There is nothing that children can connect more solidly to everyday life than measurement. Give even a very young child a ruler and they will try to determine how "big" they are. By the end of the second grade students should learn which units are appropriate for measuring something less than a foot long (inches or centimeters) or great distances (miles and kilometers). Besides length, students they should also learn to measure weight and capacity of objects. They will learn what attributes (tools) are available for measuring linear dimensions, weight, capacity, and temperature. They also learn to use clocks and calendars to measure times. They are taught the concept of minutes, quarter-hours, half-hours, hours, days, weeks, months, and years. By this time they should be able to use both digital and analog clocks and be able to determine 5 minute intervals. Another aspect of measurement they should know would be temperature, using both Celsius and Fahrenheit. By linking measurement to the world around the student, we can draw them into the curiosity of how big something is, how much it can hold, how hot is is, or how long it will take to do something. This helps them relate the attributes, units of measure and the tools we use to find them out, rather than being some sort of abstract concept.
Here is a link to some effective ways to introduce measurement into your students vocabulary.
Teaching Ideas
I have also included some links to some fun games that elementary students will totally enjoy.
Liquid Measure Game
Funbrain
Gameqaruim
Friday, July 15, 2011
Friday, July 8, 2011
1512 - Common Core Standards
When I first read about the Common Core Standards, I found it very intriguing. The mission statement of the Common Core State Standards reads as follows:
The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. Common Core State Standards Initiative
That is perfect! Isn't that what we all want? A clear concise outline of what each student should know and work they should be capable of, at each specific grade point? I certainly thought that was the way to go, when I first read about it. But now that I've had time to think it over, I have to wonder if it would be such an easy solution. We all want our children to have the best education available to them, and have them be competent and able to conform to a national standard that would be appropriate for their age. But kids are different — not only from one another, but when it comes to their own varying facility across subjects as well. Any single set of age-based standards, no matter how thoughtfully conceived, will necessarily be too slow or too fast for most children. Why can't we come up with a system that addresses what each child independently needs to succeed. I've often wondered why we can't come up with a system of IEP's (Individual Education Plans) for all of our kids. Not just the students with a "Special Ed." label. A plan that addresses their strengths and weakness and tailors their education to fit them specifically. Under a system like this, each child might not meet a specific criteria at a specific age. However, I do think you could test for competency and make sure of mastery before promoting them on (or graduation).
In his article "The False Premise of National Education Standards" Andrew J. Coulson writes: "There is a far better alternative: group students based on their level of mastery in each subject, instead of strictly by age, so that each can progress as fast as he or she is able. By doing so, all children are taught the things they are ready to learn at any given time. No one need be bored into a stupor nor left hopelessly behind".
There has to be a better way.
Update on the Common Core State Standards At this time, Minnesota is not adopting the Common Core State Standards for mathematics. The commissioner of education revises the academic standards according to a timetable specified in state statute (Minn. Stat. § 120B.023, subd. 2). The Minnesota mathematics standards were revised in 2007 and are not scheduled to be revised again until 2015. Since the commissioner does not have authority to revise mathematics standards at this time, legislative action would be needed in order for the state to adopt the Common Core State Standards for mathematics. MDE will continue to analyze the Common Core and Minnesota mathematics standards in order to provide information to the legislature, as requested.
The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. Common Core State Standards Initiative
That is perfect! Isn't that what we all want? A clear concise outline of what each student should know and work they should be capable of, at each specific grade point? I certainly thought that was the way to go, when I first read about it. But now that I've had time to think it over, I have to wonder if it would be such an easy solution. We all want our children to have the best education available to them, and have them be competent and able to conform to a national standard that would be appropriate for their age. But kids are different — not only from one another, but when it comes to their own varying facility across subjects as well. Any single set of age-based standards, no matter how thoughtfully conceived, will necessarily be too slow or too fast for most children. Why can't we come up with a system that addresses what each child independently needs to succeed. I've often wondered why we can't come up with a system of IEP's (Individual Education Plans) for all of our kids. Not just the students with a "Special Ed." label. A plan that addresses their strengths and weakness and tailors their education to fit them specifically. Under a system like this, each child might not meet a specific criteria at a specific age. However, I do think you could test for competency and make sure of mastery before promoting them on (or graduation).
