Grade+3+Math+Curriculum+Map

and Subtraction || x || x ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   || and Division ||  ||   || x || x ||   ||   ||   ||   ||   ||   ||   ||   ||
 * || O || N || D || J || F || M || A || M || J || J || A || S ||
 * Whole Numbers: Addition
 * Whole Numbers: Multiplication
 * Geometry and Measurement ||  ||   ||   ||   || x || x ||   ||   ||   ||   ||   ||   ||
 * Fractions and Decimals ||  ||   ||   ||   ||   ||   || x || x ||   ||   ||   ||   ||
 * Data Analysis ||  ||   ||   ||   ||   ||   ||   ||   || x || x ||   ||   ||
 * Algebra: Patterns ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   || x || x ||

> _asid_318_g_2_t_4.html Elapsed time > problems using two clocks, both analog and digital > activities/ElapsedTime/?version=disabled > &browser=MSIE&vendor=na&flash=10.0.32 > Several activities surrounding elapsed time > using analog or digital clocks. > Printable blank clock faces.
 * =**1: Whole Numbers: Addition & Subtraction**= ||
 * # Addition means the joining of two or more sets that may or may not be the same size.
 * 1) Subtraction has more than one meaning. It not only means the typical “take away” operation, but also can denote finding the difference between sets, such as, in a set of 2 red balloons and 6 green balloons, how many more balloons are green? What is the difference between the number of red and green balloons? (Diminution)
 * 2) Addition and subtraction are inverses; one undoes the other.
 * 3) We can verify the results of our computation by using the inverse operation.
 * 4) Place value is crucial in operating on numbers.
 * 5) Estimation helps us see whether our answers are reasonable.
 * 6) Adding zero to a number or subtracting zero from a number does not change the original amount.
 * 7) The value of a digit is determined by the place it occupies.
 * 8) The value of a given place is constant.
 * 9) Addition can be used to check subtractions
 * 10) Subtraction can be used to check addition || # How do we use addition and subtraction to tell number stories?
 * 11) How are addition and subtraction alike?
 * 12) How are addition and subtraction different?
 * 13) In what type of situations do we subtract?
 * 14) In what type of situations do we add?
 * 15) What are some ways we use estimation in everyday life?
 * 16) Why is place value important?
 * 17) How is zero different from any other whole number you might add or subtract?
 * 18) Why do we need to know place value?
 * 19) When is appropriate to estimate sums and differences? || * Whole numbers
 * Operations
 * Estimation
 * Rounding
 * Sum-total amount added, Total number of elements in a set that were combined
 * Difference-The answer obtained when 2 numbers are subtracted
 * Equal
 * Addend: A number being added
 * Associative Property of Addition: When there are three addends, the sum does not change regardless of which two numbers you group together first. As in: 3 + 5 + 2 = (3 + 5) + 2 = 3 + (5 + 2) = 10; 8 + 2 = 3 + 7 = 10
 * Commutative Property of Addition: The order in which two numbers are added does not change the sum. As in: 9 + 7 = 16 and 7 + 9 = 16
 * Doubling: Adding the same amount twice; or, two times a number
 * Identity Property of Addition: When zero is added to any number, the sum is the original amount. Or, adding zero to any number does not change a number.
 * Inverses: Operations that undo each other, such as addition and subtraction as well as multiplication and division. || * DOE Unit on Addition and Subtraction
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html"]] http://nlvm.usu.edu/en/nav/frames
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.shodor.org/interactivate/activities/ElapsedTime/?version=disabled&browser=MSIE&vendor=na&flash=10.0.32"]] http://www.shodor.org/interactivate/
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://donnayoung.org/math/clock.htm"]] http://donnayoung.org/math/clock.htm

