Unit Title: The Long and Short of It
Delaware Curriculum Unit Template
Preface: This unit has been created as a model for teachers in their designing or redesigning of course curricula. It is by no means intended to be inclusive; rather it is meant to be a springboard for a teacher’s thoughts and creativity. The information we have included represents one possibility for developing a unit based on the Delaware content standards and the Backward Design framework and philosophy.
Subject/Topic Area: Math Trailblazers Unit 6: Measurement--Length
Grade Level(s): 1st grade
Searchable Key Words: Measurement; length; geometric reasoning; quantitative reasoning; standard and nonstandard units; data (collect; represent; analyze);
Designed By: Kathy Dulis District: Seaford
Time Frame: 6 lessons (approximately 11 classroom sessions)
Reviewed by: Date:
Brief Summary of Unit (This should include a brief unit summary including a description of unit goals, rationale for the approach taken, and where it appears in the course of study.)
The students completing this unit will have had previous practice reading and creating color data tables and graphs. In this unit, the students will focus on the concepts of measurement. The students will learn to measure various objects using both standard and nonstandard units. The concept of yielding different results by using different sizes of units for measuring is also introduced. In the transfer task students will complete a lab assignment where they will be required to collect, record, and interpret data. The students will then have to use a graphing program to present their data to the class. (It may be helpful to collaborate with another teacher—media specialist or computer teacher—in order to teach the student how to use the graphing program you choose.)
Stage 1: Desired Results(Determine What Students Will Know, Do and Understand)
Delaware Content Standards (This should include a list of the DE Content Standards for which instruction is provided in this unit and which are ultimately assessed in the unit.)
Primary Standards Addressed:
Standard 3: Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree of accuracy by selecting appropriate tools and units.
GLE’s:
· Compare the length of two objects by aligning them
· Put objects in order according to their length
· Use nonstandard units to represent how long an object is
Standard 4: Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences and to present convincing arguments; and to model mathematical situations to determine the probability.
GLE’s:
· Collect categorical data (observe and count frequencies) to answer a question posed by the teacher
· Organize and informally represent categorical data (2 or 3 categories) using drawings or physical objects
· Interpret data by making comparisons between frequencies of data (e.g. how many more)
· Explore events as likely or unlikely, possible or impossible based on shared or personal experience
Secondary Standards Addressed:
Standard 1: Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.
GLE’s:
· Count sets of objects up to 50 by 1s, 2s, 5s, and 10s.
· Sequence numbers and explain which is larger, which is smaller, and what is between other numbers up to 100.
Standard 7: Communications: Students will develop their mathematical Communication ability by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral, and visual formats.
Big Idea (This should include transferable core concepts, principles, theories, and processes that should serve as the focal point of curricula, instruction, and assessment. Ex: Manifest Destiny, fighting for peace.)
Measurement can be used to compare and contrast objects.Unit Enduring Understandings (This should include important ideas or core processes that are central to the unit and transferable to new situations beyond the classroom. Stated as full-sentence statements, the understandings specify what we want students to understand about the Big Ideas Ex: Inverse operations are helpful in understanding and solving problems.)
Students will understand that…
· Objects can be compared by using measurement.
· Objects can be measured using standard and nonstandard units.
· The size of the unit of measurement effects the results of data collection
· Technology can be used to represent information from an experiment
Unit Essential Question(s) (This should include open-ended questions designed to guide student inquiry and focus instruction for “uncovering” the important ideas of the content. Ex: What is healthful eating? What is the relationship between fiction and truth?)
· How are measurement and counting related?
· How does what we measure affect how we measure?
· How do we compare, contrast and classify objects?
· What is the best way to represent data collected during an experiment?
· What is the best technology to use to represent data collected?
Knowledge & Skills (This should include key knowledge and skills that students will acquire as a result of this unit. Ex: Factors affecting climate, The causes of World War II.)
It should also include what students will eventually be able to do as a result of such knowledge and skill Ex: take notes, complete a bent-arm pull, compare fiction to nonfiction.)
Students will know….
· Objects can be measured using standard and nonstandard units (e.g. paper clips, chains, etc.)
· There is a relationship between the size of the units used to measure and the size of the object to be measured
· Patterns can be formed based on the data recorded on a chart, table or graph
· Data can be used to solve problems involving length
· Technology can be used to more easily represent our data
Students will be able to…
· Measure various objects using different units (chains; rulers; paper clips, etc.)
· Collect and record data in a chart, table or graph
· Analyze and interpret information from a chart, table or graph
· Use data to solve problems involving length
· Use a simple graphing program to represent the data they have collected
Stage 2: Assessment Evidence
(Design Assessments To Guide Instruction)
(This should include evidence that will be collected to determine whether or not the Desired Results identified in Stage One have been achieved? [Anchor the unit in performance tasks that require transfer, supplemented as needed by other evidence –quizzes, worksheets, observations, etc.]
Suggested Performance Task(s) (This should include suggested authentic tasks and projects used as evidence of student competency in the skills and knowledge deemed important in the unit. Ex: a written composition, speeches, works of art, musical performances, open-ended math problems.)
