Lesson Plans: How Small Can You Cut? | Where will it go? | Charge Challenge | Invisible Investigations | Magnet Mania | Pea Brain! Explorations in Estimation | What Shape is it?
Use two different techniques to estimate how many little things fit into a bigger thing.
Grades: 4-8 (National Standards)
Time: 45 minutes to an hour
Scientists use estimation when they just need a “ball park figure” to get them started. They may ask how many stars exist in our galaxy or how many galaxies exist in our Universe. It would be complex and not necessary to find the exact number, and so a close guess would be sufficient. This is known as order of magnitude, which just means how many times bigger or smaller something is, for example, a grapefruit is about 1000 times bigger than a pea. Similarly, if a doctor needs to know how many red blood cells that you have, the doctor wouldn't try to count every single one – there are far too many. In this lesson, we demonstrate two different techniques of estimating how many smaller things fit in a bigger container to help give students a sense of size.
This lesson can be combined with viewing the Eat your peas video Eat your peas video. In this video, Ushi estimates how many peas are inside of Danny's brain. The adult human brain is between 1200-1500 cm3 in volume and weighs about 1400g. To come up with the number of peas in Danny's brain of 10,000 in the video, Ushi made some assumptions. Some assumptions are normally necessary in scientific estimates. These assumptions can include an estimate of size, rather than using an actual measurement. Scientists should state these assumptions and explain how they used them to get the result, so that other people double check the accuracy of their estimate or prediction. In the video, Ushi makes an order of magnitude assumption, meaning that she only is trying to be accurate to a factor of 10 – like we would round up 98 to 100. Ushi uses 0.125cm3 = 0.5cm × 0.5cm × 0.5cm for the average size of a pea. This is an assumption, based on what we know about actual size peas from real observations, to make an estimate. Then she divides the volume of Danny's brain (1,200 cm3) by the average size of a pea (0.125cm3) to get an estimate of 9,600 peas. Ushi then rounds it up to about 10,000 peas.
Scientists estimate all of the time. They do this for many reasons such as to figure out how long an experiment will take to do, how many people they need to do it, how many times they can repeat an experiment, if the experiment they are trying to do is possible, and have useful numbers for things that are impossible to measure or count. For example, you want to know how many fish there are in the ocean – you cannot count them all, so you come up with a system to estimate the number of fish. Particle physicists, like all scientists, use estimation for many things such as: to scale up the results of their tests – because the experiments can be very expensive to do on a large scale, and estimate some properties of matter (e.g mass) because they are difficult to accurately measure.
Estimate the number of peas that will fit into something the size of a small paper cup. Estimate A uses volume and Estimate B uses weight. Students can calculate the number of peas in a human brain by following the procedures outlined in Estimate C.
(if time is limited or you do not have access to a food scale, use Estimate by Volume as a stand alone activity)
Each pair of students needs:
Questions for discussion with your group might include:
Each pair of students needs:
Questions for discussion with your group might include:
The estimate by weight is likely to be more precise because of empty space between the peas in the volume estimate (peas are not square), and the cup is not completely cylindrical, so it can be difficult to estimate volume accurately.
The estimate by weight is sensitive to the quality of the scale available – small differences in the weight of a small object (one pea) result in large errors when you multiply it many times. The calculation of the number of peas in a cup would be more accurate if you subtract the weight of the cup from the weight of the cup filled with peas and then divide this number by the weight of one pea.
To estimate the number of peas in a human brain using weight: divide the average weight of a human brain (1,400g) by the weight of one pea (Step 2 in Estimate by Weight).
To estimate the number of peas in a human brain using volume: have students calculate the volume of one pea by measuring the dimensions of the cup to estimate its volume (length × width × height or diameter × diameter × height) and then divide this number by the number of peas that fit in the cup. This is an estimate of the volume of one pea. Divide the average volume of a human brain (1,300 cm3) by the volume of one pea.
Science
Math
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Compute fluently and make reasonable estimates
Understand measurable attributes of objects and the units, systems, and processes of measurement
Apply appropriate techniques, tools, and formulas to determine measurements
Data Analysis and Probability Standard