Unit 5: Finding Area

What Students Should Know

M5G1

Congruent is having exactly the same size and shape. The point at which two line segments, lines, or rays meet to form an angle is the vertex. An angle is two rays that share an endpoint. Sides are line segments connected to other line segments to form a polygon. Not all geometric figures will have sides, angles and vertices. Polygons are closed plane figures formed from line segments that meet only at their endpoints. Congruent figures have corresponding sides, vertices, and angles. Similar figures have the same shape but not necessarily the same size.
M5G2

Circumference is the perimeter of a circle. A circle is a closed curve with all its points in one plane and the same distance from a fixed point (the center). A diameter is a chord that goes through the center of the circle. Pi (л ≈ 3.14) is the ratio of the circumference of any circle to its diameter. Radius is the line segment from the center of the circle to any point on the circle. A compass is a tool for making circles and arcs.
M5M1.a

Estimation is an answer close to the exact answer, found by rounding or by using compatible numbers. Area is the number of square units needed to cover a surface. Geometric plane figures are closed figures that lie on a flat surface. Geometric figures are: irregular and regular polygons.
M5M1.b

Area is the number of square units needed to cover a surface. The formula for finding area of a rectangle is length times width. (A= L W) The formula for finding the area of a parallelogram is base times height. (A= B H) A parallelogram is a quadrilateral with opposite sides parallel and congruent. A rectangle is a parallelogram with four right angles.
M5M1.c

The formula for finding area of a parallelogram is (A=B x H). The formula for finding the area of a triangle is (A=1/2b x h). Two congruent triangles can be arranged to form a parallelogram which can be arranged to form a rectangle. A triangle is half the area of a parallelogram.
M5M1.d

Area is the number of square units needed to cover a surface. The formula for finding area of a parallelogram (a=b x h) is base times height. The formula for finding the area of a triangle is (a=1/2 x b x h).
M5M1.e

Estimation is a number close to the exact answer, found either by rounding, using front-end digits, or by using compatible numbers. A circle is a flat, round shape that has all points in one plane and the same distance from the from the center point. Partitioning is used to divide objects. Tiling is a way of determining area using manipulatives. Pi is the ratio of the circumference of any circle to its diameter. (approximately equal to 3.14) Radius is the segment or the length of the segment from the center of a circle to any point on the circle. Circumference is the perimeter of a circle.
M5M1.f

Regular polygons are polygons with all sides the same length and all angles the same measure. Irregular polygons are polygons with sides that are not the same length. A square is a polygon with four congruent sides and dour right angles. A rectangle is a polygon with two pairs of congruent, parallel sides and four right angles. A triangle is a polygon with three sides and three angles. Area of a square and rectangle is found by using the formula (a=b x h). Area of a triangle is found by using the formula (a=1/2b x h). Area is the measure, in square units, of the interior region of a 2-dimensional figure.


What Students Should be Able to Do



M5G1

Identify vertices, sides, and angles of a polygon Identify corresponding sides, angles, and vertices of geometric shapes. Construct congruent shapes Communicate understanding of terminology (vertices, sides, angles, congruency, and polygons). Analyze different geometric shapes to find similarities and differences.
M5G2

Discover Pi by measuring the circumference of many circles and comparing it to the circle’s diameter Communicate understanding of circumference, diameter, pi, and circle Calculate the diameter of a circle with a given circumference. Calculate the circumference of a circle with a given diameter.
M5M1.a

Estimate the area of a geometric plane figure Use appropriate units for measurement. (Ex. The object is 5 paper clips long.)
M5M1.b

Cut the parallelogram apart and rearrange it into a rectangle of the same area Derive the formula of a parallelogram
M5M1.c

Derive the formula for the area of a triangle Compare and contrast the relationship of the area of a rectangle and parallelogram with the triangle
M5M1.d

Find the area of triangles and parallelograms using formulas
M5M1.e

Estimate the area of a circle using partitioning and tiling Estimate the area of a circle using the formula A= ∏r2
M5M1.f 

Create illustrations of irregular and regular polygons Use appropriate formulas for appropriate polygons Calculate the area of a triangle, rectangle, and square

Metric & Customary Units of Capacity

The capacity unit test is Tuesday, Nov. 6th.  Below is the study guide for it.