DOE UNIT Addition and Subtraction ||
 * =**2: Whole Numbers: Multiplication and Division**= ||
 * * Multiplication can be thought of as repeated addition.
 * Multiplication facts can be deduced from patterns.
 * The associative property of multiplication can be used to simplify computation.
 * The distributive property of multiplication allows us to find partial products and then find their sum.
 * Patterns are evident when multiplying a number by ten or a multiple of ten.
 * Multiplication and division are inverses; they undo each other.
 * Multiplication and division can be modeled with arrays.
 * Multiplication is commutative, but division is not.
 * There are two common situations where division may be used.
 * Partition (or fair-sharing) - given the total amount and the number of equal groups, determine how many/much in each group
 * Measurement (or repeated subtraction) - given the total amount and the amount in a group, determine how many groups of the same size can be created.
 * As the divisor increases, the quotient decreases; as the divisor decreases, the quotient increases.
 * There is a relationship between the divisor, the dividend, the quotient, and any remainder. || * How are multiplication and addition alike?
 * How are multiplication and addition different?
 * What are strategies for learning multiplication facts?
 * How can we practice multiplication facts in a meaningful way that will help us remember them?
 * How can we connect multiplication facts with their array models?
 * How is the commutative property of multiplication evident in an array model?
 * What patterns of multiplication can we discover by studying a times table chart?
 * How can we determine numbers that are missing on a times table chart by knowing multiplication patterns?
 * What role can arithmetic properties play in helping us understand number patterns?
 * How can we model multiplication?
 * How are multiplication and addition related?
 * How can we write a mathematical sentence to represent a multiplication model we have made?
 * Is there more than one way of multiplying to get the same product?
 * What patterns can be found when multiplying numbers?
 * What pattern is there when we multiply by ten or a multiple of ten? By one? By zero?
 * What math is involved in the study of Georgia animals?
 * How can multiplication help us repeatedly add larger numbers?
 * How does the order of the digits in a multiplication problem affect the product?
 * How does understanding the commutative property help us multiply?
 * How is multiplication like repeated addition?
 * How many different ways can you arrange 24 chairs?
 * How does drawing an array help us think about different ways to decompose a number?
 * How can multiplication and division be used to solve real world problems?
 * How can we use patterns to solve problems?
 * How can base-ten blocks help us understand how to multiply a two-digit number?
 * How does understanding the distributive property help us multiply large numbers?
 * How are multiplication and division related?
 * How can the same array represent both multiplication and division?
 * How do the parts of a division problem relate to each other?
 * What is the relationship between the divisor and the quotient?
 * What happens to the quotient when the dividend increases or decreases?
 * What do the parts of a division problem represent?
 * How can we model division?
 * How are multiplication and division related?
 * How are subtraction and division related?
 * How can we write a mathematical sentence to represent division models we have made?
 * How can we divide larger numbers?
 * What is the meaning of a remainder?
 * Does a remainder mean the same thing in every division problem?
 * How do estimation, multiplication, and division help us solve problems in everyday life? || * **Array:** A rectangular arrangement of objects or numbers in rows and columns.
 * **Associative Property of Multiplication:** The product of a set of numbers is the same regardless of how the numbers are grouped.
 * //Example: If (3 x 5) x 2 = 15 x 2 = 30, and 3 x (5 x 2) = 3 x 10 = 30, then (3x5) x 2 = 3 x (5 x 2)//
 * **Commutative Property of Multiplication**: The product of a group of numbers is the same regardless of the order in which the numbers are arranged.
 * //Example: If 8 x 6 = 48 and 6 x 8 = 48, then 8 x 6 = 6 x 8.//
 * **Distributive Property:** A product can be found by multiplying the addends of a number separately and then adding the products.
 * Example: 4 x 53 = (4 x 50) + (4 x 3) = 200 + 12 = 212
 * **Dividend:** A number that is divided by another number.
 * //Example: dividend ÷ divisor = quotient//
 * **Division:** An operation in which a number is shared or grouped into equal parts.
 * **Divisor:**(1) In a fair sharing division problem, the divisor is the number of equal groups. In a measurement (repeated subtraction) division problem, the divisor indicates the size of each group.(2) A number by which another number is to be divided.
 * //Example: dividend ÷ divisor = quotient//
 * **Equal:** Having the same value.
 * **Factor:** A number that is multiplied by another number to get a product. To “factor" means to write the number or term as a product of its factors.
 * **Identity Property of Multiplication:** Any number that is multiplied by 1 results in the number itself.
 * //Example: 1 x 5 = 5 x 1 = 5//
 * **Measurement Division (or repeated subtraction):** Given the total amount (dividend) and the amount in a group (divisor), determine how many groups of the same size can be created (quotient).
 * **Multiplicand:** The number in a multiplication equation that represents the number of objects in each (equal-sized) group.
 * **Multiplication:** The operation of repeated addition of a number.
 * //Example: 3 x 5 = 5 + 5 + 5 = 15//
 * **Multiplier:** The number in a multiplication equation that represents the number of (equal-sized) groups.
 * **Partial Products:** The products that result when ones, tens, or hundreds within numbers are multiplied separately.
 * //Example: When multiplying 63 x 37 = 1800 + 420 + 90 + 21 = 2,331//
 * //60 x 30 = 1800//
 * //**Partial Products**//
 * //60 x 7 = 420//
 * //30 x 3 = 90//
 * //3 x 7 = 21//
 * //The resulting partial products are 1800, 420, 90, and 21.//
 * **Partition Division (or fair-sharing):** Given the total amount (dividend) and the number of equal groups (divisor), determine how many/much in each group (quotient).
 * **Product:** A number that is the result of multiplication.
 * **Quotient:** The result of a division problem.
 * //Example: dividend ÷ divisor = quotient//
 * **Remainder:** The part of the dividend that is left after all possible equal sized groups are created. || * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.multiplication.com/"]] http://www.multiplication.com/ Practice games for multiplication facts as well as teacher resource pages with instructional ideas on how to introduce multiplication.
 * Students visualize the multiplication of two numbers as an area.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/vlibrary.html"]] http://nlvm.usu.edu/en/nav/vlibrary.html Rectangle Multiplication is one of the many applets from NLVM that allows students to experiment with multiplication using manipulatives.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.funbrain.com/math/index.html"]] http://www.funbrain.com/math/index.html One of many game sites designed to support student understanding of multiplication. Note: This site contains advertising.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.shodor.org/interactivate/activities/WholeNumberCruncher/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc"]] http://www.shodor.org/interactivate/activities/WholeNumberCruncher/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc Provides additional practice with the concept of an input-output machine; enables students to discover for themselves the patterns among numbers.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.naturalmath.com/mult/mult5.html"]] http://www.naturalmath.com/mult/mult5.html A series of web pages describing patterns and techniques (starting with the commutative property) that can be used to learn the basic multiplication facts
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://illuminations.nctm.org/LessonDetail.aspx?id=U109"]] http://illuminations.nctm.org/LessonDetail.aspx?id=U109 Numerous ideas for introducing multiplication, including the array model.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html?from=category_g_2_t_1.html"]] http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html?from=category_g_2_t_1.html Base-ten model using virtual grid paper. Click on the “Common” button to allow the use of numbers larger than 10 and remember to keep one dimension less than 10.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.eduplace.com/math/mw/background/3/08/te_3_08_overview.html"]] http://www.eduplace.com/math/mw/background/3/08/te_3_08_overview.html Provides background information on the relationship between multiplication and division.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.softschools.com/math/games/division_practice.jsp"]] http://www.softschools.com/math/games/division_practice.jsp Division practice; the student or teacher can determine the parameters for the divisor, dividend, and number of problems
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.thinkingblocks.com/ThinkingBlocks_MD/TB_MD_Main.html"]] http://www.thinkingblocks.com/ThinkingBlocks_MD/TB_MD_Main.html This website supports students solving multiplication and division word problems with the use of interactive models.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://mason.gmu.edu/%7Emmankus/whole/base10/asmdb10.htm#div"]] http://mason.gmu.edu/~mmankus/whole/base10/asmdb10.htm#div A site for teachers and parents provides information on using base 10 blocks to solve division problems with an area model.