In his article "The False Premise of National Education Standards" Andrew J. Coulson writes: "There is a far better alternative: group students based on their level of mastery in each subject, instead of strictly by age, so that each can progress as fast as he or she is able. By doing so, all children are taught the things they are ready to learn at any given time. No one need be bored into a stupor nor left hopelessly behind".
There has to be a better way.
Update on the Common Core State Standards At this time, Minnesota is not adopting the Common Core State Standards for mathematics. The commissioner of education revises the academic standards according to a timetable specified in state statute (Minn. Stat. § 120B.023, subd. 2). The Minnesota mathematics standards were revised in 2007 and are not scheduled to be revised again until 2015. Since the commissioner does not have authority to revise mathematics standards at this time, legislative action would be needed in order for the state to adopt the Common Core State Standards for mathematics. MDE will continue to analyze the Common Core and Minnesota mathematics standards in order to provide information to the legislature, as requested.
Math 1510 - Prealgebra
"As long as algebra is taught in school, there will be prayer in school. "
– Cokie Roberts
– Cokie Roberts
Sunday, July 3, 2011
1510 - Multiplication
Standard long multiplication algorithm? Partial products? Lattice? Fingers? Calculators? Any way they come up with on their own? I never knew there were so many ways to multiply! Thank you to 360 for the summary listed below.
Procedures:
- Repeated Addition
- On the fly shortcuts to Addition
- Doubling and Halving (Egyptian, Ethiopian?, Russian?)
- Doubling and Adding or Duplation (Egyptian)
- Shift and Add
- Grid or Lattice Multiplication (Arabic, Indian?)
- A variation on Grid Multiplication (medieval Italian or earlier)
- “Traditional” or Long Multiplication (medieval Italian or earlier)
- Crocetta, or Vertically and Crosswise Multiplication (Indian)
- Digit-reverse and shift, by Pappus (Greek)
- The Method of the Cups (Spain or the Americas?)
- per Repiego, or multiplying by factors (medieval Italy or earlier)
- Drawing lines like on that YouTube video
- Babylonian(?) (First Formula)
- Babylonian(?) (Second Formula)
- A third difference of squares (Greek) [
- Prosthaphaeresis or Trig Tables (Europe)
- Logarithm Tables (Europe)
- Physical Objects:
- Napier’s Rods (Scotland)
- Genaille-Lucas Rulers (France)
- Gunter Scale [here]
- Slide Rule
- Abacus (Chinese)
- “Prosthaphaeretic” Slide Rule (based on similar triangles)
![[here]](http://www.pballew.net/gunterscale.jpg){kind=link}
- Similar Triangles (Greek)
- Finger Multiplication by 9
- Finger Multiplication between {5, 6, 7, 8, 9, or 10} (medieval Europe
- Finger Multiplication between {10, 11, 12, 13, 14, or 15} (medieval Europe?)
So, which approach is the right way? The way that teaches your student so she to truly understands. It will be my job to help each student find what method works best for them and to keep it relevant.
I like this approach to introductory multiplication (very early elementary). You start off teaching the idea of "groups of", (you have 2 groups of 3 grapes) even before you introduce any tables or problems. Then, when the student is ready, you will just let them know that multiplication is just a shortcut for "groups of". This website lists a variety of introductory multiplication lessons, and has very clear and basic guidelines. Mathcats
The following Minnesota state standard encompasses part of the 2nd and the 3rd grade:
3.1.2.3 Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
The 2010 Common Core State Standards and the 2007 Minnesota standards state that in the second grade we should introduce multiplication sentences, multiplication tables up to 10, and divisors and quotients up to 10. (See these standards outlined at IXL) My son will be in 4th grade this coming September,and they just finished this past year with multiplying to 10, not even addressing division. I know they are well behind these standards, and I wonder when they will have the big push to catch up.
Saturday, July 2, 2011
1512 - Geometry
ge·om·e·try/jēˈämitrē/Noun
1. The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.
Who doesn't love the word hypotenuse? The hypotenuse is the long side of a triangle that contains a right angle. The word derives from the Greek hypo- ("under") and teinein ("to stretch"). I even wrote a learning poem to remind myself of the Pythagorean theorem, which helps us solve for the length of the hypotenuse. It goes like this.
"Hypotenuse, Hypotenuse, its such a silly word.
You take the squares of the right angle legs,
to find the square of the third."
