Laura Pakaln

Standard 1: Analysis, Inquiry, and Desipn:
Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard 2: Information Systems:
Students will access, generate, process, and transfer information using appropriate technologies.

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.

Standard 6: Interconnectedness: Common Themes:
Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

Abstraction and symbolic representation are used to communicate mathematically. Deductive and inductive reasoning are used to reach mathematical conclusions. Critical thinking skills are used in the solution of mathematical problems.
Information technology is used to retrieve, process and communicate information and as a tool to enhance learning.
Students use mathematical reasoning to analyze mathematical situations, make conjectures,gather evidence, and construct an argument.
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 of numbers in the development of mathematical ideas.
Students use mathematical operations and relationships among them to understand mathematics.
Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.
Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; realizing 'ideas; making connections among the common themes of mathematics, science and technology; and presenting results.

Students use special mathematical notation and symbolism to communicate in mathematics and to compare and describe quantities, express relationships, and relate mathematics to their immediate environments.
Students explore and solve problems generated from school, home, and community situations, using concrete objects or manipulative materials when possible.
Students use a variety of equipment and software. packages to enter, process, display, an communicate information in different forms using text, tables, pictures and sound.
Students telecommunicate a message to a different location with teacher help.
Students use models, facts, and relationships to draw conclusions about mathematics and explained their thinking.
Students justify their answers and solution processes.
Students use logical reasoning to reach simple conclusions.
Students relate counting to grouping and to place value.
Students add subtract whole numbers.
Students construct tables, charts and graphs to display and analyze real-world data.
Students use multiple representations (simulations, manipulative materials, pictures, and diagrams) as tools to explain the operation of everyday procedures.
Students use different types of models, such as graphs, sketches, diagrams, and maps, to represent various aspects of the real world.
Students make informed consumer decisions by applying knowledge about the attributes of particular products and making cost/benefit tradeoffs to arrive at an optimal choice.
Students work effectively; gather and process information; generate and analyze ideas; observe common themes; realize ideas; present results.

will learn that a penny is worth one cent.
will add pennies and determine how many cents they have altogether.
will understand that when a penny is tossed, it will not always land on the same side.
will understand that I 00 pennies has the same value as $ 1.00, a dollar bill.
will predict and count the number of pennies that fit inside of their footprints.
will learn the value of a dime.
will determine the value of objects to be sold in a class store.
will learn to add together coins of different value.
will group coins by value.
will examine coins closely and investigate qualities that are the same and different.
will make a coin graph in more than one way.
will add together coins of different values to make $ 1.00.
will learn how to make change.
will shop in and run their own class store.

Level 1: Beginner
Student has difficulty grasping the concept of coin value. The student may be able to identify coins by name, but unable to explain its value. This student will have more success in enabling activities that emphasize one-to-one correspondence such as counting pennies.

Level II: Intermediate
Student grasps concepts of coin value and can identify values of different coins, but has difficulty accurately finding sums of mixed coins. Student will have more success in adding coins that are the same, such as only nickels or only dimes.

Level III: Mastery
Student grasps all concepts presented 'tn unit and is able to accurately add and subtract when using coins of different value.

Objectives: Children will learn that a penny is worth one cent. Children will add pennies and determine bow many cents they have altogether.

Materials:
containers of pennies for each child (approx. 10 pennies)
overhead projector and transparency extra pennies for overhead
overhead markers
Peter's Pockets, by Eve Rice portion cups chart paper spare shirts or smocks

Procedure:
Read the story Peter's Pockets to the children. Discuss the ways that Peter used his pockets. Ask the children bow many objects be could carry in each pocket. Could they determine how many pockets Peter had?

Explain to the children that they are going to be using their pockets to put pennies in. Ask if they know what a penny is? How much is it worth? Use the overhead and place one penny on the transparency. Ask the children how much money is there. After they answer, write "I cent" below the penny. Rewrite the amount, using the cent sign, and discuss why we use the symbol in place of the word.

