Elementary Math Support Session 2: Measurement Sara Snyder SS 2013

What is Measurement? Discuss as a group… The irony of a “Google search” Simple Version: compare how long, deep, big, tall, much, heavy, far, old, etc. Formal Version: Measurement involves a comparison of attributes of an item or situation with a unit that has the same attribute. (length to length, area to area)

Before anything can be measured meaningfully, it is necessary to understand the attribute being measured

Activity Measure the bucket… Measure the bucket…

Common Core Standards Measurement Strand K-5 nt/MD nt/MD

Comprehending Measurement 1) Recognize that objects have measurable properties and know what is meant by “how long?” “how heavy?” and other expressions referring to properties 1) Recognize that objects have measurable properties and know what is meant by “how long?” “how heavy?” and other expressions referring to properties 2) Make comparisons (longer, shorter, etc) 2) Make comparisons (longer, shorter, etc) 3) Determine an appropriate unit and process for measurement. 3) Determine an appropriate unit and process for measurement. 4) Use standard units of measurement 4) Use standard units of measurement 5) Create and use formulas to count and compare units (tools) 5) Create and use formulas to count and compare units (tools)

Expanding on Critical Skills Making comparisons Units: critical to accurate measurement is consistency in the size and unit used to make the measurement. Choosing an appropriate tool, and using it in a way that yields an accurate measurement Using estimation: In many situations exact measurement is not necessary or even possible. Estimation is useful in these situations, and to check to make sure the results are reasonable.

Developmental Focus on Key Concepts & Skills Comparison & Ordering Length and Area Capacity and Volume WeightTimeTemperature Conservation (Knowing that even if a pipe cleaner is bent, it is still the same length.) Transitive Reasoning (Comparing one object to two others, then making a judgment about the relationship of the three objects: If Tim is taller than Jim, and Jim is taller than Steve, then Tim too is taller than Steve.)

Let’s See it in Action Example 1: Teaching “length” (Compare, Units, Standard Units, Tools) Length is usually the first attribute children measure, but be aware it is not immediately understood. Length is usually the first attribute children measure, but be aware it is not immediately understood. (Compare) Children should begin with direct comparisons of two or more lengths. (Compare) Children should begin with direct comparisons of two or more lengths. (Compare) It is important to compare lengths that are not straight (tape or rope). (Compare) It is important to compare lengths that are not straight (tape or rope).

Looking at Length Contd. (Units) Students can use informal units to begin measuring length (footprints, paperclips, straws) (Units) Students can use informal units to begin measuring length (footprints, paperclips, straws) (Units) Move toward “standard units” when children discover there is a need. (Units) Move toward “standard units” when children discover there is a need. (Tools) Rulers, tape measures, etc. (Tools) Rulers, tape measures, etc. (Tools) Understanding there is more than one way (cm, ft, in, etc) (Tools) Understanding there is more than one way (cm, ft, in, etc)

Two Piece Shapes Example 2: Area Take a rectangle of construction paper. Take a rectangle of construction paper. Cut it across the diagonal, making two identical triangles. Cut it across the diagonal, making two identical triangles. Rearrange the triangles into different shapes. Rearrange the triangles into different shapes. The rule is that only sides of the same length can be matched up, and must be matched exactly. The rule is that only sides of the same length can be matched up, and must be matched exactly. Find all the possible shapes that can be made following this process. Find all the possible shapes that can be made following this process.

Area Continued… Discussion: Two Piece Shapes Share the size and shapes of various results. Share the size and shapes of various results. Is one shape bigger than the rest? Is one shape bigger than the rest? How is it bigger? How is it bigger? Did one take more paper to make, or do they all have the same amount of paper? Did one take more paper to make, or do they all have the same amount of paper? Conclude: All of the shapes have the same area. Who can explain why? Conclude: All of the shapes have the same area. Who can explain why?

Thinking About Formulas The relationship between measurement and geometry is most evident in the development of formulas. Formulas help us use easily made measures to indirectly determine another measure that is not so easily found. Children should never use formulas without participation in the development of those formulas!! Developing the formulas, and seeing how they are connected/interrelated is significantly more important than blindly plugging numbers into formulas. Many children become so encumbered with the use of formulas and rules, that an understanding of what these formulas are all about is completely lost.

Let’s Try One Area of Parallelograms Draw a parallelogram on a piece of paper. Examine ways the parallelogram is like a rectangle, or think about how it can be turned into a rectangle. How does this help you find the area of a parallelogram? Can you determine a formula that would work for all parallelograms? How might this exercise relate to finding the area of triangles?

Parallelogram Image Area = base x height (same as a rectangle) Area = base x height (same as a rectangle) Can you see why?

Thoughts About Conversions The US uses the Customary System of measurement, while the rest of the world uses the Metric System. The Customary System involves an unfortunate variety of conversion factors, and as long as the US continues to use it, teachers will have to deal with helping children commit the most commonly used factors to memory. This procedural aspect of unit familiarity has been overworked in the curriculum, largely due to ease of testing, rather than need to know. “Soft” or “Friendly” estimations are more useful than exact calculations in everyday life.