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There are Seven Major Points in the Chapter

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There are Seven Major Points in the Chapter

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Meaning & process of measuring: Measurement is a number that indicates a comparison between the attribute of the object being measured and the same attribute of a given unit of measure

The role of estimation & approximation: The process of using mental and visual information to measure or make comparisons without using measuring tools.

Length: Is found by locating two endpoints and examining how far it is between those two points.

Area & Perimeter: Is the measure of two-dimensional space inside a region. Length measure of the distance around a region.

Volume/Capacity & Weight/Mass: The amount of space occupied by three-dimensional objects or the amount that a container will hold. Measure of the pull or force of gravity on an object and the amount of matter in an object and a measure of force needed to accelerate it.

Angles: Measure of rotation between two lines that meet at a point.

Time & Money: The duration of an event from its beginning to its end. Its units are;  seconds, minutes, hours.

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Time is the duration of an event from its beginning to its end.
Units: seconds, minutes, hours.

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An approach to measure angles is by using an angle maker which will help with mental images of angle sizes

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Weight is a measure of the pull or force of gravity on an object.
Mass is the amount of matter in an object and a measure of the force needed to accelerate it.

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Volume & Capacity are terms for measures of the "size" of three-dimensional regions.

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Comparison activities, like area, are great ways to help students distinguish the concept of Volume & Capacity

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Area is the measure of two-dimensional space inside a region.

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- Tiles are a common tool to help students understand area, but you can use anything (EX. sticky notes, newspaper, playing cards)

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Comparison activities with area should help students distinguish between size and shape, length, and other dimensions.

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Length is usually the first attribute studnets learn to measure

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Students can begin to measure length using nonstandard units.
-Giant footprints
-Measuring ropes
-Drinking straws
-Short units (toothpicks, paper clips)

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Goals of teaching standard units: familiarity with the unit, ability to select an appropriate unit, knowledge of relationships between units.
* Students need to be familiar with standard units in order to understand measurements correctly.

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Benefits: focuses on the attribute being measured, avoids conflicting objectives in introductory lessons, provides a good rationale for using standard units
Ex: shoe, toothpick, an arm

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The process of using mental and visual information to measure or make comparisons without using measuring tools.

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https://docs.google.com/presentation/d/1WNzmA5hWHXNqnJqOnkEhMgQ9UnsTCr55p5WZlJgxKg4/edit?usp=sharing

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-Helps students focus on the attribute being measured and the measuring process.
-Provides an intrinsic motivation for measurement activities.
- Develops familiarity with standard units.
-Promotes multiplicative reasoning through using a benchmark.

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- Liquid medicine cups
- Plastic jars & containers
- Wooden cubes or same sized blocks
- Styrofoam packing peanuts

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When you have students echo back a word or phrase, it exposes them to new vocabulary and serves as a model for correct pronunciation, syntax, and grammar.

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Partner talk allows more students to participate in classroom discussions, and eliminates the pressure that comes with speaking alone in front of a large group.

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Consider students language/math skills when grouping

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Consider students language/math skills when grouping

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There are times when grouping students with similar abilities in math makes sense, but often students benefit from working in groups where participants have varying skill levels in mathematics. Students also benefit from working in groups where participants have different levels of English language competence.

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Use clear prompts to support students responses

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Use clear prompts to support students responses

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Prompts can help students get started when responding to a question. If you encourage them toward an answer, they are more likely to follow your lead and respond with confidence.

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Nonverbal responses will help you check for understanding without requiring students to produce language. ELLs can participate and show that they understand a concept, or agree or disagree with an idea, without having to talk. This is especially important for students whose comprehension of English is more advanced than their ability to speak the language

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Design questions/prompts for different proficiency levels

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Design questions/prompts for different proficiency levels

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Questioning students lets them reveal what they have learned. Use a prompt that requires a physical response, like "Show me the circle" or "Touch the larger number." Or make them a bit more challenging like "How did you solve the problem? What did you do first, second, and third to solve the problem?"