DOE Framework ||
 * =3: Geometry and Measurement= ||
 * * Standard units provide common language for communicating measurements.
 * Geometric figures can be classified according to properties
 * Acute, right, and obtuse angles can be identifies based upon appearance and comparison of their angles
 * Geometric figures can be combined or separated to form different geometric figures
 * An inch or centimeter would be a good unit to measure small objects such as a pencil
 * A yard or meter would be an appropriate unit to use when measuring length of rooms
 * A mile or kilometer would be appropriate to use when measuring the distance from one city to another.
 * Length around a polygon can be calculated by adding the length of its sides
 * The space inside a rectangle or square can be measured in square units
 * Objects can be measured in standard units.
 * Triangles can be classified according to the lengths of its sides.
 * A circle has a diameter, radius, and center || * How can I use attributes to compare and contrast shapes?
 * How can angles be classified?
 * How can triangles be classified according to the length of their sides?
 * How can shapes be combined to create new shapes?
 * Can a shape be represented in more than one way? How and why?
 * How can I compare measurements?
 * What determines the choice of a measurement tool?
 * What estimation strategies are used in measurement?
 * How is the appropriate unit for measurement determined?
 * How is the reasonableness of a measurement determined?
 * Why are units important in measurement?
 * How are the perimeter and area of a shape related?
 * How does combining and breaking apart shapes affect the perimeter and area?
 * How can rectangles have the same perimeter but have different areas?
 * How does estimating length change with more frequency of measurement?
 * How do the measures of lengths change when the unit of measure changes?
 * What methods can I use to determine the area of an object?Wh
 * ere are radius, center, and diameter located on a circle and how can they be used to show distance on a map?
 * How can we communicate our thinking about mathematical vocabulary?
 * How can I demonstrate my understanding of the attributes of two-dimensional figures and the measurement of length, perimeter, area, and time? || * **acute angle:** an angle whose measure is between 0 degrees and 90 degrees
 * **angle:** the region between two rays
 * **area****:** a measurement of the region enclosed by the sides of a polygon Area is always expressed in squared units.
 * **centimeter:**a metric unit of length; 1/100 of a meter
 * **circle:**the set of all points in a plane that are the same distance (called the radius) from a given point (the center)
 * **diameter:**a line segment passing through the center of a circle with endpoints on the circle.
 * **edge:**the intersection of a pair of faces in a three-dimensional figure
 * **equilateral triangle:**a triangle with three equal sides and three equal angle
 * **face:**the plane figures that make up a solid figure
 * **foot:**a customary unit of length 1 foot = 12 inches
 * **hexagon:**a polygon with six sides
 * **inch:** a customary unit of length 12 inches = 1 foot
 * **isosceles triangle:**a triangle with at least two equal sides and two equal angles
 * **kilometer:**a unit of measurement for length in the metric system. 1 kilometer = 1000 meters
 * **meter:**the standard unit of length in the metric system 1 meter = 100 centimeters
 * **millimeter:**A metric unit of measurement for length. 1 meter = 1000 millimeters
 * **obtuse angle:**An obtuse angle is greater than 90 degrees but less than 180 degrees
 * **parallelogram:**A quadrilateral with opposite sides that are parallel and of equal length and with opposite angles that are equal
 * **perimeter:**the distance around the outside of a shape
 * **plane figure****:** a figure of which all points lie in the same plane
 * **polygon****:** a closed plane figure (no gaps or openings) made with 3 or more sides and angles
 * **quadrilateral:** a four-sided polygon
 * **radius:**the distance from the center of a circle to any point on the circumference
 * **rectangle:** a quadrilateral with 4 right angles and two pairs of opposite equal parallel sides
 * **rhombus:** a parallelogram with four equal sides and equal opposite angles
 * **right angle:** an angle that measures exactly 90 degrees.
 * **scalene triangle:** a triangle in which all three sides are different lengths.
 * **side:** A line or curve on the edge of a shape that joins the vertices.
 * **solid figure:** a 3 dimensional figure havign length, width and height
 * **square:** a quadrilateral with 4 equal sides, 4 right angles and opposite sides that are parallel.
 * **triangle:** a polgon with 3 sides
 * **trapezoid:** a quadrilateral with 2 parallel sides
 * **vertex(of 2-D figures):** The common endpoint of two line segments that serve as two sides of a polygon.
 * **Vertex (of 3-D figures):** The point where 3 or more edges intersect.
 * **Yard:** distance that is equal to 36 inches or 3 feet. || * //[[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities"]] http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities - Interactive Pentomino//
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.incompetech.com/beta/hexagonalGraphPaper/hex.html"]] http://www.incompetech.com/beta/hexagonalGraphPaper/hex.html - Print hexagon graph paper
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities"]] http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities - virtual manipulatives
