I have just glanced at the Quantile Framework website and was amazed at the enormous amount of information available. I was given the link by Jim Monahan, Grade 7-8 Math teacher, who uses the CMP-2 Program. If you use a popular program, such as CMP2, this site will directly link you to units within the program. Since I work with a lot of schools who use different programs…or no programs at all…I am not going to go into how to use the program resources in this post.
It appears that training is needed in order to be able to use the Quantile system of targeting instruction for students. The website can be overwhelming. In fact, I found some great resources, which is why I created this post. Then, when I tried to find the resources again, I couldn’t. The link I used links to the site’s homepage, while the resources I found were deeply imbedded in the site. I’ll try to find them again and update this post…
Okay, I’m starting to figure out how to navigate this site. Bear with me as I write this post while discovering how to move around the site myself. If you go to the link above, which is the Home Page, one option is to “Search the Math Skills Database”. I entered “fractions”. Under “State”, I selected CCSSI, which links to the Common Core State Standards. I got a lot of hits. I scrolled down to a specific skill, QT-N-231 “Add and subtract fractions and mixed numbers with unlike denominators.”
The skills are called QTaxons and are arranged by strands such as Numbers and Operations, Algebra, etc. The QTaxon number for the skill I chose is QT-N-231, which indicates that it is in the strand Numbers and Operations and it is the 231st skill under that strand.
When I clicked on that skill, I was taken to another page, where there were details on that one skill. The details include:
The QMeasure (quantile measure) for this skill is 790Q, which is a measure determined, I suspect, by the Q-gods. (You can read more to find out how this measure is created if you want.) I am choosing not to go into the QMeasures at this point, because to do so would take a lot more research and practice. The QMeasure is supposedly the raison d’être for the whole site. However, I am looking at this site as a way to find resources around a specific math topic.Below the details are links to several headings: Knowledge Cluster | Related Terms | State Standards | Textbook Lessons | Resources.
You can either click on the heading link or simply scroll down the page.
Under “Knowledge Cluster” are “Prerequisite QTaxons” and “Supplemental QTaxons”. These are simply what you would expect. The prerequisites are skills that are needed before a student can master the given skill. The supplemental skills are ones that will reinforce the given skill.
The “Related Terms” are self-explanatory.
When I got to the “State”, I had to enter CCSSI again and then hit “Return to Top”. The computer worked a bit and then appeared the following related CCSS Grade 5 standards having to do with this skill:
|5.NF.A1||Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.||5|
|5.NF.A2||Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.||5|
|5.MD.B2||Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for the grade to solve problems involving information presented in line plots.||5|
The “Resources” were divided into “Web Resources” and “Downloadable Resources”
I clicked on the first web resource:
|Conceptua Math: Adding Fractions with Uncommon Denominators (login) Show Directions||http://www.conceptuamath.com/FractionMats.html#tool=additionWithEquivalenceMat|
I clicked on the link to the Conceptuamath website. I had to register, but access to the site was free. The applet was interesting in that you could choose different representations for fractions…circle, rectangle, number line. For showing addition of fractions or mixed numbers that had a common denominator less than 24, the applet worked well. However, I tried to add two fractions with denominators 5 and 8. The least common denominator of 40 was not an option.
I did not take the time to look at other resources, but noticed that there were many from Khan Academy and two from Shodor Interactive, in addition to other sites.
Below the resources was a long list of “Textbook Lessons”. I scrolled down to a program that I am familiar with, Connected Math Program 2. The skill was listed in several places in the CMP2 Program. I chose the Grade 6 Unit Bits and Pieces II. All of the Investigations in the Unit were listed. When I chose “Expand All QTaxons”, I noticed that the skill I am looking for, Qtaxon-N-231, appeared in all four lessons in Chapter 2 and nowhere else. (See below.)
|Chapter 2 – Adding and Subtracting Fractions|
|Lesson Details||1 – Land Sections: Writing Additions and Subtraction Sentences(Show QTaxons)||790Q|
|Lesson Details||2 – Visiting the Spice Shop: Using Addition and Subtraction(Show QTaxons)||790Q|
|Lesson Details||3 – Just the Facts: Fact Families(Show QTaxons)||790Q|
|Lesson Details||4 – Designing Algorithms for Addition and Subtraction(Show QTaxons)||790Q|
When I scrolled over to the “Lesson” column on the far right, the only lesson that appeared is shown below:
High School Math Skills
I decided to look for a high school skill and see where it took me. I went back to the Home Page and to the Search the QTaxon database. I entered “solving quadratic equations” and did not get a hit. I simplified it to “quadratic equations” and got a lot of hits, many of which involved solving quadratic equations. I chose to look more closely at solving quadratic equations by completing the square because it is my favorite way to solve a quadratic equation. I was curious to see if there were any links showing the area model method for completing the square, rather than the algorithmic algebraic model.
I checked out a few of the Resources listed and was underwhelmed. While I know that the algebraic way to complete the square is more efficient, I would love to at least see a site that shows why we do the steps that we do. We are actually “completing a physical square”, an idea which tends to get lost in the algorithm. I guess I’ll just have to create my own post on this topic!
In conclusion, the Quantile Framework site contains an enormous amount of information and resources. The resources are not all good, but there are enough that you can usually pick and choose.