Homework Depends on in class Student Performance...


Date: Week of June 1st 2015

MATH

Vocabulary

MathVideos, Resources

Concepts

M-Step


https://www.youtube.com/watch?v=kmVfZ9o-2gg

M-Step




Equivalent Fractions/Comparing Fractions


https://www.youtube.com/watch?v=9me_tSRN2Z8

Decimals


https://www.youtube.com/watch?v=_jcW-ZgpRbM




https://www.youtube.com/watch?v=qmfXyR7Z6Lk

Tessalations


http://www.maths-pro.com/tessellations.htm

https://www.youtube.com/watch?v=Tceuvg9vjyc

Date: Week of May , 2015

MATH

Vocabulary

MathVideos, Resources

Concepts




https://www.youtube.com/watch?v=kmVfZ9o-2gg









http://mrnussbaum.com/symmetry/




http://www.abcya.com/measuring_angles.htm




https://www.ixl.com/math/grade-4/fractions-review




http://www.ixl.com/math/grade-4/measure-angles-with-a-protractor




http://tube.geogebra.org/student/mmZjE7SCY?mobile=true




Flexigons is iPad app for $0.99. This title uses rules like translation, reflection and axis shifting to create tricky puzzles. It has different levels for different learners. In addition to teaching children about shapes, axis usage, size and other fun geometry topics, there are three fun modes of game play here for even more challenge.







Date: Week of May 18th, 2015

MATH

Vocabulary

MathVideos, Resources

Concepts

Monday
M-Step
Homework: Fat Journal: Pages Review+Review Packet of Definitions



Tuesday
M-Step



Wednesday
M-Step



Thursday
Review and Packet Due-Review and begin Test



Friday
Test: Chapter 8 Geometry

















Math Test Week of May 18th

Date: Week of May 11th , 2015

MATH

Vocabulary

MathVideos, Resources

Concepts






Monday
Write Definitions down8-7
Parallel Lines
Perpendicular Lines

https://www.youtube.com/watch?v=yiREqzDsMP8
Students correct errors on homework papers (fractions)
Go over Friday's Homework in Skinny Journal
Students write definitions of Parallel Lines and Perpendicular Lines in Journal
Complete Pages in fat Journal: 297, 298, 299, 300
Homework: H&R skinny: Pages 187-188 (skip 1: decimals)
http://bit.ly/1ccCxWx
Review: Fractions
http://www.commoncoresheets.com/Math/Fractions/Fractions%20to%20Whole%20Numbers/English/1.pdf
http://www.commoncoresheets.com/Math/Fractions/Comparing%20Numerical%20E2/English/1.pdf

Tuesday
Classify Quadirilaterals
https://www.youtube.com/watch?v=yiREqzDsMP8
Lesson Focus: Name and clssify quadrilaterals based on sides and angles
Vocabulary: Write definintions in Math Journal
Quadrilateral
adjacent
opposite
trapezoid
parallelogram
rhombus
rectangle
square
Classwork:
301, 302, 303, 304, 304A
Homework: Skinny: Page 189, 190 (skip: decimals)
Worksheet
http://www.superteacherworksheets.com/geometry/quadrilaterals1_TZFNM.pdf
Quadrilateralshttps://www.youtube.com/watch?v=yiREqzDsMP8


Wednesday
Decompose Quadrilaterals and Triangles
Vocabulary:
Diagonal
congruent
vertex
Classwork: 305-310
Homework and Remembering (Skinny) 191-192 (Skip Decimals)



Thursday
Quick Quiz 3?
Classify Polygons
https://www.youtube.com/watch?v=IaoZhhx_I9s
Vocabulary: Polygons
Classwork: pages 311-312A
Homework and Remembering (Skinny) 193-194 (skip Decimals)



Friday
Line Symmetry
Vocabulary: line symmetry, line of symmetry
Fat Journal pages: 313-316
Review Packet for Test Thursday and Friday May 28th and 29th
Homework and Remembering (Skinny) pages 195-196









Date: Week of May 4 , 2015

MATH

VocabularyXXXXXXXXXXXXXX

MathVideos, Resources

Concepts

Homework for Monday, May 4th:


Entrance Ticket:
  • measure angles
  • identify angles
  • identify triangles

Classwork:
Pages 289-290

Homework from Thursday:

Skinny: 181-182

All Definitions and examples should be written in your Math Black and White Math Journal Notebook.

