Use the properties of operations, and the relationships between multiplication and division, to solve problems and check calculations
Recall and demonstrate multiplication facts of two, five, and 10, and related division facts
Use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 1000, and explain the strategies used
Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 1000, using various tools and algorithms
Represent multiplication of numbers up to 10 × 10 and division up to 100 ÷ 10, using a variety of tools and drawings, including arrays
Primary: Data Management
Use mathematical language, including the terms “impossible”, “unlikely”, “equally likely”, “likely”, and “certain”, to describe the likelihood of events happening, and use that likelihood to make predictions and informed decisions
Use non-standard units appropriately to estimate, measure, and compare capacity, and explain the effect that overfilling or underfilling, and gaps between units, have on accuracy
This book offers a wide range of entry points into the curriculum. You may choose to use this text as an introduction to one or more specific expectations, or you may spend additional time on a specific activity and develop it into a lesson.
Due to the amount of content in this lesson, it has been divided into a two-day activity.
Book: How Many Seeds in a Pumpkin? by Margaret McNamara
One small cardboard box, taped shut, with popcorn kernels inside
One medium cardboard box, taped shut, with the same number of popcorn kernels inside is as the small box has. In this box, however, the kernels have been popped. Ideally, the kernels are packed tightly into the box so they are unable to move. This will also prevent them from breaking too much.
If you have difficulty sourcing a box that allows popcorn to be packed in this manner, secure the popped popcorn kernels in a sealed plastic bag and place the bag into the box.
Gather the class, and announce that today you will be reading a story called, “How Many Seeds in a Pumpkin?”
Ask students: Has anyone seen a pumpkin before? When did you see it? What’s inside of a pumpkin?
Students should identify that seeds are one of the things that can be found in a pumpkin. Ask them to think about how many seeds might be inside a pumpkin and to keep that estimated number to themselves for just a moment.
Begin reading the story, stopping at the end of page 12, after: “Tonight your homework is to think about how we should count all the seeds.”
Ask students: How would you count all the seeds in a pumpkin?
Ask students to brainstorm strategies with a classmate. When appropriate, bring the class back together for a group discussion.
Ask students to share their ideas with the class, and record their plans on the board.
The class discussion about these strategies can be as long or as brief as you like. Questions you may want to ask include: How did you think of this strategy? Why do you think this strategy will work? What is a strength of this strategy? What might be a weakness of this strategy? When you were brainstorming your strategies, did the number of seeds you thought you were going to count influence how you decided what to do?
Note: If you will need to erase the details of the students’ counting strategies between the conclusion of this lesson and the start of the next, record the information so that you can re-write it on the board for the next lesson.
After recording all the strategies, ask students: Which pumpkin do you think has the most seeds? The big, medium, or small one? What information are you using to determine your answer?
Students start to consider the concept of estimation, and how to make reasonable/informed guesses.
Next, present the two opaque, closed boxes of popcorn to the students and have them pass the boxes around the group from person to person (don’t reveal what’s inside!). Allow students to examine and manipulate the boxes.
Ask students which box they think has more things inside of it. What are they observing (seeing, hearing, feeling, etc.) that helps them estimate? Does everyone agree that certain properties mean certain things (ie. a larger box means there are more objects inside of it)? Why or why not?
Take the class through the process of opening the boxes and counting what’s inside – depending on your class, you might split the students into two groups and have each group open a box and record the contents, or you might open the boxes one at a time yourself and show the entire class what you are finding (perhaps by counting the popcorn kernels out into students’ hands).
Record what you find inside the boxes on the board so that students have both heard and seen that there are the same number of popcorn kernels inside each box.
Note: This activity can lay the groundwork for future lessons about mass and volume or could simply be used to provoke student explorations and observations about the properties of objects and what assumptions they make about those properties.
Conclude the lesson with a class discussion in which students discuss the results:
Were their predictions correct? What observations/features of the boxes had helped them estimate correctly? What observations ended up being unhelpful? Why did the same amounts of popcorn need two differently sized boxes? What does this activity tell us about the relationship between the size of a container and its capacity?
