Math  /  1st Grade  /  Unit 5: Data Investigations

Data Investigations

Students build on their understanding of classification by organizing, representing, and interpreting data in up to three categories. They ask and answer questions about the data and solve related problems using addition and subtraction. The unit also introduces new compare problem types and emphasizes using tools and visual models to make sense of data.

Math

Unit 5

1st Grade

Unit Summary

In Unit 5, students develop the ability to organize, represent, and interpret categorical data with up to three categories. They ask and answer questions about the total number of data points, how many are in each category, and how many more or fewer are in one category than in another. Students represent data using tables and tallies, and begin to make sense of simple visual representations, establishing the groundwork for formal work with picture and bar graphs in 2nd grade.

In Kindergarten, students classified and counted objects into two given categories, laying the foundation for this unit’s work with organizing, representing, and interpreting categorical data with up to three categories. In earlier 1st grade units, students engaged with most story problem types, with the exception of the two compare subtypes identified in the Progressions as particularly challenging. Building on this experience, students now apply familiar problem-solving strategies to new contexts involving data. They revisit problem types such as put together/take apart with total unknown and compare with difference unknown, now framed within data sets. This unit also introduces the final two problem subtypes new to 1st grade, compare with bigger unknown and compare with smaller unknown, where the language of the problem suggests the “wrong” operation. These subtypes require students to reason flexibly about the relationship between quantities and deepen their understanding of comparison.

Throughout the unit, students use a range of tools and representations, including linking cubes, drawings, tallies, and graphs, to collect, organize, and analyze data MP.5 Use appropriate tools strategically. . Teachers support students in making sense of how data can be used to tell a story, answer questions, and draw conclusions, while encouraging precision in how data is collected and interpreted MP.6 Attend to precision. .

This unit supports important mathematical thinking that extends across domains. As students solve problems involving data, they continue to apply and strengthen their understanding of addition and subtraction within 20 1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.  and the relationships between numbers. Looking ahead, this work lays the foundation for future units in which students will represent and solve more complex problems, including those involving two-digit numbers and place value 1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:   1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. , and prepares them to engage with bar graphs and scaled picture graphs in 2nd grade 2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. .

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Assessment

The following assessments accompany Unit 5.

Student Observational Spreadsheet

Print the Student Observational Spreadsheet to use as a formative tool to monitor the progress of students throughout the unit.

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Unit Prep

Intellectual Prep

Unit-Specific Intellectual Prep

  • Read and annotate the "Unit Summary" and "Essential Understandings" portions of the unit plan. 
  • Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind. 
  • Take the Post-Unit Assessment.

Unit-Specific Intellectual Prep

Essential Understandings

  • Data can be organized and represented in different ways to help us see patterns, make comparisons, and ask and answer questions.
  • Story problems connected to data can be solved using addition and/or subtraction.
  • Compare story problems require flexible thinking, especially when the language of the question is misleading.

Materials

  • Bag of math tools (1 bag of 10-20 math tools per group of 2-4 students) –bear counters, linking cubes, two-sided counters, paper clips, etc.
  • The Day You Begin by Jacqueline Woodson and illustrated by Rafael López (Nancy Paulsen Books, 2018) (1 per class) –or alternate book
  • Enemy Pie by Derek Munson (Chronicle Books, 736th edition, 2000) (1 per class) –or alternate book
  • Optional: Clipboards (1 per pair of students)
  • Chart Paper (1 per group of 4-6 students and 1 for class strategies chart)
  • Markers (1 per group of 4-6 students)
  • Duck! Rabbit! by by Amy Krouse Rosenthal and illustrated by Tom Lichtenheld (Chronicle Books, 2014) (1 per class) 
  • Sticky notes (1 per student)
  • White board (1 per student for Warm Up)
  • Dry erase marker (1 per student for Warm Up)
  • Scissors (1 per student for Problem Set)
  • Glue stick (1 per student for Problem Set)
  • Crayons (1 yellow crayon and 1 green crayon per student for Problem Set)
  • Optional: Materials from previous Center Activities –See Set Up in Anchor Tasks for list of materials

Vocabulary and Models

Unit Vocabulary

data

tally

Foundational Vocabulary

category

To see all the vocabulary for Unit 5, view our 1st Grade Vocabulary Glossary.

Access foundational vocabulary for Unit 5 in the same 1st Grade Vocabulary Glossary.

Unit Practice

Fluency Activities

Access a full library of standards-aligned activities to engage students in practicing and strengthening their procedural skills and fluency.

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Lesson Map

Topic A: Categorical data: two categories

Topic B: Categorical data: three categories

Topic C: Story problems about categorical data

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

Measurement and Data

  • 1.MD.C.4 — Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Operations and Algebraic Thinking

  • 1.OA.A.1 — Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • 1.OA.A.2 — Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • 1.OA.C.5 — Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
  • 1.OA.C.6 — Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Foundational Standards

Counting and Cardinality

  • K.CC.C.6

Measurement and Data

  • K.MD.B.3

Operations and Algebraic Thinking

  • K.OA.A.2

Future Standards

Measurement and Data

  • 2.MD.D.10

Operations and Algebraic Thinking

  • 2.OA.A.1

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

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