Put two pennies on the overhead. Ask how much money there is now. Write the amount. Continue in this manner until you reach 10 cents.

Explain to the children that they are going to place only one penny in each of their pockets. If a child does not have any pockets, allow the child to wear a jacket, sweater, smock, etc. After they complete this task, tell the children you want them to count out how many pennies they have altogether. Demonstrate by putting your pennies on the overhead and counting them. Write down the amount.

Next, have the children work in small groups to combine their pennies, putting 10 pennies into each portion cup. When they're finished, ask the children how they could find out how many pennies the class has altogether. If counting by tens is not suggested, you can suggest that it would be the fastest way.

On a piece of chart paper, write the days of the week (Monday-Friday) in a column. Next to Monday, write the amount of pennies that you and the children counted. Explain that they will do this every day for one week. Have them discuss how they might end up with more pennies on another day.

Children will accurately count pennies: Every day of the week, have three or four children take turns counting out their individual pennies on the overhead.

Objective: Children will understand that when a penny is tossed, it will not always land on the same side.

1 hand lens for each pair of students one penny for each pair one recording sheet for each pair two different colored crayons overhead projector and transparency of recording sheet two vis a vis markers, different colors
chart paper

Children will work in pairs. Tell the children to look carefully at both sides of their penny with the band lens. Ask them what they notice about the different sides. On chart paper, list the children's observations using one side of the paper for each side of the penny Tell the children that we call the side of the penny with Abraham Lincoln's head, the "heads" side. The other side we call the "tails" side. Label the chart paper accordingly.

Explain to the children that they are going to play a probability game, or a game of chance. Using the overhead and the recording sheet, ask for two volunteers to come up. Ask one child to toss the coin onto the overhead. Ask which side is showing. Have the child color in the first penny on either the head's side or tail's side (use different colors for each side). Player two tosses the penny and colors in the corresponding penny on the recording sheet. Tell the partners to repeat this four more times (two tosses per child), but before they do, ask the class to predict which side they think will show up more times.

Have the children play in pairs. Tell them to toss the penny and record, 10 times altogether. Have them predict after their first or second turn. When done, have the pairs sit in a circle with the class to share their findings. Ask the children what they discovered. Ask them what might happen if they tossed the penny more than IO times? Would they get the same results?

If there is time, let the children continue playing to see what would happen. Put this game in a center so that children can play this game as many times as they wish. Encourage them to find out what happens when they toss the penny more times.

Assessment: Children can accurately explain and show the "head's and "tail's" side of a penny,
Children can correctly describe what will happen if you toss a penny more than one time.
Children can accurately record observations on recording sheet.
Race to $1.00

Objectives: Children will understand that 100 pennies has the same value as $1 .00. Children

Materials:
Arthur's Funny Money, by Lillian Hoban large photograph of 100 pennies, in rows of 10 x 10 a $ 1. 00 bill
"Race to $1.00" gameboard
I pair dice for each group numbered 0-5 chart paper
overhead projector
gameboard for overhead

Procedure:
Read the story Arthur's Funny Money. Have the children recall what items Arthur bought with his money. Ask the children what they would buy if they bad $1.00? Explain and show that 100 pennies is the same as $1.00.

Tell the children that they will be playing a game called "Race to a Dollar". The object of the game is for your group to get 100 pennies as quickly as they can. Using an overhead projector and copy of the gameboard, ask for three volunteers to play a demonstration game. Player one rolls the dice, adds the numbers, and puts that number of pennies on the gameboard. Players continue taking turns until they have filled the board. A single die may be used to modify the game.

Have the children play in groups of three. If time allows, they can play the game again. They can also play "Race to 0", going backwards.

Assessment: Children will accurately add numbers and count out the same number of pennies. Children will correctly place pennies on the gameboard. Children will correctly state that 100 pennies is the same as $1.00, or a dollar bill.

