This engaging 3 Act Task is a great way to add rigor to your instruction! This file is editable, so you can (and may need to!) adjust the numbers of seeds to make this appropriate and challenging for your students. Directions are below and on the first 3 slides of the PPT. This activity usually takes an hour or longer but can easily be adjusted to take more or less time. Enjoy!
P.S. Don't let the lengthy directions fool you, this activity is a lot of fun and is pretty simple to implement! :)
Act 1: This is the introduction to the task. Students see pictures of 3 pumpkins and are asked to share what they notice and wonder. The teacher should record this information in the table on this slide. Any observations should be added! This portion helps students to focus in on the important details once the task has begun and it encourages them to connect math to real life situations. When the list of items students notice and wonder is complete, the teacher can either ask what wonderings we could use math to investigate (settling on the number of seeds in each pumpkin) OR the teacher can tell students that today they will use math to determine the number of seeds in each pumpkin.
Estimate: Now students see the same picture of the pumpkins, but they are asked to estimate how many seeds are in the middle pumpkin (with the question mark on it). They should work in a small group to come up with 3 different estimates. 1 that is reasonable but may be a little low, another that is still reasonable but may be a little high, and one that they think is just right. This works best if you have done some work with pumpkins already so the kids have an idea of how many seeds there could be (my class always reads by Margaret McNamera and we do some work with actual pumpkins prior to this activity). I typically write "too low, just right, too high" on some extra board space and have the kids write their estimates on stickies and put them in the correct columns but you can also record their estimates on the slide in the boxes provided. Students will use their estimates to help determine if their answers later on are reasonable.
Act 2 Part 1: Students are now given the number of seeds one pumpkin has and the total number of seeds of all 3 pumpkins. They should work in small groups to figure out how many seeds the middle pumpkin could have. As groups think they have the answer, ask them if there could be other answers (they could be at this point!) and challenge them to come up with some alternatives. As groups work, make sure they have access to manipulatives and large paper to work through this problem collaboratively. Ask groups what they are doing and why. If some groups are struggling, suggest some ways they could get started (could you build/show the total number of seeds first and then take away the number of seeds you know are in pumpkin 1? what would you have left? could you build/show the number of seeds in pumpkin 1 and add up until you reach the total number of seeds? how could that help you find a solution?). Encourage students to think back to their estimates, are their answers reasonable?
Act 2 Part 2: After most students have come up with some possible answers to how many seeds are in each pumpkin, show them this slide. Now we KNOW how many seeds are in pumpkins 1 and 3 and in all three pumpkins together. Have students work with their tables to find out how many seeds are in pumpkin 2. This time, there should be only 1 correct answer! Again, allow students to use manipulatives and large paper for their team. Students should use their estimates from before to assess whether their answers are reasonable. Ask students who are struggling some guiding questions to help them solve this problem (see suggestions in Act 2 Part 1).
Before moving on to Act 3, give groups a chance to share their thoughts. You could give each group a chance to share out to the whole class or you could give groups a few minutes to take a gallery walk and see what other groups did. Take a moment to point out some of the different strategies used and remind students that while there may only be one right answer, there are usually many ways we can get there! Commend students on their perseverance and flexible problem solving skills.
Act 3: Show students the final slide which reveals the answer! Give students a chance to discuss. Did they find the correct answer? If not, were they close? Did the correct answer align with their estimates? If they could do this again, would the use the same strategy or something different?