Measurement Data Geometry Wiki with resources and PowerPoint:
http://elementary-math- resources.wiki.inghamisd.org/home
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1. What are the key questions that focus student's thinking and
organize their learning? 2. What are the key activities that
promote thinking? 3. What are the key strategies that have proven
effective for learning about fractions, area and perimeter, and
geometric shapes?
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Overview Review of addition/subtraction and
multiplication/division Concepts AND Procedures Measuring length,
volume, mass, time Geometric shapes and their attributes Fraction
concepts First, time for sharing
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Concepts and Procedures As a review, what do students need to
know conceptually in order to add two-digit numbers? 24 + 51 = ___
What do students need to know conceptually to multiply single-digit
numbers? 5 x 6 = ___ What do students need to do in order to get
good at these two things (after they learn the concepts?) develop
procedures, practice
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3.OA.6 Understand division as an unknown-factor problem. For
example, divide 32 8 by finding the number that makes 32 when
multiplied by 8.
Math Work StationsMath Work Stations, Debbie Diller Developing
Number Concepts, Kathy Richardson Teaching Student- Centered
Mathematics, Van de Walle and Lovin Georgia Common Core lessons New
York Common Core lessons
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Measuring length in 2 nd and 3 rd grade According to the CCSS,
what length-measuring activities should 2 nd grade students be
doing? Do you have the tools they need? What about measuring
lengths in 3 rd grade? Look at the graphing standards (3.MD.4) What
tools are needed? (see the wiki for half-inch and quarter-inch
rulers)
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inches x x x x
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Line plot of measurements How is 2.MD.9 different from 3.MD.4?
Rulers (black line masters) are on the wiki.
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Measuring area in 2 nd and 3 rd grade What area-measuring
activities should 3 rd grade students be doing? What tools are
needed?
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Measuring mass and volume 3.MD.2 Measure and estimate liquid
volumes and masses of objects using standard units of grams (g),
kilograms (kg), and liters (l). (Excludes compound units such as cm
3 and finding the geometric volume of a container.) What tools are
needed? What might be measured?
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3.MD.2 continued: Add, subtract, multiply, or divide to solve
one-step word problems involving masses or volumes that are given
in the same units, e.g., by using drawings (such as a beaker with a
measurement scale) to represent the problem. (Excludes
multiplicative comparison problems involving notions of times as
much.) Develop 4 such problems.
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Telling time 2.MD.7 Tell and write time from analog and digital
clocks to the nearest five minutes, using am and pm How do children
come to learn that 5 on the clock means 25 minutes after the hour?
3.MD.1 Tell and write time to the nearest minute and measure time
intervals in minutes. Solve word problems involving addition and
subtraction of time intervals in minutes, e.g., by representing the
problem on a number line diagram. What tools do you need for
measuring time intervals in minutes? How can number lines be used
for solving elapsed time problems? See Georgia Measurement Units 2
nd grade page 57
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Field trip to the zoo Georgia 3 rd grade Measurement pp.
84-91
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Using money 2.MD.8 Solve word problems involving dollar bills,
quarters, dimes, nickels, and pennies, using $ (dollars) and
(cents) symbols appropriately. Example: If you have 2 dimes and 3
pennies, how many cents do you have? What does it take to solve
these problems? Develop three more problems. Web pages with money
activity ideas are on the wiki.wiki
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Area standards 3.MD.5 Recognize area as an attribute of plane
figures and understand concepts of area measurement. a. A square
with side length 1 unit, called a unit square, is said to have one
square unit of area, and can be used to measure area. b. A plane
figure which can be covered without gaps or overlaps by n unit
squares is said to have an area of n square units. 3.MD.6 Measure
areas by counting unit squares (square cm, square m, square in,
square ft, and improvised units).
