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Mrs. Phillips Mrs. Phillips

Welcome to Mrs. Phillips's  

5th Grade Math Page

Please feel free to contact me at any time via email at phillipsa@duvalschools.org or call me at 992-6390 x2007

May 30-June 2  

Last Week of 5th Grade 

Sign-Up Genius for our Tuesday pizza lunch & Thursday ice cream party:

http://www.signupgenius.com/go/904084ca5ac238-last 


Tuesday9:00 AM Awards Ceremony, Pizza luncheon 
Field Day & OMC  (Nash homeroom-RED, Phillips- BLUE, Price- Light Blue)

Wednesday- Early Release Day (Dismissal at 2:00 PM)

Thursday-  Health Lesson & Ice Cream Party 

Friday-  Clap Out (11:30 AM) & Dismissal (12:00 Noon)


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Hands on Equations 
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We were able to explore the first 9-10 lessons in a pre-algebra unit entitled "Hands on Equations".
This fun unit of study offers a whole-brain approach to algebraic equations and word problems.

These lessons will help build the students' confidence for pre-algebra studies in middle school. 




There will be no homework assigned this week. :-)

 

There are no math assessments scheduled for this week. 

Please remember to review/sign and and return all previous math assessments to school. These are referenced and reviewed for reteaching purposes after parents have a chance to review them at home. 

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Content from Previous Weeks: 
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We have spent a lot of time discussing attributes of quadrilaterals.
   

As a review, we have learned that SQUARES are pretty special because they are also rhombuses, rectangles, parallelograms, trapezoids, kites, and (ofcourse) quadrilaterals!
Check out each definition above and you will see that the square fits EACH and EVERY one!
(We call him "Mr. Perfect"!)
 

We have challenged many of our new understandings with True/False statements in recent lessons.
Each 5th grader should be able to correctly respond to each of the following statements and explain WHY or WHY NOT!

TRUE Statements:

Al quadrilaterals have four sides.
(QUAD means 4.)
All parallelograms are quadrilaterals. 
(Parallelograms have 2 pairs of parallel sides and 2 pairs = 4 sides.)
All squares are parallelograms. 
(Squares have 2 pairs of parallel sides.)
All squares are rhombuses. 
(Rhombuses are parallelograms with 4 congruent sides....Squares have 4 congruent sides!) 
All rhombuses are parallelograms.
(Rhombuses have 2 pairs of parallel sides.)
Parallelograms are always trapezoids. 
(Trapezoids have "at least one pair" of parallel sides, and parallelograms have "2 pairs", which is at least one pair.)
All squares are rectangles.  
(Rectangles are parallelograms with 4 right angles....Squares have 4 right angles!)


FALSE Statements:

Trapezoids are always parallelograms. 
Nope. A trapezoid may only have one pair of parallel sides. 
  

Kites cannot have four congruent sides. 
Sure they can. To be a kite, you need 2 pairs of adjacent (adjoining, neighboring) sides that are congruent (equal) in length. Squares and rhombuses fit this rule. 
  

All trapezoids have at least one right angle.
Nope. They may only have acute and obtuse angles.
 
All rhombuses have only 1 set of equal length sides.
Nope. Rhombuses have 2 sets/pairs of equal length sides. 
 

All rectangles have 4 sides that are equal length. 
Nope. Squares are rectangles with equal length sides, but many rectangles (like the one below) have a pair of longer sides and a pair of shorter sides. 
 


All quadrilaterals are trapezoids. 
Nope. There are many quadrilaterals that ARE trapezoids because they have at least one pair of parallel sides (parallelograms, rhombuses, rectangles, and squares), but some ARE NOT....such as kites and other quadrilaterals. 
  


There are many other examples like these in your child's Math Notebook and on recent homework. This information will be assessed on our next assessment on Wednesday, March 15th.

Note that there is a lot of VOCABULARY in this module.
Your child should study his/her homework, Math Notebook notes, and Flip Book in preparation for this test.

Flip Book: 

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A great website to visit for Geometry is  http://www.mathsisfun.com/geometry/index.html
Students, if you visit this website, have your parent write a note in the planner and earn some extra (SECRET....Shh!) Behavior Bucks!
 
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Coordinate grids: 
 x then y      (x,y)
The horizontal axis is the "x" axis.
The vertical axis is the "y" axis. 

The following points were plotted on the above grid and then connected in order to make the isosceles triangle: (5, 3), (1,3) and (3,7)






VOLUME

        


Each 5th grader should be able to:
  • Find the total volume of solid figures composed of two non-overlapping rectangular prisms.
  • Apply concepts and formulas of volume to design a sculpture using rectangular prisms with given parameters.

Fraction Division 
We are using number lines in class to help visualize problems with dividing fractions. 

 

This number line illustrates how when 5 wholes is divided into groups of one-third, the result is 15 equal sized parts. Therefore, 5 divided by one-third equals 15.
We are also rewriting our division equations as multiplication equations using a "keepchangeflip" method. 
The total (divided) is kept the same (5), 
the operation is changed to the inverse (division to multiplication) 
and the fraction is flipped (changed to it's reciprocal). 

 

Fraction Multiplication 
In addition to working with fraction division, we are also continuing to review fraction multiplication and the approach of "simplifying before you multiply".

