4th grade study link pdfs have been added

Who is Mr. Nale is and why he is here?* I don't know but I do know that he has decided to post pdf version of all the 4th Grade Everyday Math Study Link assignments.

So if your 4th grader forgets his or her Study Link assignment for the day pay Mr. Nale a virtual visit and your problem is solved.

This post will migrate down the page soon so I have created a permanent page called 4th Grade Study Link PDFs on the right for your convenience.




*Kudos if you caught the Admiral Stockdale reference.

Helpful Resources

This blog is to forgotten homework assignments as the hot iron and blowdryer are to leftover pizza.

There are a couple of resources on this blog that might help students and parents.

As a teacher and a parent I know that most students need to hear information 3 times before it sinks in.  When I assign homework I write the assignment on the board and read the assignment out loud.  I then ask students to tell me what the assignment is for the day.  In the case of the 4th and 5th graders I ask Rose to repeat the assignment to the group.  She also instructs them to write the assignment in their planners.

But I know that probably isn't enough for 100% of the students to remember various assignments.  So to add one more reminder/resource the Recent Homework Assignments page is updated (almost) daily.  Yesterday I could not update the page due to a connectivity issue.  The updated edits were eaten by an error message from blogger.

That said if you do have a question about homework assignments you can always go to that page and know what exactly students should be doing.

Another resource is the grade specific video pages.  If you or your student is not sure about a concept please look for a video on the topic.  Some videos are embedded on the page and others are linked within the text.

If you don't find a video that is directly on point please feel free to use Goggle or one of the links I provide in the Useful Links section of this blog on the right hand side.  Cool Math, Purple Math and Khan Academy have excellent instructional videos.

7th Graders - Watch this Lesson with Headphones on and Take Notes

Watch the video on evaluating expressions twice.  The first time mostly listen and pay attention.  You can make a few notes but the purpose of the first time is to absorb the main ideas.

The second time through take notes using the provided template.

When finished grab your Mad Lib answer sheets and go figure out the Mad Libs posted in the first floor hallway.

Fact: Talking Crabs Improve Math Fact Fluency

It's true.  Read on and find out why.

Math fact fluency is a key skill that all late elementary and middle school students must possess in order to succeed in mathematics. Siegler et al (2012) found that understanding of fractions and division at age 10 strongly predicted students' high school success in algebra at ages 15 - 17.

Let me repeat that finding - how well a 5th grader knows division and fractions predicts high school success in math 5 - 7 years later.  Getting those basic skills in place for all of our students is a crucial aspect of my job.

The picture above shows the current fact fluency of a relatively high achieving middle student here at Kazoo School from a report I generated using Reflex Math.  One of the reasons I like Reflex Math is access to detailed progress reports including usage and current levels of fluency.  I can see how much students are practicing and how they are progressing.

As you can see from the report above Reflex Math's initial assessment of middle school and late elementary students indicates a low level of math fact fluency.    Even our best students have a lot of room to grow!

Unfortunately this is a fairly typical situation in today's schools.  But don't worry. I have a plan to address this issue and it's a fun one.  

Hello Mon, Crabby here!

Perhaps you have noticed a new addition to homework assignment namely time allotted to Reflex Math.  Students love the games and feel of the program.  Crabby is the tour guide for tutorial and the creature students see when they log on.  I think he's pretty funny.  Who doesn't like a crab that has a Jamaican accent?  I encourage you to sit down with your child for a few moments just to see how the program works for yourself.

My sense is that this will be a very effective program for increasing fact fluency and that by the end of this year students will be much better at knowing their math facts.  I can't wait to see the results!

I am determined that all Kazoo School students leave knowing their fractions and are fluent with multiplication and division.  Making sure that all Kazoo School students are prepared to succeed in high school math is my goal.

It's fun and amusing to me that we have a friendly talking crab helping us meet one important aspect of that goal - math fact fluency.

What we studying in each class

4th grade:  Geometry

• Angles, rays, lines, triangles and quadrilaterals 
• Pipe cleaners and straws make awesome shapes
• Equilateral, isosceles and scalene triangles
• We started using Reflex Math to improve math fact fluency

5th grade:  Numbers and Operations

• Arrays (think 15 poker chips arranged into a 3 x 5 grid, so 3 x 5 = 15)
• Talked about columns and rows in a table (so this can be generalized beyond arrays)
• Factors and fact families
• 3 x 5 = 5 x 3?!  Who knew?!
• We started using Reflex Math to improve math fact fluency

6th grade:  Integer Operations

• After meditating do 4 - 5 quick problems of the day (POD)
• This week's POD have showed me that we need to shore up multi-digit multiplication and division
• As a result we mostly did multi-digit division using worksheets with visual cues
• Continued building intuition using poker chips to model positive and negative number differences and sums
• Introduced explicit rules to pair with intuitive exercises to build in 2 levels of understanding
• Completed a puzzle with different integers sums and products were matched up to "fit" pieces together
• We started using Reflex Math to improve math fact fluency

7th grade:  Order of Operations

• Difficult and pedantic but necessary
• We are labeling one side of the board P(parenthesis), E(exponents), MD (multiply and divide) and AD (addition and subtraction)
• We cross off each letter from top to bottom as we complete all the operations of each kind before proceeding to the next
• Order of Operations Scavenger Hunt!
• Took Quiz 1

8th grade:  Adding, Subtracting, Multiplying and Dividing Polynomials

• We played Red Fish, Blue Fish, Yellow Fish, Blue Fish Polynomials!
• Reviewed and further practiced polynomial addition and subtraction
• Practiced using the box method for polynomial multiplication
• Took Quiz 1!