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Area of a rectangle Fill this shape with tiles so that none are
overlapping. Count how many tiles you have. Can you find a quick
way to count the tiles? 7 4
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Area standards 3.MD.7 Relate area to the operations of
multiplication and addition. a. Find the area of a rectangle with
whole-number side lengths by tiling it, and show that the area is
the same as would be found by multiplying the side lengths. b.
Multiply side lengths to find areas of rectangles with whole-
number side lengths in the context of solving real world and
mathematical problems, and represent whole-number products as
rectangular areas in mathematical reasoning. 3 4
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A shape puzzle Fill this shape with two different color tiles
or counters, making two rectangles. Represent the total number of
tiles or counters with a number sentence that uses multiplication.
7 4
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A shape puzzle Fill this shape with two different color tiles
or counters, making two rectangles. Represent the total number of
tiles or counters with a number sentence that uses multiplication.
4 x 7 = 4 x 5 + 4 x 2
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Area standards 3.MD.7 Relate area to the operations of
multiplication and addition. (contd) c. Use tiling to show in a
concrete case that the area of a rectangle with whole-number side
lengths a and b + c is the sum of a b and a c. Use area models to
represent the distributive property in mathematical reasoning. 4 x
7 = 4 x 5 + 4 x 2 7 = 5 + 2 4
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Area standards 3.MD.7 Relate area to the operations of
multiplication and addition. (contd) d. Recognize area as additive.
Find areas of rectilinear figures by decomposing them into
non-overlapping rectangles and adding the areas of the
non-overlapping parts, applying this technique to solve real world
problems.
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Scaled Picture Graph How many books did Nancy read? How many
more books did Juan read than Nancy?
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Bar Graph with Analysis How is 2.MD.10 different from
3.MD.3?
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Geometric Shapes Find all the different combinations of pattern
blocks that can be used to make the hexagon.
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van Hiele Levels of Geometric Thought Level 0: Visualization
Students recognize and name figures based on the global, visual
characteristics of the shape. Students at this level are able to
make measurements and even talk about the properties of shapes, but
these properties are not abstracted from the shape at hand. It is
the appearance of a shape that defines it for a student. A square
is a square because it looks like a square. Other visual
characteristics may include pointy, fat, sort of dented in.
Classification of shapes at this level is based on whether they
look alike or different. from Van de Walle and Lovin, 2006
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Recognizing and analyzing shapes K.G.1 Describe objects in the
environment using names of shapes K.G.2 Correctly name shapes
regardless of their orientations or overall size. K.G.4 Analyze and
compare two- and three-dimensional shapes, in different sizes and
orientations, using informal language to describe their
similarities, differences, parts (e.g., number of sides and
vertices/corners) and other attributes (e.g., having sides of equal
length).
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Found on Peace, Love and First Grade, a blog by LauraPeace,
Love and First Grade Original on Ashley Hughes Teachers Pay
Teachers storeAshley Hughes Teachers Pay Teachers store
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Color the Shapes Color all the triangles green. Color all the
rectangles red. Color all the circles blue. Are there some shapes
you havent colored?
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Shapes All Around Us The Shape of ThingsThe Shape of Things, by
Dayle Ann Dodds
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van Hiele Levels of Geometric Thought Level 1: Analysis
Students are able to consider all shapes within a class rather than
a single shape. By focusing on a class of shapes, students are able
to think about what makes a rectangle a rectangle (four sides,
opposite sides parallel, opposite sides equal, four right angles,
etc.) Irrelevant features (e.g. orientation or size) fall into the
background. Students begin to appreciate that a collection of
shapes goes together because of its properties. from Van de Walle
and Lovin, 2006 =
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Attributes 1.G.1 Distinguish between defining attributes (e.g.,
triangles are closed and three-sided) versus non-defining
attributes (e.g., color, orientation, overall size); for a wide
variety of shapes; build and draw shapes to possess defining
attributes. 2.G.1 Recognize and draw shapes having specified
attributes, such as a given number of angles or a given number of
equal faces. Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes. (Sizes are compared directly or visually, not
compared by measuring.)
