#
Math Performance Task Samples, K-5

**Yours to try—free: **These engaging, differentiated instructional tasks and summative assessments 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**, which is organized by rich Units of Study inspired by the NCTM Focal Points and leading state standards.

## Kindergarten

### Addition and Subtraction Unit

#### Addition and Subtraction Unit

The 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?
- How can you use place value to explain the strategies you used to solve this addition (subtraction) problem?
- Given an equation, can you create an addition or subtraction situation to match it? How can you prove your situation matches the equation?
- What addition or subtraction strategy did you use and why?

## Grade 1

### Equivalence Unit

#### Equivalence Unit

The Equivalence Unit involves understanding the meaning of the equal sign in order to answer questions such as:

- If I have 5 red counters and 4 yellow counters on one side of the equal sign, how many yellow counters must I put with 2 red counters to equal the number of counters on the other side of the equal sign?
- If I have 7 on this side of the equal sign, what numbers can I put on the other side of the equal sign to make a true statement?
- What does the = symbol mean?
- When is it correct to use the equal sign?
- Is there another combination of numbers you can use to find the same total?

## Grade 2

### Addition and Subtraction Unit

#### Addition and Subtraction Unit

The 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?
- How can you use place value to explain the strategies you used to solve this addition (subtraction) problem?
- Given an equation, can you create an addition or subtraction situation to match it? How can you prove your situation matches the equation?
- What addition or subtraction strategy did you use and why?

## Grade 3

### Comparing Fractions Unit

#### Comparing Fractions Unit

The Comparing Fractions Unit involves representing fractional parts of whole objects, lines, and sets in order to answer questions such as:

- Why must we use the same whole when comparing fractional parts?

- How can you prove that fractions are equivalent when using an area model such as pattern blocks or tangrams?

- How can you prove that fractions are equivalent when using a linear model such as a strip or number line?

- How can you prove that fractions are equivalent when using a set model such as 2-color counters?

## Grade 4

### Adding and Subtracting Fractions Unit

#### Adding and Subtracting Fractions Unit

The Adding and Subtracting Fractions Unit involves using a variety of methods to join or separate fractional parts referring to the same whole. Methods may include replacing mixed numbers with equivalent fractions; using properties of operations and the relationship between addition and subtraction; and using visual models of fractions. Questions to answer may include:

- Why must we use the same
*whole*when adding or subtracting fractional parts?

- How can a number line be used to represent adding or subtracting fractions?

- How can benchmark fractions help to determine whether a sum or difference makes sense?

## Grade 5

### Products and Quotients with Decimals Unit

#### Products and Quotients with Decimals Unit

The Products and Quotients with Decimals Unit involves using patterns and place value to develop strategies to multiply and divide decimals. Questions to answer may include:

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

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

- Given an equation involving finding products and/or quotients with decimals, how can you create a situation to match it?