Last updated: 5/21/2014 ## NYS Common Core-Math-Grade 5 -Quarter 3

 (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 two-dimensional 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:

1. Classify polygons by the number of sides they have.

2. Determine to which categories a given quadrilateral belongs.

3. Classify triangles by side length and angle measure.

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Assessments

Benchmark Assessment Items:

Assessment using Standardized Test Items from NYLearns:

 (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?

(2 weeks)

Students will be able to:

1. Determine the least common multiple of two numbers.

2. Add and subtract fractions with unlike denominators.

3. Represent fractions using visual models such as fraction bars.

4. Estimate the magnitude of fractions by referring to benchmark fractions.

5. Solve word problems involving addition and subtraction of fractions using both visual fractions models as well as equations to represent the problem.

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Related Activities & Resources:

Assessments

Benchmark Assessment Items:

Assessment using Standardized Test Items from NYLearns:

 (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:

1. Determine the product of two fractions or a fraction and a whole number by representing the problem using visual models and reasoning with them.

2. Determine the product of two fractions or a fraction and a whole number using symbolic methods.

3. 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.

4. Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models or equations to represent the problem.

5. Given a fraction, compute an equivalent one by multiplying the original by a fractional version of 1.

6. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

7. Solve word problems whose information is presented as a line plot with fractional vertical axis intervals.

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Assessments

Benchmark Assessment Items:

Standardized Test Items:

 (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 50-pound 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 non-zero 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 non-zero 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 1/3-cup 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:

1. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

2. Divide whole numbers by unit fractions and unit fractions by whole numbers using visual fraction models as well as symbolic methods.

3. Solve word problems involving division of unit fractions by whole numbers and of whole numbers by unit fractions.

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Common Core Suggested Glossary

This glossary contains those terms found in or associated with the Common Core State Standards.  The glossary includes terms that are essential to understanding and developing mastery of the Standards. For additional definitions and terms, please refer to the appropriate Appendices for the ELA/Literacy or Math Common Core State Standards.

Grades 3—8 Mathematics Testing Program Guidance:

Grades 3—8 Mathematics Testing Program Guidance:

In order to assist schools and districts in the curriculum planning process for the April 2013 test administration, the New York State Education Department (NYSED) has developed the following guidance for the Grades 3 - 8 Mathematics Testing Program.

• MEMO: Math 3-8 Pre & Post Assessment (August 2012) 1
• DRAFT: Testing Guidance Document (August 17th, 2012) 2
• TESTING GUIDANCE: Math 3-8 Pre & Post Standards (posted 11/26/12) 3

1From New York State Education Department. Math Pre-Post Memo. Internet. Available from http://e2math.weebly.com/uploads/8/4/6/7/8467476/math_pre-post_memo_-_8-17-12.pdf; accessed 22, March, 2013.

2From New York State Education Department. Math Pre-Post Draft. Internet. Available from http://e2math.weebly.com/uploads/8/4/6/7/8467476/math_pre-post_attachment_-_draft_8-17-12.pdf; accessed 22, March, 2013.

3From New York State Education Department. NYS Grades 3-8 Mathematics Common Core Learning Standards Testing Program Guidance—September-April/May-June. Internet. Available from http://www.p12.nysed.gov/assessment/ei/2013/math-sept-april-may-june.pdf; accessed 22, March, 2013. 