Lisa lwanowski

Standard 1: Analysis, Inquiry, and Design-Students will use mathematical analysis and 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.

Benchmark standards: Elementary
Content standards
Standard 1: Analysis, Inquiry, and Design
Mathematical Analysis - Number 3: Critical thinking skills are used in the solution of mathematical problems.

Scientific Inquiry
Number 1: The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process.

Number 2: Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the conventional techniques and procedures and usually requiring considerable ingenuity.

Number 3: The observations made while testing proposed explanations, when analyzed using conventional and invented methods, provide new insights into phenomena.

Number 1: Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

Number 2: Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use.
Standard 3: Mathematics

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

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

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

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

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 data.

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

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

Students will ask "why" questions in attempts to seek greater understanding concerning objects and events they have observed and heard about.
Students will question the explanations they hear from others and read about, seeking clarification and comparing them with their own observations and understanding.
Students will develop relationships among observations to construct descriptions of objects and events and to form their own tentative explanations of what they have observed used of what they have observed.
Students will explore and solve problems generated from school, home, and community situations, using concrete objects or manipulative materials when possible.
Students will carry out their plans for exploring phenomena through direct observation and through the use of simple instruments that permit measurements of quantities.
Students will organize observations and measurements of objects and events through classification and the preparation of simple charts and tables.
Students will interpret organized observations and measurements, recognizing simple patterns, sequences, and relationships.
Students will share their findings with others and actively seek their interpretations and ideas.
Students will adjust their explanations and understandings of objects and events based on their findings and new ideas.
Students will understand that computers are used to store personal information.
Students will demonstrate ability to evaluate information.
Students will use a variety of equipment and software packages to enter, process, display, and communicate information in different forms using text, tables, pictures, and sound.
Students will use patterns and relationships to analyze mathematical situations.
Students will justify their answers and solution processes.
Students will use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances.
Students will develop strategies for selecting the appropriate computational and operational method in problem solving situations.
Students will construct tables, charts, and graphs to display and analyze real-world data Students will use variables such as height, weight, and hand size to predict changes over time.
Students will understand that measurement is approximate, never exact Students will select appropriate standard and nonstandard measurement tools in measurement activities.
Students will estimate and find measures such as length, perimeter, area, and volume using both nonstandard and standard units.
Students will collect and display data
Students will develop a wide variety of estimation skills and strategies.
Students will determine the reasonableness of results.
Students will interpret graphs.

Day 1: Concept Web Chart: Students will list at least four things that they know about apples. There should be four items under each heading: types, locations, uses, and attributes.

Day 2: Apple Recording Sheet: Students will be able to accurately record their estimations and draw/write accurate appearances of the apples throughout the week on their apple recording sheet.

Day 3: Apple Sense Matrix: Students will correctly identify and record how each type of apple/apple product looks, smells, feels, tastes, and sounds.

Day 4: Estimation of Apple Circumference and Number of Seeds: Students will accurately construct a bar graph based on the weight of each students apple and write a few sentences explaining why they could have overestimated or underestimated the number of seeds in their apple.

Day 5: Johnny Appleseed: Students will list at least three correct contributions that Johnny Appleseed made that effect us today.

Day 6 and 7: Timeline: Working in groups, students will create a timeline that includes the beginning of Johnny Appleseed's life, the middle, and the end of his life. Students will complete the group reflection sheet.

Day 8: Apple Exemplar This problem allows students to define the task by allowing different family members to pick different numbers of apples. Each individual may pick up to 2 apples. The students must give a clear explanation with a drawing that shows the students reasoning.

Day 9: The Season's Of Arnold's Apple Tree: Students must correctly label, write, and draw how their apple tree would look throughout the year, in their Seasons of "Student's Name" Tree book.

Day 10: Line graph: Students will correctly construct a three color line graph based on the results of the apple recording sheet.

Materials needed:
blank concept web chart
*If available software titled, The Graph Club

Begin the lesson by engaging in a class discussion about apples, specifically having students share what they know about apples. Have each student work individually, in pairs, or in small groups to complete a concept web based on apples. If you have the program The Graph Club available to you, students can complete the concept web using the graphic organizer provided on the program. Students will then share what they know about apples and the teacher can record this information onto a class concept web. The class concept web can then be typed into the graphic organizer provided on The Graph Club program.

Materials needed: 3 apples (1 with all the skin on, 1 with partial skin on it, and 1 fully peeled)
Scale
Recording Sheet

Time Frame: Approximately 25 minutes (observations recorded throughout the week)

Begin the discussion questioning students what makes up an apple. What kinds of substances are in an apple? For example; seeds, water, meat, and fruit. Have students estimate how much they think an apple weighs. They should record their estimation on their recording sheet. Pose the question, do you think an apple that has some of its skin peeled away would change the weight of an apple? Have them record their estimation of the partially peeled apple on their recording sheet. Do the same for the apple that is fully peeled and has no skin. Once all estimations have been recorded weigh each apple and students write down the actual weight of all three apples. Every day throughout the week the weight of each apple should be estimated and then weighed for the actual weight. In addition, the students need to observe the outward appearance of each apple and write/draw the changes that take place. All of these results are recorded on their observation sheet. A class recording sheet should also be kept and up in the classroom for consistency. See Day 10 for follow-up activity.
Day 3:

