Eureka Math and Assessment for Learning

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Assessments for learning are formative assessments. Formative assessments are a way to get information about student comprehension to make instructional decisions. Examples of formative assessments include in-the-moment questions we ask students, problems students work on in class, fluency activities, and Exit Tickets. Even summative assessments can be formative! What makes an assessment formative is when it results in decisions about how to adjust instruction to meet students’ needs.

“An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have made in the absence of that evidence.”

Dylan, William. 2011. Embedded Formative Assessment. Bloomington, IN: Solution Tree Press.


Make the most of Eureka Math assessments.

Formative assessments are embedded in Eureka Math®, so you don’t have to spend lots of time creating new assessments. Some resources are easily recognizable as assessments, such as Exit Tickets, the topic quizzes in Eureka Math Affirm®, Mid-Module Assessments, and End-of-Module Assessments. Other formative assessment opportunities are part of your daily instruction. When you engage students in Sprints, White Board Exchanges, or discourse about the Concept Development or Application Problems, you’re gathering information about what students know and are able to do.

Here are a few tips to get the most out of these assessments:

  • Before engaging in the math activity, consider what outcomes you expect.
  • Use the data gathered, whether formal or informal, to understand your students better. What strategies do they use to do the math? Are the students accurate with their math? Do they solve problems efficiently? What types of problems are easy for them, and which do they get stuck on?
  • Make teaching decisions based on the data. What questions will you ask students to advance their learning? What scaffolds will you offer? What prior knowledge will you bring to the forefront? How will you present the next task to ensure that students get the support they need to apply learning from one context to the next?


Use assessment to guide instruction.

What does assessment for learning look like in practice? It’s using what you observe about students’ mathematical knowledge to make teaching decisions. Consider this Application Problem from Grade 1 Module 4 Lesson 7 of Eureka Math.

Benny has 4 dimes. Marcus has  4 pennies. Benny says, “We have the same amount of money!” Is he correct? Use drawing or words to explain your thinking.

When you treat this problem as a formative assessment, you pay attention to how students are thinking and adjust your teaching accordingly.

Sample Response


Teaching Decision

Benny and Marcus have the same amount. They both have 4. So Benny is right.

The student is not attending to the value of the unit.

Step back to focus on units. Ask, “If Benny had 4 large pizzas and Marcus had 4 small pizzas, would they have the same amount of pizza? Are pennies and dimes worth the same amount? How much is a dime worth? How much is a penny worth?”

Dimes and pennies are not worth the same amount. So Benny is wrong.

The student understands the values are different for pennies and dimes. However, the student may not know the specific value of each coin.

Press for more information. Ask, “Which is worth more, pennies or dimes? How much is a penny worth? How much is a dime worth? How much money do Benny and Marcus each have?”

Benny is wrong. Dimes are worth 10 cents, and pennies are worth 1 cent. 10 cents is more than 1 cent, so Benny has more money.

The student understands that the units are different and calls out the specific differences.

Use questioning to extend the problem. Ask, “How much money do Benny and Marcus have altogether? How much more money does Benny have than Marcus? What other combinations of coins make 40 cents?”


Here’s another example. It comes from the Closing questions in Grade 7 Module 2 Lesson 6 of Eureka Math.

What does it mean to find the absolute value of a number?

Sample Response


Teaching Decision

It means to take the opposite of the number.

The student has a misconception and doesn’t understand that absolute value represents a distance from 0.

Refocus the student’s conceptual understanding of absolute value as a distance from 0. Ask, “Can distance be negative?” Guide students to understand that a number’s opposite can be negative, so opposite isn’t the same as absolute value.

It means you get a positive number.

The student is not considering the absolute value of 0 and may not understand that absolute value represents a distance from 0.

Check whether the student has conceptual understanding by asking why you get a positive number. Guide students to understand that the absolute value of 0 is neither positive nor negative.

It means you find the distance the number is from 0 on the number line.

The student understands the concept of absolute value.

Challenge the student to provide examples of when absolute value can be used in the real world.


Formative assessment provides valuable data to help you identify and meet students’ needs during the learning process. Data from the Concept Development, Application Problems, Sprints, White Board Exchanges, or debrief questions will help you plan your next question or task during instruction. Data from Exit Tickets will help you plan for the next day’s lesson. Topic quizzes and Mid-Module and End-of Module Assessments will help you plan the next series of lessons.

Whether you use informal or formal assessments, the key is to decide how the information from the assessments guides instructional choices to meet students’ needs. While there is certainly a time and a place for summative assessments, it’s the formative assessments that drive the learning and move it forward. If we do a good job with our formative assessments (assessments for learning), then we’ll see the results on our summative assessments (assessments of learning).


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