Why Part 1: Place Value Concepts Through Metric Measurement and Data

During the first week of school, teachers and students spend time establishing a classroom community. By launching with categorical data, teachers can leverage getting-to-knowyou activities to generate student data, create graphs, and answer questions.

Bar graphs provide students with a concrete and visual experience of comparison. Comparing categories on a bar graph sets up students for solving compare word problems by using a more abstract model, the tape diagram. Labeling the categories on a bar graph supports the practice of labeling tape diagrams, where students must visualize the amount or length.

Students revisit strategies for answering questions by using bar graphs to solve word problems. When students count on, take away, or use matching to answer how many more or how many fewer questions, they may use simple addition or subtraction to solve, which is a precursor to work in topic D. Moreover, when students find the total number of data points, they combine up to four addends, which prepares them for solving put together problems with four 2-digit addends in module 2.

The linear nature of bar graphs also supports students in understanding measurement, and it helps them transition from work on the number path in kindergarten and grade 1 to work on the number line in grade 2. The count scale on a bar graph primes students for using the ruler as a number line to solve problems.

After much consideration of our students’ learning, teachers’ input, and research on how students learn and how mathematical concepts progress, we decided it makes the most sense to include measurement in module 1. Why?

1. One of the major areas of emphasis of grade 2 math standards, as noted by the content standards, is measurement. By focusing on the relationship between metric units, students begin to develop key place value understanding that is inherent in the base-ten number system; more specifically, that 10 smaller units make 1 of the next larger unit.

2. When students begin the year with a concrete measurement experience that highlights the relationship between 100 cm, 10 cm, and 1 cm, they are able to work more flexibly and make explicit connections to place value units in module 1 part 2.

3. Once students have an understanding of the meaning of the spaces and tick marks on a ruler, they are ready to use the number line as a tool for solving addition and subtraction problems in topic D. After its introduction in this module, the number line becomes a reliable tool for students to use when solving problems throughout the year.

Through the concrete experience of creating a ruler, rather than using a standard tool, students come to see that length is the number of same-size units from zero, as opposed to the number of tick marks. Students iterate a centimeter cube to create a 10 cm ruler. Then they iterate ten 10 cm rulers to create a meter stick. In doing so, students internalize the proportionality of units. This early experience of building measuring tools, rather than working with standard ones, lays the groundwork for deeper place value understanding when students compose and decompose units in module 1 part 2.

In addition, the double-sided meter stick, an innovative, new measuring tool in Eureka Math2, reinforces Say Ten counting and the base-ten structure of the number system. When students use this tool, they focus on units of ten, as opposed to each number. Students also notice relationships between units. For example, a student may correctly claim to be 120 cm tall, twelve 10 cm rulers tall, or 1 m two 10 cm rulers tall.

Beth and Kate measure the same desk. Beth says the desk is 1 m 2 cm. Kate says it is 102 cm. Who is correct?

Which word problem types, or addition and subtraction situations, are used in this module?

The table shows examples of addition and subtraction situations.1 Darker shading in the table indicates the four kindergarten problem types. Students in grades 1 and 2 work with all problem types. Grade 2 students reach proficiency with the unshaded problem types.

Grade 2 students are expected to master all addition and subtraction problem types by the end of the year. They revisit types that were introduced and mastered in kindergarten and grade 1. However, in grade 2, the problems are one- and two-step, and use numbers within 100 (not just within 20).

Students use graphs to solve take from and put together/take apart problems in topic A.

• Take from with result unknown:

6 red balloons pop. How many red balloons are there now? (Lesson 3)

• Put together/take apart with total unknown: Up to four parts are given. No action joins or separates the parts. Instead, the parts may be distinguished by an attribute such as type, color, size, or location.

How many balloons are there in all? (Lesson 3)

• Compare with difference unknown: Two quantities are given and compared to find how many more or how many fewer.

Ling’s plant is 64 cm tall. Alex’s plant is 39 cm tall. How much taller is Ling’s plant than Alex’s plant? (Lesson 18)