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Attributes Give each student a set of shapes. Have them
brainstorm ways to describe the shapes. Record their responses on
chart paper. Guide students to look for ways other than color and
size when describing the shapes such as by number of sides, number
of corners, or no corners. Make a class chart.
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van Hiele Levels of Geometric Thought Level 2: Informal
Deduction Students are able to develop relationships between and
among properties of shapes. They recognize sub-classes of
properties: If all 4 angles are right angles, it is a rectangle.
Squares have 4 right angles, so squares must be rectangles. from
Van de Walle and Lovin, 2006 5.G.4 Classify two-dimensional figures
in a hierarchy based on properties.
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Attributes 3.G.1 Understand that shapes in different categories
(e.g., rhombuses, rectangles, and others) may share attributes
(e.g., having four sides), and that the shared attributes can
define a larger category (e.g., quadrilaterals). Recognize
rhombuses, rectangles, and squares as examples of quadrilaterals,
and draw examples of quadrilaterals that do not belong to any of
these subcategories. Quadrilaterals Measuring and classifying
angles starts in 4 th grade Why can we say that a rectangle is a
category of shapes?
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Shapes by grade K: squares, circles, triangles, rectangles,
hexagons, cubes, cones, cylinders, and spheres 1 st : rectangles,
squares, trapezoids, triangles, half- circles, and quarter-circles
2 nd : triangles, quadrilaterals, pentagons, hexagons, and cubes 3
rd : rhombuses 4 th : parallelogram is implied by classifying
figures based on parallel lines
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Shape sorts 1.Take any shape. Tell one or two things you find
interesting about the shape. 2.Choose two shapes. Find something
alike and something different about the two shapes. 3.The group
selects one shape and places it in the center of the workspace.
Find all other shapes that are like this shape according to the
same rule. 4.Do a second sort with the same target shape but using
a different property.
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Shape sorts 5.Groups share their sorting rules with the class
and show examples. Everyone draw a new shape that will also fit in
the group according to the same rule. 6.Do a secret sort by
selecting about 5 shapes that fit a secret rule, leaving some
similar shapes in the pile. Others find similar shapes and try to
guess the rule. 2.G.1 Recognize and draw shapes having specified
attributes, such as a given number of angles or a given number of
equal faces. Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes.
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Match the Rule
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Attributes In your small group, look at the pictures of the
shapes on your page. List all the attributes you can find that all
the shapes share. Sides Corners (Measurement and classification of
angles starts in 4 th grade) (Diagonals and symmetry are introduced
in 4 th grade) The rhombus has 4 sides 4 corners opposite sides are
the same length
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Attribute Blocks
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Orientation Draw a triangle. Does it look like one of these
triangles?
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Whats my shape? One student will come to the front of the room
and reach into a bag of shapes. The student will pick out one
shape, but keep her/his hand in the bag so no one can see the
shape. The student then describes the shape, talking about
attributes. After describing the shape as completely as possible,
the student says Whats my shape? All of the other students think
silently about what the shape might be and put their thumb up on
their chest when they have an idea. The teacher calls on several
students, drawing each shape they suggest on the board. When enough
shapes have been drawn, the first student pulls the shape out and
names it. Teacher-led discussion can continue about how the target
shape matches or doesnt match the shapes on the board.
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Build a Shape Read The Greedy Triangle (on wiki)on wiki Ask
students if they can make shapes with their bodies and a piece of
yarn. Use straws, pipe cleaners, or other manipulatives to create a
triangle, rectangle, square and trapezoid. Model how you connect
the straws and pipe cleaners to create a shape (sample below). Read
The Greedy Triangle again. Have students create the shapes as you
come to each shape in the book. Georgia Common Core first grade
workbook p. 29
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Georgia lesson plans on wiki wiki
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Build a cube It is often difficult for students to visualize as
it requires a coordination of both two and three- dimensional
shapes. Activities which require students to think about,
manipulate, or transform or a shape mentally will contribute to
students overall visualization skills.