Consider the following set of stem statements as you construct a scenario for a performance task:
G – Goal—Ex: Reflect character’s motivation and predict his actions
R – Role—Ex: A character in Of Mice and Men
A – Audience—Ex: A family member or close friend
S – Situation—Ex: Creating a scrapbook chronicling a character’s life, real and inferred
P – Product, Performance, and Purpose—Ex: Scrapbook
S – Standards and Criteria for Success—Ex: Your scrapbook should include all components on included rubric
Task: You have been hired by the Seaford Car Test Company to test the distances that several models cars can travel on the test ramp. The car that travels the farthest will be sold by the company next year. You will be completing an experiment using cars and a ramp called Rolling Along with Links found in your Math Trailblazers Student Guide. You will be required to measure the distance that three cars will travel on a ramp, giving each car three trial runs. Using the median of the trials, you will record your information on a data table and then complete a graph using paper and pencil. The graph will then be transferred to the computer using a graphing program. You will present your findings to your class and propose which car should be sold next year during a class meeting. (See Appendix for complete instructions for the task.)
Goal: The goal of the task is to successfully collect, graph, interpret and present data from an experiment.
Role: You are the scientist who will collect the data for the Seaford Car Test Company.
Audience: Your audience is your teacher and your class (Seaford Car Test Company).
Situation: Testing three cars and determining the best car to use for the company based on your findings.
Product/Presentation: Using your graphs created in class and in the computer lab, you will make a proposal for which car should be sold next year.
Standards and Criteria for Success: Successful completion of the experiment and all components included in the rubric. (See Appendix for the rubric for the task.)
Rubrics/checklists for Performance Tasks (This should include holistic or analytic-trait rubrics used as a scoring guide to evaluate student products or performances.)
See appendix for Rubric for Task
Other Evidence (This could include tests, quizzes, prompts, student work samples, and observations used to collect diverse evidence of student understanding.)
Observational Record
DPP’s
Two Car Roll-Off
Brian’s Class
Stepping Out with My Family
Measuring at Home
Comparing Links to Chains
Could Be or Crazy?
Student Self-Assessment and Reflection (This should include opportunities for students to monitor their own learning. Ex: reflection journals, learning logs, pre- and post-tests, editing own work.)
Math Journal Prompt (Lesson 2)
See Appendix for Student Self-assessment/evaluation (How Did I Do?)
Stage 3: Learning Plan
(Design Learning Activities To Align with Goals and Assessments)
Key learning events needed to achieve unit goals
(This should include instructional activities and learning experiences needed to achieve the desired results (Stage 1) as reflected in the assessment evidence to be gathered (Stage 2).
The acronym WHERETO summarizes key elements to consider when designing an effective and engaging learning plan for ALL students.
W – Help the students know Where the unit is going and What is expected? Help the teachers know
Where the students are coming from (prior knowledge, interests)
H – Hook ALL students and Hold their interest?
E – Equip students, help them Experience the key ideas and Explore the issues?
R – Provide opportunities to Rethink and Revise their understandings and work?
E – Allow ALL students to Evaluate their work and its implications?
T – Be Tailored (personalized) to the different needs, interests, and abilities of ALL learners?
O – Be Organized to maximize initial and sustained engagement as well as effective learning?
Guides for each lesson are included in the Unit Resource Guide (URG) for Unit 6.
Lesson One (1 day): Linking Up
1. Daily Practice Problem: DPP A: Skip counting by 5’s with leftovers by ones
2. This lesson focuses on the concept of measuring length and the use of nonstandard units for measuring length.
3. Each student will need to make a chain using 45 connecting links. (It is helpful to have the students sort the connecting links into groups of 5 of the same color. You could also have the students compare their chains to make sure that they are all the same.)
4. Have the students practice counting by 5’s by holding up a chain and counting the groups on their chain. (5, 10, etc.). Then have the students count the links by 5’s with leftovers by ones. (Mark a chain with a piece of tape or yarn and have the students count. For example, 5, 10, 15, 16, 17, 18)
5. Focus the children back on the concept of measurement by asking them how they would use the chain to measure different objects in the room. (See page 17 of the URG for ways to guide the discussion with the students.)
6. Reinforce the concepts—URG page 17.
7. Group activity: Measuring Our World (Page 100 in the Student Guide):
8. Discuss the activity using the guiding questions on page 18 of the URG.
9. Introduce the term perimeter to the students. Demonstrate how to measure perimeter using a large object (e.g. a large book; chart paper)
10. Have the student pairs to complete page 101—Measuring Ourselves for more practice.
11. Homework/Practice: DPP B.
12. Assessing the lesson:
a. DPP A (Skip count by 5’s with Leftovers by ones)
b. Observational record (Pages 5 & 6 in the URG)
Lesson Two (3 days): Rolling Along With Links (Transfer Task)
1. DPP C—Story Problems/Addition in measurement context
2. This lab focuses on the concepts of measuring length; “fairness”; and collecting, recording and analyzing data. It is completed in three classroom sessions. In the first session (#3-#9), the teacher will discuss and model the investigation. Using information they have learned in previous units about controlled variables and recording data, the students will collect data during the second session (#10-#14). In the third session, students will complete the graph and analyze the results (#15-#20). (Additional sessions may be needed to complete the technology piece of the transfer task. Working with the computer teacher or media specialist to complete this piece is highly recommended so that loss of classroom instructional time is minimal.)
3. Using the information on URG page 22, prepare the experiment for demonstration to the class. Use the illustration in Figure 1 (URG p.22) to help with the set-up if the lab.
4. Model the procedure for selecting cars for the experiment. Use the prompts on URG p.23 to discuss the concept of “fairness” when choosing cars.
5. After the five cars have been selected, create the chart shown in Figure 2 (URG p.23).