While learning about different kinds of angles, I had asked my students to find examples around the classroom. We then thought, ” Where else we might find them ‘in real-life’ ?” The obvious next step was to look outside.
I like to have students use non-standard measuring tools to estimate dimensions (something many of us have done in a pinch). So before we headed out, I posed the question, “If you do not have a protractor, what else might you use?” Your hand was one of the responses.
Students had already estimated that the angle made by their thumb and index finger was about 90º. We measured it with a protractor to see how close each student’s hand was, wrote it down and then headed into the woods.
Each student had a recording sheet with their hand angle measure on the top and a table for recording objects and their angle measures. They ran excitedly about the woods measuring things such as veins on leaves, branches on a tree , veins on a rock and boards on the bridge. A few brave souls tried measuring branches high above their heads and the angle formed by two tree trunks in the distance.
Initially, they began with just 90º and 45º angles, but then they wanted to measure whatever angle they could find. Thus we had a short problem-solving session on breaking 90 and 45 into smaller measures or adding onto the 90. It did not take the students long to fine-tune a process between themselves. Armed with this knowledge, off they went to try it.
Some students asked for a challenge, so I told them to look for objects that contained more than one angle, such as a leaf. Students used added and subtracted angle measurements to create acute, right, obtuse and straight angles. Once other students saw this happening, they began to challenge each other to find ways to create specific angle measurements. A bit of a scavenger hunt was created!
Once we had finished our activity, the students began to brainstorm other measurement activities we might do on our next trip into the woods. Math outside never fails to spark their imaginations.
Meroby Elementary, 4th grade
We have been learning about what arrays are and how to use them to represent multiplication equations. Last week, my class went into the woods to take on the challenge of creating arrays themselves with the help of the natural resources around them. Students worked in teams of two to use natural objects to create arrays that represented the equations 4×5 and 5×5.
Part of the challenge was for them to try to create it with their partner, and then show their array to either myself or another teacher. It brought me so much joy when my students ran up to me and proudly showed me the arrays they created. My students enjoyed the activity, and were excited to explain their thinking behind their arrays.
This challenge was fun and it brought out the creativity in my students. Some students used pinecones, some used leaves, and some used sticks. When I asked a team of students about their 5×5 array, one of them replied “We made it with teamwork and sticks!” and went on to say how creating their own array helped them better understand what an array is.
Meroby Elementary School, Grade 3
When learning about multiplication you have to understand the concept of equal groups. When you have equal groups it has the same number of items as all of the other groups.
In order for the students to understand what I meant, I had the students arrange themselves into equal groups. However, they could only have 2 people in a group. The students quickly realized there would be 5 groups of 2 because of the total number of students in class (10 in all). Next, I had them put the groups of 2 into columns and rows and asked the dimensions of their array and most of them said “It’s a 5 by 2!” or “It’s a 2 by 5!” I then took time to show them the difference on how the arrays look.
We all went into the woods and I asked them to collect natural objects (all the same) to build an array just like we did with ourselves. I didn’t tell them any specific instructions on how many items to get or even how to build the array based on the number of items they chose. In the end, they were able to explain to me about how they arranged their items into equal groups and why they chose to build that particular array.
It was amazing to see how many different arrays the students came up with after collecting their natural objects.
Meroby Elementary School, Grade 3
Kindergarten brought their collecting baskets to the woods, ready to embark on a nature adventure. The closer we got to our outdoor classroom, their excitement grew and grew. Once there, children moved freely around the forest, collecting small, medium, and large leaves of various colors and types. Children shared about their own leaf collections, and were naturally curious about what leaves their friends chose to collect.
“I see a hole in it!”
“The stem is so long!”
“I found a big red leaf!”
We took our leaf collections back to school, where we examined them closer and decided to use them as counters on large ten frames. Since we enjoy being outside, we carried our baskets and ten frames to the playground. While there, I wrote one number at a time on a white board, describing how to form the number while writing. Children shared with one another what the number was and then used their leaves to show how many.
We enjoyed this activity because it was outdoors and we got to use our own leaf collections! Creating a fun and meaningful hands on activity.
Meroby Elementary School, Kindergarten
“The only way to learn math is to do math.” Paul Halmos
On a rainy Friday afternoon when you have been stuck inside for days, it is hard to hook your students into a lesson of any sort. What is a teacher to do! We haven’t had recess, no woods day, no fresh air inside the walls of our classroom.
This teacher decided it was a great time to teach her first graders about estimating! We looked out the window at a freshly created puddle and I asked them how many sticks they thought it would take to go the length of the puddle. The students all guessed an amount: “5!” “30!” “14!” We grabbed our jackets and out we went!
It took the kids less than one minute to collect 5 sticks each, and less than a minute (using great teamwork) to spread their sticks the length of the puddle. They took turns counting and WALAH! The puddle was 17 sticks long!
We loved this activity because it was outside, it was quick, and it taught us that doing math is a lot of fun!
Kati Mazza, Meroby Elementary School, Grade 1
This week, first graders went to the woods with collecting on their mind. Sitting in the outdoor classroom in the crisp air students were asked to work in teams to gather natural objects that we could use as manipulative’s for math time. Some groups chose to collect leaves, some groups chose to collect sticks, and others collected items like pinecones and small rocks. The kids ran around with their bags and their group finding the best sticks and the best leaves to collect to use.