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://incompetech.com/beta/plainGraphPaper/"]] http://incompetech.com/beta/plainGraphPaper/ dot and graph paper
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://mathforum.org/trscavo/geoboards/dot1.html"]] http://mathforum.org/trscavo/geoboards/dot1.html - Geoboard dot paper 20 up
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://math.arizona.edu/%7Eondrus/teaching/302Bsum05/resources/10x10dot.pdf"]] http://math.arizona.edu/~ondrus/teaching/302Bsum05/resources/10x10dot.pdf -10 x 10 Geoboard
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.wiu.edu/users/mfjro1/wiu/graphics/pdf-files/dotpaper5x5.pdf"]] http://www.wiu.edu/users/mfjro1/wiu/graphics/pdf-files/dotpaper5x5.pdf - small geoboard paper
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://highered.mcgraw-hill.com/sites/dl/free/0072532947/78543/InchGrid.pdf"]] http://highered.mcgraw-hill.com/sites/dl/free/0072532947/78543/InchGrid.pdf -
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathName"]] http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathName- What's in a Name video
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://standards.nctm.org/document/eexamples/ch0."]] http://standards.nctm.org/document/eexamples/ch0.
 * “Making Triangles” applet and background information.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm"]] http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm “Creating Polygons” applet and background information.
 * Interactive geoboard from the National Library of Virtual Manipulatives [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/"]] http://nlvm.usu.edu/
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_271_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html"]] http://nlvm.usu.edu/en/nav/frames_asid_271_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html Students follow a pattern to create attribute trains based on color, shape, or the number on the shape (e.g. triangle, square pattern; red, red, blue pattern; triangle, square, square pattern; 2,3,1 pattern).
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/7_Tangrams/"]] http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/7_Tangrams/ An animated movie that discusses the attributes of the pieces of tangrams and asks students to create different shapes while showing how to make the seven tangram pieces.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://pbskids.org/cyberchase/games/area/tangram.html"]] http://pbskids.org/cyberchase/games/area/tangram.htmlVirtual tangrams with several pictures for students to build.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_289_gChallenge_2_t_3.html?open=activities"]] http://nlvm.usu.edu/en/nav/frames_asid_289_gChallenge_2_t_3.html?open=activities Interactive tangram puzzles
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://standards.nctm.org/document/eexamples/chap4/4.4/part2.htm"]] http://standards.nctm.org/document/eexamples/chap4/4.4/part2.htm Tangram challenges from the National Council of Teachers of Mathematics.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm"]] http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm Interactive tangram pieces.
 * __[[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.innovativeclassroom.com/Files/Worksheets/AmIaSquare.pdf"]] http://www.innovativeclassroom.com/Files/Worksheets/AmIaSquare.pdf__ “Am I a Square?” measurement and graphing activity.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities"]] http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities Interactive pentomino tasks
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html"]] http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html Provides several beginner problems with solutions for pentominos.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://puzzler.sourceforge.net/docs/pentominoes.html"]] http://puzzler.sourceforge.net/docs/pentominoes.html Solutions to several pentominos puzzles such as the one below.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities"]] http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities Geoboard with area/perimeter activity (Look for the activity titled, “Shapes with Perimeter 16.”)
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://highered.mcgraw-hill.com/sites/0072532947/student_view0/grid_and_dot_paper.html"]] http://highered.mcgraw-hill.com/sites/0072532947/student_view0/grid_and_dot_paper.html Printable dot and graph paper
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.shodor.org/interactivate/activities/ShapeExplorer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.32"]] http://www.shodor.org/interactivate/activities/ShapeExplorer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.32 Randomly generated rectangles for which the perimeter and the area can be found
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html"]] http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html Instruction on finding area and perimeter of shapes with practice. Levels 2 and 3 for area require finding the area of several rectangles and adding the areas together. ||
 * =4: Fractions and Decimals= ||  ||
 * * Fractional parts are equal shares of a whole or a whole set.
 * The more equal sized pieces that form a whole, the smaller the pieces of the whole become.
 * When the numerator and denominator are the same number, the fraction equals one whole.
 * When the wholes are the same size, the smaller the denominator, the larger the pieces.


