deep dive: measurement and data grades 3 5 · pdf fileelementary math coach ... deep dive:...

Bhavna VaswaniElementary Math Coach

Newton Public Schools, [email protected]

Deep Dive: Measurement and Data Grades 3‐5

Acknowledgement

STEM project at Michigan State University.Strengthening Tomorrow’s Education in Measurement.

https://www.msu.edu/~stemproj/2

Reflect for a moment…

• What are the key ideas you want your students to know about measurement?

• What do you find challenging about teaching length, area and/or volume?

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Grade 4 Grade 8

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2000 2003 2005 2007 2009 2011 2013

Algebra

Data Analysis,Statistics,Probability

Geometry

Measurement

NumberProperties andOperations

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NAEP Results, 2000‐2013

Analysis of Curriculum Involving Measurement

Percentage of Curriculum that is Procedural

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Grade Length Area Length Area Length Area

K 79 100 97 98 98 100

1 70 97 93 100 80 99

2 80 88 89 97 85 92

3 75 92 80 88 87 94

4 ‐ 89 ‐ 94 ‐ 90

Grade C o n ce p t ua l

C o n ce p t ua l

Conceptual

K 0 2 0

1 3 0 1

2 7 3 1

3 6 10 3

4 8 5 2

Percentage of Curriculum that is Conceptual

Mathematics Teaching Practice

Build procedural fluency from conceptual understanding.

Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

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Deep Dive Objectives

• Know the essential understandings of measurement

• Understand the development of measurement concepts and skills K‐5 and beyond

• Link CCSS Math Practices and NCTM Process Standards to measurement understanding

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Today’s Agenda

• Conduct an experiment involving valves and an IV drip

• Collect and record data from the experiment

• Create a list of measurement understanding or skills needed or used during the experiment

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Equipment & TaskTask:1. Identify the head height of the drip to allow a flow rate of 6 liters per hour. 2. Record data on chart paper. 3. As you work through this investigation, record in your small group any

understanding and measurement skills that you notice being utilized.

Equipment:• Valves 4 for each group• IV drip• Water• 3‐D geometric shapes containers• Measuring tools (e.g., measuring tape, stop‐watch, clock, rulers, calculators)

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Reflecting on the Experiment…

5 minutes of individual think time:‐What conclusions can you make about the flow rate of any specific valve?

15 minutes with your group:‐ Create a poster that

i. Justifies a conclusion madeii. Lists the measurement understanding and skills used

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Mathematical Practices

1. Make sense of problems and persevere in solving them2. Reason abstractly and quantitatively3. Construct viable arguments and the reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

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Today’s Agenda

• Identify the essential understandings of measurement; length, area, volume

• Work on math tasks involving length, area, volume

• View video clips of students at work

• Understand the trajectory of measurement skills as CCSS has outlined from K‐8

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Quick Task

Using paper clips, measure the length of your table. How many paper clips long is your table?

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Can you find another way to measure the length of your table using the same size paper clips?

Measurable attributes are quantifiable characteristics of objects or events. Students need opportunities to explore how an object or an event can have many different measurable attributes. What are some measurable attributes of this ice‐cream cone?

"Image courtesy of foodclipart.com"

Measurable Attributes

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What were the measurable attributes yesterday’s experiment?

Measurable Attributes

Math Tasks

Spend about 10 minutes on each task. As you work through the task, think about the following questions:

• What are some key ideas about measurement this task helps to elicit?

• What misconceptions might make this task particularly challenging?

• What features of these tasks might be helpful in teaching/learning measurement

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Area Question

What is the area of this pentagon?

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Draw another pentagon with the same area.

Both parts incorrect: 48%Partial incorrect: 47%Omitted: 2%

Both parts correct:

NAEP, Grade 8, 2005

2%

Iterating vs. Tiling

Iteration is the underlying concept of measurement; a unit measure repeats itself with no gaps or overlaps.

Iterating however involves using the actual same unit measure to find the length, area, or volume of an object, shape, or distance. i.e. the number of iterations needed to cover the length, area, or volume.

What could be a benefit of giving students more experience with iterating? How is this experience different than tiling?

Student at Work‐ Iterating

Volume

Typically standard units of measure are used when discussing volume with students. Are there any benefits for using non‐standard units when studying volume?

Students at Work‐ Volume

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CCSS Progression of Measurement Standards

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Kindergarten: Describe measurable attributes of objects, directly compare two objects with common measurable attributes (including 3‐D shapes). Compose simple shapes to form larger shapes.

Grade 1: Order 3 objects by length, using whole units, understand unit measure has to be the same size, placed end to end with no gaps. Students begin to partition shapes into halves and fourths.


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Grade 2: Iteration of units, use appropriate tools, use different length units to measure the same object, estimate lengths (inches, feet, centimeters, meters), addition/subtraction word problems within 100 using lengths, represent whole numbers on a number line, generate data using whole numbers and display data on a dot/line plot. Partition circles and rectangles into two, three, and four equal shares. Partition rectangles into rows and columns of same‐size squares and count to find the total number of them.