“WOW! Look how HUGE this leaf is.”
“I bet I have 100 sticks in my bag!”
“My bag has 3 different colors of leaves in it!”
Students talked to each other about their collections and were very curious about how we would be using these collections later during math.
Fast forward through the day to math time. Two of the first-grade classes met outside where there were 10 different “flap cards” drawn in chalk. Flap card and dominoes have been a topic in math for several weeks. All of the kids partnered up and were asked to use natural objects from their collections to make their own flap cards to match the whole number that was written above their flap card. This resembles a part-part whole mat. To take it to the next step partnerships worked together to write out the fact family that matched their creations on a white board. The level of student understanding for this lesson was amazing and the level of engagement shown was proof, in itself, that with a little fresh air and choice of manipulative’s students can succeed.
Karri Hall, Meroby Elementary, Grade 1
This week our 4th graders headed out into the woods at our Principal’s home to explore and learn about Maine’s natural environment. Seeing the kids outside was energizing. They came alive, running, hopping, and skipping. They wanted to inspect at everything!! They were fascinated with mushrooms and different tree varieties, and crossing a rushing brook was an epic adventure with shrieks of delight. The children definitely thrived in this new outdoor classroom.
“Whoa, look at that tree!!”
“Wow, it’s HUGE?”
“I’ve never seen a tree so big!!!”
“Why does it have red paint on it?”
Our Principal went on to explain that it was a property boundary tree, so the land around the tree had been logged, but they didn’t cut down this particular pine because it was a boundary marker between property lines. Seeing how curious the students were their teacher asked, “What do you think the diameter of that tree is? Can we estimate?”
Previously back in the woods at school, students had made estimates in the forest using their hand spans as a measure. They knew their spans were about a foot, so they could use that information to estimate how many feet long something was. Immediately they ran to the tree and tried to see how many of their hand spans it would take to go all the way around. They were short a small section, so the Principal joined them to close the gap. They discovered that it took the hand spans of 11 people to go around the tree, so the diameter was close to 11 feet!
The entire day was exciting, but this small connection of math with nature was one of many academic connections made that day. They measured their heart rates before and after their hike, and they tracked the number of steps they walked during the day. They also used a phone app to create a map of the hike and see how far the hike was. All of this math was done with inquisitive attitudes and smiles.
Yes, you can lead your students across water, and you can get make them think!
Karen Wilson, Meroby Elementary School Math Coach
It’s autumn, the colorful leaves are falling in the outdoor classroom, and 2nd graders need practice with skip counting, flexible addition/subtraction strategies, and using models to show their work. I had noticed that the concept of 100 was not yet solid. Students were using millions and thousands to describe much smaller amounts. To address their math needs, along with their desire to be in nature, we visited our outdoor classroom to gather 100 leaves in three minutes. The students were paired and had drawn out their strategy before going outside. Counting one by one was NOT an option. Their strategies included:
<p”>After the first trial, the results were: 8, 18, 25, 51, and 140. A class reflection followed to generate new and improved ideas. As it turns out many pairs had resorted to counting one by one.
<p”>The second time, the students were more efficient and used estimation and skip counting to get closer to 100. One pair conducted a divide-and-conquer approach. They made a group of 10 together by finding two groups of five leaves. Once they had 10, they duplicated that by making a pile that appeared to be the same height.
The results were much closer the 2nd time:
82, 91, 94, 97, 100* (* there may have been some leaves added at the end, but they were certainly close to 100).
Laura Waite, Otisfield Community School, Grade 2
Oscar Wilde once said, “Two men look out a window. One sees mud, the other sees the stars.” What do you think a class of curious Kindergarteners sees when they look through a window in the woods? Can you imagine what kinds of math opportunities a window can provide?
I put 4 meter sticks down on the ground in our classroom space in the woods. I asked my students, “What do you notice? What do you wonder?” The first time I did this with my class, their responses were very hesitant. “Um pine needles and leaves?” “Why is there a stick in there?” We tried the activity a few more times and each time we got better at noticing and wondering. A week ago, I did it again and I heard more excitement, engagement, and vocabulary use. “I noticed that there are some leaves that have many different colors!” “I noticed there is a footprint in the corner. I wonder what made it!”
After we notice and wonder as much as we can, I ask them to think of some math questions we could ask. This activity has led us to counting leaves, estimating how many pine needles were inside the window, and measuring the length of a footprint with acorns. By laying down a clear visual that represents a window, the math opportunities are as endless as students’ wondering will take you. This activity can be easily used by students of all ages, grades, and abilities. Each age group will approach it at the level where they are, so the maths may be as simple or as complicated as would be appropriate for the ages. Changing window size and adding inside grid work is a great way to keep the activity fresh. Putting the window down in unique and different areas is also a great way to keep students wondering.
We love this activity because it lets us look closer, to wonder and to hear what others are also wondering, and to find math where we just played. It might be mud, it might be stars, but either way we are happily mathing!
Maggie Corlett, Kindergarten, Meroby Elementary, Mexico, ME
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