CCSS Gr. 3 Fractions and Area

Jack D. Gittinger, Oct 29, 2015

[i][b]Common Core Standards for Grade 3-Geometry[/b] [/i] [b]Reason with shapes and their attributes.[/b] 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. [b] [color=#1551b5]Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.[/color][/b] [i][b]Common Core Standards for Grade 3-Geometric Measurement [/b][/i] [b]Geometric measurement: understand concepts of area and relate area to multiplication and to addition.[/b] Recognize area as an attribute of plane figures and understand concepts of area measurement. [color=#1551b5][b]---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][/color] ---[color=#1551b5][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.Measure areas by counting unit squares (square cm, m, square in, square ft, and improvised units). [/b][/color]Relate area to the operations of multiplication and addition. ---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. ---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. ---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. ---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. [b]Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.[/b] Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Table of Contents

  1. Correcting Fractions
    1. Correcting Fractions
  2. Finding Halves
    1. Finding Halves
    2. Finding More Halves
    3. Finding Halves with Unit Squares
  3. Finding Fourths
    1. Finding Fourths
    2. Finding More Fourths
    3. Finding Fourths with Unit Squares
    4. Finding 3/4 with Unit Squares
  4. Finding Thirds
    1. Finding Thirds
    2. Finding More Thirds
    3. Finding Thirds with Unit Squares
    4. Finding 2/3 with Unit Squares

1.

Correcting Fractions

  • 1. Correcting Fractions

1.1.

Correcting Fractions

Instructions
[b]Introduction and Background[/b][br]Some people think that dividing a polygon in four pieces means that you have divided it into fourths. That’s not necessarily true! The pieces must be the same size, have the same area.  We sometimes say they must be “fair shares.”  Some people think that if you divide a polygon into, say, fourths that all the pieces must look alike.  Again, not necessarily true![br][br][b]The Challenge[/b][br]Some students made a few mistakes in creating fractional parts.Use the MOVE (pointer) tool to move the lines on each shape to fix the shapes so that they are more correctly divided.[br][b][br]Print and Discuss[/b][br]When you have found made all of the necessary corrections, print the GeoGebra screen.Find a partner who is also finished and compare your line segments.Do you agree with each other?  Did you find different solutions?
– Jack D. Gittinger

2.

Finding Halves

  • 1. Finding Halves
  • 2. Finding More Halves
  • 3. Finding Halves with Unit Squares

2.1.

Finding Halves

Instructions
[b]Introduction and Background[/b][b] [br][/b]In this activity you will find a way to divide some polygons in half, but you might have to be creative! Remember, the halves of a polygon don’t necessarily have to look exactly alike (be congruent). [br][br][b]The Challenge [br][/b]Use the SEGMENT BETWEEN TWO POINTS tool to construct a line segment that divides each polygon into equal halves. Is there more than one way to do this? If possible, use another line segment to divide the polygon in another way. [br][br][b]Print[br][/b]When you have found all the ways you can to divide each polygon into halves, print[br]the [i]GeoGebra[/i] screen. Find a partner who is also finished and compare your line segments. Do you agree with each other?   If you see a line segment that you think does not really divide the polygon into halves, fair shares, and then discuss why you feel that way.
Finding Halves
– Jack D. Gittinger

2.2.

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2.3.

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3.

Finding Fourths

  • 1. Finding Fourths
  • 2. Finding More Fourths
  • 3. Finding Fourths with Unit Squares
  • 4. Finding 3/4 with Unit Squares

3.1.

Finding Fourths

[b]Introduction and Background[/b][br]In this activity you will find a way to divide some polygons into fourths, but you might have to be creative! Remember, the fourths of a polygon don’t necessarily have to look exactly alike (be congruent).[br][br][b]The Challenge[/b][br]Use the SEGMENT BETWEEN TWO POINTS tool to construct a line segment that divides each polygon into fourths.Is there more than one way to do this? If possible, use another line segment to divide the polygon in another way.[br][br][b]Print[/b][br]When you have found all the ways you can to divide each polygon into fourths, print the [i]GeoGebra [/i]screen.Find a partner who is also finished and compare your line segments. Do you agree with each other?  If you see a line segment that you think does not really divide the polygon into fourths, four fair shares, and then discuss why you feel that way.
Finding Fourths
– Jack D. Gittinger

3.2.

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3.3.

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3.4.

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4.

Finding Thirds

  • 1. Finding Thirds
  • 2. Finding More Thirds
  • 3. Finding Thirds with Unit Squares
  • 4. Finding 2/3 with Unit Squares

4.1.

Finding Thirds

Instructions
[b]Introduction and Background[/b][br]In this activity you will find a way to divide some polygons into thirds, but you might have to be [br]creative![br]Remember, the thirds of a polygon don’t necessarily have to look exactly alike (be congruent).[br][br][b]The Challenge[/b][br]Use the SEGMENT BETWEEN TWO POINTS tool to construct a line segment that [br]divides each polygon into thirds.[br]Is there more than one way to do this?[br]If possible, use another line segment to divide the polygon in another way.[br][br][b]Print[/b][br]When you have found all the ways you can to divide each polygon into thirds, print the [br]GeoGebra screen.[br]Find a partner who is also finished and compare your line segments.[br]Do you agree with each other?  [br]If you see a line segment that you think does not really divide the polygon into fourths, four [br]fair shares, and then discuss why you feel that way.
– Jack D. Gittinger

4.2.

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4.3.

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4.4.

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Information