 * The fraction name (half, third, etc) indicated the number of equal parts in the whole.
 * decimal point can be used in a number to name a part smaller than one whole.
 * If a whole is divided into ten equal parts, the parts can be named with tenths. || * How can we be sure fractional parts are equal in size?
 * What does each term in a fraction represent?
 * How does the number of equal pieces affect the name of a fraction?
 * What do I know about a fraction that has the same numerator and denominator?
 * What are the important features of a unit fraction?
 * Why is the size of the whole important?
 * How can I write a fraction to represent a part of a group?
 * How can I represent a fraction of a discrete model (a set)?
 * How are multiplication, division, and fractions related?
 * How can I be sure fractional parts are equal in size?
 * What do the numbers (terms) in a fraction represent?
 * How does the number of equal pieces affect the fraction name?
 * How can I write a fraction to represent a part of a group?
 * How are multiplication, division, and fractions related?
 * Why does the denominator remain the same when I add fractions with like denominators?
 * How do we add fractions with like denominators?
 * Why is the number 10 important in our number system?
 * How are tenths related to the whole?
 * How can you use decimal fractions to solve addition and subtraction problems?
 * How are decimal fractions and common fractions used in problem-solving situations?
 * How are decimals and fractions related?
 * Why is the number 10 important in our number system?
 * How can I write a fraction to represent a part of a group?
 * When we compare two fractions, how do we know which has a greater value?
 * What happens to the denominator when I add fractions with like denominators? || * **Common Fraction:** A number used to name a part of a group or a whole containing a fraction bar, a numerator and a denominator.
 * **Decimal Fraction:** A fraction with a denominator as a multiple of 1
 * **Decimal Place:** The number of digits to the right of the decimal point (Ex.~ 8.604 has 3 decimal places
 * **Decimal Point:** The period placed in a base 10 number that separates the whole number digits from the fraction digits
 * **Denominator:** The lower number of a fraction that represents the number of equal fractional parts a whole has been divided int
 * **Divide:** To separate into equal part
 * **Equivalent Sets:** Sets containing the same number of objects
 * **Increment:** the amount or degree by which something changes
 * **Numerator:** The top number in a common fraction representing the number of equal parts of a whole or group under consideratio
 * **Term:** The number in the numerator and denominator of a fractio
 * **Unit Fraction:** Any common fraction with a numerator of on
 * **Whole Number:** A counting number from 0 to infinity || * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_102_g_2_t_1.html"]] http://nlvm.usu.edu/en/nav/frames_asid_102_g_2_t_1.html -Manipulatives for fractions