Homework for Monday:

292

http://bit.ly/1E3yVwt (Find missing Angles)
http://bit.ly/1JYeK7M (Measuring with Protractors)

https://www.youtube.com/watch?v=_n3KZR1DSEo

8-1

point

line

line segment

endpoint

angle

ray

vertex

right angle

acute angle

obtuse angle

straight angle

ray

8-2

degree

protractor

8-3

circle

reflex angle

triangle

right triangle

obtuse triangle

acute triangle

congruent

equilateral triangle

equilateral

isosceles

scalene

8-5
adjacent angles
compose
decompose
8-7
Parallel Lines
Perpendicular Lines

http://bit.ly/19Dh2vX (Virtual Protractor)



Math Antics Points, Lines & Planes- Skip/Stop when you get to the plane part:https://www.youtube.com/watch?v=k5etrWdIY6o
Math Antics Angle Basics: https://www.youtube.com/watch?v=DGKwdHMiqCgMath Antics Angles & degrees: https://www.youtube.com/watch?v=_n3KZR1DSEo


Draw and describe points, rays, angles, and other simple geometric figures.

Use protractor to measure angles

Draw angles of a given measure

Identify, measure, and draw angles in a circle

Draw and clssify triangles by their angles and sides.

Make triangles and name them by their angles

Find unknown angle measures
Recognize that the measure of an angle is the sum of the measures of its parts.

Unit 8 Geometry Plan
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
CCSS.Math.Content.4.G.A.1

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
CCSS.Math.Content.4.G.A.2

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
CCSS.Math.Content.4.G.A.3

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Geometric measurement: understand concepts of angle and measure angles.
CCSS.Math.Content.4.MD.C.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
CCSS.Math.Content.4.MD.C.5.a

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.
CCSS.Math.Content.4.MD.C.5.b

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
CCSS.Math.Content.4.MD.C.6

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
CCSS.Math.Content.4.MD.C.7

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Tuesday

Quick Quiz 1

Adding & subtracting angles- https://www.youtube.com/watch?v=7gV6aemCz8Y


Wednesday

Skinny: 183-184



Thursday

Quick Quiz 2
No Homework



Friday

Homework (skinny journal page 185 and page 185 Numbers 4-6)










Date: Week of May , 2015

MATH

Vocabulary

MathVideos, Resources

Concepts







Write Definitions down8-7
Parallel Lines
Perpendicular Lines
http://bit.ly/1ccCxWx




https://www.youtube.com/watch?v=yiREqzDsMP8


















Date: Week of May , 2015

MATH

Vocabulary

MathVideos, Resources

Concepts




https://www.youtube.com/watch?v=kmVfZ9o-2gg




























Date: Week of May , 2015

MATH

Vocabulary

MathVideos, Resources

Concepts
































Date: Week of April 27th

Lesson 7

Classwork and Homework

Definitions Vocabulary:


Monday

Homework-


Date: Week of February 23

Classwork and Homework

Definitions Vocabulary:

Due by Feb. 13th, 1015

Monday

Homework-

  • e number:

Tuesday

Review 1 in Class

Review 2 HW

composite numbers.JPG
composite numbers.JPG


prine numbers
prine numbers


Wednesday

Second Review

http://www.teachertube.com/video/prime-numbers-rap-typography-245376

http://www.teachertube.com/video/multiples-and-factors-194220
**Finding factors of a number**: To find the factors of a number means to find all the whole numbers that the number in question is divisible by. Can you help us find the factors in this example?
Thanks to Jack for suggesting this video!

New Concepts

Review Concepts;

Math videos, games, practice and resources

Thursday

Quiz Multiples and Factors

Classwork: Fraction Pretest - Begin Unit 6

No Homework





Friday

Classwork Fat Journal

Homework:
4nf3b using visual fraction strips to compare

http://illuminations.nctm.org/Activity.aspx?id=3510




factors.JPG
factors.JPG


composite numbers.JPG
composite numbers.JPG


prine numbers
prine numbers


Wednesday

Second Review

http://www.teachertube.com/video/prime-numbers-rap-typography-245376

http://www.teachertube.com/video/multiples-and-factors-194220
**Finding factors of a number**: To find the factors of a number means to find all the whole numbers that the number in question is divisible by. Can you help us find the factors in this example?
Thanks to Jack for suggesting this video!

New Concepts

Review Concepts;

Math videos, games, practice and resources

Thursday

Quiz Multiples and Factors

Classwork: Fraction Pretest - Begin Unit 6

No Homework





Friday

Classwork Fat Journal

Homework:
4nf3b using visual fraction strips to compare

http://illuminations.nctm.org/Activity.aspx?id=3510

Date: Week of April 20th

Classwork and Homework

Math videos, games, practice and resources


Monday

Homework-
Geometry: Unit 8
Homework and Remembering (Skinny)
Pages 175 and 176)


https://www.youtube.com/watch?v=_n3KZR1DSEo (variety)
https://www.khanacademy.org/math/basic-geo/basic-geo-angles/basic-geo-angle-basics/v/angle-basics

Tuesday

Measuring Angles
Skinny: 177-178


Wednesday

Circles and Angles
Skinny 179-180



Thursday

Name Triangles
Skinny 181-182


Friday








Date: Week of April 13th

Classwork and Homework

Definitions Vocabulary:

Resource

Monday

Worksheets
Estimating Capacity:

Cup
Pint
Quart
Gallon

Tuesday

Worksheets:
Measuring Units Worksheet
Homework:
Worksheet
equivalent fractions
(Later in Week

Wednesday

Homework:

Continue Measuring Units Worksheet
Converting Standard Units of Measure


New Concepts


Converted Minutes to Hours

Review Concepts;

Thursday

Classwork:

Fat Journal Page

Homework: skinny

h

Friday









Date: Week of March 9th

Classwork and Homework

Review Concepts;

Math videos, games, practice and resources


Monday

Homework-
Classwork: Entrance Ticket Review Fraction Comparisons
6.3 Pages 203-206
Homework: Skinny 133 (1-9)
Quick Quiz 1 Fractions
http://app.discoveryeducation.com/player/view/assetGuid/256A00C1-697A-4F39-B5DF-F14109EDF28F

Tuesday

Homework: Skinny 133-1-9)
Common Core Math Sheet
Improper Fractions
Improper Fractions



Mixed Fractions

Wednesday

Homework: Skinny
6-4
Pages 135-136 Improper to Mixed Numbers




Thursday

Homework

6.5
Page 137 Skip 7,9,10,12 (We are teaching Subtracting with regrouping Friday
Page 138 Skip 4-6


Fri

Homework: Finish page 137

Subracting Fractions with Regrouping worksheet

h

0ttttday

Subtracting Mixed Numbers with Like Denominators with Regrouping



Reducinjg to lowest terms: https://video.search.yahoo.com/video/play;_ylt=A2KLqIKoseZUcEoAoVD7w8QF;_ylu=X3oDMTBzZzJoNGtoBHNlYwNzcgRzbGsDdmlkBHZ0aWQDBGdwb3MDMTY-?p=adding+%26+subtracting+unit+fractions&vid=9eeecd99181e49b4f19b0a4ce5fad85a&l=7%3A18&turl=http%3A%2F%2Fts1.mm.bing.net%2Fth%3Fid%3DVN.608044408970807740%26pid%3D15.1&rurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DRBjEWQJqkgA&tit=Adding+and+Subtracting+Fractions+Part+1%3A+The+Basics+%28Simplifying+Math%29&c=15&sigr=11b44eulv&sigt=12667vka0&sigi=11rnb5dfp&age=1349192518&fr2=p%3As%2Cv%3Av&hsimp=yhs-001&hspart=mozilla&tt=b

Date: Week of March 2

Classwork and Homework



Monday

Homework-
Math-No Homework


Tuesday

Fraction Worksheet


Wednesday

Homework: Skinny129-130 (6.1)



Review Concepts;

Math videos, games, practice and resources

Thursday

Classwork: Went over Pages:
195, 196, 197, 198,199,200,
Homework: Skinny- Pages 131-132 (1-10) (6.2)

https://learnzillion.com/lessons/1630-decompose-a-fraction-into-a-sum-of-fractions-using-an-area-model

Friday

–Homework: Complete Page

201-202 (Finish Page 131 Skinny Journal)

Play this Math Game:
http://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/common/itools_int_9780547584997_/fractions.htm







Date: Week of March

Classwork and Homework



Monday

Homework-



Tuesday




Wednesday





Review Concepts;

Math videos, games, practice and resources

Thursday



https://learnzillion.com/lessons/1630-decompose-a-fraction-into-a-sum-of-fractions-using-an-area-model

Friday


















Date: Week of February 23

Classwork and Homework

Definitions Vocabulary:

Due by Feb. 13th, 1015

Monday

Homework-
Math Mansion 2
e and Composite Numbers
United Streaming: Math Mansion Video #24 Prime #s
http://app.discoveryeducation.com/player/view/assetGuid/52435DB1-3D08-4CF7-A683-80C1FF2A3890
Entrance and exit
How do you know you have every factor of a given number?
What is the rule for a prime number and composite number?
Pg 154 in class
Homework: Skinny Journal 107
Factor Game
http://illuminations.nctm.org/Activity.aspx?id=4134
  • Expression
  • equation
  • Simplify: is to make easier
  • simplify in Multiplication
  • term
  • Order of Operations
  • factor: A factor is one (part) number of a multiplication problem (not the product…factor x factor = Product.
  • factor pair
  • multiples: are the products of skip counting.
  • Distributive Property ex. from last Friday
  • Prime number: A number greater than 1 that has 1 and and itself as its ony factor pair is a prime number. Some prime numbers are 2, 5, 11, and 23.
  • composite number: A number greater than one that has more than one factor pair. Some Composite numbers are: 4, 12, 25, 100.
  • square number:

Tuesday

Review 1 in Class

Review 2 HW

factors.JPG

composite numbers.JPG

prine numbers

Wednesday

Second Review

http://www.teachertube.com/video/prime-numbers-rap-typography-245376

http://www.teachertube.com/video/multiples-and-factors-194220
Finding factors of a number: To find the factors of a number means to find all the whole numbers that the number in question is divisible by. Can you help us find the factors in this example?
Thanks to Jack for suggesting this video!