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Making Shapes What can students learn from using Geoboards?
National Library of Virtual Manipulatives
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Pattern Blocks - Composing
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National Library of Virtual Manipulatives
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Math Playground
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Tangrams
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Fractions of a shape 2.G.3 Partition circles and rectangles
into two, three, or four equal shares, describe the shares using
the words halves, thirds, half of, a third of, etc., and describe
the whole as two halves, three thirds, four fourths. Recognize that
equal shares of identical wholes need not have the same shape.
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Fraction Fill In Game Students will work with a partner to play
Fraction Fill In to develop proficiency with fractions. To use
spinner, put a paperclip in the middle. Hold it in place with the
tip of the pencil. Have the student thump the paper clip to spin
and see where it lands. pp. 55-56 Georgia 1 st grade lessons
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Sharing a Cake pp. 58-61 Georgia grade 2 unit 5
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Key Strategies for Fractions Base early understanding on fair
shares Cookies, candy bars, geometric shapes Use representations of
different kinds Circles, rectangles, bars, number lines
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pp. 63-70 gr. 2 unit 5
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Key Strategies for Fractions Develop the meaning of a fraction
as a number (a place on the number line); connect a point on the
number line to a fraction of a whole through the meaning of
denominator and numerator Use real-world examples including
measurement 1st grade: measure by placing unit bars on an object
without gaps. 2nd grade: measure using rulers; know feet and inches
3rd grade: solve problems involving perimeter of polygons; measure
using rulers to 1/2 inch and 1/4 inch.
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Key Strategies for Fractions Develop estimation skills for
comparing fractions by basing comparisons on benchmark fractions
such as 1/2.
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Fractions 3 rd Grade Goal How do each of the 3 rd grade CCSS
for fractions contribute to being able to do this? 3.NF.1 use
manipulatives to model 3/8 and 5/8 (A) 3.NF.2 use a number line to
show 3/4 and 3/5 (B) 3.NF.3 a, b show how 3/4 and 6/8 are
equivalent using manipulatives and drawings (A) 3.NF.3 d solve the
problems above and explain your reasoning (B)
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Number Talks questions: Draw a picture to show 3/4. Which is
larger, 3/4 or 1/2? How would you prove this? How much more is
needed to make 1? How do you know? Draw a picture to show 3/5. How
did you decide where to put 3/5? Which is larger, 3/5 or 1/2? How
would you prove this? How much more is needed to make 1? How do you
know? How would you show or explain which is larger? Lets try some
more: 1/2 and 1/3. 1/4 and 2/4. 4/6 and 4/8. Dolphin Racing Game
Fractions 3 rd Grade Goal
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Which Common Core standards can this help students learn?
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The 10 Instructional Shifts 1.Incorporate ongoing cumulative
review into every days lesson. 2.Adapt what we know works in our
reading programs and apply it to mathematics instruction. 3.Use
multiple representations of mathematical entities. 4.Create
language-rich classroom routines. 5.Take every available
opportunity to support the development of number sense.
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6.Build from graphs, charts, and tables. 7.Tie the math to such
questions as: How big? How much? How far? to increase the natural
use of measurement throughout the curriculum. 8.Minimize what is no
longer important. 9.Embed the mathematics in realistic problems and
real-world contexts. 10. Make Why? How do you know? Can you
explain? classroom mantras.
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1. What are the key questions that focus student's thinking and
organize their learning? 2. What are the key activities that
promote thinking? 3. What are the key strategies that have proven
effective for learning about fractions, area and perimeter, and
geometric shapes?
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At least one big idea for each topic Measuring and estimating
length, volume and mass Tell and write time and solve problems
Solve problems involving money Draw graphs, use measurement data
Shapes and their attributes