Negative Numbers and Subtraction Are Not the Same Thing

One of the frustrating things about teaching math occurs when students encounter unnecessarily confusing math symbols. This week the 6th graders have been struggling with understanding how to use the subtraction operation with negative numbers. Subtraction and negative numbers share the identical notation but are very different concepts.

Subtraction is an action, what mathematicians call an operation.  For instance 6 - 2 = 4 means start with the number 6 then do the action of removing 2 objects. The remaining number is equal to 4.

This is represented by the symbol -.

A negative number is the opposite of a number in the sense that under addition the two cancel each other exactly. A negative number is a thing, a place on the number line, not an action.  The opposite of 3 is -3 because 3 + -3 = 0.

Negative numbers are distinguished from positive with the symbol -.  See the problem?

Subtraction is a verb.  Negative numbers are nouns.  But the math language is the same. Imagine how awful the English language would be if nouns and verbs of related concepts were the same words and we all had to figure out which one was in use by the context of the sentence. For example what if "baker" and "baking" were combined into one word "bakering". "John is baking" would be indistinguishable from "John is a baker" because both would read "John is bakering". It would drive everyone nuts.


Our poor 6th graders have to confront this noun/verb conflation in expressions such as 6 - (-2). 6 - (-2) means "start with 6, now take away (minus sign) the opposite of 2 (-2)". Taking away the opposite of 2 can be a tricky idea.

Black chips are positive 1s and red chips are negative 1s.  The circled red chips represent physically removing or subtracting -4.

I have found that one great way of teaching tricky ideas is by using manipulatives - physical objects that kids can touch and, well, manipulate that stand in for mathematical ideas.  This week we have been using poker chips and drawings of circles with + and - in the middle to visualize this relatively complex combination of concepts.  The picture above is an illustration of 2 - (-4) = 6.  The black chips are positive 1s the red negative 1s.  A black chip and a red chip together make a "zero pair".  So the picture starts with 4 zero pairs of black chips and red with 2 unpaired black chips left over.  Hence, the number 2.

Taking away (-4) is represented by physically removing 4 red chips.  Now there are no more zero pairs, just 6 black chips by their lonesome.

By Friday I got the sense that the ideas were beginning to click.

Now on to 6 x (-2) and how that can be understood as repeated addition:  (-2)  + (-2) + (-2) + (-2) + (-2) + (-2) = -12.


On Edit:  Look out 7th and 8th graders because this exact problem is found in square roots.  There is an action called taking a square root and there is a number concept with the same name and notation.  Nice job mathematicians, nice job.

Standards Based Grading is Coming

Standards based grading is a change from the grades with which we parents and teachers are familiar.  In regular grading the scores for various quizzes and tests are weighted and average over a semester to form an aggregate percentage.  Percentage cutoff values then determine a letter grade - 90% for an "A", 80% for a "B" and so forth.  What we see is that our son or daughter got an "A" or a "B".  Recently I have become uneasy with how little information is conveyed by a letter grade.  If someone gets a "B" in Algebra 1 do they understand polynomials?  What about absolute values?  Inequalities? The variation in understanding across concepts that all math students possess is hidden by a simplistic letter grade.  There must be a better way.  Of course I wouldn't be writing this if there wasn't.  There is.

Standards based grading is a type of assessment in which data on student understanding from quizzes and tests is organized into important skills. Student data remains relatively disaggregated. Assessments are focused on critical mathematical domains in the curriculum and specific skills within the domain are laid out for the students before assessments take place.

Here is one example of what this looks like in practice for a 4th grade classroom.

In this case the specific skills are link to the Common Core State Standards.  There are a few new things to notice.  First, what you see is a relatively detailed list of skills rather than entries like "Unit 1 Test".  Second, the evaluation is related to levels of understanding.  In principle it is a qualitative measure but in math often it is tied to a quantitative outcome (percentage on a quiz).

With standards based assessment a student and parent receives an inventory of strengths, weakness and material already mastered or at least covered so far.  This may or may not be in addition to an overall course grade.

In my opinion the main advantages of standards based assessment are:

• students and parents have a clear picture of course expectations and required skills for the duration of the course
• 
  
• students know what they are supposed to be learning at any point in time
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• future teachers can look at the grade book and know what the students needs and accomplishments are prior to beginning instruction in the new year.

Above is a screenshot of the standards based grade book for 6th grade that I developed this week. The first page of the document shows five 6th grade skills.  The second page has my rubric for scoring each mathematical domain that is assessed.

I look forward to passing out standards based assessment forms to all students soon so that everyone knows what we are working on and what is expected.  I hope that by going to a standards based grading system parents and students will have a better understanding of both the courses I teach as well as what their students have learned.