Money Matters
Group Members:
Kelley McCall
Mark Janne
Dana Hageman
Jenae Crowley
Grade level: 2
Standards:
· Measurement- Pre-K-2: Understand measurable attributes of objects and the units, systems, and processes of measurement; Compare and order objects according to these attributes; Understand how to measure using nonstandard and standard units.
· Representation: Create and use representations to organize, record, and communicate mathematical ideas.
· Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others; Recognize and use connections among mathematical ideas; Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
· Reasoning and Proof: Make and investigate mathematical conjectures.
· Problem Solving: Build new mathematical knowledge through problem solving AND solve problems that arise in mathematics and in other contexts.
· Connections: Recognize and apply mathematics in contexts outside of mathematics.
Explanation of how each lesson fits into the unit:
· Dana’s lesson begins by introducing the students to exchanges in the base 10 number system and encourages students to discover that numbers can be represented in various ways. Students have the opportunity to practice exchanging 1’s for 5’s with two different colors of blocks. This lesson provides the knowledge base for the remainder of the lessons within this unit.
· Jenae’s lesson fits into the unit because it draws on the student’s previous knowledge of exchanging in the base 10 number system that Dana’s lesson provided the day before. This lesson also integrates with literacy as the children are listening to “Pudge’s Problem”. Students then have to use the information from “Pudge’s Problem” and apply it to a mathematical concept. It then provides the students with a concept of money and gives them an opportunity to trade their “money” for an item of a certain price.
· Mark’s lesson is appropriate for our math unit because it connects money value to everyday life. Connecting the idea that money is used to buy everything that people need to live is one of the main points of this lesson. The students will know what each coin looks like and the characteristics of each coin. The student will be able to identify each coin and know the exact value for that coin. In the lesson, there are places where the student will be using both pictorial and concrete representations. Children need to realize that knowing the value of money and the differences between the different coin is an important part of their learning.
· As the fourth lesson plan for this particular unit, Kelley’s lesson gives an opportunity for the students to practice with exchanging and counting money. While reading the story, Alexander, Who Use to be Rich Last Sunday, the students have the chance to work with a partner to pay for items that Alexander had bought throughout the story. This part of lesson asks for one partner to put money on the spent pile while the other student keeps a journal of what the money was spent on. At the end of the game, they should only have bus tokens. Next, we play a game that requires them to not only count to 25 cents, but also gives them the opportunity to exchange coins. This lesson raps up our unit on exchanges and introduces them to counting money.
Unit Reflection
This unit on money is a good unit because each lesson builds upon the skills learned in the previous lesson. The students progress from a concrete representation of exchanging with blocks to the abstract concept of exchanging within the monetary system. The lessons helped to accomplish instilling the sense of exchanging, first with blocks and then with actual money, so that students can fully understand trading and exchanging various coins and monetary values.
Arrangements of Ten
Name: Dana Hageman
Date of Lesson: September 28, 2004
Subject Area/Topic: Math/Measurement
Grade Level: 2nd Grade
Standards:
· Measurement: Understand measurable attributes of objects and the units, systems, and processes of measurement
· Reasoning and Proof: Make and investigate mathematical conjectures.
· Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Outcomes/Objectives:
· The main idea that the students will understand is that they can use exchanges to represent the number ten in different ways.
Vocabulary:
· value
· exchange
· representation
Materials/Technology:
· Interlocking blocks in yellow and blue (10 yellow and 2 blue for each pair)
· Paper and crayons for recording possible patterns
· Newsprint
Procedure:
The students will work in pairs.
ENGAGE
· What does ten look like? (a 1 and a 0, 10 tally marks, 10 items grouped together)
· Students discuss the question with their shoulder partner.
· Each pair share one idea with the class.
1. How does it represent the number 10?
EXPLORE
· Each pair will be given ten yellow interlocking blocks and paper to record answers.
· One student will arrange the yellow blocks in an arrangement of ten (concrete).
· The other student will record the pattern on paper (pictorial).
· They will switch jobs until no more patterns can be made.
EXPLAIN
· One pair at a time will come to the front of the room and draw one of their patterns on newsprint. (pictorial)
· The class will discuss each configuration.
1. Does it represent 10? (yes)
2. Does it look differently from the others? (yes)
3. Did the shape of the pattern change the value? (no)
4. What determined the value of the pattern? (The number and value of each block)
EXPAND/EXTEND/APPLY
· Give each pair 4 blue blocks.
· If the blue block equals five, will this change how your arrangements of ten look? (yes)
· How many white blocks would you have to “exchange” or “trade” for one blue block? (five)
· This time only focusing on the number and value of blocks, how many representations could you make for the number ten? (three)
· Still in pairs, one student makes an arrangement representing “10” using the yellow blocks to represent “1” and the blue blocks to represent “5” (concrete).
· The other student draws a picture of the arrangement on their paper (pictorial).
· How many patterns could you make for the number fifteen? (four)
· Pick one number between ten and twenty and draw the different patterns of yellow and blue blocks that represent that number.
EVALUATE
Given prior knowledge from the lesson, the student will complete a worksheet matching pictorial representations (yellow and blue blocks) of a number to the number with 90% accuracy.
EXPAND/EXTEND/APPLY (2)
· Students are given numbers from six to twenty-five and ask to represent that number using the fewest number of blue and white blocks as possible.
