#
Non-Common Core Math Samples

**Yours to try****—****free:** Math performance tasks that are organized by rich Units of Study inspired by the NCTM Focal Points and leading state standards. 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 include problem-solving performance tasks, teacher planning sheets, rubrics, student anchor papers, and scoring rationales. They reflect just a few of the 350+ tasks in **Problem Solving for the 21st Century.**

## Kindergarten

### Comparing Numbers Unit

#### Comparing Numbers Unit

The Comparing Numbers Unit involves understanding the relative position and magnitude of whole numbers, and their relationships within the numeration system. Students will answer questions such as:

- How do you know which group has more? How do you know which group has less?

- Do any groups have the same number? How do you know?

## Grade 1

### Strategies for Addition + Subtraction Unit

#### Strategies for Addition & Subtraction Unit

The Strategies for Addition and Subtraction Unit involves understanding the processes of addition and subtraction in order to solve problems and answer questions such as:

- If we know all of the parts, how can we find the whole?

- If we know the whole and one of the parts, how can we find the missing part?

- Given an equation, can you create an addition or subtraction situation to match it? How can you prove it matches the equation?

## Grade 2

### Algebraic Reasoning Unit

#### Algebraic Reasoning Unit

The Algebraic Reasoning Unit involves understanding number patterns within properties of numbers and operations in order to answer questions such as:

- How can you prove this number is odd or even?

- How can you use the relationship between addition and subtraction to solve problems in which the unknown may be any one of the terms in the equation?

- Give an equation in which the unknown may be any one of its terms, how can you create a situation to match it? How can you prove that your situation matches the equation?

- How can you show ___ is an even/odd number?

- What strategies can you use to determine a number is odd or even?

- What happens when you add two like odd or even numbers?

## Grade 3

### Place Value Unit

#### Place Value Unit

The Place Value Unit involves understanding and representing the relative position, magnitude, and relationships within the numeration system in order to answer questions such as:

- How can you use the additive property of place value (expanded notation) to decompose the number 54,321?
*(50,000 + 4,000 + 300 + 20 + 1)*

- How can you use the base ten property of place value to explain the relationship between each of the digits in the number 55,555?
*(Each number is worth 10 times the number to its right and one-tenth the number to its left.)*

- How can you use the multiplicative property of place value to describe the meaning of each digit in the number 54,321?
*(Since the 4 is in the thousands place, multiplying the 4 times 1,000 gives the value of the 4 in the number.)*

- What other ways can you use ten thousands, thousands, hundreds, tens, and ones to represent a number without changing its value?
*(Methods might include using objects, pictorial models, and numbers, including non-standard partitioning of the number in a variety of ways.)*

## Grade 4

### Multiply and Divide Whole Numbers Unit

#### Multiply and Divide Whole Numbers Unit

The Multiplying and Dividing Whole Numbers Unit involves using patterns and place value to develop strategies to multiply and divide whole numbers. Questions to answer may include:

- How are models useful for representing the processes of multiplication and division?
*(Models might include equal jumps on a number line, arrays/area models, or base ten materials.)*

- How are the properties of place value (additive, multiplicative, base-ten & positional) useful in developing efficient procedures for multiplying and dividing whole numbers?

- How can mental math, rounding, and/or the use of compatible numbers help to determine whether the solution to a multiplication or division problem is reasonable?

## Grade 5

### Decimal Place Value Unit

#### Decimal Place Value Unit

The Decimal Place Value Unit involves understanding and representing the relative position, magnitude, and relationships within the numeration system in order to answer questions such as:

- How can you use the additive property of place value (expanded notation) to decompose the number 0.123?

- How can you use the multiplicative property of place value to describe the meaning of each digit in the number 0.123?

- How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5.555?