   


We are also working on Order of Operations in class and "Aunt Sally" is reminding us of how to proceed:
 

Fraction Addition & Subtraction 
We are still reviewing addition and subtraction of fractions / mixed numbers through math centers and homework. 

See the anchor charts from our classroom below:
  

We are also STILL emphasizing the importance of putting our final answers to addition and subtraction problems in "simplest form". 
See the related anchor charts below:
  

Through centers, we will continue to work on division strategies and representations for remainders (left-overs).



We will continue to use estimation to help justify the reasonableness of our quotients. For example, in the problem above we would know that our answer should be about 9,000 since 63,000 divided by 7 is 9,000. We will round the divisor or the dividend to help make these determinations. 


 

Look at the example for 45 x 32 below (45 groups of 32)-
The array model on the left shows the partial products when both factors are decomposed into their place value parts.
The traditional algorithm is shown on the right. Notice the similarities between the two approaches.   

                 

The distributive property for this problem could be represented as: 
45 x 32 
45 x (30 + 2)
45(30 +2) 
(45 x 30) + (45 x 2)


Multiplying DECIMAL fractions by multi-digit whole numbers:

 

As you can see in the example above, the standard form of 13.5 was converted to unit form as 135 tenths. This allowed the problem to be solved without worrying about the placement of the decimal point. After finding the product, the unit form answer (5805 tenths) was then converted to standard form 580.5.
   
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Writing and converting numerical expressions and comparing expressions:

Examples: 
"the sum of 10 and 9, doubled" .............
2(10 + 9)  
and 
"30 fifteens minus 1 fifteen"..............(30 x 15) - 15

                                              
Converting numerical expressions into unit form as a mental strategy for multi-digit multiplication:

31 x 8 is "30 eights plus 1 eight". 
This problem can be solved using MENTAL MATH strategies since 30 is a nearby landmark to 31. 
30 x 8 = 240, so 31 x 8 is 240 +8 or 248.


The Distributive Property 

  

With this property, as in the example shown above, a number "a" is being multiplied by both "b" and "c", so it is being "redistributed". 
Changing the grouping of factors (numbers being multiplied) does not change the product (answer), so both expressions are EQUAL (as shown in the balance). 

Here is a great "real-world" example that I found on a google search from www.profteacher.com: 
 


This mathematical property is useful for many reasons. Right now, our focus will be on how it is useful for decomposing a factor to make it easier to solve for in a multiplication problem. 

For example, 5 x 32 can be rewritten as 5(32) or 5(30 + 2).
Then, we can rewrite the expression as (5 x 30) + (5 x 2).
These two "mental math" problems can then be easily solved to get the final product. 
5 x 32 or 5(32)
5(30 +2)
(5 x 30) + (5 x 2)
150 + 10 = 160 

If your child would like to earn $20 Behavior Bucks, have him/her SECRETLY provide me with a written real-world example of the distributive property (one like the taco & soda example shown above).

                  The Associative Property
                           
                      

This property, as shown in the example above, simply demonstrates that changing the order of the factors being multiplied does NOT change the product. :-)


With adding and subtracting decimals, "dot models" are used to illustrate how our base 10 number system works. When we "regroup" between place values, we exchange "one" larger unit for "ten" smaller units (or vice versa). These models support the traditional algorithms, which are also shown.
  


Strategies for multiplication are shown below. The color changes help to emphasize connections between the non-traditional approach and the traditional algorithm. This example shows whole numbers, but we have extended this work to multiplying decimal numbers. 
  


 
Students are encouraged to "strive for 45" minutes each week on I-Ready Math. They are provided some time in class to help achieve this goal during math centers and they are encouraged to also log on at home if/when time permits. Thank you to those families who are encouraging the use of I-Ready Math at home!!!



 
Student fluency with basic multiplication and division facts is necessary in 5th grade. If your child is not yet fluent, please have him/her log into Reflex Math at home until fluency is achieved. 

                                                                            

Multiplication of whole numbers by decimals:
Area models are used to show how to decompose a decimal into its place value parts to find the partial products of those parts and then combine (+) those parts together to get the total (product).

Look at the example below. 

                                                                               


Conceptual rounding strategy:

    

The above example shows how 49.67 is rounded to the nearest ten.
 
Since this number is between "4 tens" and "5 tens", these values are placed at opposite ends of the vertical  number line. Next, the midpoint is determined: "4 tens + 5 ones", or "45" (as 45 is halfway between 40 and 50). 

Since the number 49.67 has "4 tens" and "9 ones", it is well above the midpoint and will round to "5 tens" (50), the "nearest ten". 

Students will learn to round numbers to "any place"- developing more flexibility and fluency with our base ten number system. 
                                                                            


 Our students know how to reason about place value understanding by relating adjacent base ten units (for example, one hundred is ten times greater than one ten). We have explored and discussed place value units from millions to thousandths 


            10 = 1 x 10
          100 = 10 x 10 
       1,000 = 10 x 10 x 10 
     10,000 = 10 x 10 x 10 x 10
   100,000 = 10 x 10 x 10 x 10 x 10
1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 
 
 
To see all of the math standards for 5th grade, please visit the site listed below:










5th Grade - Chets Creek Elementary
Duval County
13200 Chets Creek Boulevard
Jacksonville, FL 32224
(904) 992-6390