 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.coolmath4kids.com/fractions/fractions1.html"]] http://www.coolmath4kids.com/fractions/fractions1.html

//Find more Candy Fractions at these sites:// // * http://www.instructorweb.com/lesson/candyfractions.asp //


 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://mathforum.org/paths/fractions/hershey.frac.html"]] http://mathforum.org/paths/fractions/hershey.frac.html


 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.teach-nology.com/teachers/lesson_plans/math/fractions/"]] http://www.teach-nology.com/teachers/lesson_plans/math/fractions/

> > > > > > > > > >
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.primarygames.com/fractions/1a.htm%C2%A0"]] http://www.primarygames.com/fractions/1a.htm -Select the correct name for a region
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.picadome.fcps.net/lab/currl/math/fractions.htm"]] http://www.picadome.fcps.net/lab/currl/math/fractions.htm
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html?from=category_g_2_t_1.html"]] http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html?from=category_g_2_t_1.html Allows students to practice naming fractional parts of a whole.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://gingerbooth.com/flash/patblocks/patblocks.php"]] http://gingerbooth.com/flash/patblocks/patblocks.php - Manipulate pattern blocks online and easily print, and then label their work from the following website.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.primarygames.com/fractions/question1.htm"]] http://www.primarygames.com/fractions/question1.htm In this game, students are asked to identify remaining fraction of a pizza. Note this site contains advertising.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.mattnelson.com/dee/fractions/Fractions_Lesson_Plan_2.pdf"]] http://www.mattnelson.com/dee/fractions/Fractions_Lesson_Plan_2.pdf - More activities about __The Doorbell Rang__. (Note – use toothpicks instead of the matchsticks referred to in this lesson.)
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.visualfractions.com/Identify_sets.html"]] http://www.visualfractions.com/Identify_sets.html This website could be used as an intervention. Students determine the fraction of a set.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.widro.com/throwpaper.html"]] http://www.widro.com/throwpaper.html - Students can play the waste basket basketball virtually. This is very challenging because a virtual fan is blowing. Note – web site contains advertisements.
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://nlvm.usu.edu/en/nav/frames_asid_107_g_2_t_1.html?from=category_g_2_t_1.html"]] http://nlvm.usu.edu/en/nav/frames_asid_107_g_2_t_1.html?from=category_g_2_t_1.html

