by Scott Baldridge and Ben McCarty

**Intended Audience:** Parents, teachers, and other educators involved in the Eureka Math/EngageNY Curriculum.

In this article, we simply discuss types of math problems from a state assessment and then show similar problems from the Eureka Math curriculum. We focus on the new TCAP Achievement Test (called TNReady Math), mainly because one of the authors of this article (Ben McCarty) is an assistant professor of mathematics at the University of Memphis. The format of this post is simple: we will discuss features of the TCAP and then show examples that match those features in the Grade 3 Eureka Math curriculum.

**Example 1: Language**

From the old Grade 3 TCAP sample test:

and a similar problem from Eureka Math Grade 3 (Module 1, Lesson 13):

Note the similarity in the language of “number sentence” between the two problems. Language like this will very likely continue to be used in the new TNReady assessments. Students using Eureka Math will be prepared for that language. This aspect is particularly important for fractions in 3rd and 4th grade where Eureka Math uses the exact same language (like “unit fraction”) as specified in the Tennessee Academic Standards.

**Example 2: Explain-Your-Reasoning Problems**

As explained in the “Seven Things You Need to Know About TNReady Math” document, the new TNReady assessments will no longer be all multiple-choice and instead will have a variety of formats:

**3. TNReady will replace the state’s multiple choice only test in math and will include a variety of questions.**

Eureka Math teaches a variety of answer formats that should mesh well with the types of questions asked on TNReady. Eureka Math also gives insight and guidance to the teacher in how to model ways to answer these problems (cf. the teacher-student vignette on the left hand side):

This problem was taken from Grade 3, Module 3, Lesson 11. This one explanation describes three different models/strategies that students can use in explaining their answer: (1) The tape diagram at the top, (2) the use of letters to represent unknowns, and (3) several mental math strategies for finding 72-28. Taken altogether, and enacted in daily use over the entire year, these explanation strategies become part of the bread-and-butter methods students can use to answer TNReady assessment problems.

**Example 3: Multi-step Problems**

Also explained in the “Seven Things You Need to Know About TNReady Math” document, the new TNReady assessments will have many more multistep problems than the old assessments:

**4. TNReady will ask students to solve multi-step problems, many without using a calculator, to show what they know.**

Multistep problems are one of the prominent features of the Eureka Math curriculum; it truly exceeds other curricula in preparing students for multistep problems. The problem in Example 2 above is one such example, but for good measure, here is another example:

The tape diagram (the picture between the two paragraphs) helps students convert this multistep problem into pictures they can use to solve the problem. The TNReady assessments will expect students to be fluent with answering word problems using tape diagrams and other models because they are part of the standards at every grade. Compared to the mostly-one-step problems of the old TCAP, students using the Eureka Math curriculum will be ready to excel on the new TNReady assessments.

Scott Baldridge

Distinguished Professor of Mathematics,

Louisiana State University

Lead Writer and Lead Mathematician, Eureka Math/EngageNY Curriculum

ScottBaldridge.net (This article and other *Engineering School Mathematics* articles can be found at this website)

Ben McCarty

Assistant Professor Mathematics

University of Memphis

Mathematician, PK-5, EngageNY Mathematics Curriculum

http://umdrive.memphis.edu/bmmccrt1/public/

CHANNEL: *Engineering School Mathematics
*© 2015 Scott Baldridge and Ben McCarty

1. The term “number sentence” does not appear anywhere in the CCSSM document. If we must shove equations at these little kids why invent a new term?

2. I would be more impressed with a kid’s number fluency if he said 6×4 = 3×8, done!

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Question (1): Good question. The term “sentence” is not invented, but an integral part of interpreting equations in mathematics. See for example, http://en.wikipedia.org/wiki/Sentence_(logic). The concept is needed to distinguish between equations that are boolean-valued and those that are not, which is part of understanding what it means to solve an equation—the very heart of Algebra.

Question (2): Sure, but that is a separate issue from the one discussed in the article. Eureka Math also works extensively on number sense—see https://scottbaldridge.net/2015/02/23/fluency-without-equivocation/ for example.

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