# Standard Algorithm for Multiplication: Math in the Natural World

## Math in the Natural World: Standard Algorithm Multiplication 5th Grade

The natural world is a fantastic vehicle for getting kids to think deeply about the Standard Algorithm for Multiplication. When I show a nature video at the beginning of class, I get immediate buy in because they are all fascinated, especially when it has to do with animals. They ask a million questions about them and then they want to find the answer. Why wouldn’t they love it? It is fascinating and ripe with mathematical concepts. The natural world holds so many wonders and amazing examples of survival. It is inspirational for adults, as well as children.

One of the fascinating parts of the natural world are the numbers. From the very small to the very big, we can quickly get absorbed in the numbers; the number of a species, the amount of bacteria in a tablespoon of seawater or the number of eggs laid by insects. One of the more impressive sets of numbers is the migratory patterns of the Monarch Butterfly.

This butterfly makes the migratory trip from Canada and the US to Mexico each year. Granted, it may take a few generations for them to reach their destination, but they do it nonetheless. They return each year to the same locations, and even sometimes the same tree. Amazing!

## Set Up for the Lesson: Standard Algorithm for Multiplication

● Each student will need a Monarch Multiplication Activity Worksheet.
● Create three teams. Each team will work with one data set.
● Predetermine the groups based on who works best together.
● Each student needs a sticky note to record their questions.

## Launch the Lesson

Show the students the video Watch a Breathtaking Monarch Butterfly Swarm. Ask them to write as many questions as they may have about the butterflies.

### Questions may include:

● Where did they come from?
● How did they get there?
● What are they doing there?
● What do they eat?
● Why are there so many in one place?

Allow students to share some of their questions after the video. Don’t answer the questions. Just let them ask. Let them know that some of their questions will be answered during the lesson. Others will not. Ask the class to mark with a star any questions that might address a mathematical concept or be answered mathematically.

Then show the video Monarch Butterflies Begin Annual Migration from Cape May to Mexico.

See if students have any new questions about the math involved in the Monarch Butterfly Migration.
Record their questions and mark them with a star.

Note that the distance some Monarch butterflies travel to get to Mexico is more than 2,000 miles. Ask students to think about the greatest number of miles they have ever walked. How did they feel at the end of that journey? Was the journey anywhere near 2,000? What if they had to fly that distance like a butterfly? How many times would they have to flap their wings to make it 2,000 miles?

Ask students to stand up and put their arms out to make sure they are not touching anyone. Tell them to practice “flapping their wings” by flapping their arms up and down. Encourage them to do it as fast as they can. Time them for one second to see how many flaps they can do in that time. They will say things like, “This is impossible!” Ask how many they were able to do. Let them know that Monarch butterflies flap their wigs 5-12 times per second. Try again and see how long it takes students to flap their arms up and down 5 times, then 12 times. Record the class’s lowest and highest numbers on the board.

## The Lesson: Standard Algorithm for Multiplication: Math in the Natural World

Review multi digit multiplication with the class. Using ideas from the video, write this problem on the board: If there are 57 trees in a grove and there are 543 butterflies on each tree, how many butterflies would there be in the entire grove? Have students work through the problem in their math notebooks as you work it out on the board. Ask different students to explain how they set the problem up and to give each step in the process of solving it in order to check on the understanding of as many students as possible.

Divide students into groups of three. Give one data collection sheet to each group. Each group will be working with a different set of data. They will share out with the other groups at the end of the class period. You can break the groups down into pairs. We know that too many students working in one group usually ends up with some kids not participating. I also like to require each student to have their own worksheet. If you break each group into partners, they can come together at the end to check each other’s work, and they can help each other if they get stuck.

Assign each group a data set, # of wing flaps, speed of flight and distance traveled, or number of monarchs. Students should use the data tables provided to gather information for their question set. All work should be done by hand – no calculators. Students should use the standard multiplication algorithm to complete each question. All work must be shown. They cannot do the work in their heads. You may wish to review the standard algorithm with them before they begin. This activity should take place after students have had explicit instruction in multiplying multi-digit numbers.

Walk around as students work, checking on their ability to generate the correct conversions of time. For example, did they correctly convert hours to days? When a group finishes, have them get together with the other partner group and check each other’s work. Prompt partner groups to discuss how they got their answer if they have different products and determine how to get both sets of partners using the same strategy to solve so they arrive at the same product.

If time allows and your class is comfortable discussing their mistakes as opportunities to learn and grow, ask a partnership who had an incorrect product share out to the class what went wrong, how they figured it out, how they fixed it, and what it taught them.

## Reflecting on the Activity: Standard Algorithm for Multiplication

Have each group of students share out the answers they found for their data sets. Record these numbers on a large chart at the front of the room or use a document camera so all students can see the numbers. Discuss the impact small numbers have when multiplied by larger numbers.

Students will most likely be surprised at the large numbers they will produce in their work. Let them marvel at the impressive math involved in the natural world. Discuss the questions they wrote at the beginning of class and see if any of them have answered their questions through their work. What questions still remain? Have other questions arisen during the activity? If there are questions remaining, consider offering extra credit to any student who brings a correct answer back to class the following day, accompanied by a reliable source.

## Extensions/Next Steps: Standard Algorithm for Multiplication

You could generate another set of questions based on the table below. This could be a review and/or tie-in to the last unit, to practice using Multiplicative Patterns on the Place Value Chart. The students would recognize 3,000 as 3 X10 X10 X10. You could work through a problem with them like, if there were 100 butterflies, how many total miles did they travel? This is yet another opportunity to look at the enormity of some of the numbers we come across in nature. Another possible extension of this work is to use the following data table to connect to powers of ten and scientific notation.

1. If the total population of Monarchs was at 303 million (2018-19), how many total miles (if you combined the miles traveled by every Monarch butterfly in the population) would be traveled from Canada to Mexico?

2. From Cape May, NJ to Mexico?

3. If the total population was 124 million (2017-18), how many total miles (if you combined the miles traveled by every Monarch butterfly in the population) would be traveled from Canada to Mexico?

4. From Cape May, NJ to Mexico?

## Resources: Standard Algorithm Multiplication 5th Grade

https://monarchbutterflygarden.net/8-things-know-monarch-migration/
https://journeynorth.org/tm/monarch/FlightPoweredSlowMotion.html

10 Things You Might Not Know about Fall’s Annual Monarch Migration? 🤔

https://www.sciencedaily.com/releases/2005/08/050814173536.htm

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