Pumpkin Problems: Estimates to Actuals

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Objective

SWBAT estimate, round, and subtract using a place value strategy of breaking apart numbers into tens and ones.

Big Idea

Critical to mathematical success is developing the sophistication of students’ strategies simultaneously with the teaching and application of key mathematical knowledge.

Warm Up

10 minutes

First, I review the process of mental math subtraction of breaking apart numbers using place value with a word problem using both rounded numbers and actual numbers.  

An example of this would be 53 - 28 = ______.  Rounded, this would be 50 - 30 = ____.

Rounding also supports the students confidence in subtraction by providing friendly numbers to subtract. 

Because I know the students need to practice their skills with subtraction, using place value, I have taught the students to separate the tens and ones to subtract.  For example, if the subtraction sentence is 53 - 28 = _____, the students would subtract 53 - 20 = 33, and then 33 - 8 = 25.  

The reason I use this strategy is I find students will rely on the steps of the "standard" algorithm, rather than thinking about changes in the value of the numbers.  I have also found my students are still switching the order of ones digits to put the larger number first.  For example, in the problem 53 - 28, when using the standard algorithm some students will think, "Well, I can't take away 8 from 3, so I'll do 8 take away 3. That way it works."

I chose to have the students use individual whiteboards and markers for this type of problem because I can see their work easily and they can make corrections quickly.  This also gives me a cue about who may need additional help throughout the lesson, and who will benefit from more challenge. 

Introduction to Today's Lesson

10 minutes

Because some of my students expressed they had not ever carved a pumpkin before, I knew I needed to provide some background information about how pumpkins grow.  I explained how pumpkins grow from seeds  about the size of the fingernail of your thumb. I displayed a pumpkin in front of the students and asked them to estimate how many seeds would fit inside of the pumpkin?  I asked them to estimate the weight of the pumpkin by lifting it.  Because the students are growing up in an urban area with few gardening experiences and some in poverty, I decided to provide some additional information about the pumpkin and also have them hold the pumpkin.  This knowledge of students' background and potential experiences was needed to support the progression of the lesson.

I feel it is so important children are given the opportunity to examine and explore some of these common seasonal items thoroughly.  They all could name a pumpkin, but many of my students had never experienced the slimy, stringy insides of a pumpkin.  This lesson combines different math skills and allows students  to work in groups allowing for different levels of abilities to work together and all students contributing to the group work.

After some discussion, I explained the students would be making estimates about various types of information about the pumpkin, and then they would measure using tools including rulers, tape measures, and a scale.  The students at my school had previous experiences using measuring tools in second grade with building simple machines and measuring lengths in a science unit.  This activity provided students with an opportunity to become familiar again with the measuring tools we will use throughout the school year in math and science.   

Because the Common Core standards require students to work with metric measurement in third grade, I displayed a textbook and demonstrated its weight using kilograms.  I then weighed the same book in US standard customary measurements in pounds. I explained how the students will need to use mental math subtraction to compare their estimates to the actual measurements.  

 

Guided Instruction

10 minutes

First, I asked the students to show me the gestures we have established for some measurement vocabulary.  For weight we pretend we are holding something really heavy, height the students extend their hands high above their heads, circumference is drawing a circle out in front of their body (as the equator is around the earth), and for diameter the students draw a horizontal line in front of himself/herself.  

Depending on the number of pumpkins for the activity, students work in either groups, partners, or individually.  My students were working in groups of about 4 students each.

The student groups record their estimates about the weight, height, circumference, diameter, and the number of seeds on the recording sheets together.  Because I want the students to estimate, I did not have the measuring tools on their desks at this time. 

Students can use the textbook from the warm up section to help make their estimations for weight and height.  

If needed, demonstrate how to use the scale, which side of the measuring tape, and ruler to use for metric measurement (MP5 - Use appropriate tools strategically).  It is helpful to discuss the differences between an inch and a centimeter, by comparing them. 

The vocabulary we are using, weight, height, circumference, diameter, were words introduced/used earlier in the year. If this vocabulary is new to your students, I suggest you couple these words with "kidspeak" versions, such as "how tall" with height. Using the words, coupled, when speaking and in writing, will assist students to learn this vocabulary within the context of this lesson.

I have my students use their math journal to record new mathematical terms, definitions, and create illustrations or examples.  My experience is that math journals are more meaningful than posting vocabulary on a wall, because the students create their own resource that is meaningful to them.  

The size of pumpkin does not matter.  Because of safety requirements,  adults cut the tops of the pumpkins prior to beginning the lesson. 

Explore

25 minutes
Weight and Measurement
Students working in groups, partners, or individually: 
    1. Estimate the weight of your pumpkin and record
    2. Weigh the pumpkins on the scale and record
    3. Determine difference between actual weight and estimate using mental math strategies.
    4. Repeat the steps of estimating, measuring, and subtracting with mental math strategies for the circumference and  diameter of the pumpkin. 

Seeds 

    1. Open the pumpkin, observe, describe, and record information about your pumpkin on the recording pages. 
    2. Scoop out one handful of seeds from the pumpkin 
    3. Count the number of seeds. 
    4. Estimate and record how many handfuls/seeds will be removed from the pumpkin. 
    5. Scoop out all remaining seeds and collect into a pile. 
    6. Group seeds into piles for skip counting/multiplying 
    7. Determine the difference between the actual number of seeds and the estimated number of seeds. 

Questions: 

How much did you estimate your pumpkin to weigh?  Was that in pounds or kilograms?  About how many pounds are in one kilogram? What do you think is the reason for measuring in metric?  Why is it important to measure in metric?   What was the difference between your estimate of seeds to the actual number of seeds.  How do you describe the inside of your pumpkin? How did you group your seeds for counting? Why did you choose that way?  Can you think of another way to group the seeds?  Do you think you could use the scale to measure the seeds?  How would you use the scale to measure the seeds?  

Wrap Up (Closer)

15 minutes

To finish the activity, the students were given a graph to compare and find the difference between the estimates and actual measurements from their pumpkins. Because we have used bar graphs in the class before and compared numbers this was a familiar activity to my students.  

Prior to completing this section of the activity, the students cleaned up and the parent helpers had said good bye to the students.  Having the parents/assistants leave before this part of the lesson is important because I want the students to independently apply their math strategies.

The objective of the lesson is to find the difference between two numbers and subtract using a place value strategy.  The groups are given the task of writing subtraction sentences to find the difference between each estimate and actual weight.  

First, students identify the larger of the two numbers by circling it.  Next, each team draws a box around the smaller of the two numbers.  Because I am asking them to compare, and because each group could have either an actual number or an estimate number as the larger number, I provide a model for the number sentence:  circle - box = ________. 

Each group chooses a graph and subtraction sentence to explain and present to the classroom. Students are asked to explain how they subtracted, and the steps of breaking apart the number into their place value (tens, ones).  For each step described, we take peer questions.  If there are no questions, then I ask the questions. This helps to guide the students with framing questions.

The cleaned out pumpkins are sent home at the end of the day with each of the students. We do not carve jack-o-lanterns for reasons of safety, and religious beliefs of some of my students.  It may be an activity to consider if appropriate, and when adult helpers are available.