The following document provides a detailed explanation of an answer to a capacity word problem.  Though it is a sample, it shows you the level of detail/clarity for explaining an answer that the kids are to be doing on assignments.

Here's the website we went on today to practice converting customary units.

http://www.mce.k12tn.net/measurement/volume_customary.htm

Metric System - great website!

 http://www.mce.k12tn.net/measurement/volume_metric.htm

Unit 3: Capacity

(Information taken from a Fulton County Website)

What Students Should Know:

M5M3.a

Capacity is the amount of liquid a container can hold. Fluid ounces, cups, pints, quarts, and gallons are customary units for measuring capacity. A milliliter, liter, and a kiloliter are units for measuring capacity in the metric system.
M5M3.b

Capacity is they amount of liquid a container can hold. Fluid ounces, cups, pints, quarts, and gallons are customary units for measuring capacity. 8 fluid ounces equals 1 cup, 2 cups equals 1 pint, 2 pints equals 1 quart, 4 quarts equals 1 gallon. A milliliter, kiloliter, and a liter are units for measuring capacity in the metric system. 1 kiloliter is 1,000 liters, 1,000 milliliters is 1 liter
 

What Students Should Be Able To Do:  

M5M3.a

Measure the amount of capacity in an object using size appropriate tools (ex. use cups to measure a pitcher of water) Determine which unit of capacity is most apppropriate for measuring the capacity of a given vessle
M5M3.b

Compare one unit to another within a single system of measurement (e.g. 1 quart= 2 pints) Order the customary units of capacity from smallest to largest

Unit 4: What's That Proportion?

What Students Know

M5N4.a

Division of two numbers can be written as a fraction in which the dividend represents the numerator and the divisor represents the denominator.  
M5N4.b

A fraction has two parts, the top number is a numerator and the bottom number is the denominator. The numerator represents how many parts of the whole are present. The denominator represents what fractional part is being counted (how many parts in a whole). A number over itself in a fraction is equal to one. (e.g. 2/2 = 1) Any number multiplied or divided by 1 keeps the same value. To get an equivalent fraction, multiply (or divide) the numerator and denominator by the same nonzero number.
M5N4.c

Equivalent fractions are fractions that name the same number or amount. Multiply or divide the numerator and denominator by the same number to get an equivalent fraction.  Simplest form is when the numerator and denominator of a fraction have no common factor other than 1.
M5N4.e

A whole number that is a common multiple of the denominators of two or more fractions is a common denominator. A concrete model uses manipulatives to represent parts of a whole (example: fraction bars, pattern blocks) A pictorial model is represented with pictures or grids. A computational model uses numbers.
M5N4.f

Less than is represented by the symbol: < Greater than is represented by the symbol: > Equal is represented by the symbol: = When fractions are equal, they represent the same amount. All fractions exist between zero and one on a number line.
M5N4.g

A common fraction is any fraction whose numerators and denominators are whole numbers. A mixed number is a whole number and a fraction. To add and subtract fractions with unlike denominators a common denominator needs to be found and then the rules of addition and subtraction of fractions with the same denominator should be followed. A common denominator is a whole number that is a common multiple of the denominators of two or more fractions.
M5N5.a

Percent is a special ratio that compares a number to 100 using the symbol %.  Percents are fractions with a denominator of 100. The word percent means hundredths or out of 100 or a number divided by 100. A 10 by 10 grid equals 100 units.
 

What Students Should be able to do

 

M5N4.a

Given a fraction, write it as a division problem Give a division problem, write it as a fraction
M5N4.b

Write one as a fraction in multiple ways (e.g. 4/4 = 1, 16/16 = 1) For a given fraction calculate two equivalent fractions
M5N4.c

Rename fractions to simplest form Create equivalent fractions
M5N4.e

Find common denominators using models
M5N4.f

Compare, order and justify fractions
M5N4.g

Add and subtract fractions and mixed numbers with unlike denominators Identify mixed numbers and fractions Identify unlike denominators
M5N5.a

Given a percentage shade a 10 by 10 grid Given a shaded grid, state the percentage represented
 

Paragraph.