Grade 3: There is an explicit focus on area. Identify perimeter and area as an attribute of polygons, distinguish between linear and area measures, solve problems involving area and perimeter. Draw scaled graphs, generate and plot data with lengths that involve ½ and ¼. Estimating and measuring liquid volume is introduced.

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Grade 4: No explicit mention of area but symmetry and angles are introduced. Length is refocused with regards to conversion between units. Solve problems involving measurement and unit conversations from a larger unit to a smaller unit, know relative sizes of metric as well as the U.S. Customary units, solve word problems involving distance, time, liquid volumes, mass, money, apply area and width formulas, represent data using fourths, halves, and eighths, and use the data to add/subtract (i.e. number operations involving fractions).


Grade 5: Convert measurements within a given measurement system including from a smaller unit to a larger unit, represent and interpret data using fourths, halves, and eighths, solve word problems using this data. Find area with side lengths that include fractions. Introduction to volume measurement. Volume seen as an attribute of 3‐D space that can be determined by finding the total of number of same‐size units to fill the space without gaps or overlaps.

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.Grades 6: Students are introduced to the concept of ratio, rate, and proportional reasoning which could include calculations involving length, speed, time. Students continue work on area and volume measurement.

Grade 7: Students are introduced to length in the form of circumference. Students continue work on area, surface area of 3‐D shapes, and volume measurement. Geometry standards call for students being able to calculate the area and circumference of circles.

Grade 8: Length is now seen in the form of distance. Students are expected to perform operations with numbers expressed in scientific notation while using the appropriate unit of measurement for very large and very small numbers. They use their understanding of of distance and angles to deepen their understanding of geometric concepts (e.g. congruence, similarity, proof of Pythagorean Theorem).

Resources

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• Implementing the Common Core State Standards through Mathematical Problem Solving Grades 3-5 by Mary Q. Foote, Darrell Earnest and Shiuli Mukhopadhyay

• Developing Essential Understanding of Multiplication and Division Grades 3-5

• Multiplication and Division into Practice 3-5

Squares Within a Rectangle…

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This rectangle has been dissected into nine non‐over‐lapping squares. Given that the width and the height of the rectangle are positive integers with greatest common divisor 1, find the perimeter of the rectangle. (from the 2000 American Invitational Mathematical Examination)

Today’s Agenda

• Explore fraction opportunities within the measurement standards

• Analyze student work to unearth common misconceptions.

• Wrap‐up

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“If students are going to understand the number line in rich and meaningful ways, they should understand how numbers represent accumulated quantities of lengths.”

https://www.msu.edu/~stemproj/teaching.html

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CCSS Development of Measurement Data

Grade 2: Moving from categorical data to measurement data, students measure and generate data whole numbers, use line plot to display data (aligns with work that is being done with whole numbers and the number line)

Grade 3: Students use their developing understanding of of fractions and number lines and apply it to measurement data involving fractional measurement values. Students are work with measurements to the nearest ½ and ¼

Grades 4: Students use the measurement data to solve problems as well as for analysis purposes (e.g. the difference between the greatest and least value). Students work with fractions to the nearest 1/8

Grade 5: Students grow in their skill and understanding of fraction, and apply these skills to analysis of measurement data. (Able to multiply a fraction by a fraction, divide a unit fraction by a whole number or a whole number by a fraction, add and subtract fractions with unlike denominators)

Grade 6 & 7: Statistical reasoning, distributions, bivariate measurement data where they are representing two sets of data at the same time

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Consider…

i. 1/3 + 1/5

ii. 1/3 – 1/5

i. 1/3 1/5

i. 1/3 ÷ 1/5

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×

A. 1/3 + 1/4

A. 1/4 + 1/5

A. 1/6 + 1/3

B. 1/6 + 1/4 + 1/3

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Using Cuisenaire Rods, try to solve:

Analyzing Student Work

As you look through the packet of student work, think about…

• What concepts around measurement are understood?

• What misconceptions around measurement do you notice?

• How might you address the misconceptions in your classroom?

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Wall Ball Wall

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One gallon of Interior BEHR PREMIUM PLUS ULTRA Paint and Primer in One, or BEHR PREMIUM PLUS is enough to cover 250 to 400 Sq. Ft. of surface area with one coat.

Dimensions of the wall: 12½ feet by 18½ feet

Reflect back…

• What are the key ideas you want your students to know about measurement?

• What do you find challenging about teaching length, area and/or volume?

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• One key idea or essential understanding that you hope to implement

DisclaimerThe National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students. NCTM’s Institutes, an official professional development offering of the National Council of Teachers of Mathematics, supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of viewpoints. The views expressed or implied in the Institutes, unless otherwise noted, should not be interpreted as official positions of the Council.

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deep dive: measurement and data grades 3 5 · pdf fileelementary math coach ... deep dive:...

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