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Math sentence frames serve a variety of purposes, and they provide the support English language learners need in order to fully participate in math discussions.

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Charts that contain key math vocabulary words and phrases are helpful references for students when discussing or writing about their math thinking, especially if the words are accompanied by illustrations.

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V-The amount of space occupied by three-dimensional objects.
C-The amount that a container will hold.
W-Measure of the pull or force of gravity on an object.
M-Amount of matter in an object and a measure of force needed to accelerate it.

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Students focus on ending point of a ruler rather than the length

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Students focus on ending point of a ruler rather than the length

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-Move items along a ruler and ask students if they believe the item has changed size.
-Iterate unites to show how long the item is and then show how those units match the units on the ruler.

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Ruler, tape, balances, cylinders, measuring spoons, cups, jars, clocks, measuring grid, protractor

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https://www.geogebra.org/search/broken%20rulers
https://www.mathplayground.com/area_blocks.html

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How to measure everything by D.K Publishing

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How to measure everything by D.K Publishing

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(July 31, 2018)

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Students will measure perimeter by counting two sides

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Students will measure perimeter by counting two sides

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-This is an artifact of the problem having only two sides labeled with numbers. Have students draw a line around the rim to show what is being measured. Then suggest each side is labeled before adding the lengths.

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Time is different from most other attributes commonly measured in school because it cannot be seen of felt. This makes is more difficult for students to comprehend units of time or how those units are matched against a given period or duration

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As soon as students can differentiate between a long and short angle, you can move on to measuring angles.

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Use physical models of Weight & Mass Units

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Use physical models of Weight & Mass Units

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Any collection of uniform objects with the same mass can serve as nonstandard weight units.
For lighter objects try large paper clips, wooden blocks, or plastic cubes or coins.

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Use physical models of Volume & Capacity

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Use physical models of Volume & Capacity

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Two types of unit can be used to measure volume & capacity (liquid volume): solid units and containers.
-Liquid medicine cups
-Plastic jars and containers of almost any size
-Wooden cubes or same sized blocks of any shape
-Styrofoam packing peanuts

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Students think bigger units result in a larger measure

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Students think bigger units result in a larger measure

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-Provide many experiences where the students measure the same object's attribute with two different sized units. Have the students predict how the measures will relate to the size of the units.

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Have students time familiar events in their daily lives; brushing teeth, eating dinner, riding to school, doing homework.
This will help develop some concept of how long these units are.

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Money ideas & skills required in primary grades

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Money ideas & skills required in primary grades

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-recognizing coins & identifying their value
-counting and comparing sets of coins
-creating equivalent coin collections
-selecting coins for a given amount
-solve words problems involving money

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A number that indicates a comparison between the attribute of the object (situation or event) being measured and the same attribute of a given unit of measure.

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- the attribute of angle size is often misunderstood
- protractors are used without students understanding the concept behind how they work

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Manipulatives are important tools that make math content comprehensible.

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Me and the measure of things by Joan Sweetney

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Me and the measure of things by Joan Sweetney

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(2001)

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Students will count tick marks rather than units

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Students will count tick marks rather than units

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-Have students iterate units; for example to see how a ruler is made. Then emphasize that units are what we are counting and how the number or tick mark indicates the end of the unit.
-Have students make their own ruler.

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Length is found by locating two endpoints and examining how far it is between those two points.

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The most efficient way to compare weights of two objects is to hold one in each hand, extend your arms and and see which ones "pulls" your arm downwards.

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One method to compare is to fill one container with something then pour that amount into the comparison container. By primary grades most students understand the concept of "holds more" when referencing containers.

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Units that can be used to measure volume and capacity: solid units and containers.
solid units example: wooden cubes

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-Length
-Area & Perimeter
-Volume & Capacity
-Weight & Mass
-Angles
-Time
-Money

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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 using some other method - with the attribute of the object being measured

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1. Develop benchmark or referents
2. Use "chunking"
3. Iterate units