Last updated: 4/26/2016

## NYS Common Core-Math-Grade 6 -Quarter 1

 (1) 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. (1) 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

How does representing quantities in different ways reveal different information about the quantities?

Numerical Expressions

(3 weeks)

Students will be able to:

1. Find the greatest common factor of two whole numbers less than or equal
to 100.

2. Find the least common multiple of two whole numbers less than or equal to 12.

3. Factor addition expressions using the distributive property and the GCF.

4. Write and evaluate numerical expressions involving whole-number
exponents.

Milestone Lessons:

Pre/Post Assessment:

Ongoing Skill Assessment:

Problem Solving Assessments:

 (2) 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

In what different ways can parts and wholes be combined?  Which ways are the most effiicient and why?

(1.5 weeks)

Students will be able to:

1. Add multi-digit decimals using the standard algorithm.

2. Subtract multi-digit decimals using the standard algorithm.

Milestone Lessons:

Pre/Post Assessment:

Ongoing Skill Assessment:

 (1) 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. (2) 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

In what different ways can parts and wholes be multiplied and divided?  Which ways are most efficient and why?

Multiplication and Division of Whole Numbers and Decimals

(2 weeks)

Students will be able to:

1. Multiply multi-digit whole numbers using the standard algorithm.

2. Divide multi-digit whole numbers using the standard algorithm.

3. Multiply multi-digit decimals using the standard algorithm.

4. Divide multi-digit decimals using the standard algorithm.

Milestone Lessons:

Pre/Post Assessment:

Ongoing Skill Assessment:

 (1) 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. (1) 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. (1) 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

How can areas of simple shapes be used to find areas of more complex shapes?

Area and Surface Area

(2.5 weeks)

Students will be able to:

1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

2. Solve real-world problems involving finding the area of polygons.

3. Draw polygons in the coordinate plane given coordinates for the vertices.

4. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

5. Solve real-world problems involving polygons and distance in the coordinate plane.

6. Represent three-dimensional figures using nets made up of rectangles and triangles.

7. Use nets to find the surface areas of three-dimensional figures.

8. Solve real-world problems involving the surface area of three-dimensional figures.

Milestone Lessons:

Pre/Post Assessment:

Ongoing Skill Assessment:

Problem Solving Assessments:

 (1) 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

How is finding volumes with fractional units similar to and different from finding volumes with whole number units?

Volume

(1 week)

Students will be able to:

1. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.

2. Find the volume of a right rectangular prism by multiplying the three edge lengths of the prism.

3. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths.

4. Solve real-world problems involving finding the volume of right rectangular prisms.

Milestone Lessons:

Pre/Post Assessment:

Ongoing Skill Assessment:

Common Core Suggested Glossary