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Math FUNdations for 5th and 6th graders Blog

The focus of this class is to provide a foundation in math for 5th and 6th graders. Learners will be introduced to math concepts as another way to explore our world and to enjoy ourselves as creative problem solvers. We'll investigate mathematical patterns that are found in problem solving, adding, subtracting, time, fractions, decimals, multiplying, dividing, time, money, geometry, logic, spatial understanding, shapes, and patterns. We'll use geoboards, cards, dice, graph paper, and play games from around the world.

From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 10

Statistics and Probability
Homework: 105, 107, 113 You may also finish any other part of the book that you’d like to try.


Notes from Class
Probability: If there are n equally likely outcomes, then the probability of any given outcome is 1/n
Probability of an Event: If all the outcomes of a sample space (data) S are equally likely, the probalility of an event E is

P(E)= number of outcomes in E
Number of outcomes in S

For two stage experiments, such as the number of children in a family make a tree. Like we did in class.

Thank you all so much for a wonderful year! Enjoy your summer vacations, reunions, soccer playing, dog training, and all the sunshine.
Blessings,
~rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 9

MEAN; MEDIAN; MODE
Mean: of a set of data is the sum of all the measurements (or numbers) divided by the total number of measurements
X= X1+X2+X3+… Xn
____________
N

Median: of a set of data is with an odd number of measurements is the middle number when the measurements are listed from smallest to greatest
For a set of even measurements, also list the numbers from least to greatest, then find the mean of the two middle numbers.


Mode: of a set of data is the measurement that occurs most often


Challenge of the week: Find the mean, median and mode of the ages of your family members, then bring it to class to share.

Homework: Page 105-106, complete at least three problems on each page.





From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 8

Tessellations

Homework: pages 86-91 please try one problem from each page
Create your own tessellation to share with the class

The Dutch artist M.C. Escher created unique tessellations by using translations, rotations, and reflections to reshape polygons such as squares, equilateral triangles, and regular hexagons, which are known to tessellate [think about a honeycomb].
Translation tessellation: begins with a regular shape, cut one side then tape it to the other and map them next to each other. This is the same process that we did in class.
Rotation Tessellations: created by cutting one side and rotating it to the next side of the polygon.
Reflection Tessellations: Cut out the side of a polygon figure, now reflect the whole thing down or side to side like a lake or mirror.

Challenge of the week: Make an Escher type tessellation using two different colors and going to different directions. This process is similar to what we did in class today, but taking it to the next level.


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 7

translations and reflections

Homework: Use the graph paper and tracing paper to make your own translations, rotations and reflections. Bring it to class next week to share.

Notes from class

Translations: is a special kind of mapping that can be described as a sliding motion. Make sure you move each piece the same distance and the same direction

Reflections: about a line is a mapping that can be described by folding. Remember that the fold is the line of reflection. A mirror or lake would also be called a plane of reflection.

Rotations: which for plane (flat, one dimensional) figures can be described as turning about a point. Most rotations occur at 90 degree intervals.


Challenge of the week: What year and what country was M.C. Escher born?


Have a great weekend!
~rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 6

Symmetry & Reflection

Homework: pages 83, 84, 85 Complete at least three problems from each page
Symmetry:
*When the shape is ‘folded’ it will be the same on both sides of the ‘fold’.
*If the shape is not the same, and a piece hangs over or sticks out, then the shape is NOT symmetrical.
*Lines of symmetry occur along the ‘folds’ (remember the example of our shapes in class and the example that one learner drew on the board)
Reflection:
*Think about what happens to a shape when it is set near water
*remember that it is backward, like in a mirror

Challenge of the week: How many lines of symmetry does a circle have?


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

week 5: Surface Area

Homework: page 101

Surface Area: L*W of each of the six sides added together

For example (L*W of side A) + (L*W of side B) + (L*W of side C)+ (L*W of side D)+ (L*W of side E) + (L*W of side F)= Surface area (of a rectangular shape)

*Recall the example with the boxes in class and let this be your guide

Challenge of the week: Measure the surface area of a box in your home (like the battleship game box) and share it with your ‘square buddies’

Bonus Challenge: Find the surface area of a cylindrical oatmeal container with a radius of 5cm and a height of 18cm. [hint see the notes on circumference found in week 2]


