This activity introduces children to sampling with replacement as a way to predict how many of each color are in a bag of color tiles.
Math by All Means: Probability Grades 3-4 by Marilyn Burns
About Teaching Mathematics: A K-8 Resource, 2nd Edition by Marilyn Burns
This activity engages children in taking samples and analyzing data, and provides them with opportunities to think proportionally. Students discuss and define words such as certain, impossible, likely, unlikely, 50/50 chance, etc.
1. Demonstrate a positive learning attitude toward mathematics.
3. Reason mathematically.
Invitation to Learn
Show students a paper bag and tell them you have placed color tiles in the bag. (Put 12 tiles of the same color in the bag, for example: 12 yellow tiles). Walk around the room letting children look into the bag. After everyone has had a chance to see inside the bag, tell students you are going to shake the bag up, and without looking inside you will put your hand into the bag and take out one tile. Ask students to predict what color of tile they think you will pull from the bag. You should hear a chorus of YELLOW. Hold a discussion about why it would be yellow. Ask students how likely it would be that you would draw a yellow tile from the bag. Students might respond by saying it is very likely,
extremely likely, highly likely, etc. If students do not say the word CERTAIN, add that to the discussion. Tell students there is a numerical way to write the chance of pulling a yellow tile from the bag; write 12 out of 12. Then write 12/12 and say 12 out of 12. Then write 12:12 and say 12 to 12.
Math/ScienceRead Probably Pistachio by Stuart Murphy. This is the story of Jack a young boy who thinks nothing is going his way. Will he get what he wants in his lunch? Probably not! This story centers on probability and Jacks chances of things going his way.
Pair up students. Have each pair put 12 tiles of two different colors into a bag, discussing their choices. Have partners trade their bag with another pair. Partners conduct an experiment by sampling with replacement. After 12 draws, have students record their predictions of how many of each color tile are in the bag. Students then draw 12 more times, making another prediction and explaining their thinking in a paragraph. Finally, have students dump the contents of the bag to reveal the correct combination of color tiles.
Homework & Family Connections
Have students conduct an experiment at home similar to the one done in class. Students gather two different items to put in a paper bag in varying quantities. For example: 4 matchbox cars and 3 fingerboards (toy skateboards). Next, students can sit with a family member and assist them in randomly selecting one item at a time from the bag (without looking at the contents). The student explains how to record their choice on a T-chart. The student (or family member) continues selecting items from the bag, recording it on their chart, and then replacing it. Instruct students to select items and replace them at least 12 times. Students then ask their family member to predict the contents of the bag after considering the results on their T-chart. This activity has many possibilities for length (number of draws from the bag) and options for selecting items to go into the bag. After the family member has completed the activity, ask them to write a short paragraph explaining their thoughts or feelings. Students can share responses with class the following day.
Students should keep a log of what happened in their experiment. They can use the T-chart or construct their own way of displaying the information they gathered. After they have completed the assigned number of pulls from the bag and recorded their results, ask students to discuss these questions with their partner.
Ask students to write their explanation to the following questions and be prepared to share their responses in a class discussion: