 6 and 8 close behind.
To make sure this is true, have students write out all of the possible combinations. It makes for an interesting pattern, and kids love patterns.
2 (1+1)
3 (2+1) (1+2)
4 (2+2) (1+3) (3+1)
5 (3+2) (2+3) (4+1) (1+4)
6 (3+3) (4+2) (2+4) (5+1) (1+5)
7 (4+3) (3+4) (6+1) (1+6) (5+2) (2+5)
8 (4+4) (6+2) (2+6) (3+5) (5+3)
9 (4+5) (5+4) (6+3) (3+6)
10 (5+5) (6+4) (4+6)
11 (5+6) (6+5)
12 (6+6)
The tally marks students record on their charts will tend to look a lot like this pattern, given enough rolls. Is it a sure thing 7 will come up when you roll dice? No, but it has a better probability than all the other options. No betting please! This is strictly mathematical. ;)
Here's the link to the record sheet. https://drive.google.com/file/d/1r81N879HrLiXMmLyjres3js-urqLylW7/view?usp=sharing
Have fun with this!
Best,
Bob
From Reteaching Math: Data Analysis and Probability Grades 2-4 by Maryann McMahon-Nester and Bob Krech (Scholastic, 2008)
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