(1) 
5.G.3 
Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 
(1) 
5.G.4 
Classify twodimensional figures in a hierarchy based on properties. 

In what ways can we place shapes into categories? What is the best way?

Properties of Polygons
(2 weeks)

Students will be able to:
 Classify polygons by the number of sides they have.
 Determine to which categories a given quadrilateral belongs.
 Classify triangles by side length and angle measure.

Resources
Milestone Lessons:
 NCTM  Polygon Capture
 NCTM  Rectangles and Parallelograms
 NCTM  Shape Up
Related Activities & Resources:
 NCTM  Sorting Polygons
 NCTM  Shape Sorter
 NLVM  Tangrams

Assessments
Benchmark Assessment Items:
 Kuta  Classifying Polygons
 Learner.org  Classifying Polygons Assessment
Assessment using Standardized Test Items from NYLearns:
 Polygons  Student
 Polygons  Teacher

(1) 
5.NF.1 
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in
such a way as to produce an equivalent sum or difference of fractions
with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In
general, a/b + c/d = (ad + bc)/bd.) 
(1) 
5.NF.2 
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the
problem. Use benchmark fractions and number sense of fractions
to estimate mentally and assess the reasonableness of answers. For
example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that
3/7 < 1/2. 

How can parts of a whole be combined to form new quantities?

Addition and Subtraction of Fractions
(2 weeks)

Students will be able to:
 Determine the least common multiple of two numbers.
 Add and subtract fractions with unlike denominators.
 Represent fractions using visual models such as fraction bars.
 Estimate the magnitude of fractions by referring to benchmark fractions.
 Solve word problems involving addition and subtraction of fractions using both visual fractions models as well as equations to represent the problem.

Resources
Milestone Lessons:
 Understanding Fractions  Addition & Subtraction
 Shodor Interactive  Addition & Subtraction of Fractions
 Jamit  Adding & Subtracting Fractions
Related Activities & Resources:
 NCTM  Equivalent Fractions
 NCTM  Fraction Models
 NCTM  Fractions
 Nullo  A Fraction Game
 Math Fact Cafe  Practice Worksheets

Assessments
Benchmark Assessment Items:
 Kuta  Adding and Subtracting Fractions
 FCIT  Adding Fractions Performance Assessment
 Kuta  Least Common Multiple
 MathSalamander  Benchmark Fractions
Assessment using Standardized Test Items from NYLearns:
 Add Subtract Fractions  Student.pdf
 Add Subtract Fractions  Teacher.pdf

(1) 
5.NF.4 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 
(1) 
5.NF.4.a 
Interpret the product (a/b) * q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of
operations a * q / b. For example, use a visual fraction model to
show (2/3) * 4 = 8/3, and create a story context for this equation. Do
the same with (2/3) * (4/5) = 8/15. (In general, (a/b) * (c/d) = ac/bd.) 
(1) 
5.NF.4.b 
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying
the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas. 
(1) 
5.NF.5 
Interpret multiplication as scaling (resizing), by: 
(1) 
5.NF.5.a 
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the
indicated multiplication. 
(1) 
5.NF.5.b 
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as
a familiar case); explaining why multiplying a given number by
a fraction less than 1 results in a product smaller than the given
number; and relating the principle of fraction equivalence a/b =
(n*a)/(n*b) to the effect of multiplying a/b by 1. 
(1) 
5.NF.6 
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 

How can we represent portions of a whole in ways that make sense to us?

Multiplication of Fractions
(3 weeks)

Students will be able to:
 Determine the product of two fractions or a fraction and a whole number by representing the problem using visual models and reasoning with them.
 Determine the product of two fractions or a fraction and a whole number using symbolic methods.
 Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models or equations to represent the problem.
 Given a fraction, compute an equivalent one by multiplying the original by a fractional version of 1.
 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
 Solve word problems whose information is presented as a line plot with fractional vertical axis intervals.

Resources
Milestone Lessons:
 Multiplying Fractions
 Understanding Fractions  Multiplication
 Shodor Interactive  Fraction Multiplication
Related Activities & Resources:
 NCTM  Fraction Models
 NCTM  Fractions
 Cynthia Lanius  No Matter What Shape Your Fractions Are In
 Math Fact Cafe  Practice Worksheets
 NLVM  Fractions  Parts of a Whole
 NLVM  Fractions  Visualizing

Assessments
Benchmark Assessment Items:
 Harvard's Balanced Assessment  At the Grocery Store
 Kuta  Multiplying Fractions
Standardized Test Items:
 MultiplyFractions  Student.pdf
 MultiplyFractions  Teacher.pd

(1) 
5.MD.2 
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example,
given different measurements of liquid in identical beakers, find the
amount of liquid each beaker would contain if the total amount in all the
beakers were redistributed equally. 
(1) 
5.NF.3 
Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers,
e.g., by using visual fraction models or equations to represent the
problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting
that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared
equally among 4 people each person has a share of size 3/4. If 9 people
want to share a 50pound sack of rice equally by weight, how many
pounds of rice should each person get? Between what two whole numbers
does your answer lie? 
(1) 
5.NF.7 
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 
(1) 
5.NF.7.a 
Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) / 4, and use a visual fraction model to show the quotient.
Use the relationship between multiplication and division to explain
that (1/3) / 4 = 1/12 because (1/12) * 4 = 1/3. 
(1) 
5.NF.7.b 
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 / (1/5), and use a visual fraction model to show the quotient. Use
the relationship between multiplication and division to explain that
4 / (1/5) = 20 because 20 * (1/5) = 4. 
(1) 
5.NF.7.c 
Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to
represent the problem. For example, how much chocolate will each
person get if 3 people share 1/2 lb of chocolate equally? How many
1/3cup servings are in 2 cups of raisins? 

How can we determine how parts fit inside other parts?

Division of Fractions
(3 weeks)

Students will be able to:
 Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
 Divide whole numbers by unit fractions and unit fractions by whole numbers using visual fraction models as well as symbolic methods.
 Solve word problems involving division of unit fractions by whole numbers and of whole numbers by unit fractions.

Resources
Milestone Lessons:
 Understanding Fractions  Division
 Shodor  Fraction Division
 HomeSchool  4 Ways for Fraction Division
Additional Resources:
 NLVM  Fraction Bars
 Shodor  Converter