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Math websit

http://udltechtoolkit.wikispaces.com/Math+tools

I hope you all find this very useful.
~rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Notes Week 4

Homework: p99-100 complete at least three problems from each page

Volume= LxWxH
The measurement is always cubed.
For example, the volume of a room measured in units of feet would be
12 feet x 14 feet x 8 feet = 1344 ft3

Challenge of the week: measure the volume of a cereal box and share it with your buddy

~rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Week 3 Notes

Area= 2L*2W
Perimeter= L1+L2+W1+W2
Remember to ADD the sides to find perimeter

Area units are always squared. For example the area of a room equals 1200ft2 (also 1200sq.ft)
For Homework: Find the area and perimeter of a room in your home. Make sure you write the unit of measurement that you used.

Challenge of the week: How many post-it notes will fit perfectly on your workbook?

~rebecca



From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Week 2 notes

Homework: p78, p95, p96, p97
Complete at least three problems from each page.

Notes from class:

C=circumference=the measurement around the outside of the circle
d=diameter=the measurement across the circle
r=radius=half of the diameter, OR from the center to the edge of the circle

pi=3.141593…the number continues indefinitely without ever repeating

To solve the calculations on the homework pages use 3.14

Pi was a number discovered by the Greeks who measured both the circumference and the diameter of circles. They discovered that the ratio C/d=3.14 again, and again, and again; just like we did in class with our cylinders.

To find the area of a circle:
A=pi*r^2 (3.14 times the radius squared)
Remember that exponents are the number multiplied by itself! Found in the class blog under Fall week 8.

Challenge of the week: Measure the circumference and diameter of a circle at home. See if the ratio C/d =3.14. Try a tire, a drinking glass, a pool. Share it with your buddy on Tuesday.

~rebecca




From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Week 1 notes

Pythagorean Theorem a^2 + b^2 = c^2

Exponent: a number times itself, ie 3^3=3*3*3=27 OR 2^2 = 2*2 =4

To find the square root of a number you break the number down into prime numbers then take out PAIRS.
For example: the square root of 25 is broken down into 5*5, thus it is 5 because you have one pair
Another example: The square root of 18 can be broken down into 2*3*3 thus it is 3 square root 2. Only the pair of 3’s can come out of the square root, the 2 must stay inside of it because it is not part of a pair.

We spent a lot of time on our community building activity and did not have a chance to go over this process in depth. Please do your best on the homework found on page 77.

Challenge of the week: Use a thick piece of yarn to tie knots every six inches. Can you take this piece of yarn with the knots and build a 3, 4, 5 triangle like we did in class with the geoboards??? Bring it to class and show us!

As always you can email me or call if you have further questions.
Have a great week!
~rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Spring Syllabus

1] Pythagorean Theorem
2] Circles (circumference and area)
3] Perimeter and Area
4] Volume
5] Surface Area
6] Symmetry & Reflection
7] Translations & Transformations
8] Tessellations (M.C. Escher)
9] Mean/Median/ Mode
10] Probability and Statistics




From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Winter Week 7

Notes

Right Triangle- contains one right angle (90)
Equilateral Triangle- all three sides or of equal length and all three angles are equal
Scalene Triangle- all three sides or different lengths (looks obtuse)
Isosceles Triangle- at least two sides are equal length (looks acute)

Trapezoid- exactly one pair of opposite sides are parallel
Rhombus- opposite sides parallel and all sides of equal length (leaning square)
Parallelogram- pairs of opposite sides parallel and of equal length (leaning diamond, either vertical or horizontal)
Rectangle- pairs of opposite sides parallel and of equal length, and all right angles (can be a square)
Square- all sides of equal length and all right angles (cannot be a rectangle)


A straight line is equal to 180 degrees
Complementary angles add up to 90 degrees
Supplementary angles add up to 180 degrees
Alternate Interior Angles --If two lines are intersected by a transversal, the lines are parallel if and only if the alternate interior angles created by the transversal have the same measure
Right angle- is 90 degrees, always and is represented by the tiny square
Acute angle- is less than 90 degrees (its small and cute)
Obtuse angle – is bigger than 90 degrees
Reflex angle –is greater than 180 degrees (like the outside measure from an obtuse angle)
The interior angles of any triangle add up to 180 degrees
The interior angles of any quadrilateral add up to 360 degrees
A pentagon’s interior angles will add up to 540 degrees 

HOMEWORK: Complete pages 66-69
If this is easy (great!) try to create a problem using a triangle or a quadrilateral and stump me!