Ask students if, based on their discoveries from opening the boxes of popcorn, any of them would like to revise their hypothesis about which pumpkin in the story will contain the most seeds? What rationale are students using when amending their guesses?
Remind students of the counting strategies they came up with during the previous class.
Ask students: Did anyone think of any other strategies that they would like to add to our board before we begin reading?
Continue reading How Many Seeds in a Pumpkin through to the end, including “Charlie’s Pumpkin Facts” and “A Note from Mr. Tiffin.”
Ask students whether they were surprised by the number of seeds each group counted.
Discussion points for younger grades:
Have students share whether or not they were surprised by the discovery that Charlie’s pumpkin contained the most seeds, and their reasoning. Some may have been hypothesizing that the size of the pumpkin would matter. Others may have been thinking about the popcorn kernel activity from the last lesson and wondered if there might be more to the pumpkins than meets the eye.
Explore the counting strategies the students used in the story. Did any of their strategies match ones that your students brainstormed?
Remind the students that Robert’s pumpkin had the most groups of seeds. Ask students how it is possible that Robert had the most groups of seeds, but Charlie had the most seeds in total. Give students time to discuss their ideas with a classmate.
When appropriate, bring the class back together for a group discussion. Ask students to share their ideas with the class and explain why they think their reasoning is correct.
If necessary, re-read pages 19-21, pausing at the end of each page to highlight the number of seeds in each group. Add information to the board (307 groups of 2, 63 groups of 5 [plus one left over], and 35 groups of 10). Guide students to recognize the significance of how many seeds are in each group using skip counting – for example, 8 groups of 2 vs 4 groups of 5.
Discussion points for older grades:
Follow-up on the initial question by having students discuss why they were or were not surprised by the outcome of the story. Did anyone agree with Robert that the number of groups was the most important information? Did anyone see any hints that there might have been other information to consider?
Continue by asking students what strategies they were using when following along with the story to determine which pumpkin would have the most seeds. Possible answers are adding groups, skip counting, or multiplying.
Conclude the lesson by leading a conversation about key ideas in the book. Depending on the lesson, your discussion might focus on:
Addition – Which counting strategy did students find most effective (2s, 5s or 10s)? Why did they like that strategy? Have students share when else they might use skip counting or “adding equal groups” to help them figure out how much of something them have.
Multiplication – Which counting strategy did students think was most effective (2s, 5s or 10s)? Have students explain why it was faster for Charlie to multiply than the other students. Explore as a class when might it be best to multiply by 10s the way Charlie did, and when might it be better to multiply by 2s like Robert.
Data analysis – What information did students use as they were reading to help them determine which pumpkin would have the most seeds? Did any students try to use the pictures of the seeds in the book to help them assess the totals, and did they find the images to be helpful? Note: Robert’s 307 groups of 2 appear to take up much more space on the table than Charlie’s 35 groups of 10. As a class, discuss how you might visually represent the information to make it clearer.
Attributes – Have students consider and discuss which features of the pumpkins they used to predict which one would have the most seeds. As a class, compare this with the features that ended up being more important. Link this conversation to the previous lesson’s popcorn kernel activity and think about the many different ways we try to infer knowledge about something from various aspects of its physical appearance. Have students discuss the pros and cons of these strategies.
Divide the class into groups and ask them to take the data collected from the story and represent it in a graph. Depending on their age, this might be a bar graph or pictograph. Students will need to determine which scale to use for their graph, and how to represent the data so it clearly communicates how many seeds were in each pumpkin.
Can students successfully communicate their observations of the pumpkins in the story, their predictions for what will happen, and provide reasoning for their predictions?
Are students able to skip count, add equal groups, or multiply when prompted to confirm how many seeds are in each pumpkin?
Are students able to recognize how both the number of groups and the number of items within each group are important pieces of information when totaling large collections of items?