New Concepts

Review Concepts;

Math videos, games, practice and resources

Thursday

Quiz Multiples and Factors

Classwork: Fraction Pretest - Begin Unit 6

No Homework





Friday

Classwork Fat Journal

Homework:
4nf3b using visual fraction strips to compare

http://illuminations.nctm.org/Activity.aspx?id=3510


Date: Week of February 2nd

Notes from top didn't get to
Classwork 4.3

Definitions
Fat Journal: 130
Fat Journal: 133

Homework:

Skinny Journal 4.3
Page 93


Date: Week of February 9

Classwork and Homework

Definitions Vocabulary:

Due by Feb. 13th, 1015

Monday

Homework-
No Homework

  • Expression
  • equation
  • Simplify: is to make easier
  • simplify in Multiplication
  • term
  • Order of Operations
  • factor: A factor is one (part) number of a multiplication problem (not the productfactor x factor = Product.
  • factor pair
  • multiples: are the products of skip counting.
  • Distributive Property ex. from last Friday
  • Prime number: A number
    greater than 1 that has 1 and and itself as its ony factor pair is a prime number. Some prime numbers are 2, 5, 11, and 23.
  • composite number: A number greater than one that has more than one factor pair. Some Composite numbers are: 4, 12, 25, 100.
  • square number:

Tuesday

Review Story Problems and Variables
'[


Wednesday

Homework:

Finish Fat Journal Pages 151, 152
Then complete Identifying factor worksheet
Finding factors of a number: To find the factors of a number means to find all the whole numbers that the number in question is divisible by. Can you help us find the factors in this example?
Thanks to Jack for suggesting this video!

New Concepts

Review Concepts;

Math videos, games, practice and resources

Thursday

Classwork:

Fat Journal Page 153

Homework:

Identifying Multiples and finish 153


Friday

Practice Multiplication facts if needed!


Date: Week of February 2nd

Notes from top didn't get to
Classwork 4.3

Definitions
Fat Journal: 130
Fat Journal: 133

Homework:

Skinny Journal 4.3
Page 93


Monday

Snow Day


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Snow Day


Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Expressions vs. Equations & Review of the Different Properties

1. Operations inside parentheses are performed first.

2. The multiply and divide from left to right.

3. Then add and subtract from left to right.

  • Properties and Algebraic Notation p. 127
  • Parenthesis in Equations p. 128
HOMEWORK: 4.1

Vocabulary: Expression
equation
simplify
term

New Concepts

Review Concepts;

Math videos, games, practice and resources

Thursday

Classwork:


Equalities and Inequalities
  • Discuss = and not = Signs p. 129
  • Inverse Operations (fact Families) p. 130
  • Write equations to solve problems p.
  • FAt: 127
  • Skinny Finish 89

Homework:



evaluate
Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Friday

Homework:
128 Fat Journal

Classwork:


Equalities and Inequalities
  • Discuss = and not = Signs p. 129
  • Inverse Operations (fact Families) p. 1Properties and Algebraic Notation p. 127
    • Parenthesis in Equations p. 128
    30
*

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0



Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities



Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6



Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities



Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6



Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

http://app.discoveryeducation.com/player/view/assetGuid/9EAD89AB-CBEE-4923-AF2A-F155B6E11AF9

Continue to practice multiplication facts to increase speed.


*I am going to try to post the homework for the week, however, it may change depending on student performance in
class.

Unit 3 Objectives:

3A: Divide with up to 4- Digit Dividends and 1 digit Divisors
3B: Use rounding and estimating to check quotients
3C: Understand remainders and use division to interpret remainders in the context of a problem.
3D: Solve one step and multi-step problems
3E: Solve real world problems.

Mathematical Practices:

  • Make sense of problems and persevere in solving them
  • Reason abstractly and quantitatively
  • Construct viable arguments and critique the reasoning of others
  • Model with Mathematics
  • Use appropriate tools strategically
  • Attend to precision
  • Look for and make use of structure

Unit 3 Test : Tuesday, January 27th


Date: Week of January 26th, 2015

Math

New Concepts

Review Concepts;

Math videos, games, practice and resources

Monday

Classwork:

Check Review Packet

Homework:

Unit 3Test Form B

Problems: 3, 4, 7, 8, 12, 14, 16, 17, 18, 20

You can complete the packet if you wish.
The answers are below:

3. D
4. K
7. C
8. H
12. H
14. K
16. G
17. D
18. F
20. G

Extra Practice

Print as needed:

http://www.commoncoresheets.com/Math/Division/Word%20100d1w/English/All.pdf


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

TEST: UNIT 3

Review Division

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

TEST: Continued

Review Division

Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

International Celebration-No Class

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc


Date: Week of January 19th, 2015

Math

New Concepts

Review Concepts;

Math videos, games, practice and resources

Tuesday

Classwork: Checked Homework

Reviewed Multistep Story Problems
Began Fat Journal Page 120

Homework:


  • Skinny; Homwork & Remembering:
    • pages 87-88

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Wednesday

Classwork:

Fat Journal 120

Quick Quiz 2

Homework:

(Skinny-Homework and Remembering) pages
Review 123-124 Fat Journal

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Thursday

Classwork:

Review Homework Book Review:

Math Review Packet (ONLY NUMBERS)
2, 7, 8, 9, 10, 11, 12

Homework:


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Friday

Classwork:

Review Packet

Homework:

Review packet, all but #16


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Monday

Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Date: Week of January 12, 2015

Math

New Concepts

Review Concepts;

Math videos, games, practice and resources

Monday

Classwork:

  • Quick Quiz #3-1
  • Review Friday’s lesson
  • Discuss why estimates maybe too low
  • Fat pages 113-114
  • Will get to 114 Tuesday...


Homework:


  • Skinny; Homwork & Remembering:
    • pages 79 (1-3) -80 (all)

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Classwork:


  • Review yesterday’s lesson
  • Different kinds of remainders
  • Real World Division Problems

Extra Practice: Everyday Math

Extra Practice: Common Core Sheets 3 ÷ 1 (With Remainder) 4nbt6

Classwork: p. 114

Homework:

(Skinny-Homework and Remembering) pages finish page 79. Do page 82

Promethean Planet: Slides 9-14 **http://www.prometheanplanet.com/en-us/Resources/Item/168771/4-6-interpreting-the-remainder-everyday-math-5th-grade#.U2bysFNvDLQ**

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Classwork: Page 115,



Homework: (Skinny) 81


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork: Finish page 115

Do 116, 117

Homework: Skinny 83-84


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework&Remembering-

Skinny Pages 85-86

Quick Quiz 2 Monday, January 18th

Unit 3 Test (next week Thursday-Friday or Monday-Tuesday the following week…)

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc
Unit 3 Test on Tuesday, January 20th

Week of January 19th

Math

New Concepts

Review Concepts;

Math videos, games, practice and resources

Monday

Classwork:


No School


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Classwork:

Test on Unit 3

Homework: Relax…you just completed a test :)

No Homework!


Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Classwork: Unit 4 Page


  • Review yesterday’s lesson


Homework: (Skinny)


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork:


  • Review yesterday’s lesson

Homework:

Homework&Remembering-pages


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework:


Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc








Date: Week of January 5th

Math

New Concepts

Review Concepts; Math videos, games, practice and resources

Monday

Classwork:

  • Page 101 Fat Journal
2-Digit and 4 Digit Quotients
  • Page 102 Fat Journal
Finding Group size
  • Discuss Division Practice Packets given before vacation

Homework:

(Skinny)
Homework and Remembering:
Pages 71 Try solving the problems using Place Value Sections Model, the Expanded Notations Methods Model, and the Digit-by-Digit Method aka Traditional Division Model I9f you know how to do this method) (reference page 105 in the fat journal)
Digit-by-Digit Method

Fat Journal Page 105
[[image:/file/view/Slide1.jpg/535959006/503x378/Slide1.jpg width="503" height="378"]]

Digit-byDigit Model
http://www.khanacademy.org/math/arithmetic/multiplication-division/long_division/v/division-2

http://www.khanacademy.org/math/arithmetic/multiplication-division/long_division/v/division-3-more-long-division-and-remainder-examples

http://www.khanacademy.org/math/arithmetic/multiplication-division/long_division/v/division-3-more-long-division-and-remainder-examples
[[image:/file/view/Expanded%20Notation.jpg/535956208/Expanded%20Notation.jpg]]

[[image:/file/view/place%20value%20sections%20poster.jpg/535956198/place%20value%20sections%20poster.jpg]]

[[image:/file/view/division%20poster.jpg/535956182/division%20poster.jpg]]
[[image:/file/view/mult%20and%20division%20poster.jpg/535956174/mult%20and%20division%20poster.jpg]]

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Classwork:

  • Check Homework (pg. 71)
  • The Digit-by-Digit Methods - Page 105
  • Pg. 106 Practice on Boards
  • Practice on Boards pg. 107
    • evens

Homework: Skinny Homework and Remembering Pg. 72

  • Pg 107 odds depending on progress in class.