Have a good week,
Rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Winter Term Homework Week 4

Hi,
We are working on pages 61-63. Please have the learners try at least one Function table from each of the pages.

We have succussfully completed the inequalities section!!!!! Congratulations everyone you earned it!

Rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Winter Term Syllabus

1] Inequalities
2] Functions
3] Venn Diagrams and Graphing
4] Polygons
5] Geometry (Angles)
6] Triangles
7] Quadrilaterals
8] Similar & Congruent Figures
9] Prisms
10] Cylinders/Cones


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Where everyone should be for Winter Term

Hi learners and families,
I hope you all had an excellant Thanksgiving and are thouroughly enjoying your break.

When we return in January everyone should have completed the pages up to 54. If we skipped over a page you don't have to finish it unless you want to. We did cover the material so you can.

Have a good break and see you all next year,
Rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Notes from Week 8 and homework

Hmwk wk 8
p.43-48

Notes from class:

Order of Operations
Parantheses
Exponents
Multiplication
Division
Addition
Subtraction

EXPONETS
10^0=1
10^1=10
10^2=10*10=100
10^3=10*10*10=1000
ETC
b^n= b*b*b*b*b...*b
b occurs n times

Commutative Porperties--> addition and multiplication are commutative. For any rational numbers a and b, a+b=b+a and a*b=b*a

Associative Properties--> Addition and mulitplication are associative. For any rational numbers a, b, and c,
(a+b)+c=a+(b+c)

Distributive Property--> Mulitplication is distributive over addition. For any rational number a, b, and c
a*(b+c)=a*b+a*c

Email me if you have questions


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Homework Week 7

Please comlete pages 30-32, also complete 28 and 29 if you did not get to them last week.

Mulitiplying Fractions
Whole number
K* a/b = ka/b

Fraction times a fraction
a/b * c/d = ac/bd

Dividing Fractions
a/b divided by c/d =a/b * d/c =a*d/b*c


Let me know if you have questions


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Homework Week 6

Hello Math Fundations III learners,

This weeks homework:
Page 26 adding fractions
Page 27 subtracting fractions

and please try pages 25, 28 and 29. We covered this briefly in class so you should be able to do a few of them.

See you all next week!
Rebecca


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Prime Numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

The Sieve of Eratosthenes
Eratosthenes (275-194 B.C., Greece) devised a 'sieve' to discover prime numbers. A sieve is like a strainer that you use to drain spaghetti when it is done cooking. The water drains out, leaving your spaghetti behind. Eratosthenes's sieve drains out composite numbers and leaves prime numbers behind.
To use the sieve of Eratosthenes to find the prime numbers up to 100, make a chart of the first one hundred positive integers (1-100):

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100


Cross out 1, because it is not prime.


Circle 2, because it is the smallest positive even prime. Now cross out every multiple of 2; in other words, cross out every second number.


Circle 3, the next prime. Then cross out all of the multiples of 3; in other words, every third number. Some, like 6, may have already been crossed out because they are multiples of 2.


Circle the next open number, 5. Now cross out all of the multiples of 5, or every 5th number.
Continue doing this until all the numbers through 100 have either been circled or crossed out. You have just circled all the prime numbers from 1 to 100!


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Syllabus for fall

1] Place Value
2] Mental Math & Scientific Notation
3] Fractions
4] Decimals to Percents to Fractions
5] Multiples, LCM, GCF
6] Adding and Subtraction Fractions
7] Multiplying and Dividing Fractions
8] Order of Operations and Exponents
9] Algebra with variables, adding and subtracting
10] Algebra with variables, multiplying and dividing


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Math homework and books

Hello everyone,
The books should be here Tuesday afternoon at the latest. I will have photo copies of that class day's homework available to take home. You may pick up the books in the office at your convenience. Thank you all for your patience in this matter.


From: Rebecca Krantz            Updated:
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Wed Dec 31, 1969 04:00pm

Tuesday's homework and Books

Hi families,
I am sorry the homework pages did not work. I don't use the scanner portion of my printer very often. I did speak with the director and photo copies of the same pages for pick up in the office. The Director will email everyone when they are ready.
Thank you for bringing this to my attention.
The books should be here for next Tuesday's class.