References:
Economopoulos, K. & Russell, S. J. (1998). Investigations in number, data, and space: Coins, coupons, & combinations (Grade 2). Dale Seymour Publications: White Plains, NY.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics: Reston, VA.
Reflection: I think the lesson will go well. I think the students will be able to understand that one blue block is the same as five white blocks. The only problem that I can anticipate is asking the students represent a number using the fewest number of blocks possible. However, with practice, I think that they will be able to master this as well.
Write the number that each picture represents. Remember blue = 5 and yellow = 1
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Exchanges & Money
How many ways can you pay for an item?
Jenae Crowley
September 15, 2004
Mathematics: Money & Measurement
Grade level: 2
Standards:
· Measurement, Pre-K-2: Understand measurable attributes of objects and the units, systems, and processes of measurement
· Representation: Create and use representations to organize, record, and communicate mathematical ideas.
· Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Outcomes/Objectives:
· The main ideas that students will understand is that exchanges, or trades, can be made and the concept of money and how it is used.
· Students will exchange chips for equal values.
· Students will then extend this concept of exchanging into the monetary system.
Vocabulary:
· Money
· Exchange
Materials:
· “Pudge’s Problem”
· 4 different colors of counting chips
· Number Cube
· Different objects with a number (price)
· Worksheet about Exchanges
· Various coins
Procedure:
The learning cycle is the format for this lesson plan. Concrete and pictorial representations will be implemented.
Engage:
· Read the story, “Pudge’s Problem” to the class. Then tell them that Pudge needs their help solving this mystery.
· Encourage the students to think about which color Pudge should take.
· The teacher should play a very minimal role in this discussion and the students should all share their input.
· Once a color has been decided, encourage the students to share their reasoning.
Explore:
· The teacher says, “Now we are going to play a game with the colorful circles. I will give each group the 4 different colors of circles. Each chip will be worth the same amount as in “Pudge’s Problem”. Each person will roll the cube and get that number with the colored circles. Once all of the colored circles you have add up to 25, trade it in for a green colored circle. You have just won the first round. Continue playing. Remember, here is how much each chip is worth”:
o Yellow: 1
o Blue: 5
o Red: 10
o Green: 25
· Give the students about 10 minutes to complete this game.
Explain:
· Ask the students, “Was there more than one way to get to each number? How do you know?” Encourage conversation among the students. Try to lead them to the idea that five yellow were equal to one blue, etc.
· Introduce the concept of exchanging.
Extend:
· Introduce the concept of money. Tell the students that Pudge’s colored circles were actually a type of money because they represent a certain number.
· Hand students various objects with price tags on them (only in cents).
· Using their colored circles, have each individual student try to come up with enough “money” to pay for that item. Then, as a group, go around the table and share how each student was able to pay for that item. Repeat with a few different items.
Evaluate:
· Have student complete the Exchanges worksheet independently with 90% accuracy.
References
Economopoulos, K. & Russell, S. J. (1998). Investigations in number, data, and space: Coins, coupons, & combinations (Grade 2). Dale Seymour Publications: White Plains, NY.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics: Reston, VA.
Reflection
I believe that this lesson is appropriate for second grade students because it introduces the concept of exchanges and then relates that to the monetary system. By breaking this process in two separate pieces, students are fully able to grasp the concept of exchanges prior to learning about money itself. Therefore, students have prior knowledge to build upon before even learning about money. Younger children would probably not have the ability to exchange beyond two different values. This lesson plan incorporates both concrete and abstract representations and the learning cycle is a useful tool because it emphasizes building upon previous knowledge, which is crucial to this lesson.
Hi! My name is Pudge and I am a blowfish that lives in the Atlantic ocean. I am quite a friendly fish, but today I ran into some trouble. That is why I need you, boys and girls, to help me solve my problem.
Well, I was swimming along, just minding my own business, when I saw a huge basket filled with colorful circles. There were four different colors of circles: yellow, blue, red, and green. I had never seen anything like them before, they were beautiful! Well, I put them all in a large knapsack and headed on my way. All of a sudden, out of nowhere, I was bombarded with sting rays! I don’t know if you know about sting rays, but they are some mean and nasty creatures! They were surrounding me and I had not idea why. Then, I remembered the colorful circles. Maybe those are what they want. Slither, the head sting ray of this pack, began to circle around me. He told me that those colorful circles were his. I begged to differ by saying, “Finders, keepers, losers, weepers.”
Slither began to see that I was not going to back down. Because our ocean community promotes peace, we had all recently attended a lecture on compromise. Slither and I decided to put our new knowledge into practice.
Slither began to tell me that these colorful circles could be used to trade for other things such as seaweed mattresses, glow worm lamps, and even food. As he was telling me this, I logged on to my laptop and began researching. I found that each color represented a different number. Yellow was equal to 1, Blue was equal to 5, Red was equal to 10, and Green was equal to 25. The bigger number, the more items you can trade them for. I of course did not share my new information with Slither.
Instead, I convinced Slither to split the colored circles in half. He could take half and I could take half. The only catch was that I can only take one color. Now, here is where I need you, boys and girls. Which color should I take?
Name:______Date:______
Directions: Use your crayons. Beside each number, see how many different ways you can use the colored circles to get that number by drawing the colored circles on each row.
Number
/ 1 / 5 / 10 / 2526
58
79
103
Coins & Combinations
Mark Janne
September 16, 2004
Mathematics: Money & Measurement