Not terribly inventive, but it works for me!
Again a nice example from brainpop.com, and also a song about triangles... Thanks James Blunt.
A triangle is a polygon. Polygons are closed plane figures formed by segments. They can be classified based on the number of sides (or angles) they have. A polygon with two sides does not exist. Below you see a sample of the most common geometric shapes. I wish I would have had this chart before I took my last test!
A triangle is a polygon with three sides and three angles.
A quadrilateral is a polygon with four sides and four angles.
A pentagon is a polygon with five sides and five angles.
A hexagon is a polygon with six sides and six angles.
A heptagon is a polygon with seven sides and seven angles.
An octagon is a polygon with eight sides and eight angles.
A nonagon is a polygon with nine sides and nine angles.
A decagon is a polygon with ten sides and ten angles.
A dodecagon is a polygon with twelve sides and twelve
1. The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.
Who doesn't love the word hypotenuse? The hypotenuse is the long side of a triangle that contains a right angle. The word derives from the Greek hypo- ("under") and teinein ("to stretch"). I even wrote a learning poem to remind myself of the Pythagorean theorem, which helps us solve for the length of the hypotenuse. It goes like this.
"Hypotenuse, Hypotenuse, its such a silly word.
You take the squares of the right angle legs,
to find the square of the third."
Not terribly inventive, but it works for me!
Again a nice example from brainpop.com, and also a song about triangles... Thanks James Blunt.
A triangle is a polygon. Polygons are closed plane figures formed by segments. They can be classified based on the number of sides (or angles) they have. A polygon with two sides does not exist. Below you see a sample of the most common geometric shapes. I wish I would have had this chart before I took my last test!
A triangle is a polygon with three sides and three angles. A quadrilateral is a polygon with four sides and four angles. A pentagon is a polygon with five sides and five angles. A hexagon is a polygon with six sides and six angles. A heptagon is a polygon with seven sides and seven angles. An octagon is a polygon with eight sides and eight angles. A nonagon is a polygon with nine sides and nine angles. A decagon is a polygon with ten sides and ten angles. A dodecagon is a polygon with twelve sides and twelve
Math 1512 - Graphs and Charts
I feel that most elementary children are very visual learners. Charts and graphs are amazing learning tools because they communicate information visually. This is a very effective way to show the student the meaning behind the figures. If you can connect the math problem to a real life situation, the problem won't appear pointless. It helps us to understand reality. A classic example is if a student is learning about percentages, using a pie chart (or a pizza chart) will show what the percentages really mean. Do you think you can really eat 1/2 of the pizza? Or would you be full after 1/4? A chart can help tie that foreign concept of a fraction together with a real world situation. Check out this link for Brainpopjr.com for another real life situation utilizing a chart and graph. Brainpopjr.com has a fantastic age appropriate video that explains tally charts and bar graphs, and this example uses dinosaurs and a robot. I think you could grab some attention with that!
Graphs and charts are great because they communicate information visually. For this reason, graphs are often used in newspapers, magazines and businesses around the world. This learning aid doesn't stop at the elementary level.
Here is a fantastic software download for producing your own charts and graphs. Amcharts You can download and use Amcharts for free, but there will be a small icon that shows on every page to advertise and link back to the home company. A very nice tool for older grades.
Math 1510 - Understanding Place Value
My research shows that some children have trouble grasping the basic concept of place value. This basic number concept is so important for math success later down the line. The result of a child not fully understanding place value could lead to problems when he/she is faced with fractions, division or other more challenging problems. For children to understand place value, they first need to name numbers, do simple small number addition and subtraction, and understand about groups.
If you are teaching place value or other number sense concepts, children's books can make the difference between comprehension and confusion for students who are visual or verbal in nature. A great place to start with lower elementary levels would be the following children's books.
Children's Math Books
These books children's are excellent for teaching place value, odd and even numbers, and other basic number sense concepts.
Here is a look at a lesson plan on place value I think we all would enjoy!
If you are teaching place value or other number sense concepts, children's books can make the difference between comprehension and confusion for students who are visual or verbal in nature. A great place to start with lower elementary levels would be the following children's books.
Children's Math Books
These books children's are excellent for teaching place value, odd and even numbers, and other basic number sense concepts.
Here is a look at a lesson plan on place value I think we all would enjoy!
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