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Classwork:

  • Fat Journal (pg. 108)
    • Storyproblems
    • Partners
    • Key words
      • Circle the numbers
      • Underline the unit
      • Box the key words
      • Evaluate the problem(operation?)
      • Solve

Homework:

  • Homework and Remembering (Skinny) pages 73 & 74


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork: (Fat)Page 109-110

Homework:

Homework&Remembering-pages

Page 75-76

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Classwork: 111-112 (fat)

Homework: Skinny 77-78

Quick Quiz- #3-1 (Monday)

Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc
Unit 3 Test on Tuesday, January 20th

Week of January 19th

Math

New Concepts

Review Concepts;

Math videos, games, practice and resources

Monday

Classwork:

No School

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Classwork:

Test on Unit 3

Homework:

(Skinny)-Homework and Remembering pages

Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Classwork: Unit 4 Page

  • Review yesterday’s lesson


Homework: (Skinny)


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork:

  • ** Review yesterday’s lesson

Homework:

Homework&Remembering-pages


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Classwork:

  • ** Review yesterday’s lesson

Homework:


Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc



Blank Calendar

Date: Week of January, 2015

Math

Concepts


Vocabulary

Math videos, games, practice and resources

Monday

Snow Day!



Tuesday

Snow Day!



Wednesday

Class Work 127

xpressions vs. Equations & Review of the Different Properties

  • Whenever you follow the order of operations, you should first perform the operations inside the parentheses.

  • Second, they should multiply and divide from left to right.

  • Then, addition and subtraction are performed fro left to right.

  • =Properties and Algebraic Notation p. 127=

  • =Parenthesis in Equations p. 128=

HOMEWORK: 4.1

Homework: Pages 89,90

Vocabulary:
Expression
equation
simplify
term
Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork: Page


Equalities and Inequalities
  • Discuss = and not = Signs p. 129
  • Inverse Operations (fact Families) p. 130
  • Write equations to solve problems p. 131-132

Homework:

Homework&Remembering-pages 91 and 92

Evaluate
Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework:

Homework&Remembering-


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc
class.

I am going to try to post the homework for the week, however, it may change depending on student performance in

Date: Week of December 15, 2014

Math

Concepts


Vocabulary

Math videos, games, practice and resources

Monday

Homework:


Review Math Videos of Place Value Sections Model and Expanded Notation if you are still confused.
(That Quiz) Practice Multiplication)
Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc

Tuesday

Homework:

Fat Journal page 100

Review Videos on place value model of division and expanded notation model of division if needed.
Thatquiz.com 15 minutes of practice.
Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Homework:

Finish Math packet from Classwork.


Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

No Formal Homework

  • Practice multiplication facts if needed over vacation
  • Practice Place Value and Expanded Notation Division Models if needed over vacation

Classwork: Page

Homework:

Homework&Remembering-pages


Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework:

Homework&Remembering-pages 2


Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc
class.

Date: Week of December 8, 2014

Math

Concepts


Vocabulary

Math videos, games, practice and resources

Monday

Homework:

Using the glossary in the back of the "fat" journal write the definitions and the examples of the following Division Words:
  • divisor
  • dividend
  • quotient
Watch Video: What is Division?

Homework&Remembering-pages: 67, 68

If students do not understand after watching the video how to divide with remainders...do not have them do page 67...they should give it a try, but not worry if they are confused...we will go over it in class tomorrow!

What is Division?
https://www.khanacademy.org/math/arithmetic/multiplication-division/long_division/v/introduction-to-remainders

Tuesday

Homework:

Fat Journal page 95


Division With Remainder Video
https://www.youtube.com/watch?v=-yJqO9aOHG0

Wednesday

Homework:


Fat Journal page 96



Use these sites to help you with your division work.
Use these sites to help you with your division work.

Division Fact Practice
Learning Games for Kids Great for fact practice by digits
Fun4theBrain
HOODA Math Fact Practice
Woodlands Math Activities

Thursday

Classwork: Page 97, 98

Homework:

Homework&Remembering-pages

69 #1
70 #1-8

Place Value Section Model for Division Video

http://www.showme.com/sh/?h=xkzwpkG

Place Value Model Video
https://www.youtube.com/watch?v=GLbbjAuamA4

http://www.showme.com/sh/?h=ijtWPz6

Friday

Homework:

Homework&Remembering-pages 69 #2&3,

Page 70 #9-12

Expanded Notation Method for Division
https://www.youtube.com/watch?v=-PoArz2KP_U

https://www.youtube.com/watch?v=0yBAv8ijCZc


Math Test for Unit 2: Thursday, December 4th

Date: Week of December 1, 2014

Math

Concepts

Vocabulary

Math videos, games, practice and resources


Monday

Homework:


Homework and Remembering (Skinny)


57,58

3 digit x 2 digit Video
https://www.youtube.com/watch?v=PNJWENtXiog

Review:

multiplying 4 digits x 1 digit visual model
http://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-mult-div-topic/cc-4th-area-models/e/multiplying-by-4-digit-numbers-with-visual-models

multiplying multidigit numbers (2digitx2digit, 3 digitx2 digit, 3 digit x3 digit numbers)
https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/v/multiplication-6-multiple-digit-numbers