Objectives: Children will predict and count the number of pennies that fit inside of their footprints.

colored construction paper, 9x 1 2 drawing or writing materials overhead projector overhead transparency of a footprint Graph Club CD ROM

Procedure: Explain to the children that they are going to work in pairs to help each other trace their footprints. They can take their shoes off or leave them on. Ask for two volunteers to demonstrate for the class. Then, ask the children to predict how many pennies they think will fit inside of their footprints. Put the transparency up and make a prediction for your own footprint. Write the number somewhere in the border of the page. Explain that after they make their own predictions, they will fill their footprints with as many pennies as they can, without going over the outline. Pennies should be placed side by side. Show on the overhead how they will do this. Then, count the number of pennies and write the number in the border. Discuss with the children beforehand whether they should count the pennies that go over the edge of the footprint. Circle the actual number of pennies.

When the children finish this task, they can share their predictions and results with the class. Ask what might happen if they did this again with or without shoes on. Would there be a difference?

Help the children enter the results on the computer, using a graphing program such as Tom Snyder's "The Graph Club". Create different types of graphs to show the results in a variety of ways.

Assessment: Children will correctly count the number of pennies in outlines of their -feet.

Material:
Jelly Beans for Sale, by Bruce McNfillan
large paper coins
coin paper money
real coins (100 pennies, 2 half-dollars, 3 quarters, 5 dimes, 5 nickels per pair of students) 3x5 index cards on which are written values to be used (for example, show 25 cents; show 25 cents using only nickels; show 25 cents using no nickels) 81/2 x I I boards on which are written the words, "Put It Here"

Procedure:
Read and discuss Jelly Beans for Sale.
Attach large paper coins to strips of paper and place the strips at various places along the floor. Select a sum of coins from one of the strips and ask the children to find the strip that matches that sum. Try this with some of the other strips.

Give each pair a bag of assorted coins.
1. Have the students sort the coins by value.
2. Have the students select one coin from each pile and arrange them from smallest to largest.
3. Have students select another coin from each pile. Beside each coin use pennies to demonstrate the value of each coin.
4. Have the students arrange the second set of coins in a column from largest to smallest.
Using the index cards, read one to the class. Children will place that card's value on their desk. Explain to the children that they are going to play a game. When you read one of the index cards, you want the students to place coins equal to that value on the "Put It Here" board.

When each space on the board has been filled, a new caller can be chosen for a new game.

Assessment: Children will identify specific coin values and add a random set to determine their value.
Observing Coins

Objective:
Students will examine pennies, nickels, and dimes closely and Investigate the qualities that are the same and different among them.

Materials:
One for each student:
8 1/2 x 14 photocopy paper, folded in half (short way) a penny, a nickel and a dime magnifying lens pencil
chart paper, ruled into two columns

Procedure:
Place student materials at each desk. Have children work in small groups. Give the children a few minutes to use the hand lenses to explore the coins. Have them stop, and explain that when you say "Go!" you want them to continue their exploration of the coins in a special way. Tell them that you want them to look at the coins and find out all of the ways they are the same. As an example, you could say that you noticed all of the coins had the word "liberty" written on them. On the chart paper, write the word "same" at the top of the left side of the paper. Underneath, write "all say liberty". Tell the children that you also want them to find ways in which the coins are different. As an example, explain that you noticed the coins each have different dates on them. Write "different" at the top of the right column. Below, write "all have different numbers". Explain to the children that as they are working, they should share their discoveries with others in their small groups. Tell the children to "Go!"

Let the children explore for a little while. Then, ask them if anyone found something that was the same about all three of the coins. Continue with things that are the same, then ask about differences. Write the children's responses on the chart paper.

After this task, have the children unfold their paper. tell them to make their own chart of things that are the same and different about the coins. They can write things from the class list or they can write other things that they discovered.

Assessment: Children can accurately describe different ways in which the three coins were alike or different.

People Coins

Children learn to add together coins of different values. ChiIdren will learn how to group coins by value to make them easier to count.

