Mathematical measurements and patters are vital in describing the world around us...and what better place to explore number, operations and even algebra than in the garden? Numbers are everywhere...not only in all areas of mathematics, but also in our daily lives. It's vital children understand what numbers represent and how they are used. Children learn about numbers through concrete, real-world experiences, such as counting objects of interest....like the number of petals on a flower. Numbers are also used to measure in units (such as how many feet tall a sunflower measures) or to make comparisons (such as which sunflower is tallest).
Estimations allow children to gauge an approximate quantity without counting precisely. Opportunities to practice making estimates helps children gain a deeper understanding of the magnitude of numbers and measures as well as assess the "reasonableness" of an answer.
In today's activity, children will measure the area of a leaf with nonstandard units, such as beans, buttons, and bottle caps. The sky is the limit when it comes to units of measurement for this activity. Once the surface area of various leaves is determined, the children will compare those areas.
Each pair of children will need:
- overhead transparency
- white paper
- transparency pen
- about 1cup of small, flat objects (like the beans, buttons or bottlecaps discussed above). Dried lima beans work well
- journal for recording observations
- Select a plant whose leaf area is smaller than a standard sheet of paper. Select a leaf that will hold a countable number of objects within it's area. Younger children will need to use smaller leaves to be successful at counting. A spinich leaf might be a good choice for a 5-year odl, for example.
- Select a flat surface, such as a picnic table or level area of ground, where the group can gather to set out their clipboards and compare areas.
- Either provide each pari of students with the steps for measuring area or write it on a large poster board, chalboard or easel where all students can see the step. (See below)
- Trace a leaf
- Place 1 bean inside traced leaf.
- Estimate how many beans will fit inside the leaf.
- Put 10 beans inside the leaf.
- Revise your estimate and write it down.
- Fill the area of the leaf with beans.
- Count the beans using groups of 10.
- Write down the number of beans.
Conducting the activity:
- Walk through the garden asking kids to look at the variety of sizes and shapes of leaves. Have them use their hands to show the size of the largest and smallest leaves they find.
- Tell them they will be exploring different sizes of leaves. Use your pre-selected leaf to demonstrate how to trace the leaf onto an overhead trasparency. (Carefully place the leave between the transparency and clipboard, then gently trace around the leaf with the transparency pen. This allows the leaf to remain on the plant and lets you kep the outline.
- Hold the transparency up for everyone to see. Point to the space inside the leaf and ask the children if they knwo the mathematical name for the space inside. It's called the "area."
- Hold up a lima bean (or other unit of measure) and ask how many beans they think it will take to cover the area.
- Have the children discuss their estimates, share them with each other, and explain their thinking.
- Demonstrate the steps for measuring area outlined above letting the children make the estimates. Ask if their estimates became more accurate as they gathered more information.
- Go over the steps for measuring area one more time; make sure each pair of students has access to or can see a copy of the steps.
- Have the pairs select their leaves. If they are having trouble tracing a leaf on the plant, have them select a fallen leaf to trace. Guide them through the measuring steps and assist if necessary.
- Regather and have a group show their leaf outline while the other children make estimates cbout the area. Have the group revela the actual area in beans.
- Record that number inside the leaf outline and place that paper in the center of the group.
- Continue with another group. Have them show their leaf in comparison. Is it larger, smaller, or about the same size? You can place the transparencies one on top of the other to help estimate the area.
- Have the children estimate the area of the second leaf, then share the actual number of beans and record that number in the center of the leaf tracing.
- Continue until all the groups have shared their leaves. Line the leaf tracings up in order of smallest to largest area.
- Ask questions such as: What helped you make your estimate? How many leaves have about the same area? What do you notice about the size and shape of leaves? How do you think leaves help the plant grow?
- This activity is designed to arress the math standards of number, operations and algebra and well as geometry and pattern.
- It is particularly relevant for students ages 5-8
- You can use transparencies with a centimeter grid to compare areas using standard units of measure, then compare the results of the standard and nonstandard units of measure.
- Use string to measure the perimeter of the leaves. Modify the shapes encompassed by the string to see how the areas are affected.