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1. “MeasureWorks!” Developing Understanding Melisa Hancock
KSU-Teacher in Residence Director
3. A few Metric Conversions 2000 mockingbirds = two kilomockingbirds
1 millionth of a fish = 1 microfiche
8 nickels = 2 paradigms
4. Almost all division explorations with fractions found in the elementary and middle school curriculum involve the measurement concept.
5. Overview of “MeasurementWorks!” (Time, Length, Area/Perimeter, Volume/Capacity, Weight, Temperature, Angles, Assessment) 1. “Big Ideas” of Measurement
3. Meaning & Process of Measurement
4. Plan for Measurement Instruction
6. Developing Measurement Concepts Big Ideas: 1. Before anything can be measured meaningfully,
students must recognize that objects have
Measurement involves a comparison of an attribute of
an item or situation with a unit that has the same
attribute. Lengths are compared to units of length,
areas to units of area, time to units of time, and so on.
7. Big Ideas Cont. 2. Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit measure being used.
3. Estimation of measures and the development of personal benchmarks for frequently used units of measure help students increase their familiarity with units, prevent errors in measurements, and aid in the meaningful use of measurement.
8. Determine an appropriate unit and process for measuring an object.
Measurement instruments replace the need for
actual measurement units. It is important to
understand how measurement instruments work so
that they can be used correctly and meaningfully.
Understand and Use Formulas
Area and volume formulas provide a method of
measuring these attributes by using only measures
of length. Big Ideas Cont.
9. Area, perimeter, and volume are related to each other, although not precisely or by formula. For example, as the shapes of regions of three-dimensional objects change but maintain the same areas or volumes, there is a predictable effect on the perimeters and surface areas.
Ex: Explore Area and Perimeter Lesson Big Ideas Cont.
10. “MeasureWorks” Activity As we do one of the “MeasureWorks” activities, think about the following:
“Big Ideas” of measurement addressed
in this activity
The meaning and process of measurement addressed in this activity
Alignment to Standards at your grade level
11. To measure something, what do students have to do? (Think-Pair-Share)
12. To measure something, what do students have to do? (Think-Pair-Share)
1. Decide on the attribute to be measured.
2. Select a unit that has that attribute.
3. Compare the units, by filling, covering, matching, or some other method, with the attribute of the object being measured.
13. Step 1
Goal: Students will understand the attribute measured.
Type of activity: Make comparisons based on the attribute. Example: longer/shorter, heavier/lighter. Use direct comparisons whenever possible.
Notes: When it is clear that the attribute is understood, there is no further need for comparison activities.
14. Step 2
Goal: Students will understand how filling, covering, matching, or making other comparisons of an attribute with measuring units produces a number called a measure.
Type of activity: Use physical models of measuring units to fill, cover, match, or make the desired comparison of the attribute with the unit.
Notes: In most instances it is appropriate to begin with informal units. Progress to the direct use of standard units when appropriate and certainly BEFORE using formulas or measuring tools.
15. Step 3
Goal: Students will use common measuring tools with understanding and flexibility.
Type of Activity: Make measuring instruments and use them in comparison with the actual models to see how the measurement tool is performing the same function as the individual units. Be certain to make direct comparisons between the student-made tools and the standard tools.
Notes: Student-made tools are usually best made with informal units. Without careful comparison with the standard tools, much of the value in making the tools can be lost.
16. Theory into Practice: Measurement Experiences in MeasureWorks Length
18. MeasureWorks “Tool Kit” The “Tool Kit” shows and overview of manipulatives needed for each concept.
(ie. Time Length, Area/Perimeter, Volume/Capacity, Weight, Temperature, and Angles)
19. MeasureWorks! “Lesson Plan at a Glance”
20. Fraction Questions (Getting at Depth of Knowledge) If you are scared half to death twice, what does that mean?
If three out of four people suffer with diarrhea, does that mean that one out of four people actually enjoy it?
It has been said that five out of four teachers struggle with fraction concepts, what does that mean?
21. Instrumental Understanding (Procedural)
22. Relational Understanding (Conceptual)
23. Manipulatives When deciding to use manipulatives with students.....................consider the following questions:
1. Will the manipulative help achieve my objective?
2. Which manipulative will work best to develop the CONCEPT?
3. Should students work alone? In pairs? In groups?
4. Do I have the time to appropriately use manipulatives?
5. Can this lesson be done using a demonstration with manipulatives or an overhead or is the objective best achieved through a hands-on experience?
24. Reflections: Procedural vs. Conceptual Understanding 1.Conceptual Knowledge (logical relationships, representations, an understanding and ability to talk, write and give examples of these relationships, etc.)
2. Procedural Knowledge (knowledge of rules and procedures used in carrying out routine mathematical tasks and the symbols used to represent mathematics)
25. Overview of “FractionWorks!” (Understanding, Equivalent, Comparing, and Computation) 1. “Big Ideas” for Fraction Concepts (Building Background)
26. Understanding: Fractions Concepts Partitioning
This is fundamental to the understanding of fractions
Regions, sets, number lines (multiple context)
Fractions that name the same amount
Students with instrumental understanding see only the numbers and not the meaning
Compare and Order
Students should be able to compare and order fractions with the same denominators or the same numerators.
Students should be able to use benchmarks such as ˝ and interpret the relationship between the fractions.
27. Lesson at a glance Fractions Near One-Half
Objective: Find fractions near one-half
Objective: Compare fractions
Note: In second lesson the instructional method is utilizing a strategy of moving from a concrete manipulative to a symbolic representation. This is represents an opportunity for informal assessment. Students who abandon the manipulative are demonstrating mastery of the concept.
28. Questions related to activities Describe the kind of model used
Can this activity be done using another model? What other models might you use?
What is the advantage of using the linear model as an introduction to the concepts?
What extensions do you see for these lessons?
29. Assessment Compare Fractions Test
Summative assessment tool is provided for teachers
Correct responses are mark
For incorrect selections the tool provides insight into why the student may have selected that answer choice.
Teachers can assess misconceptions related to concepts and group students for reteaching.
30. Final Reflections/Questions????? It is generally accepted that procedural rules should never be learned in the absence of a concept.
(John A. Van De Walle)
Manipulatives are the vehicle for building conceptual understanding.