Materials:
large paper coins in respective sizes, labeled I cent, 5 cent, and IO cents

Procedure:
Ask for seven volunteers to come up in front of the class. Pass out pennies and nickels in a random order to the children. Ask the rest of the class to find the sum of the coins. Ask the children if they could think of an easier way to count the coins? Direct their discussion so that they try their different ideas, but ultimately group the nickels together, followed by the pennies.
Ask for a different group of volunteers and repeat this process, gradually adding the dimes.

One variation of this activity Is to have the children record the counting patterns on chalkboards. They can work individually or with a partner. To make the activity more challenging, add quarters.

Assessment:
Children will accurately group coins by value and correctly find the sums of mixed values.

Objectives:
Children will learn the value of a dime. Children will begin to think about the value of objects that might be sold in a store.

Benny's Pennies, by Pat Bn'sson
chart paper
coin stamps: pennies, nickels, dimes an enlarged photograph of a dime an enlarged Photograph of 10 pennies chart paper
drawing paper

Show the coin photographs to the children. Explain that 10 pennies has the same value as one dime. Read the story Benny's Pennies to the children. As you read, ask them to predict what they think Benny will buy on each page. Re-read the story, asking how much Benny has left after each purpose. Write a number sentence on the chart paper to show the amount.

After the story, ask the children to brainstorm a list of things that they would like to buy if they had their own money. After a list is compiled, ask the children to think about how much each item costs and why they think so. Write the amount next to the item on the list.

Tell the children they can choose one thing from the list to "buy". Model the activity first by choosing an item from the list. Take a piece of paper and draw a picture of the item on the paper. Write the value. Fold the paper into fourths. Unfold the paper. Rewrite the value. Ask the children to help you use the coin stamps to show how much the item costs in one box. Then, have them help you show the amount in a different way with different coin combinations. Continue until all four boxes are done.

Tell the children to pick one item that they would I Iike to buy and have them complete the task. Share when finished.

Assessment:
Children will correctly identify the value of a dime. Children will show one amount of money using different coin combinations.

Objectives: Students will be able to:
1. Determine how much money they have in hand.
2. Find and read the price of a product.
3. Determine which product they would like to buy.
4. Determine if they have enough money for the item.
5. Count out the exact change or determine how much change they are due.

Materials:
Sheep in a Shop, by Nancy Shaw
Clean trash (empty soup cans, cereal boxes, vegetable cans, etc.) stickers to use as price tags calculators
computers with an internet server

Read and discuss Sheep in a Shop. Explain to the children that they will be going shopping in their classroom. If possible, involve the children beforehand in collecting and pricing items to sell in their store. Involve all of the children in discussing how the store should be set up. Make a rotating schedule so that all of the children have a chance to work in the store. Have them brainstorm a list of different jobs that need to be done in the store.

While the class is working on individual projects, send two or three students at a time to go "shopping". Give them a set amount of money to shop with. The shoppers need to figure out what items can be purchased with the amount of money they have. They need to tell the cashier how much change, if any, they should get. Students can check their figures using calculators. Take photographs of the children while they are shopping and working in the store. Use the pictures to make a class book. If you have the capability, use the Photographs on a school web page. Have the children write about their store.

Young children love to play store. Leave your store up as a center. Have a supply of real or plastic coins for the children to use. Have the children think of a name for their store.

Children can communicate with children from other schools via the internet, telling them about their store.

Children will correctly add and subtract using a variety of coins.
Students will correctly use a calculator to check their work.

Resources
Hoban,Tana. 26 Letters and 99 cents. 1987. WilliamMorroNv. N.Y.
Lewis,Brenda Ralph. Coins and Currency. 1993. RandomHouse. N.Y.

Additional Children's Literature
Adams,BarbaraJohnston. The Go-Around Dollar. 1992. MacMillan PublishingCo. N.Y.

Rodriguez, Anita. Aunt Martha and the Golden Coin. 1993. Clarkson Potter. N.Y.