Model One-Digit by Two Digit Multiplication
Learn Zillion Use an Array to Multiply a Two Digit by One Digit Number-https://learnzillion.com/lessons/1875-use-an-array-to-multiply-a-two-digit-number-by-a-one-digit-number
YouTube https://www.youtube.com/watch?v=a0MwnLNln4k

2 digit x 2 digit Short-Cut Model or Traditional Model
http://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/e/multiplication_3

2 digit x 2 digit Area Model and partial products
http://www.khanacademy.org/math/arithmetic/multiplication-division/area-models-multiplication/e/multiplying-2-digit-numbers-with-area-models

Multiplying by multiples of 10
https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/e/multiplication_1

Tuesday

Homework:


Review packet-all

Posters are for Review:

[[image:/file/view/Algebraic%20Notation%20Method.jpg/532346994/Algebraic%20Notation%20Method.jpg width="271"]]

Wednesday

Homework:

2nd Review (complete at least half, selecting the problems that you need the most support.)
[[image:/file/view/partial%20products%20poster.jpg/532346500/273x361/partial%20products%20poster.jpg width="273" height="361"]]

Thursday

Homework:

No formal homework. Students can review using the review packet. They will finish their test tomorrow.
[[image:/file/view/shortcut%20model.jpg/532346772/280x365/shortcut%20model.jpg width="280" height="365"]]


[[image:/file/view/expanded%20notation%20method.jpg/532347118/expanded%20notation%20method.jpg width="273"]]


[[image:/file/view/place%20value%20sections%20method.jpg/532347210/place%20value%20sections%20method.jpg width="270"]]


[[image:/file/view/multistep%20word%20problems.jpg/532347312/multistep%20word%20problems.jpg width="279"]]

Friday

Homework:


No Formal Homework. Students should continue to practice their multiplication facts. We will retest Monday.


Date: Week of November 21, 2014

Math

Concepts

Vocabulary

Math videos, games, practice and resources


Monday

Homework:


Homework and Remembering (Skinny)


Pages: 53-54

Factors
Products
Array
Area Model
Associative Property
Commutative Property
Distributive Property
Estimate
Rounding
Partial Products
Algebraic Notation Method
Place Value Section Method
Expanded Notation Method
Shortcut Method (New Groups Above/New Groups Below)
Decompose
Inverse Operations
2 digit x 2 digit Short-Cut Model or Traditional Model
http://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/e/multiplication_3

2 digit x 2 digit Area Model and partial products
http://www.khanacademy.org/math/arithmetic/multiplication-division/area-models-multiplication/e/multiplying-2-digit-numbers-with-area-models

multiplying 4 digits x 1 digit visual model
http://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-mult-div-topic/cc-4th-area-models/e/multiplying-by-4-digit-numbers-with-visual-models

Tuesday

Homework:


Homework&Remembering

(skinny) -Pg. 55&56



Finish (fat) Journal Page

2 digit x 2 digit Short-Cut Model or Traditional Model
http://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/e/multiplication_3

2 digit x 2 digit Area Model and partial products
http://www.khanacademy.org/math/arithmetic/multiplication-division/area-models-multiplication/e/multiplying-2-digit-numbers-with-area-models

multiplying 4 digits x 1 digit visual model
http://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-mult-div-topic/cc-4th-area-models/e/multiplying-by-4-digit-numbers-with-visual-models

Wednesday

Homework:

Skinny: Page

Finish (fat) Journal Page

Thursday

Homework:

Please double check homework sheet for assignment).

Homework&Remembering (skinny) -pages



Finish (fat) Journal Page

Friday

Homework:


Skinny page
see Dylan's video tutorials to the right!
2 digit x 2 digit multiplication
Traditional Model


2 digit x 2 digit multiplication
ModelRectangle Model



Date: Week of November 17, 2014

Math

Concepts

Vocabulary

Math videos, games, practice and resources

Monday

Homework:

Finish (fat) Journal Page:

Page 65

Factors
Products
Array
Area Model
Associative Property
Commutative Property
Distributive Property
Estimate
Rounding
Partial Products
Algebraic Notation Method
Place Value Section Method
Expanded Notation Method
Shortcut Method (New Groups Above/New Groups Below)
Decompose
Inverse Operations

Tuesday

Homework:

Homework&Remembering

(skinny) - Page 49-50



Finish (fat) Journal Page


Wednesday

Homework:

Skinny: Page

Finish (fat) Journal Page

Thursday

Homework:

Please double check homework sheet for assignment).