// DOE Framework 08-09// // Fraction strip on smartboard// // adding and subtracting decimals student46.pdf// // adding subtracting decimals teacher46.pdf// // COmparing Fractions student 41.pdf// // Comparing Fractions Teacher41.pdf// // Decimal concept student44.pdf// // Decimal Concepts teacher 44.pdf// // subtracting Fractions42.pdf// // subtraction Fractions student42.pdf// ||
 * =5: Data Analysis= ||  ||   ||
 * * graphs are visual representations of data
 * represented data allows the asking and answering of questions
 * scales remain constant within graphs
 * different graphs can have different scale increments
 * graphs can provide a simplified representation of complex data
 * Bar graphs and tables may be used to display data.
 * One way to compare data is by using a bar graph.
 * The scale used when making a bar graph is determined by the data being graphed.
 * A bar graph's scale can affect how the data is interpreted || * How are bar graphs and tables useful ways to display data?
 * How does the scale affect bar graph?
 * How do I decide what interval to use for my scale?
 * Why do we use graphs?
 * Why would we use different scales?
 * Where are graphs found? || * **Increment:** value assigned to a fixed distance on an axis of a graph
 * **Bar graph:** A way of displaying data using horizontal or vertical bars so that the height or length of the bars indicates its value.
 * **Scale:** The numbers along the axes on a graph. The numbers are arranged in order with equal intervals.
 * **Line Plot:** shows data on a number line with x or other marks to show frequency
 * **Pictograph:** A graph that represents statistical data using symbolics figures to match the frequencies of different kinds of data. A pictograph uses pictures or symbols to represent an assigned amount of data.
 * **Interval:** A regular distance or space between values. The set of points between two numbers.
 * **Mathematical arguments and proof:** Explaining, supporting, justifying or stating your thinking about why you think or believe something is true || Attachments:

- has various graphing activities you may want to supplement

-
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.studyzone.org/testprep/math4/d/pictograph4p.cfm"]] http://www.studyzone.org/testprep/math4/d/pictograph4p.cfm
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.studyzone.org/testprep/math4/e/readpicto3p.cfm"]] http://www.studyzone.org/testprep/math4/e/readpicto3p.cfm
 * [[image:http://clarke-public.rubiconatlas.org/common_images/attach.png?v=Atlas7.1.1b10703 link="@http://www.superteacherworksheets.com/pictograph.html"]] http://www.superteacherworksheets.com/pictograph.html

data grade 3 10 minute review.notebook || The product of a given whole number and an integer. Or the result of a number adding to itself repeatedly **Factors:** A whole number that divides exactly into another number, a whole numbers that can be multiplied together to make a third number. "To factor" means to write the number or term as a product of its factors. For example, 4 and 5 are factors of 20 since 20 = 4 x 5.
 * =6: Algebra:The Study of Patterns= ||  ||
 * * graphs are visual representations of data
 * represented data allows the asking and answering of questions
 * scales remain constant within graphs
 * different graphs can have different scale increments
 * graphs can provide a simplified representation of complex data
 * Bar graphs and tables may be used to display data.
 * One way to compare data is by using a bar graph.
 * The scale used when making a bar graph is determined by the data being graphed.
 * A bar graph's scale can affect how the data is interpreted || * How can numerical, geometric, or time patterns be extended and described?
 * In what ways can a numerical pattern be associated with a geometric pattern?
 * How can a term in a pattern be found without finding every term that precedes that term?
 * How can various patterns be described, i.e. with words, geometrically, with mathematical notations?
 * How do tables and graphs help organize mathematical thinking? || * **Sum****:** the total or whole amount as a result of adding. The answer in an addition problem.
 * **Addend:** The number(s) being added together to get the sum.
 * **Difference:** The number that is the result of subtracting one number from another. The answer to a subtraction problem.
 * **Product:** A number that is the result of multiplying two or more numbers together. The answer to a multiplication problem.
 * **Multiple:** (repeated addition). For example, the multiples of 3 are: 3, 6, 9, 12, 15, etc.

**Pattern** **: A** set of numbers or objects that are generated by following a specific rule. Patterns can be //numerical, i.e. 2, 4, 6, 8,// geometrical, i.e. as a tile pattern on the floor with 2 blue tiles followed by 1 white tile, etc. Patterns //alternating, i.e., 1, 5, 2, 6, 3, 7, 4 (add four, subtract three).// ||  ||