Center Street Elementary School

Horseheads, NY

Horseheads is the only town or village in the United States dedicated to the honor of the American Military Horse. Horseheads was named for the military horses in the army unit commanded by General John Sullivan during the American Revolution. In 1779 General Sullivan and his five thousand soldiers were fighting against the British soldiers and the Iroquois Indians who were helping them. After the Battle of Newtown on August 29, 1779 the British and the Indians were fleeing north toward Seneca Lake and General Sullivan followed after them. It had been a very rainy season and the area was very swampy, so the horses had a very difficult time carrying all the military supplies along the trails. Finally on September 24, 1779 General Sullivan and his army returned to our area. By this time there was little food left for the horses and many of them were ill or wounded from the battle. Many horses were so worn out that they cold not go on any farther. General Sullivan was forced to kill them for humanitarian reasons so they would not suffer.

A year or so later the Indians returned to this area and found all the horse bones. They arranged the skulls along the trail and called this area the “Valley of the Horse Heads.” Early settlers who came to this area many years later saw the horse skulls along the trail in this wilderness area. They decided to keep the Indian name and in 1837 the village of Horseheads was established.

New York State Science, Math and Technology Standards

Standard 1: Analysis, Inquiry and Design

Mathematical Analysis - Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Standard 3: Mathematics

Students will: understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

3.1 Mathematical Reasoning

Students use mathematical reasoning to analyze mathematical situations make conjectures, gather evidence, and construct an argument.

3.2 Number Sense and Numeration

Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use numbers in the development of mathematical ideas.

3.3 Operations

Students use mathematical operations and relationships among them to understand mathematics.

3.4 Mathematical Modeling/Multiple Representation

Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

3.5 Measurement

Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and

3.6 Uncertainty

Students use ideas of uncertainty to illustrate that mathematics involves more then exactness when dealing with everyday situations.

3.7 Patterns/Functions

Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patters simply and efficiently.

Mr. Berger’s Class Mathtrail Problem	N. Y. State Math, Science, Technology Standards
Slap! Slap!	1, 3.3
Leaves	1, 3.3
Leg Problems	1, 3.3
Arrowheads	1. 3.2
Longhouse #1	1, 3.3
Longhouse #2	1, 3.5
Geoanimal	1, 3.7
Quilt Array	1, 3.5
Freedom Trail	1, 3.5
Geometry for the Art Gallery	1, 3.7
Pattern Blocks	1, 3.7
Torn Shapes	1, 3.7
Cup Cake	1, 3.1, 3.2

The Trail Begins

The idea for this Mathtrail was developed in conjunction with our participation in the Chemung River School Project. The Project gave us the opportunity to get out into our surrounding community; we used the concept of “math is everywhere” to connect math to the Project. The mathematics ideas on this Mathtrail were created using the field trips as a jumping off points for math.

Use the Answer Sheet provided and, most important, have fun! (There is an AnswerKey at the end of every section if you need!)

Chemung River School Project

The Chemung River School Project was initiated in 1994, spearheaded by the Arnot Art Museum. This nine month multidisciplinary collaborative program combines fourth grade science, natural and social history, and ecology curricula with writing, performing and visual arts. The Arnot Art Mueum works with the Chemung County Historical Society, Tanglewood Nature Center, Chemung County Environmental Management Council and Wastewater Treatment Plant.

Math along the banks of the River ….

Slap! Slap!

It’s a beautiful, sunny day on the Chemung River. 43 children are sitting quietly on the rocky shore. Slap! Slap, slap! Slap! Slap, slap, slap, slap, slap! Mosquitoes! Hundreds of mosquitoes. When the kids got on the bus each one of them had 13 mosquito bites! How many mosquito bites did the class suffer from that day?

Leaves

Elm, maple and birch trees line the river. Each tree has at least 26 branches with 59 leaves on each branch. How may leaves are on each tree? There are 14 trees in view. How many leaves are there all together?

Leg Problems

Eight kids caught 4 spiders each, seven kids caught 5 mosquitoes each, six kids caught 4 water striders each. How many pairs of legs do they have altogether?

Hint: Number of Legs

1 spider = 8 legs

1 mosquito = 6 legs

1 water strider = 6 legs

AnswerKey:

Slap! Slap! 43 kids x 13 bites each = 559 mosquito bites

Leaves 25 branches x 59 leaves = 1,534 leaves AND 1,534 leaves x 14 trees = 21,476 leaves

Leg Problems 8 kids x 4 spiders = 32 spiders

7 kids x 5 mosquitoes = 35 mosquitoes

6 kids x 4 water striders = 24 water striders

32 spiders x 8 legs = 256 legs

35 mosquitoes 6 legs = 210 legs

24 water striders x 6 legs = 144 legs

Total legs = 610 legs

610 legs divided by 2 per pair = 305 pairs

The Iroquois Nation

The Trail continues with our visit to the Chemung Historical Museum located on East Water Street in Elmira, NY. In our area there were five local Native American tribes that formed the Iroquois Nation. At the Museum, the Native Americans showed us Iroquois arrowheads and longhouses as well as other Native American Artifacts.

Arrowheads

One man told us it took 6 days to find the stone, shape it into an arrowhead and tie it to the arrow. Another man said it took him 7 days. The lady could make one in 5 days. On the average, how many days does it take to make an arrowhead?

The Longhouses

1. The Iroquois Indian longhouse was at the center of daily life. They were made of birch logs and tree bark. They sheltered the many families of a clan and it was the location of their every meal. A village might have a dozen of these houses. The first longhouse they showed us took 24 logs to make. Another longhouse used 18 logs. The biggest longhouse needed 45 logs! What was the average number of logs it took to build a longhouse?