Homework&Remembering (skinny) -pages



Finish (fat) Journal Page

Friday

Homework:

Skinny page
see Dylan's video tutorials to the right!
2 digit x 2 digit multiplication
Traditional Model


2 digit x 2 digit multiplication
ModelRectangle Model




Date: Week of November 3, 2014

Math

Math videos, games, practice and resources


Monday

Homework:

Homework&Remembering-pages 35-36

Finish Journal Page 48

http://www.amblesideprimary.com/ambleweb/mentalmaths/testtest.html This "tables tester" has three levels: easier, harder and megahard…check it out…challenge yourself to get to the next higher level!

http://www.brainormous.com - Multiflyer (can select what facts you want to practice (7s,8s) and print record!

http://www.fastertimestables.com/cool-times-tables-songs/

Math practice for 12, 13, 14, 15

Multiplication Baseball

Multiplication Facts 3 4 5 10 Times Table Rap

8 Times Table Song

Tips and tricks
Use area models to show multiplication of whole numbers
Use an array to multiply a two digit number by a one digit number

Tuesday

No Schools


Wednesday

Homework:

Finish Journal Pages 49, 50
Homework and Remembering 36

Thursday

Homework:

Journal P.g 52 and H+R P.g 37 problems 1,2,7 P.g 38 1,2,3,5


Friday

Homework:Fat Journal P.g 54 ,H+R Pgs 39,40















Date: Week of November 10, 2014

Math

Concepts

Vocabulary

Math videos, games, practice and resources


Monday

Homework:

Homework&Remembering

(skinny) -pages 41 and 42 #s 7,8


Finish (fat) Journal Page

  • Multiply using area models, expanded notation model, place value section, algebraic notation, shortcut multiplication method
  • Decompose multiplication through the use of base ten models
eg. 444= (4 x 100) + (4 x 10) + (4 x 1)
  • A digit in one place is ten times greater than the digit to the right
  • Estimate products to check the reasonableness of an answer
  • Apply multiplication methods to word problems
  • Construct a viable argument and critique reasoning of others
  • Explain the process of how to solve a problem and explain why you chose that process (written, pictorial, verbal)
  • Determine the necessary information needed to solve multiplication story problems
Factors
Products
Array
Area Model
Associative Property
Commutative Property
Distributive Property
Estimate
Rounding
Partial Products
Algebraic Notation Method
Place Value Section Method
Expanded Notation Method
Shortcut Method (New Groups Above/New Groups Below)
Decompose
Inverse Operations

Tuesday

Homework:

Homework&Remembering

(skinny) -pages 43, 44


Finish (fat) Journal Page





Wednesday

Homework:


No Homework (math was cancelled due to the field trip.

Finish (fat) Journal Page




Thursday

Homework:

Please double check homework sheet for assignment).

Homework&Remembering (skinny) -pages


Pages 45-46

Finish (fat) Journal Page



3 digit x one digit video:https://learnzillion.com/lessons/1877-use-an-area-model-to-multiply-a-three-digit-number-by-a-one-digit-number?BackLink=4077&https%3A%2F%2Flearnzillion.com%2Flessons%2F1877-use-an-area-model-to-multiply-a-three-digit-number-by-a-one-digit-number

Friday

Homework:

We began 3 digit x1 digit multiplication. If students did not finish page 63,
in their (fat) Journal
they have homework this weekend. Most students completed it in class and left their journals in school with me.



3 digit x one digit video:https://learnzillion.com/lessons/1877-use-an-area-model-to-multiply-a-three-digit-number-by-a-one-digit-number?BackLink=4077&https%3A%2F%2Flearnzillion.com%2Flessons%2F1877-use-an-area-model-to-multiply-a-three-digit-number-by-a-one-digit-number





Date: Week of November 3, 2014

Math

Math videos, games, practice and resources


Monday

Homework:

Homework&Remembering-pages 35-36

Finish Journal Page 48

http://www.amblesideprimary.com/ambleweb/mentalmaths/testtest.html This "tables tester" has three levels: easier, harder and megahard…check it out…challenge yourself to get to the next higher level!

http://www.brainormous.com - Multiflyer (can select what facts you want to practice (7s,8s) and print record!

http://www.fastertimestables.com/cool-times-tables-songs/

Math practice for 12, 13, 14, 15

Multiplication Baseball

Multiplication Facts 3 4 5 10 Times Table Rap

8 Times Table Song

Tips and tricks
Use area models to show multiplication of whole numbers
Use an array to multiply a two digit number by a one digit number

Tuesday

No Schools


Wednesday

Homework:

Finish Journal Pages 49, 50
Homework and Remembering 36

Thursday

Homework:

Journal P.g 52 and H+R P.g 37 problems 1,2,7 P.g 38 1,2,3,5


Friday

Homework:Fat Journal P.g 54 ,H+R Pgs 39,40


Fractions:
http://www.mylinkstolearning.com/nctm.htm
https://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/exp_equiv_fractions.pdf