Unit 5: Finding Area

What Students Know

M5G1

Congruent is having exactly the same size and shape. The point at which two line segments, lines, or rays meet to form an angle is the vertex. An angle is two rays that share an endpoint. Sides are line segments connected to other line segments to form a polygon. Not all geometric figures will have sides, angles and vertices. Polygons are closed plane figures formed from line segments that meet only at their endpoints. Congruent figures have corresponding sides, vertices, and angles. Similar figures have the same shape but not necessarily the same size.
M5G2

Circumference () is the perimeter of a circle. A circle is a closed curve with all its points in one plane and the same distance from a fixed point (the center). A diameter is a chord that goes through the center of the circle. Pi (л ≈ 3.14) is the ratio of the circumference of any circle to its diameter. Radius is the line segment from the center of the circle to any point on the circle. A compass is a tool for making circles and arcs.
M5M1.a

Estimation is an answer close to the exact answer, found by rounding or by using compatible numbers. Area is the number of square units needed to cover a surface. Geometric plane figures are closed figures that lie on a flat surface. Geometric figures are: irregular and regular polygons.
M5M1.b

Area is the number of square units needed to cover a surface. The formula for finding area of a rectangle is length times width. (A= L W) The formula for finding the area of a parallelogram is base times height. (A= B H) A parallelogram is a quadrilateral with opposite sides parallel and congruent. A rectangle is a parallelogram with four right angles.
M5M1.c

The formula for finding area of a parallelogram is (A=B x H). The formula for finding the area of a triangle is (A=1/2b x h). Two congruent triangles can be arranged to form a parallelogram which can be arranged to form a rectangle. A triangle is half the area of a parallelogram.
M5M1.d

Area is the number of square units needed to cover a surface. The formula for finding area of a parallelogram (a=b x h) is base times height. The formula for finding the area of a triangle is (a=1/2 x b x h).
M5M1.e

Estimation is a number close to the exact answer, found either by rounding, using front-end digits, or by using compatible numbers. A circle is a flat, round shape that has all points in one plane and the same distance from the from the center point. Partitioning is used to divide objects. Tiling is a way of determining area using manipulatives. Pi is the ratio of the circumference of any circle to its diameter. (approximately equal to 3.14) Radius is the segment or the length of the segment from the center of a circle to any point on the circle. Circumference is the perimeter of a circle.
M5M1.f

Regular polygons are polygons with all sides the same length and all angles the same measure. Irregular polygons are polygons with sides that are not the same length. A square is a polygon with four congruent sides and dour right angles. A rectangle is a polygon with two pairs of congruent, parallel sides and four right angles. A triangle is a polygon with three sides and three angles. Area of a square and rectangle is found by using the formula (a=b x h). Area of a triangle is found by using the formula (a=1/2b x h). Area is the measure, in square units, of the interior region of a 2-dimensional figure.
What Students Should be able to do



M5G1

Identify vertices, sides, and angles of a polygon Identify corresponding sides, angles, and vertices of geometric shapes. Construct congruent shapes Communicate understanding of terminology (vertices, sides, angles, congruency, and polygons). Analyze different geometric shapes to find similarities and differences.
M5G2

Discover Pi by measuring the circumference of many circles and comparing it to the circle’s diameter Communicate understanding of circumference, diameter, pi, and circle Calculate the diameter of a circle with a given circumference. Calculate the circumference of a circle with a given diameter.
M5M1.a

Estimate the area of a geometric plane figure Use appropriate units for measurement. (Ex. The object is 5 paper clips long.)
M5M1.b

Cut the parallelogram apart and rearrange it into a rectangle of the same area Derive the formula of a parallelogram
M5M1.c

Derive the formula for the area of a triangle Compare and contrast the relationship of the area of a rectangle and parallelogram with the triangle
M5M1.d

Find the area of triangles and parallelograms using formulas
M5M1.e

Estimate the area of a circle using partitioning and tiling Estimate the area of a circle using the formula A= ∏r2
M5M1.f 

Create illustrations of irregular and regular polygons Use appropriate formulas for appropriate polygons Calculate the area of a triangle, rectangle, and square