2. What is the perimeter of this Iroquois longhouse that is 250 feet long and 60 feet wide?

AnswerKey:

Arrowheads - 6 days + 7 days + 5 days = 18 days

18 days divided by 3 people = 6 days on average

Longhouse #1 - 24 logs + 18 logs + 45 logs = 87 logs

87 logs divided by 3 longhouses = 29 logs on average

Longhouse #2 - 250 feet + 250 feet + 60 feet + 60 feet = 620 feet around

“The Dish” Math Game: #1 - various, #2 - 9, #3 - Little Beaver, #4 - Lone Wolf, #5 - Bright Star = 48, Lone Wolf=26, Falling Star=42, Little Beaver=84, #6 - < (less than), Bonus - Falling Star and Little Beaver

Geometry in Nature

A local artist visited our class as part of the Chemung River Project and the kids had a chance to use geometric shapes to create animals that are found in our local habitat.

Geoanimal

Using construction paper, cut geometric shapes and create your own animal. Fill in the chart to show the body parts for your animals and the shapes you used to make them.

Body part	Geometric shape used to make it

AnswerExample:

Body part	Geometric shape used to make it
Head	circle
Leg	triangle
tail	oval

Quilts

For February, Black History Month, the Trail brought us back to the Chemung Historical Museum. We learned math by looking at quilts. The quilts, which used geometric shapes, were used as maps to guide the slaves to freedom.

Quilt Array

During the Civil War slaves from the south escaped to the North on the “Underground Railroad”. At the Historical Museum, we learned that a map of the Underground Railroad was hidden in the design of quilt. The quilt was 60 inches wide and 48 inches long. Each square was 3 inches by 3 inches. How many squares would it take to make each row? How many squares would it take to make each column? How many squares would it take to sew the whole quilt?

Freedom Trail

One route on the Underground Railroad was traced on a map of New York. The map scale read 2 inches = 60 miles. The class figured we could walk 3 miles in one hour. Using this information, finish the following chart and answer the questions that follow.

Depart	Arrive	Inches on map	Miles between Cities	Hours to walk between cities
Elmira	Ithaca	1 1/2
Ithaca	Etna	1/2
Etna	Auburn	1 1/2
Auburn	Syracuse	1 1/4
Syracuse	Rochester	4

1. How many miles is it from Elmira to Rochester?

2. How many hours would it take to walk from Elmira to Rochester?

AnswerKey

Quilt Array - 60” divided by 3” = 20 squares wide columns)

48” divide by 3” = 18 squares long (rows)

20 wide x 18 long = 360 squares all together

Freedom Trail -

Miles between Cities	Hours to walk between cities
45 miles	15 hours
15 miles	5 hours
45 miles	15 hours
34 miles	11 1/3 hours
120 miles	40 hours

1. 259 miles

2. 86 1/3 hours

Geometry in the Art Gallery

While visiting the Arnot Art Museum the students went on a scavenger hunt for geometric shapes. They were asked to find as many shapes as they could listing the work, the artist, the medium and which geometric shapes were found.

When we returned to our classroom the students created their own pictures, collages or drawings using geometric shapes. Some students used cut paper from magazines and some used pattern blacks to create animals, plants and other objects.

Pattern Blocks

Vicky uses pattern blocks to create a turtle. Fill in the chart to how many of each the shape she will need.

Erica finshes the flower. Use the picture of the turtle and the flower to complete the chart.

Picture	Hexagons	Trapezoids	Rhombus	Triangles	Square	diamonds
turtle
flower

Torn Shapes

Eric tore squares from magazine pages and created this Mahi-mahi fish. He used all squares and three different pictures/pages: black with gray, green and yellow. The Mahi-mahi has a long fin along its back, a round forehead and blunt head. The tail is triangular. Create your own animal the same way. Think about colors and shapes of the pieces of paper and the animal itself.

AnswerKey

Picture

Hexagons

Trapezoids

Rhombus

Triangles

Square

diamonds

turtle

flower

Life in the 1800’s

Our last stop took us back in time to the Browntown School House in Corning, New York. The Browntown Schoolhouse was built in 1878 and served grades 1 through 8 until 1955. A “potbellied” stove using wood or coal has always been used to heat the school. The blackboard in the school is, indeed, boards painted black. Pump organs are commonly found in one-room schoolhouses; Browntown uses an 1885 Estey Parlor Organ. A privy stands on each side of the schoolhouse; one is for boys, one for girls.

Cup Cake

A teacher helped us make “Cup Cake“, an easy to remember recipe that was used in the 1800”s. Here is the recipe for a small cake that is enough for one class.

Cup Cake

1 cup butter

2 cups sugar

3 cups flour

4 eggs

Mix all the ingredients together. Pour into an 8”x8” pan. Cook at 350 degrees for 45 minutes.

We need enough cake for 3 classes. Write the recipe for a cake that could serve 3 classes. Explain how you solved the problem.

AnswerKey:

Cup Cake- 3 cups butter, 6 cups sugar, 9 cups flour, 12 eggs

Multiplied each number by 3

Census Report - 1. 1,096, 2. 1,03, 3. 2,163, 4. 1,471, 5. 1,447, 6. 64 more men, 7. 24 more men, 8. Decreased by 11, 9. Total of 2,940 and increase of 777, 10. John Brees was 72 in 1810, he was in the 45 years or older group, 11. Sara Brees was born in 1789, so she was 21 years old in 1810 and was in the 16 to 26 year old group.