#
NYS Next Generation Learning Samples

**Yours to try****—****free: **Performance tasks that connect both the NYS Next Generation Learning Standards and Mathematical Practices. Featuring differentiated instructional tasks and summative assessments with anchor papers, these engaging tasks let every student build their skills through solving real-world DOK 3-level problems.

The samples below are aligned to NYS Next Generation Learning Standards and include problem-solving performance tasks, teacher planning sheets, rubrics, student anchor papers, and scoring rationales. They reflect just a few of the 500+ tasks in **Problem Solving for the 21st Century: Built for the NYS Next Generation Learning Standards****.**

## Grade K

### NY-K.OA.A.2a

### NY-K.OA.A.2a

Add and subtract within 10.

## Grade 1

### NY-1.OA.D.7

#### NY-1.OA.D.7

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

e.g., Which of the following equations are true and which are false?

6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

## Grade 2

### NY-2.NBT.B.6

#### NY-2.NBT.B.6

Add up to four two-digit numbers using strategies based on place value and properties of operations.

## Grade 3

### NY-3.NF.A.3b

### NY-3.NF.A.3b

Recognize and generate equivalent fractions, e.g. 𝟣/𝟤 = 𝟤/𝟦; 𝟦/𝟨 = 𝟤/𝟥.

Explain why the fractions are equivalent.

## Grade 4

### NY-4.NF.B.3c

### NY-4.NF.B.3c

Add and subtract mixed numbers with like denominators.

e.g., replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

## Grade 5

### NY-5.NBT.B.7

#### NY-5.NBT.B.7

Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations:

- add and subtract decimals to hundredths;
- multiply and divide decimals to hundredths.

Relate the strategy to a written method and explain the reasoning used.

**Notes on and/or:** Students should be taught to use concrete models and drawings; as well as strategies based on place value, properties of operations, and the relationship between operations. When solving any problem, students can choose to use a concrete model or a drawing. Their strategy must be based on place value, properties of operations, or the relationship between operations.

**Note:** Division problems are limited to those that allow for the use of concrete models or drawings, strategies based on properties of operations, and/or the relationship between operations (e.g., 0.25 ÷ 0.05). Problems should not be so complex as to require the use of an algorithm (e.g., 0.37 ÷ 0.05).

## Grade 6

### NY-6.G.A.3

#### NY-6.G.A.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.

## Grade 7

### NY-7.RP.A.1

#### NY-7.RP.A.1

Compute unit rates associated with ratios of fractions. e.g., If a person walks ½ mile in each ¼ hour, compute the rate as the complex fraction ½ ÷ ¼ miles per hour, equivalently 2 miles per hour with 2 being the unit rate. Note: Problems may include ratios of lengths, areas, and other quantities measured in like or different units, including across measurement systems

## Grade 8

### NY-8.G.B.8

#### NY-8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.