Materials needed:
Sense Matrix (chart for recording how the apple looks, smells, feels, tastes, and sounds)
Variety of apples such as; Jonathan, Red Delicious, Macintosh, and Granny Smith (to be cut into slices)
Apple cider (to be poured into individual cups for students to taste)
Applesauce (to be scooped into individual cups for students to taste)
Chart paper to record Apple Facts

Open the lesson by reviewing the class concept web that was created yesterday. Focus on the various types of apples and apple products. Depending on the information already on the web you may or may not need to have students brainstorm additional information, regarding different types of apples and apple products. Add Jonathan, Red Delicious, Macintosh, and Granny Smith if need be. Explain to the students that they will be comparing varieties of apples and apple products. Using their sense matrix they will be responsible for recording how each type of apple/apple product looks, smells, feels, tastes, and sounds. You may want to have your students sit in-groups so that each group has one plate that contains one slice of each type of apple, cups of apple cider and applesauce. Close the lesson by having the students share what they learned about each type of apple and apple product. Record this on a chart titled, Apple Facts.

Jonathan: Red color speckled with gold and green, juicy, and slightly Red Delicious: Deep red color. Has an oval shape and 5 points and the bottom. Sweet, firm, and crisp.

Materials needed:
Extra apples
Apple corer
5 or 6 small scales
Yam or string
Student recording sheet

Each student will use their apple for the following activity (have extras for those who do not bring in an apple). Discuss with the students that they will be estimating and measuring various parts of their apple. Review the term estimation and introduce the term circumference. Using their recording sheet, have the students write down their estimate for the circumference of their apple. As they are doing this, circulate around the room with the yam. Lay the yam on each student's desk and have him/her cut the length of yam they think is the circumference of their apple. The students test their estimation by putting one end of the yam in the center of their apple and placing the string around their apple, remembering to keep it on the center. If there was left over string their estimation was too much. If there was not enough string their estimation was too little. If the string fit perfectly their estimation was just right. Students then graph their estimation on a class graph using their string.

Next have students estimate the weight of their apple and record their estimation on their recording sheet. Students weight their apple on the scale and record the actual weight on their recording sheet. A class bar graph can then be created showing the students results.

Lastly, have students estimate the number of seeds in their apple and record on their recording sheet. The teacher then cores each apple and the students count the number of seeds actually in their apple.

In the students math journal have them write about their estimations and how it will help them make more accurate estimations in the future. What things will they take into consideration (size, shape, weight, prior knowledge, etc.) For example, did they overestimate and why they think they did or did they underestimate and why they think did.

Materials:
Johnny Appleseed by Stephen Kellogg Index cards
Marker
Time Frame: Approximately 40 minutes Activity:

Read aloud Johnny Appleseed by Stephen Kellogg, spend time with the illustrations and help children notice and describe the many details shown. As a class discuss the events that occurred in Johnny's life. Record these events on index cards. Discuss the contributions Johnny Appleseed has made and how they effect us today. Students can write about this in their journal.

Materials:
Timeliner software program if available Index cards from yesterday Time Frame:

Along the chalkboard ledge display the index cards. Have students choose which event occurred first, second, etc. until all the events are in correct chronological order. Number the cards accordingly. Divide the class into groups of 3. Each group is responsible for creating a detailed timeline representing Johnny Appleseed's life. Within each group one student is responsible for the beginning of Johnny's life, one student is responsible for the middle of Johnny's life, and one student is responsible for the end of Johnny's life. Students use the class timeline created plus, additional books about Johnny Appleseed. The completed timeline can be published on the software program Timeliner, if available or published using construction paper.

Day 8:
Materials:
Apple Exemplar Problem (1 for each student) Construction paper
Manipulative

Students will be given an apple exemplar problem to solve by drawing and writing how they got their answer. Read the apple exemplar problem together: Build 3 apple trees. There are at least 6 apples in each tree. A family of four wants to go apple picking. Each person may pick up to 2 apples. How many apples did. the family pick? Have the students tell about the problem in their own words and write this down on the board. Remind students to draw pictures to help them solve the problem and to use manipulative if they need to. They must also write how they solve their problem. For instance, I got my answer by....

Materials needed: The Seasons of Arnold's Apple Tree ,by Gail Gibbons
Chart showing 4 empty trees
Construction Paper

Read aloud, The Seasons of Arnold's Apple Tree and discuss the seasonal changes of an apple tree. As students are noting the changes that occur in an apple tree during each season, record these (draw) on the blank tree chart and label. Students will then create their own apple tree book which can be titled, The Seasons of "Student's Name" Tree. Each page in the book would depict what their apple tree would look like during each of the seasons. For instance page one would depict an apple tree in the Fall.

Materials needed:
Apple Recording Sheet from Day 2
Chart for line graph
Chart for three apples

Using the class recording sheet, discuss with students the changes that occurred throughout the week between the three apples. As students are sharing their observations with the class record their statements on the apple chart. The apple chart could have headings such as; Whole Apple, Partially Peeled Apple, and Fully Peeled Apple. Brainstorm why they think the changes occurred, guiding the discussion towards water weight and water evaporation. Using the Apple Recording Sheet, create a line graph depicting the change in apple weight throughout the week. The whole apple results would be one color, the partially peeled apple results would be another color, and the fully peeled apple results would be another color.

Build 3 apple trees. There are at least 6 apples in each tree. A family of four wants to go apple picking. Each person may pick up to 2 apples. How many apples did the family pick?